352-14333; THE ANALYSIS OF THE FRICTIONAL CHARACTERISTICS OF AND FORCES APPLIED TO STAIRWAY TREADS Thesis for the Degree oI M. S. MICHIGAN STATE UNIVERSITY LARRY JOHNSON SEGERLIND I962 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ \EBBB 8871 312930 \ \\\\\\\\\\\ HIGAN STATE UNIVERSITY LIBRARIES IIIIIIII I Ht:Slfi LIBRARY Michigan Saw U . . MICHIGAN STATE UNIVERSITY mar-aw MICHIGAN STATE UNIVERSITY LIBRARY ”K- A)?" tic.- ‘H‘, . . L4 L.' A" " L? M. I' I (1 THE ANALYSIS OF THE FRICTIONAL CHARACTERISTICS OF AND FORCES APPLIED TO STAIRWAY TREADS By Larry Johnson Segerlind AN ABSTRACT Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1962 t/ / x ”.4 Approved: ///~*< L ’4 .:/"~--' Cu- U L (l 2;; T r< I y I Although the stairway has been used for many years it is still not a safe means of travel. In 1959 nearly 700 farm people died as a result of falls which occurred ; on steps and stairways. To reduce the injuries and deaths giresulting from these falls an analysis of some of the ~§ifactors affecting stairway safety was performed. 3k The investigation had two objectives. The first was \g-to evaluate the coefficient of friction of different shoe sole and stair tread materials. The second was to evaluate and analyze the forces exerted by individuals when ascend— ing and descending stairways of different designs. The coefficient of friction was measured on a machine having a table which moved under a stationary holder.‘ The 'holder was fastened to two vertical bars which contained strain gages. The strain gage bridge was connected to 3 Brush amplifier and inking oscillograph. The vertical load was applied by placing weights at the end of an arm which rested on the holder. The tread material was placed on the table and moved under the holder which contained the sole material. The horizontal force was recorded on the oscillograph. New and worn specimens of six different tread materials and six different sole materials were used. The different sole materials were duplicated for two different sole sizes. The tread materials used were wood, linoleum, a non skid type paint, abrasive strip, varnish and rubber mat. The sole materials used were neoprene, neolite, crepe, leather, ripple Larry Johnson Segerlind and a hard surface sole made by B.F. Goodrich. The investigation was designed so that it could be analyzed statistically and the order in which measurements were made was determined by randomization. All the measurements were made at one table speed and one vertical. force. The magnitude, direction and point of application of the forces exerted by a person ascending and descending a stairway were measured using a force plate. ~The force plate contains five separate strain gage circuits and is capable of measuring the vertical force, both horizontal forces and the point of application of the forces with respect to the front edge and side of the tread. The output of each circuit was recorded on an inking oscillograph. To compare stairway designs nine different stairways were constructed. Stairways with 9, lO and ll inch treads were built for each of three riser heights, 6, 7 and 8 inches. Two subjects, weighing 140 and 172 pounds, Were used in the investigation. Each subject ascended and descended each stairway four times while traveling at his own natural speed. ' The coefficient of friction for the abrasive strip and rubber mat materials was higher than the coefficient of friction of the other tread materials for most all of the soles investigated. Wood, varnish and paint generally Larry Johnson Segerlind showed a decrease in the coefficient of friction with use while linoleum increased with use. The ripple sole had the highest coefficient of friction values for any of the sole materials studied. The crepe sole was the only sole which had a higher coefficient of friction value on the new material than on the worn material. The vertical force exerted on a tread had two maxi- mum values when either ascending or descending the stair- ways. The initial rate of application of the vertical force varied linearly with time when ascending or descending the stairways. ‘ The horizontal force varied considerably between both the stairways and the two subjects. The horizontal force was generally directed toward the front edge of the tread at the beginning of the step, when either ascending or descending the stairways. The forces exerted by a person when ascending or descending a stairway normally are not large enough to cause slipping. THE ANALYSIS OF THE FRICTIONAL CHARACTERISTICS OF AND FORCES APPLIED TO STAIRWAY TREADS By Larry Johnson Segerlind A THESIS Submitted to Hichigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1962 ACKNOWLEDGEMENTS The author wishes to express his appreciation to his nmjor professor, Dr. Merle L. Esmay, for his counsel and encouragement during the investigation and for his helpful suggestions on the manuscript. Grateful acknowledgement is also due to Dr. A. W. Farrall, Head, Agricultural Engineering Department and the North Central Regional Committee on Farm Housing (NC-9) for their interest and allocation of funds for this project. Appreciation is extended to Dr. W. B. Eaten, Michigan State University Experiment Station Statistician, for suggesting methods of processing the data. Appreciation is also extended to Thomas Mulvaney and Harris Gitlin for the time they spent being the lumen subjects required for part of the investigation. ii TABLE OF CONTENTS Page I INTRODUCTION . . . . . . 1 II REVIEW OF LITERATURE . . . . . 3 Stairway Accidents . . . 3 Physiological Responses of Nomen . . 4 c‘tairway Design . . .- . 4 Friction of Non-Metals. . . . 7 Human Locomotion . . . . . 9 III EXPERIMENTAL INVP‘STIGATION . . . l2 Coefficient of Friction of Tread .and Shoe Sole Materials . . . l2 Tread Covering Materials . Shoe Sole Materials . . Testing Equipment . . Procedure of the Investigation . Measuring the Forces Exerted on Stair Step Description of the Equipment . . o o o (no 0 e o o “ H (I) Bridge Output . . . . . l9 Calibration . . . . 23 Stairways . . . 29 Procedure of the Investigation . . 2 IV RESULTS . . . . 3l Coefficient of Frict on . . . . 31 Analysis of the Experiment . . . 31 Presentation of Results . . . 32 General Trends . . . . 33 Analysis of New and Worn Tread Materials for a Worn Sole Material . . . 37 Analysis of Worn Soles on Worn Tread Materials . 45 Analysis of Sole Materials Independent of Tread Materials . . . . 49 Discussion of Results . S3 Forces Exerted on a Stair Step Analysis of Experiment . Percent Error . . Time Spent on a Tread . Ascending a Stairway . Vertical Force, Ascending 'Horizontal Force, Ascending O O O O O O O O O O Q 0 O O O O O O O\ H Center of Pressure, Ascending 9 Descending a Stairway . . . . 92 Vertical Force, Descending . . . 94 Horizontal Force, Descending . . . 107 Center of Pressure, Descending . O H H . U1 iii, TABLE OF CONTENTS Page V CONCLUSIONS . . . . . . . 123 VI SUGGESTIONS FOR FUTURE INVESTIGATIONS . . 126 VII 'BIBLIOGRAPHY . . . . . . 127 iv LIST OF TABLES Tables l 10 ll 12 The mean (X), the standard deviation (S) and the interval of X S of the coefficient of friction data of the four conditions involv- ing a single sole and tread material. . The results of the factorkfl_analysis for the two surface conditions of the tread mater- ials with a worn sole. . . . Summary of the factorial analysis . . The average coefficient of friction value for worn sole materials on worn tread materials. . . . ‘ The mean (X),_standard deviation (8) and the interval of Kits for a worn sole material with the six worn tread materials analyzed together. . . . . The average coefficient of friction for the new and worn condition of each sole. .‘ The average coefficient of friction values for the shoe sole materials. . , . The analysis of variance table with degrees of freedom for the two variable classifica— tions involving stairways and present pOintSO O O . O O The analysis of variance table with degrees of freedom for the two variable classifica— tions involving stairways and forces. . The analysis of variance table with degrees of freedom for the two variable classifica- tions involving stairways and replica- tions. 0 O O O The analysis of variance table with degrees of freedom for the two variable classifica— tions involving stairways and subjects. . The average time (seconds) spent on a tread when measuring the horizontal and vertical forces, average for the nine stairways. . V Page 38 44 46 47 48 SO SO 59 59 60 64 LIST OF TABLES Table 13 The average time (seconds) spent on a tread by each subject while ascending and descend- ing each of the stairways. . . 14 The vertical force exerted at the 25 percent point while ascending each stairway. . 15 The average vertical force exerted while ascending each stairway. . . . 16 The average vertical force exerted at each percent point while ascending the nine stairways. . . . . 17 The horizontal force exerted at the 6.25 percent point while ascending each stairway. 19 The average horizontal force exerted while ascending each stairway. . . 19 The average horizontal force exerted at each percent point while ascending the nine stairways. . . . . 20 The initial point of application of the ver— tical force while ascending the stairways. Distance from the front edge, inches. . 21 The vertical force (pounds) exerted at the 12.5 and 25 percent points while descend- ing each stairway. . . . 22 The average vertical force (pounds) exerted while descending each stairway. . . 23 The vertical force (pounds) exerted at each percent point while descending the nine stairways. Average for the nine stairways. 24 The horizontal force (pounds) exerted at the 12.5 and 25 percent points while descending each stairway. . . . . 25 The average horizontal force (pounds) exerted while descending a stairway. . . 26 The horizontal force (pounds) exerted at each percent point while descending the stair- ways. Average for the nine stairways. ‘ . vi Page 64 7o 73 73' 82 8S 85 93 102 102 110 113 113 LIST OF TABLES Table Pages 27 The initial point of application of the vertical force while descending each stair- way. Distance from the front edge, inches. 121 LIST OF FIGURES Figure 1 A schematic picture of molecules in a boundary lubrication, a) surface at rest, b) surfaces in motion. . . . 2 The relationship between u and the partial vapor pressure. . . . . 3 The machine used to measure the coefficient of friction. . . ‘ . . 4 A close view of the machine used to measure the coefficient of friction showing the sole holder and the stair tread. . . 5' The calibration curve for the strain gage transducer of the friction machine. 6 The force plate in one of the experimental stairways. . . . 7 Calibrating the force plate for vertical forces and the coordinate system. . 8 The corner support for the force plate. . 9 A schematic diagram of the tread holder showing the specific dimensions. . 10 The calibration curve for the vertical force whenel is less than one half the tread Wiath. O O O O 11 The calibration curve for the vertical force when e1 is greater than one half the tread width. . . . 12 The calibration curve for e1 . . 13 The calibration curve for e4 . . 14 Calibrating the force plate for the hori- zontal forces. . . . . 15 A person descending one of the experimental stairways. . . . . 16 The calibration curve for the horizontal force directed toward the front edge of the tread. . . . . viii Page 25 26 26 27 27 28 LIST OF FIGURES Figures 17 18 19 2O 21 22 23 24 25 26 27 2R 29 The calibration curve for the horizontal force directed toward the rear edge of the tread. . . . . A schematic diagram of a 2x2 factorial analysis. . . . . The average coefficient of friction for each of the simulated surface conditions and the large neoprene sole. . . . The average coefficient of friction for each of the simulated surface conditions and the large crepe sole. . . . The average coefficient of friction for each of the simulated surface conditions and the large ripple sole. . . . The average coefficient of friction for the large soles. . . . . The average coefficient of friction for the small soles. . . . . The comparison of the stairway averages for the time spent on a tread, 140 pound subject ascending the stairways. . The basic divisions of one complete step while ascending a stairway. . . The vertical force exerted by the 140 pound subject while ascending a stairway with 6 inch risers and 11 inch treads. . Comparison of the percent point averages for the vertical force, 140 pound subject ascending the stairways. . . Comparison of the percent point averages for the vertical force, 172 pound subject ascending the stairways. . . The vertical force exerted by the two sub- jects while ascending the stairways. Average for the nine stairways. . . ix Page 28 32 34 4O 41 51 52 63 66 68 71 72 74 LIST OF FIGURES Figure 30 31 32 39 4O 41 The vertical force, as a percent of body weight, exerted by the subjects while ascending the stairways. Average for the nine stairways. . . The horizontal force exerted by the 140 pound subject while ascending three different stairways. . . The horizontal force exerted by the 172 pound subject while ascending three different stairways. . . Comparison of the stairway averages for the horizontal force, 140 pound subject ascending the stairways. . Comparison of the percent point averages for the horizontal force, 140 pound subject ascending the stairways. Comparison of the stairway averages for the horizontal force, 172 pound subject ascending the stairways. . Comparison of the percent point averages for the horizontal force, 172 pound subject ascending the stairways. The horizontal force exerted by the two subjects while ascending the stairways. Average for the nine stairways. Center of pressure while ascending a stair- way with 6 inch risers and 11 inch treads. The basic division of one complete step while descending a stairway. . The vertical force exerted by the 140 pound subject while descending a stairway with 6 inch risers and 10 inch treads. Comparison of the stairway averages for the vertical force, 140 pound subject ascending the stairways. . X Page 76 78 90 a4 84 86 9-7 88 90 95 96 100 LIST OF FIGURES Figure 42 Comparison of the percent point averages for the vertical force, 140 pound subject descending the stairways. . . 43 Comparison of the stairway averages for the vertical force, 172 pound subject ascending the stairways. . 44 Comparison of the percent point averages for the vertical force, 172 pound subject descending the stairways. . 45 The vertical force exerted by two subjects while descending the stairways. Average for the nine stairways. . 46 The vertical force, as a percent of body weight, exerted by each subject while descending the stairways. Average for the nine stairways. . . 47 The horizontal force exerted by each subject while descending a stairway with 6 inch risers and 11 inch treads. . . 48 Comparison of the stairway averages for the horizontal force, 140 pound subject descending the stairways. . . 49 Comparison of the percent point averages for the horizontal force, 140 pound subject descending the stairways. . 50 Comparison of the stairway averages for the horizontal force, 172 pound subject descending the stairways. . . 51 Comparison of the percent point averages for the horizontal force, 172 pound sub- ject descending the stairways. . . 52 The horizontal force exerted by each subject while descending the stairways. Average for the nine stairways. . . 53 Center of pressure for each subject while descending a stairway with 6 inch risers and 11 inch treads. . . xi Page 101 103 104 105 106 109 111 112 114 114 116 118 LIST OF FIGURES Figure 54 Comparison of the center of pressure 55 57 5a 59- ‘ so 61 averages, 140 pound subject descending the stairways. . . Comparison of the center of pressure averages, 172 pound subject descending the stairways. . . A schematic diagram of the instrumented stair tread. A tOp view showing the specific dimensions. . . The labeling of the Wheatstone Bridge Location of the strain gages on the corner support. . . . The strain gage circuits for determining 51 and 52. . . . The strain gage circuit for determining 63. The strain gage circuits for determining 6 4 and £50 0 o o xii Page 120 122 131 134 136 138 141 144 LIST OF APPENDICES Appendix I II III IV The Strain Gage Circuit and Bridge Output for the Transducer of the Friction Measuring Machine. . . . Force Plate Design and Operating Circuits. The Coefficient of Friction Values for the Sole and Tread Materials. . The Calculation of a Bank Correlation value. 0 O 0 O The Magnitude of the Vertical Force, Hori— zontal Force and the Point of Application of the Vertical Force. . . xiv Page 129 131 146 148 149 INTRODUCTION Ever since man has constructed buildings of more than one story he has been confronted with the problem of traveling from one floor to another. He has met this problem in several ways. He has built stairways, elevators and escalators. While elevators and escalators have re— ceived widespread usage in large commercial structures the stairway still remains the method used in his home. Although the stairway has been used for many years man still has not made it a safe means of traveling from floor to floor. In 1959 more than 2200 farm people died as a result of falls. About a third of these accidents cmcurred on steps and stairways (National Safety Council 1959). A survey of 100 stairway accidents by Miller (12) showed that 38% of the accidents were caused by slipping. ifiller also concluded that the non uniform dimensions of treads and risers was greater on the accident stairways than for a representative group of stairways reported by Velz (17). Three factors must be considered in the analysis of stairway safety: 1) the tread material and its friction Characteristics, 2) the actual forces exerted on the stair tread as a person ascends and descends the stairs, and 3) the Point of application of the forces in relation to the front edge of the stair tread. The type of shoe sole may 1 be considered a fourth factor; however, it is uncontrol- lable from the standpoint of stairway design. Since tread materials are subject to wear,_a high coefficient of friction under both new and used conditions is desirable. A trend material with a high coefficient of friction for a wide selection of shoe-sole materials is also desirable. The measurement of the forces exerted by the foot of a person is necessary to determine how high the friction value of a tread has to be to prevent slipping. The forces exerted and their point of application may depend somewhat on the dimensions of the stairway. The wide variation in stairway dimensions shown by Killer (12) snd‘Weaver and Pogue (21) suggest that no uniform con- struction pattern for stairways exists. While sets of design equations and specifications are available, they V8?! between "authorities". The objective of this thesis is two fold. The first is to evaluate the friction characteristics of various shoe sole and stair tread materials. The second is to evnluate and analyze the forces exerted by individuals ascending and descending stairs of different designs. REVIEW OF LITERATURE Stairway Accidents A survey of 100 stairway accidents by Killer (12) showed that most accidents happened in the mid-morning, mid—afternoon and early evening periods. The greatest number of accidents occurred around 10 A.M.. The fact that 81% of the accidents occurred to women and time of occurance suggests that many of the accidents occur during the process of doing household work. The rate of falls, however, did not increase with the persons age. Presumably older people were more cautious or decreased their use of the stairs. Slipping was found to be the direct cause of 38% of the accidents. lissing a step was responsible for 18% while loosing balance accounted for 16%. Hurrying and having the arms full while using the stairs were contrib- uting factors in 61% of the accidents. Twenty-four per cent of the falls caused by slipping occurred on rubber mats. Linoleum accounted for another 20%, varnish 18%, paint 16%, carpet 14% and 4% occurred on bare wood. Iiller (12) also found a wide variation in tread mate- rials‘being used. The types of finishes for 135 stairways Vere as follow: 32 Paint 13 Linoleum with no metal 2 Rubber Mat edge 18 Varnish 7 Linoleum with edge 16 Full length carpet type metal edge 10 Bare wood 6 Linoleum with surface 6. Other type metal edge 4 'Physiological Responses of Women Weaver (20) investigated the physiological responses of women while ascending and descending stairways of dif- ferent designs. Three stairways were constructed; one with a 33° slope and the other two with a 400 slope. Stairway #1, considered architecturally correct, had 7 inch risers and 11 inch treads. Stairway #2 had 7 inch risers and 9 inch treads while stairway #3 had 9 inch risers and 11 inch treads. Ten women subjects were observed ascending and descending the stairs at a rate of 2.2 m.p.h.. A statistical analysis of the investigation showed no significant difference between the three stairways. In ascending, the stairs with a 400 slope (2&3) used less energy but an increase in the heart rate and pulse pressure oc- . curred. In descending, the stairs with a 40° slope used more energy and increased both the heart rate and pulse pressure. Stairway.Design An attempt to improve the safety of stairways should include an analysis of stairway design. There is no defi- rflte set of dimensions for designing a stairway. In a Survey of housing preferences by Weaver and Pogue (21) a wide variation in stairways was disclosed. The slope of the stairways varied from 31 to 47 degrees. The treads Varied from 7 to 12.75 inches while the risers varied from 5.75 to 9.75 inches. Parker, Gay and lacGuire (13) suggest that a good 5 riser height is from 7 to 7.5 inches. They give as a set of design equations the following: 1) T J B 3 177 to 17.5" 2) T # ZR = 25" for interior stairs 3) T x R -‘70 in. to 75 in. T is the tread width (less nosing) and R is the riser height. Ierrit (11) suggests that the second equation above should be T / 28 = 24" to 25". The Forest Service of the ILS.D.A. (7) suggest that the first equation should be I dropped and the last equation should read T x R 8 75 in. The Forest Service states: There is a definite relation between the height of a riser and the width of a tread, and all stairs should be laid out to conform to well established rules governing these relations. If the combination of run to rise is too great, the steps are tiring; and if too short, the foot may kick the riser at each step and an attempt to shorten the stride may be tiring. Experience has proved that a riser 7 to 7% inches high with appropriate tread combines both comfort and safety, and these limits therefore determine the standard height of risers commonly used for principal stairs. As the height of the riser is increased, the width of the tread must be decreased for comfortable results. Coefficient of Friction of Stairway Materials Hunter (10) reported that measurements on new or unworn specimens of walkway materials gave little indica— tion of the true value of u (coefficient of friction). He states that test surfaces should be standardized with res- pect to smoothness, cleanliness and dryness to get repro- ‘ . du¢€Ible results. However, he also states that there seems t0 be no possibility of selecting a single or even a limited 6 number of surface conditions which can be defined or accu- rately produced. This is because the wear on a tread or walkway material will vary with its location in a building, thus making possible many different values of u for a single sole and tread combination. Sigler, Geib and Boone (16) have conducted friction tests on a large number of materials. A pendulum type apparatus holding a test heel was used. The test method duplicated the way a heel hits a level walkway surface. Leather and rubber heels were tested in the experiment. In all tests on dry surfaces they found that the rubber heel gave a higher coefficient of friction than the leather heel. However, on wet surfaces both heels had low coefe ficients and could be classified as potential hazards. The only wet surfaces which gave good results were those con- taining asperities that projected through the film of water. The asperities prevented the water from acting as a lubricant. A series of tests on waxed surfaces was also carried out. It was found that the coefficient of friction of a waxed surface was higher than that of a clean surface for a dry rubber heel. However, for the leather heel and both kwels under wet conditions a decrease in the coefficient (wourred on the waxed surfaces. Under continual use it tmok approximately one month to wear the wax off and return the coefficient of friction to that of a clean surface. 7 Friction of Non-Metals The friction between shoe soles and stairway treads is the result of the contact of two elastic materials. Bowden and Tabor (2) report that for elastic materials the basic laws of friction do not apply. Instead of u being proportional it is inversely proportional to the weight applied. The coefficient of friction decreases as the weight is increased. Bowden and Tabor (2) stated that all surfaces are rough on an atomic scale. As two materials are placed on one another the only contact occurs at the tips of the' asperitie.. The actual contact area is very small making the resulting pressures extremely high. Over regions of intimate contact strong adhesion occurs and the two mate- rials become a continuous body. The friction force is the ‘force required to shear this junction. With metalic mate-- rials the area of true contact is proportional to the weight applied. However, for elastic materials the true area of contact can depend on the geometry of the surface, the load or the time of loading. For elastic materials Ad: Wn Where n < l and A is the true contact area. While the area of contact and weight play an important role in the value of u, Bowden and Tabor (2) state that the most important factor is the cleanliness of the surface. They point out that surface cleanliness is far more impor- tant than surface roughness. Gomer and Smith (9) show that 8 the presence of certain types of films including water vapor will cause a decrease in the coefficient of friction. This decrease is due to a very thin film which is formed ‘ on the surface. The physical adsorption of water vapor on clean sur— faces amounts to only one or two molecular layers at the saturation pressure. However, a suitable trace of con- tamination will lead to the presence of large quantities of water on the surfaces at pressures well below saturation. Germant (8) has given a qualitative picture of this boundary lubrication. Figure 1 shows two surfaces in con- tact, each covered with a thin film two molecules deep. When the lower surface is moved, layer 1 and layer 4 will still adhere to their respective surfaces. However, the forces of attraction between subsequent layers become weaker as their distance from the surface increases. There will be moderate slippage between layers 1 and 2 and between layers 3 and 4. A considerable amount of slippage will take place between layers 2 and 3. The formation of the surface layers depends upon the attraction between the liquid and solid, as measured by the adhesion tension. The adhesion tension is particularly lugh for molecules containing polar groups such as 0H and COOH. Germant (8) also reported that where friction tests lmve been conducted the coefficient of friction drops according to a curve indicated in Figure 2. A definite lljllz/Lzljjj [ ' - e r L 2 \\\\\\\ Hi I __J 3 fl W1} 7/ I I I I7 fir/7— (a) (b) 1/////[////1/ f/f77777/fI/7 Figure l: A schematic picture of molecules in boundary lubrication, a) surface at rest, b) surfaces in motion. Germant (8) A amount of lubrication is required to cause a change. When this has been reached the friction value dimishes rapidly and later slowly with an increasing thickness of the layer. It is believed that the point of sharp drop occurs after the first layer has been formed. ? u Vapor Pressure —- Figure 2: The relationshig between u and the partial vapor pressure. Germant ( ) \ Human Locomotion A study of human locomotion while ascending and // 10 descending stairs is an important part of any attempt to improve stairways. A considerable number of investigations on human locomotion have been reported. However, most of these have been carried out on a level surface. A determination of the actual forces exerted by the foot while ascending and descending stairs would be very helpful. Eberhart and Inman (5) report that the most direct means of measuring all ground reactions is the force plate. With this plate records of the vertical force, both horizontal shears, torque, and the center of pressure of the foot can be obtained. Cunningham and Brown (3) discuss the design and operation of a force plate. They obtained the value of the forces by using strain gages on tubular columns. With the use of a force plate Rehman, Patek and Gregson (14) determined the ground reactions which occur in level walking. They state that the maximum vertical, horizontal and lateral forces occur at 22.5% and 72.5% of the full stride. The maximum vertical force is greater than the body weight due to Newton's Law, F a ma. The first half of the horizontal force is directed posteriorly as the foot pushes forward. The last half of the reaction is fOrward while the foot pushes back. The maximum horizontal reaction amounted to about 15% of the total body weight. The maximum lateral forces amounted to only four to five Percent of the body weight. Barnett (1) measured the pressures of the foot with a ll pedograph and reported that the walking stride can be divided into five phases. The phases are as follows: a) b) c) d) e) Heel Phggg - In this phase only the heel touches the ground. The whole heel bears the weight evenly most of the time. This phase occurs in the first 15 to 20 percent of the total stance. Standing ghggg - The pressure is taken by the heel, the outer side of the sole and the heads of the metatarsal bones. The center of gravity of the body is directly over the foot. This phase lasts for 30 to 35 percent of the total stance. Metatarsal - All of the weight is borne by the metatarsal heads. This phase seldom exceeds 10 percent of the total stance. zgrgfggj Ehggg — The toes and the metatarsal heads bear the weight. This phase occupies 30 percent of the total stance. Eggs; - The weight of the foot is borne entirely on the toes, especially the hallax. However, most of the body weight is on the other foot. This phase will make up from 3 to 10 percent of the total stance. EXPERIMENTAL INVESTIGATION COEFFICIENT OF FRICTION FOR TREAD AND SHOE SOLE MATERIALS Tread Covering Materials The tread materials selected for this investigation were wood, inlaid linoleum, a non-skid type paint, varnish, marblized rubber mat and an abrasive strip. The first five materials were found most often in Miller‘s (12) study. The sixth material, the abrasive strip was studied for comparative purposes. New and worn specimens of each tread material were studied. The surfaces for the new specimens of wood, linoleum, abrasive strip and rubber mat were left in their original condition. The linoleum, abrasive strip and rubber mat materials were cemented to pieces of plywood for the tests. A test surface for the abrasive strips, which were three quarters of an inch wide, consisted of two strips placed one half of an inch apart. The rubber mat, which contained surface grooves, was oriented such that the sole material .crossed perpendicularly to the grooves. Varnish and paint were applied to regular wood stair tread material according to directions. A regular wooden stair tread was used for the tests on wood. Because of the difficulty encountered in obtaining used tread materials, the worn tread materials were pre- pared in the laboratory. They were prepared by rubbing l2 13 new tread materials with a very fine sand (50 mesh) as suggested by Hunter (10). Shoe Sole Materials The shoe sole materials used in this study were n80” prene, neolite, leather, a neoprene base crepe, ripple and a hard surface sole made by B. F. Goodrich. The investi- gation was carried out using new and worn specimens for two different sole sizes for each of the six soles studied. The different sole sizes represented the worn area of an average size sole for a man and woman. The area of the two sole sizes was 16.4 and 10.7 square inches. To perform the desired tests the shoe soles had to be mounted in a metal holder (see testing equipment). The soles were mounted as follows: ' l) A sole was trimmed to the desired size. 2) A piece of plywood was cut to the same size. 3) The plywood was nailed to a wooden block approxi- mately 8% inches square. 4) The sole was cemented to the plywood and held in place by clamps until dry. The sole holder was attached to the metal holder by four small bolts. The total thickness of the shoe sole holder had to be constant because the arms connecting the metal holder to the strain gage transducer had to be level during the Operation of the testing machine. The thickness of the shoe soles varied for the different materials so the total thickness was held constant by adjusting the thickness of the plywood. The sole was oriented so the vertical force 14 applied to the metal holder was directly over its centroid. The new soles were mounted to the holding block in their original condition. Worn soles of all the materials except the hard surface sole were obtained from old shoes purchased at second hand stores. These soles were removed from the shoes and mounted to the holder. The worn B. F. Goodrich sole was obtained by rubbing a new sole with the same type of sand used on the treads. Testing Equipment The coefficient of friction was measured with the machine shown in Figures 3 and 4. This machine consisted of a movable table under a stationary holder. The holder was fastened to two vertical bars containing strain gages. The strain gage bridge was connected to a Brush amplifier and inking oscillograph. The vertical load was applied by placing weights at the end of the arm resting on the holder. This arm had a l to 3 mechanical advantage (1 pound at the end of the bar places 3 pounds on the holder). In this investigation the tread material was placed on the table and the shoe sole material was fastened to the holder. The tread materials moved under the holder at a uniform speed and the horizontal force was recorded on the oscillograph. From the horizontal and vertical forces the coefficient of friction was calculated (coefficient of friction equals the horizontal force divided by the vertical force). The dvnamic coefficient of friction was used in Figure 3: The machine used to measure the coefficient of friction. Figure #: A close view of the machine used to measure the coefficient of friction showing the sole holder and the stair tread. 16 this study. The strain gage circuit consisted of eight SR—4 (type 4-5) strain gages, two in each arm of the Wheatstone Bridge. The output of this circuit is given by the following formula: (is 6PT. EbH2 a Bridge output, in units of strain. . Horizontal force, pounds. Distance from the end reaction to the center of the strain gage, inches. Modulus of elasticity, psi. width of the bar, inches. Thickness of the bar, inches. Ilflll > mom hum diagram of the strain gage circuit and the deriva- tion of the above formula is in Appendix I. The circuit was calibrated by applying known loads to the bars and adjusting the oscillograph to read pounds per line of deflection. It was possible to calibrate using this procedure because 6 is directly proportional to P since L, E, b and H are all constant for any measurement. Once the strain gage circuit had been calibrated the internal calibration circuit of the amplifier was used before each test period to eliminate the process of manual calibration. The calibration curve for the circuit is shown in Figure 5. Procedure of the Investigation For this investigation the coefficient of friction was measured for only one vertical force and one table speed. A vertical force of 117 pounds was used. Loads 17 on» no noosommmup ommw camnpm on» you opus. OO— sa_.momou mam» 00 00 .ocdnoma ooduoaau coaueanaaeo one um onswah mm OW LP D q q 0 N ‘6 e ‘6 (D O O l. :00. aqu‘sosos oaansvaw 18 greater than this caused one of the tread materials to tear apart. Higher loads also caused considerable wear on some of the soles. The table moved at a speed of 14.6 feet per minute. Preliminary tests indicated that faster table speeds caused the vertical bars to vibrate when the horizontal force was applied. The investigation was designed so that it could be analyzed statistically. The study was run as a series of separate parts. Each part consisted of the new and used Specimens of a single sole type and size.) The coefficient of friction was measured using these soles and the twelve different tread materials. There were three duplications of each sole and tread material. The order in which the measurements were made was determined by randomization. Each individual shoe sole was tested on twelve dif- ferent tread materials during each single investigation. To prevent the sole and tread materials from becoming smooth they were brushed lightly with a piece of 3/0 sandpaper between each test. This proCedure of keeping the materials in a condition similar to that of natural walking was suggested by Hunter (10). MEASURING THE FORCES EXERTED ON STAIH STEPS Description of the Equipment The magnitude, direction and point of application of forces exerted by a person ascending and descending a stairway were measured by the force plate shown in Figure 6. 19 The force plate contains five separate strain gage circuits and is capable of measuring the vertical force, both hori— zontal forces and the point of application of these forces in relation to the front edge and side of the tread. The frame holding the instrumented stair tread is supported at each corner by small columns made from Reynolds 618T6 Aluminum. This aluminum has a yield stress of 40,000 psi. The support is 5.62 inches high with an outside diameter of 0.876 0.008 inch. The inside dia- meter is 0.787 0.002 inch. The force plate was designed to be used in stairways with different riser height and tread width combinations. A detailed drawing of the corner support is shown in Figure 8. Bridge Output Each of the strain gage circuits consisted of eight SR-4 (type A-5) strain gages, two in each arm of the Wheatstone Bridge. The equations for the bridge output of the circuits are as follows: Circuit #1 61 a P (2e2-d) . . P (d-2e1) (l) d A E d A E Circuit #2 62 .- P (Zea—L) ':.-. P (Ln2e4) (2) L {E L A E ' Circuit #3 63 a P ((u-l)(2e1e4)r‘(l-u)(e4d—e1L)/udL) dLAE‘ ' Circuit #4 6%,: Hy t c (4) EI Circuit #5 65 .. H): t c (5) EI (3) 20 Figure 6: The force plate in one of the experimental stairways. Figure 7: Calibrating the force plate for vertical forces and the coordinate system. 21 r— A —* "I Ha _ 1 I; I ——..—— —....T .0.___.—L ' \ \ T L \ ‘ 1 \ 1 *t t : . ~ . I c _ " N 860110" X-X W x ‘ N N l H : ~ ~ ‘4 : ~ J _ I w r H # . N *7 “a I I I r V 1 d —-—-- ---- we DIMENSIONS 0.876" + 0.003" T 0.787“ g 0.002" 2.365" t 0.007“ 0.376" I 0.003" LOIO" t 0.010" 0.257“ t 0.006" 5.62" t Figure 8: The corner support for the force plate. II II IO N h m X H ¢+ It c: u. 22 Bridge output in units of strain, 0 = circuit number Vertical force, lbs. Cross sectional area of one support, 9.116 in. Modulus of elasticity of aluminum, 10 psi. Horizontal force toward the front or rear edge of the tread, lbs. Horizontal force toward the right or left side of the tread, lbs. Distance from the end reaction of the supports to the center of the strain gages measuring the fix and By forces, inches. Radius of the support, inches. Poisson's ratio, 0.33 for aluminum. L, d, e , e , e and e are specific dimensions of the The frame holding the stair tread. See Figure 9. orientation of the strain gages on the supports, a diagram of the circuits and the derivation of the equa- tions are in Appendix II. Figure 9: A schematic diagram of the tread holder showing the specific dimensions. For any measurement the equations for circuits (1) and (2) contain two unknown quantities. The vertical force P and the location of the force with respect to the front 2; tion for side of the tread. For any measurement the equa— circuit (3) contains three unknown quantities. The vertical force P and the location of the force with respect to both the front and side of the tread. To de— termine the magnitude of the vex tical force, equations 23 (l) and (2) were solved in terms of el and e4 and sub— stituted into equation (3). The resulting equation was: (1K4) ’, u: €1€2(u-—l) 2 2 P 63 3 P This equation can be put into the form of a quadratic equation and solved for P. ._ E3 1163 2 _ 4(_1.'w)(1/AE) (A E€1€2(u-l)) 2 2 P - _ 2(l/AE) (1 / u) I 2 Substituting in the numerical values for u, A and E reduces the equation to: Leg“ €32 ,z 0-90 61 e2 FD== 6 1.146 x 10- Calibration 'Because equations (1), (2) and (3) contained more than 1 unknown quantity, circuits 1, 2 and 3 were calibrated so the oscillograph read 5 micro inches per inch of strain per line of deflection. The internal calibration circuit of the amplifier was used to achieve this reading. The calibration was accomplished by placing the attenuator on 20 and adjusting the oscillograph pen for 15.5 lines of deflection after the amplifier had been balanced in. The 24 attenuator was then set at 5 and the measurements were made at this attenuator setting. The relationship between the applied and measured vertical loads was determined by applying a known load at a known position as shown in Figure 7. This procedure was repeated for several different loads and positions. Cali- bration curves showing the relationship between the applied and measured vertical force are shown in Figures 10 and 11. The vertical force could not be applied to a specific point but instead had to be applied over a small area. As shown in Figure 9, the vertical force was applied by a lever arm resting on a small block which was one inch ' square. The vertical force was applied as near as possible over the center of the block. The true position of el and e4 was the distance from their respective edges of the tread to the center of the block. However, due to the difficulty of determining the exact position of the vertical force an error of 0.125 and 0.25 inches were allowed for e1 and e4 respectively. These two limits allowed for errors in measuring the center line of the block, the placing of the lever arm on the block and the reading of the oscillograph chart. A larger error was allowed for e4 because this measurement was affected more by a change in the placement of the lever arm. The relationship between the true and measured positions for e1 and e4 are shown in Figures 12 and 13. The band formed by the two lines indicate the region in which values were acceptable. 25 - r/ k .0“ . 1r .. J/ i Y 803.8 'I- |.086(X) I g 4 l A A L MEASURED FORCE, lbs, (y) 5'} LLLL o.re~v -. 40 so use use 2:00 APPLIED FORCE, lbs. (x) Figure 10: The calibration curve for the vertical ores when e1 is less than one half the tread width. S: 3‘ 20041 m e 4T c K 3" “01b ’ _k/ A m 0 / C) llmt u. i f a co~ K g T / v: -I.O7 4- 0.946(X) m ‘Oh— 1 I i <1 .4 T I ,- o + t F a : e a e 2 4O .0 Ito 1.0 200 APPLIED FORCE, lbs. (X) Figure 11: The calibration curve for the vertical force when el is greater than one half the tread width. 26 L g ' V 7 I / J 1 f inches IL (3 Z .. Q 9 t: i m 0 0 CD a: 0- .2 ‘0 yr :3 D C 0 32 t; V /A(//;;;§: 8 f "‘ r/ g 0 // + 4/? L if g r g 0 z 3 c e c TRUE POSITION 0F 3', inches Figure 12: The calibration curve for e1. U. C) l’cb :5 u 9 . t 3 " (D E l3" CD a_ .. .. / no: " //’ a=e one "ma madman BE .5393... 3:5 @3985 < sm_c..o> E3205... too; a o ’- ol 0 o :0... mNd Omd NO 00; one: 93: a co oaoo c3: 7”. one: too a co oaon one; D ouch» duos a co oHom to: E neon» ton a co oaou to: EH— NOIL OIH :1 :10 .LN BIOHdBOO l. . ..E...... r‘nfi’noflt‘ . t r. 35 These graphs show some of the general trends and particular phenomenon of this investigation. Figure 19, which is for the large neOprene sole, indicates that the abrasive strip had the highest coeffi- cient of friction value for the six tread materials. The abrasive strip had the highest friction value (the four simulated conditions averaged together) of the six tread materials for nine of the twelve soles investigated. Only with the small leather and the large and small ripple soles were there other tread materials which had a higher coeffi— cient of friction than the abrasive strip. Another trend which is apparent from Figure 19 is that the worn linoleum material had a higher coefficient of friction than did the new linoleum. When the coeffi— cient of friction was compared for the combination of a new sole material on new and worn tread materials the worn mate— rial had an equal or higher friction value for nine of the twelve soles investigated. Only for the large ripple and the large and small neolite soles was the friction value of the new linoleum higher than that for the worn linoleum. When the coefficient of friction for the worn soles on new and worn linoleum material was compared, the worn tread material had an equal or higher coefficient of friction for eight of the twelve soles investigated. The large neolite and the small neoprene, neolite and B.F. Goodrich soles had higher friction values on the new linoleum. Another trend apparent from Figure 19 is the small 36 variation between the means of the four simulated conditions of the abrasive and rubber mat tread materials. To determine the amount of dispersion in the data of each tread material the data for the four simulated conditions are combined and the mean and standard deviation of these data were computed. This analysis was performed for each of the twelve soles investigated. The standard deviation was computed from the following formula suggested by Walker and Lev (l8). 2 l - 2 (Zix) z n — l The mean (Y), the standard deviation (8) and the inter- val X S, which includes 68% of the data values, are given in Table 1. From this table it can be seen that the rubber mat material and the abrasive strip generally had the smallest standard deviation of the six tread materials investigated for the large and small neoprene, crepe and neolite soles and the small ripple sole. The abrasive strip had the smallest stand— ard deviation for the large ripple and small leather soles. The painted tread had the smallest standard deviation for the large and small B.F. Goodrich soles while the worn tread had the lowest value for the large leather sole. As a general rule the wood, linoleum and varnished tread materials had a larger standard deviation than did the abrasive, rubber mat and painted tread materials. 'For seven of the twelve soles investigated the rubber mat, 37 abrasive and paint had the three smallest standard devia- tions. For four of the other five soles one of these three tread materials had the smallest deviation of the six tread materials.‘ Figure 20, which is for the large crepe sole, reveals a phenomenon which occurred primarily with the crepe sole. For this sole the combination of a new sole material on a new tread material gave the highest coefficient of fric- tion value for the four simulated conditions. This was true for the wood, abrasive, varnish and painted treads for both the large and small crepe soles. This phenomenon occurred for other sole and tread combinations but not with the regularity that was observed with the crepe sole. Figure 21, which is for the large ripple sole, shows the high coefficient of friction values obtained with the ripple sole. It should be noticed that the highest values occur on the smooth surfaced treads. The abrasive strip and rubber mat materials have the lowest values of the six tread materials. This was true for both the large and small ripple soles. Analysis of New and Worn Tread Materials for a Worn Sole Material When a stair tread material is placed on a stairway it is expected to last for a period of years. During this period of usage the surface condition of the tread material will change. It would be desirable, however, if the coefficient of friction of the tread material either 38 0m.0u0m.0 HH.0 0e.0 05.0-«m.0 50.0 05.0 00: ampnsm 0 .0:¢0.0 50.0 mm.0 00.0-0 .0 NH.0 «.0 named Hm.0:m¢.0 a0.0 5¢.0 00.0-0m.0 0H.0 5.0 m>anaap¢ H¢.0uam.0 0H.0 Hm.0 00.0-m .0 00.0 0m.0 enacaa> 00.0-0H.0 00.0 a0.0 0m.0umm.0 50.0 ma. asmaocag 0m.020H.0 00.0 ¢N.0 0m.0|0~.0 a0.0 mm.0 000: waom honuamn H5.0amm.0 «5.0 e0.0 N5.0-00.0 00.0 00.0 pa: magnum m0.04 ¢.0 0~.0 mm.0 0m.0|m¢.0 50.0 0e.0 human em.0u00.0 00.0 05.0 em.0:05.0 50.0 55.0 asamaapa 0 .0:0¢.0 0H.0 00.0 m0.0-m¢.0 0H.0 mm.o smaca0> 00.0umm.0 HH.0 ve.0 m.0u0m.0 0~.0 0¢.0 assaocan 00.0nee.0 NH.0 00.0 00.0-0m.0 00.0 00.0 000; wfiow m who m5.0um0.0 00.0 00.0 m5.0u00.0 m0.0 05.0 00: “spasm 00.0-Hm.0 00.0 00.0 00.0-em.0 00.0 00.0 pcamm 0 .0105.0 50.0 55.0 e0.0umm.0 00.0 00.0 m>amaap< e .0:mm.0 HH.0 m0.0 00.0-0 .0 NH.0 00.0 smacaa> m0.0-m¢.0 HH.0 00.0 00.0nom.0 00.0 00.0 asmaoaaq 55.0:0¢.0 ¢H.0 m0.0 00.0-0m.0 ¢H.0 05.0 0003 Mdmm ecommoom .III. IE. 0 am 0 x 0.05 m m oaom Hanan oaom omuma Huauoumx omens .Hmahmpm: omega cam maom mamcww a wma>ao>cH acoauficcoo anon an» no «pee cofiuoapm no ucoaoauuooo on» mo mnnm.mo Ha>amucfi on» cam Amv coapaa>oa cmeccwuw on» .AMV see: was “H uqmanman< :anAw> enoaoefig coo; «~00 «Hanan pm: 000050 peaam o>wmwpn< smacmc> asmaocfin coo: onom mmwuoaou .N.m 00: magnum unwed m>ammun¢ nmficaa> EzmaocHA 000: mHom moaaomz .Hmwpopmz camps tam -wHom maucfim mcfi>ao>ca mcoauaccoo paom mg» no mama cofipowam mo pcmfionmmoo esp mo .AMV cams one «H mqm<9 MO .22 Begum 2.5 «20204 ‘02:; 60205.. @003 .oHon omen. owned emu use occauaucoo oneness copmagaan on» no some now moan-«nu no pcoauauuooo ewwaopm one now unawau .‘C‘ I O OH «em as non-8 as as. ’ 0... ... IUD“.- .l’. u. a... at as.- 0 ~00“. \l. a...” w 0.0% at‘ ”00.00 7- . o o . 4.. .- aa \ IL # ///7/// /////////Z/ I /////Z////// l //////////./ D g 0; ‘ 'o. . at \1' .-t'-~' 0: .° ‘.I '3.” .0.” '0‘: | 1' 2.0". ‘ ' s‘ .'o¢. /7]7////Z///// [M ///7////////// use: duos a so 300 2.35.. a use: no: a do 300 anon. U 00000 000. a a0 0H00 .02 00000 each” .00 0 00 .000 .00 mHHHH_ Av \L vad 7one who £00.. NOIlOIH :l :10 .L NBIOHSEOO M1 .oaom oaaaan owned on» can nmoaaaccoo commune nonmamaao one no memo non moduoaau no acoaodunooo ommao>m one "am madman Es. magnum .55 030054. :0_Eo> 500.003 0003 f O I O It’s I C. Q. o... J . a o a O C I \ 0 N0 00.0 I who .l 00.. N... use: duo: o no 300 93». 0.00.3 snot m :0 0.3m- 3.02 E use: son a no oaom duo; use: to: 0 mo oaoo to: E2: NOIlOIUJ :IO .LNHIOL-JABOO 42 remained constant or increased with use. To determine if there were significant changes in the coefficient of fric- tion between new and worn conditions of a tread material the friction values for the conditions were compared using the factorial analysis. This comparison was performed only for the worn soles. The results of the factorial analysis are in Table 2. The values given are the difference between the average coefficient of friction for the new tread material and the average value for the worn material. A negative sign indicates that the average friction value for the worn material was higher than the value of the new material. An asterisk indicates there was a significant difference between the two values at the 95% probability level. For the large geeegepe eele the new tread material had a significantly larger coefficient of friction than the worn material for the wood, varnish and painted treads. The two conditions of the linoleum tread were also signi- f‘icantly different except the worn tread had the highest coefficient of friction. For the small neoprene sole 81lig’nii‘icant differences occurred with the varnished and p31 nted treads. For both treads the new condition had the highest friction value. For the large crepe sole the linoleum and rubber mat um‘T-erials had a significant difference between their two 3\\Pface conditions. In both cases the worn material had the highest coefficient of friction. For the small crepe 43 sole there were significant differences between the two tread conditions of the linoleum varnish, paint and rubber mat materials. Except for the rubber mat material the highest coefficient of friction value was obtained on the surface . The linoleum, varnish, paint and rubber mat materials lied a significant difference between their two surface Of these four austerials, linoleum was the only one which had its highest ccaefficient of friction on the worn surface. The wood, vearnish, paint and rubber mat materials had a significant riifference between their new and worn surface condition for true small leather sole. The highest coefficient of friction runs obtained on the new surface for each of the four mate- rials. For the large neolite sole the linoleum and varnish trneads had significant differences between their two Sllxrface conditions. The linoleum had its highest value the new material while the highest friction value for The varnish on ttlea varnish was obtained on the worn surface. ”‘13 0 had a significant difference between its new and worn 3‘11‘ face for the small neolite sole. However, its highest f‘r‘iction value was obtained on the new surface. For the large giggle sole the linoleum material, which obtained its highest coefficient of friction on the Surface, was the only material which had a significant dif«- Terence between its new and worn surface. However, the 44 ma0.0- *mma.0- amma.0- *am0.0- *¢0H.0- 0H0.0a museum Hacew mm0.0 500.0: ”no.0 sm0.0 *m0H.0 a00.0 magnum magma 0H0.0 0m0.0 mH0.0 *mHH.0 H0.0 *HHH.0 nuaacooo .u.m Hausa 0N0.0- #000.0- smo.0- m¢0.0 00.0- *es0.0 sesucooo .m.m eaten Hm0.0 HH0.0 000.0 *0mm.0 em0.0 00H.0 mpaaooz Hausa 0m0.0 Hm0.0 sm0.0 *smm.0u *NNH.0 0H0.0: opaaomz omamg aoefi.0 *NNH.0 Hm0.0 * 0~.0 sm0.0s *000.0 emnpamq afieam *0¢H.0 *mmH.0 ¢m0.0 * s0.0 *H0H.0u umo.0 emanate «mama *0HH.0- *e00.0 0m0.0 woma.0 *00H.0 eH0.0 sumac Hanan *aso.0- 0e0.0- mm0.0- 000.0- *0NH.0- «No.0 mawuo mwemg HH0.0 *H00.0 ¢m0.0- wema.0 m00.0 mm0.0u memeaowz Haaam «No.0 #050.0 0H0.0u *emm.0 *e00.0- *0om.0 envenomz magma we: .mo venue .maep0 snacaas asmaocag coon .oaom ago: a spa» mamwnoua: cache 0:» mo ”coauaecoo moauesm 0:9 map you mamsaac¢ asuopoaa may go ”panama any um mamas '5 4S linoleum, abrasive and painted treads had significant differences between their two surfaces for the small ripple sole. For each of these three materials its highest friction value was obtained on the worn surface. The reenlts given in Table 2 are summarized in Table 3. Table 3 gives the number of times a tread material had a significant difference between the two surface conditions (maximum of, 12) and whether the highest coefficient of friction value was obtained on the new or worn surface. Table 3 shows that the varnished tread had the highest number of significant differences with eight and that on seven of these occasions the highest friction value was obtained on the new surface. This indicates that the varnish tread is the most susceptible to wear and that Qenerally the coefficient of friction decreases with wear. The table also shows that the abrasive strip had a signi— ficant difference only once with the highest coefficient 01' friction being obtained on the worn surface. The fact of only one significant difference for the abrasive strip 1n“Oates that it is a very stable material and behaves the Same under new or worn surface conditions for nearly all t"Ypes of sole materials. Analysis of Worn Soles on Worn Tread Materials The combination of surface conditions most often en- e Cmntel‘ed during the use of a stairway is a worn sole m alter-1&1 on a worn tread material. The average COfoiCient 46 of friction for each sole and tread combination investi~ gated under this condition is contained in Table 4. —— TABLE 3: Summary of the Factorial Analysis laterial No. of times _§ighest frietion,value on significant New surface Worn surface Wood 4 4 O Linoleum g 3 4 Varnish 7 l Abrasive l 0 1 Paint 7 5 2 Rubber Mat 4 2 2 The six tread materials were compared with respect tea a particular sole material. The worn abrasive strip fund the highest coefficient of friction for the six tread matxarials on nine of the twelve soles. For the large worn ripple sole the worn varnish tread had the highest coef- ficienrt of friction value for the small ripple sole. For the small leather sole the rubber mat material gave the highest friction value. {The data for the six worn tread materials was grouped togetdier’for each worn sole. From these data the mean and the Stnandard deviation was calculated for each of the soles. The mean, standard deviation and the interval of plus and Minus One standard deviation from the mean, (i 5), WhiCh includes 68% of the data, is given in Table 5. All of the standard deviation values were in the range Crf 0.06 to 0.14 except for the large leather sole. This 8Ole had a standard deviation of 0.21. The standard de viation obtained from the large leather sole is due to 47 00.0 0m.H so.“ 0N.H ma.H m0.H maagam Hawam 50.0 NH.H 00.0 mH.H mg.“ 0.0 manna: magma m0.0 no.0 H0.0 00.0 H0.0 0m.0 coatcooo.a.m HHmEm 0m.0 00.0 00.0 0m.0 mm.0 mm.0 noaacooo .m.m magma mm.0 no.0 00.0 no.0 sm.0 mm.0 mafiaomz aflasm 0m.0 00.0 «5.0 no.0 mm.0 0.0 cpaaomz magma 00.0 00.0 Hm.0 mm.0 0m.0 00.0 seesaw; aamam Hm.0 ee.0 em.0 em.0 me.0 em.0 0000000 «mean 00.0 me.0 00.0 0m.0 He.0 0«.0 mamso HaaEm 05.0 ue.0 «0.0 0e.0 mm.0 mm.0 sumac omega 05.0 00.0 mm.0 00.0 00.0 Hu.0 00000002 HHaEm 05.0 em.0 00.0 mm.0 00.0 0m.0 ocosaomz 00am; um: .m ucfimm o>fimwan< nmwcum> esoaocfiq coo? Egg; .mawapvaaa nevus ago; no oamaaouma oHom ago: you ofi~m> noHpoaam mo_ucwfio«umwoo omqao>< Q‘s “V mgmg& 48 Hm.0:mm.0 ea.0 um.0 ma.0-mm.0 Hm.0 em.0 amnpmmo 00.0:mm.0 .00.0 m0.0 00.0-me.0 m~.0 um.0 goa00000.a.m m0.0-0m.0 ma.0 Hm.0 00.0-me.0 HH.0 0m.0 ,mamao 50.0amm.0 00.m H0.0 H5.0nmm.0 00.0 m0u0 madaomz ss.0:sm.0 0H.0 50.0 ma.0xmm.0 ma.0 00.0 mcmtaomz mm.Hsa0.0 mH.0 0H.H m~.H-H0.0 m~.0 m0.H maaaam m x m m m x m m . maom Harem maom.mman Hawumpmfi awoke i .nmnuomou cou>H«Cm maawaouw: campy amok xfim ms» nu“: Hmaamumz maom ago: 0 you warm co Hapsmpefi 0:» 00m .Amv casuma>oo 0tm0cmpm .Amv new: one am mgm¢a ? 49 the wide difference between the coefficient of friction values on the tread materials. The large leather sole had friction values ranging from 0.34 on the wood tread'to 0.84 for the abrasive strip. This is a range of 0.50 for the leather sole while the ranges for the other soles varied from 0.11 to 0.35. The large standard deviation for the leather sole would indicate that the frictional properties of this sole change considerably with the tread material. The other soles indicate less variation between tread materials which may make them safer. Analysis of Sole Materials Independent of Tread Materials The average coefficient of friction of the sole materials investigated is illustrated graphically in Figures 22 and 23 and given numerically in Table 6. Each of the Values is an average of 108 measurements except for the 1‘L’JDIe sole and includes measurements from each of the twelve tread conditions. The values for the ripple sole are an average of 72 measurements. As a general rule the worn soles had a higher coef- f101.eernt of friction than did the new soles when comparing the ‘13vwo conditions of a particular sole material. 0f the 81x sole materials investigated the crepe "83 the only mater 131 in which the new sole had a higher coefficient of fr1°“t1t1 on than the worn sole for both sizes of sole. The large neoprene and the small ripple 30193 both had a higher co effhieien‘t of friction for the new materials. However, #9» Wu 50 there was very little difference between the new and worn conditions, 0.01 and 0.02 respectively. MW TABLE 6: The Average Coefficient of Friction for the New and Worn Condition of each Sole. Sole Material Large Sole _S_mall Sole New Worn New Worn Ripple 0.91 1.02 1.08 1.06 Neoprene 0.70 0.69 0.5 0.69 Neolite 0.61 0.66 0.5 0.64 Crepe 0.60 0.55 0.66 0.51 B.F. Goodrich 0.48 0.59 0.45 0.65 Leather 0.47 0.54 v 0.32 0.37 An average coefficient of friction value was calculated for each sole size of each sole material. This value was for the twelve tread conditions. The coefficient of friction values were ranked from highest to lowest, see Tfible 7. Although the average friction value varied between the two sole sizes the order ofarrangement was the same fVDr-‘hoth. The ripple sole had the highest friction value f‘C’llowed by the neoprene, neolite, crepe, B.F. Goodrich and leather soles . *4_ . _ ““i ——‘ .... _. .4.._ ”7 —._..~.....—.—.. ._.- _ ._...- _ __ --._.__._ .2, TABLE 7: The Average Coefficient of Friction Values __~______ for the Shoe Sole Materials. 318 Material Large Sole Small Sole -—~__2 Ripple 0.97 1.07 Neoprene 0.70 0.64 Neolite 0.64 0.61 Crepe 0.58 0.59 B.F. Goodrich 0.54 0.55 .Leather 0.51 0.35 51 .ooaom owaua on» «on coduoanu no acoaoamuooo owaaoew one .mm oaswdh 20.5.05..— ..._0 hzm_o_mn_moo N._ m... R 9.0 .v0 N6 0 P d d. 1 db ”.300 2:0; I 300 :62 U 7| ] [1 '& EMF—Run. 19008 0.0 mcmmo m._._.._ouz mzmmaomz m._n_a_m 52 .uoaou Hausa on» no“ acaouaun «o weed-«nuooo owaae>u one "mm oaswfih 202.02”: “.0 FZEOCquo m. 0... ewe 0.0 :0 mmxef1 I’our measurements. Table 12 indicates that the average 'tilnea spent on a tread was nearly the same when ascending orfl r‘?escending. However, the 172 pound subject traveled at q 1“aster rate than the 140 pound subject. Ascending a Stairway The event of ascending a stairway may be divided into ttTrwee basic periods, the "set", "lift" and "swing" periods. 64 no.0 0m.0 00.0 00.0 .0cmommo pomnnsm $0 $0 00.0 0.0.0 0:500 NOH d‘ \O O «0.0 00.0 00.0 mm.0 m0.0 No.0. 00.0 00.0 00.0 .000000 00.0 00.0 00.0 00.0 «0.0 00.0 00.0 00.0 00.0 .0000000 0000050 00000 00H 00.0 00.0 00.0 mu.0 00.0 00.0 00.0 00.0 00.0 .020000 .HH:0 0H-0 0:0 Ha-m 0H-u mum ~H-0 00:0 0-0 t mw¢smH< wne «ma mum mcfiocoomma mcficcmomc mcficcmommo maflmcmom< 0000000 02500 NBA pomnnzm eczom 00H .mm«zp«mpm mafia mnu how mmmum>m «wwonom Hmoapao> cam Haydoufiyom map wcfinsmmma awn: campy a co pcmnm Amtcoommv mafia mmwpm>¢ 0:? «NH mam¢a i I. 141.! it 65 Suppose a person standing at the bottom of a stairway decides he wants to ascend it. The person's first move would be to lift one foot from the floor and place it on the first step. The instant at which the foot is placed on the step will be called the "set" period. The forefoot shall be defined as the foot which is either stationary (yr «or: the higher of any two steps. For this example the fRJresfoot is on the first step. The rearfoot will be de- fined as the foot which is either moving or is on the lower of any two steps. For this example the rearfoot is on the floor. The person's next movement would be to apply pressure On the tread with his forefoot and lift his rearfoot off the floor. The interval during which this movement occurs will be termed the "lift" period. The final phase is m(Wine; the rearfoot forward and placing it on the next Step. The interval during which this movement occurs W111 be defined as the "swing" period. When the person's I‘Parfoot is placed on the upper step he is again at the u , set," period and tne rearfoot now bchmes the forefoot and Vice Versa. The event of ascending a stairway is simply a con- tinuous repetition of the "set", "lift" and "swing" periods. The three periods are illustrated in Figure 25. Vertical Force, Ascending The vertical force exerted by the 140 pound subject 66 a mcavcoomw oaan: noun opoaoaoo oco no ucoana>av canon one QOEMQ oz_3m OOEwn. hm... .udtnawpu "mm onswah 00.1mm Hum 67 while ascending a stairway with 6 inch risers and ll inch treads is shown in Figure 26. Figure 26 illustrates the gene ral pattern of the vertical force while ascending different stairways. . When a person ascends a stairway two relative maximum values in the vertical force occur. The first maximum takes place during the "lift" period and occurs when the E forefoot is applyimz pressure on the force plate and liftine the rearfoot from the lower tread. The first maximum value was usually greater than the body weight. A force greater than body weight occurred because the body weight is sup- \W‘ ported entirely by the forefoot and this foot is also applying a force on the tread. The first maximum value occurred approximately when 25 percent of the step had been completed. After the first maximum point was reached a depression occurs in the force curve. The depression occurs during the "swine" period. Although the total body weight was on the forefoot during this period, the total force measured was less than body weight. Since F «'3 ma (Newton's Law) the smaller force may possibly be explained by the upward acceleration of different parts of the body which produce forces that partially offset the body weight. The second maximum point occurs during, the "set" period, The body is under little upward acceleration due to the COmpletion of the "swing" period. The rearfoot which is now on the upper 'step supports little of the body .uuumu» noaa an new «Human coca 0 near smupamam a wcaocoomm oaanz pecansm fiasco osa map so ooaaoxo ocnom aaoauuop one new oaswam 005.5on 35 or: “.0 5.3me 66 00. m» on mu 0 z, .4 v a a v us a a 0m 4.0? . w AV o ’ r1 \ :00 , a , a \‘”fi/ ‘3 n? s \ a x . ..o~_ \ I . ‘A‘\ .t ow. ‘30303 wouuaw 'SB'I 69 weight. Thus most of the body weight is still on the force plate. The second maximum value is usually less than the total body weight and occurs approximately when 75’ percent of the step has been completed. Table 14 gives the value of the vertical force exerted on each stairway at the 25 percent point. This value was J the ' largest value which was calculated; however, this ”1 value was not necessarily the maximum vertical force exerted on the step. The maximum force may have been exerted either just before or after the 25 percent point. For the l40‘pound subject there was little difference * between the values at the 25 percent point. The values range from 139.7 pounds on the 6-9 stairway to 159.1 pounds on the 7-11 stairway. There was no definite relationship hathfeen the force exerted. and the riser height. However, for e‘ach riser height the maximum value occurred on the StaiPw-wy with an 11 inch tread. Iror the l72 pound subject there was a greater variation in the values with a minimum of 174.9 poun"s on the 8-9 Stair‘Way and a maximum of 215.6 pounds on the 8-ll stairway. Again there is no definite relationship between the force exerted and riser height. But for each riser height the maximilm value occurred on the stairway with an ll inch tread - ' A statistical analysis of the vertical force for the 140 Pound subject showed no significant difference be- tweefl the average force exerted on each of the nine stairways. _ pneum? o.mmH 0.0HH m.~oa 5.0HH m.eo~ H.00H m.eea o.maa o.efiameeom co e smofinem o.mam m.moH o.eua e.mom e.mmH m.mm~ o.ao- e.moH m.moHM ounce DH «ea ” exude? o.ohH m.moH m.emH e.MHH e.oo m.mn~ H.mna m.mo~ m.oo Waeom co & “mumpme mw m.emH m.mea H.@¢H H.0ma «.mmfl H.aeH m.eeH e.me~ e.omap cocoa - shim oa-m Tale as-e OHHNII axe Haze care are macemHaem .eegeampm nose cocoa Heofiuem> wee ”ea mamee searcoomm oaflna pawoa ucoogcm mm onp um eoupmxo 71 However, the analysis did show significant differences between percent points (percent of the step completed.) The analysis indicated no significant difference between the 50.0, 97.5, 12.5 and 62.5 percent points. Each of the remaining points was sianificantly different from all the other points. The highest average, 147.0 pounds, occurred at the 25 percent point. The lowest average was 27.9 pounds for the 93.75 percent point. The compari- son of percent averages is shown in Figure 27. All values under the same line are not significantly different from each other. Percent Points “,3 m to O O , o . m N dflmg h m In I l in I l 1 1 I I U W V T I I (n ‘9 0029“! sf. ‘0 O N l~ wmow m m .2 N c “0’99 9.’ '2 ‘1" Averages Figure 27: Comparison of the percent point averages for the vertical force, 140 pound subject ascending the stairways. For the 172 pound subject the statistical analysis gave nearly the same results. There was no significant difference between the average force exerted on each of thE’ nine stairways. However, there was significant dif- f'el‘ence between the averages of the percent points. The hiflflnest average, 194.0 pounds, occurred at the 25 percent poidlt. This value was significantly different from all 72 the other averages. The lowest average was 28.1 pounds for the 93.75 percent point. This value was also signi- ficantly different from all the other averages. The com- parison of percent averages is given in Figure 28. Percent Points m —- :3 8'0 gm“? “.33,- 0. N In 2’ m 0 tag”: M 5' N e :+ ::: =+ a a ”a 322:?“- °- N 8 m 9“: 2 a! 3 Averages Figure 28: Comparison of the percent point averages for the vertical force, 172 pound subject ascending the stairways. The percent point averages of the two subjects were ccnnpared using the method of rank correlation. The analysis gave a correlation value of R = 0.98. The correlation value iruiicates that the vertical force curve for each subject has the same pattern. Figure 29 indicates that the force CUIWres do follow the same pattern. The difference in the twe> curves is due to a difference in body weight. The average vertical force exerted by each subject While ascending each of the nine stairways is given in Table 15. The average vertical force exerted by each sub- 3901: for each of the percent points is given in Table 16. E3011 of the averages in Tables 15 and 16 contains thirty- 81): measurements. Figure 29 shows the average vertical force at each -'.—_d- . ,_..1___‘.‘_ —-.— -4- .”D" '-._' 73 pnwaee m.oa m.am H.ooa m.mm m.ou e.mm o.maa o.mw e.oe eeom mafia sommnsMH . p .n m H.mm H.mm m.mua a.e¢~ m.oma H.eea o.em~ m.eea m.om .oueoe cameos m.aa m.oe m.em m.mu o.mo H.mm o.moa o.we m.¢m zoom co a pomfipsw . .mpa .na oefl w.e~ m.mm m.mm~ m.eoa m.oo e.mmH o.e¢~ m.ooa m.ue .eoeoe me.mm m.ew o.me m.me 0.0m Wham o.mm “.ma mm.e mezHoa ezmommm um cmunmxo venom Hmofiuum> o .nzmshaapw ocfiz on» mchcoonw ages: ucfiom acuopmm comm umnm>¢ one "0H Names .mnH poofipsm e.ema e.ema m.em~ n.5ma m.emH m.mma e.mma m.om~ H.mma .uoeoe .nn mea .mpa womepsm v.5o H.mm m.moa m.moa o.am e.ue o.aoa 0.59 n.mo .moeoe .na oea shim calm o:w Haze oh-“ 0-5 .Haue oHre ole mweechem e i gt: 0;; .mmtpfiwpm coco wcfincoonm mews: couumxo oopom Hmofiuum> oweno>< one ”mH Names 1; 71+ .mmakaadpm can mqaucoomw .uhetnawam onus on» you cmmuo>< “mm madman mean: maoofinsm can on» an uoaaowo mono“ Hmoduuo> one OMPUJQSOQ amhm MI... “.0 Fzmumma oo. .. owe . com . 9mm x o .o -- .M 'y \“ 30¢ a . u . o . v . nl :w m o! \m :om M \v . ~ 8 c ~ 3 \ i a. m :ON. “I / 5 .Il \\‘ II \ a v ’1 p S s c s L.om_ I .n\ I: x 52.93 .mmewt\w / \ , e . ‘ lo\ . ,OON 7‘5 percent point for both subjects. It should be noted that the curves for both subjects were very similar. The rate of application of the vertical force was very rapid for each subject. The 140 pound subject applied a load that was 34.2 percent of his body weight in the first 6.25 percent of the step. The 140 pound subject had applied a load that was 72.0 percent of his body weight in the first 12.5 percent of the step. The 172 pound subject showed the same characteristic by applying loads that were 46.6 and 83.9 percent of his body weight in the first 6.25 and 12.5 percent of the step. The values for each subject indicate that the force exerted on the tread in— creases nearly linearly with time during the "lift" period. The curves in Figure 29 indicate that the "lift" period occupies the first 25 percent of the step, the "swing" period the next 50 percent and the "lift" period the last 2‘5 percent. The first "11m." period is the interval when the forefoot is applying pressure on the tread to lift the body. The second "lift" period is the interval when the rear-foot is being lifted from the tread. The "set" Period, which is the short interval between the "swing" and the second "lift" period, occurs apPI‘OX1mat91Y at the 75 percent point. The length of the "set" period is negligible compared to the other two periods. Figure 30 shows the average vertical force at each Dex-cent 901nt as a percent of the body weight. The maximum val ues 0? 105.5 and 112.5 percent of body weight for the 76 .ommkndwvm on“: on» no“ owdno>< an voanoxo .unwdot moon no advance a no .oeaon Haoauno> one owHMJQEOU awhm wt... no hzwumwa ax: mN Om b ’ & JL P mm 0 4|- .mzwknawwm on» wcaucoomw wads: opoonnso on» ”on unawah O o ’,..-i" ’ ’—' ’ e i . v a / xbowfimam .mqu 4/ v . ~ v .1 $2.03 .3 mt _ _ _ 'BOHOJ ‘WOILUBA 1H9I3M A008 so as 77 140 pound and 172 pound subjects, occurred at the end of the "lift" period. The maximua values at the "set" period were 96.85 and 100.1 percent for the 14?) and 172 pound subjects. Horizontal Force, Ascending The horizontal force exerted by the l4O pound sub- ject on three different stairways is shown in Figure 31. Each curve illustrates the general pattern of the hori— zontal force while ascendinz a stairway. However, the curves are located differently on the coordinate scale for different riser heights. The general pattern of the curve indicates that a POSItive horizontal force was applied at the beginning of the "lift" period. A positive horizontal force was directed toward the front edge of the tread. The horizontal force Changed direction shortly after the start of the "lift" period and remained directed" toward the rear of the tread until approximately a quarter of the "swing" period was completed. The force was directed toward the front edge for the remainder of the step. A ‘Dossible reason the horizontal force changed direc- tion during the "lift" period was that the centroid of the body was moving toward the rear of the tread. A move— ment toWard the rear of the tread may produce a negatively directed force which offsets any positive force produced by the forefoot. The body movement was also aided by -3 PUSh 78 i . 2e. .uhouuddvm peonounuu moan» mcducoend canal noonnsn unsoa 03H on» up consume oouou Hoanouanon one "Hm oasmuu .OMPUJQSOO am...» mt... no hzmocua 00. me On MN ’ ’ q» 4} fl ‘1 ‘ d rOd ON. ‘3030: 1V1NOZIUOH SONOOd 79 from the rearfoot. The force exerted by the rearfoot may tend to reduce the amount or force exerted by the forefoot. During the last part of the "lift" period and the start of "swing" period the centroid of the body was moving over Thus the the the point where the horizontal force was applied. positive horizontal force may he small compared to the negative force exerted by the body during its movement. The horizontal force shifts back to the positive direc— tion during the "swing" period because the centroid of the body is moving away from the forefoot. The forefoot has to exert a positive force to give the body this movement. The curves in Figure 31 indicate a slight dip at the 75 percent point. The "set" period occurs around this P011111: and some of the body weight was shifted to the foot on the upper tread. The added reaction may reduce some 0f the horizontal force needed for stability. The final P189 in the curves is due to the push off by the rearfoot ”3 the subject. moves to the next step. Although the curves in Figure 31 represent the general pattern of the horizontal force there were some stairways on Which. the horizontal force varied considerably from this Pattern. The curves in Figure 32, for the 172 pound sub— JQCt 1llustrate someof‘ the variations. The horizontal force exerted on the'8-9 stairway was positive for the complete step. The 1'72 pound subject also showed this ‘ I $81? A ‘6 characteristic on the 7-a stairway. The horizontal 80 .ohotnampm pcmaounao moan» mcauaoeum mafia: peonnsu canon NNH on» an coaaoxo venom kucoufiuon one “mm shaman / omhmdn—SOO awhm m1... “.0 Fluocmu 00. on On mm I b # d 1 4 fir db 4 - :Odl roast \/ \A ./ i.O.¢I \iT\ .. . o I \\ \‘I‘II'I p ./L \\ "\l.‘ A// \ toe. \ *1 » . i /{T\\\er*e=:.mgw . “3030:: 1VLNOZIHOH SONflOd 91 force on the 8-10 stairway was completely positive except for the 12.5 percent point. However, the horizontal force on the 94-11 stairway was negative for nearly two thirds of the step. 1 Table 17 gives the value of the horizontal force exerted on each stairway at the 6.25 percent point. The horizontal force at the 6.9.5 percent point was directed toward the front edge of the tread and was the force which would cause a person to slip when ascending a stairway. The calculated value which was given was not necessarily the maximum horizontal force exerted. A higher value could have been exerted either just before or after the 6.25 Percent point. For the 1413 pound subject there was little difference between the 6.25 percent point values on the stairways with 6 and 7 inch risers. However, the values for the Stairway'with 9. inch risers were considerably higher. The three highest values calculated occurred on the stairways with the 8 inch risers. The highest value, 9.5 pounds, Occurred on the q_9 stairway with 5.3 pounds on the 8—11 stairway. A force of 4.4 pounds was measured on the 8-10 Stairw’iY. For each set of stairways with a constant riser height, the lowest horizontal force in the set occurred on the Stairway with a 10 inch tread width. The 172 pound subject showed a greater variation in the 6'25 percent point values. The highest value, 9.2 pounds , occurred on the 8—9 stairway. However, the next . .mnn sownpsm H.c m.e m.o o.e 0.0 H.e e.a m.m a.m .mosom .pH was .mpa pomnpsm w.m e.e m.o m.m o.~ N.“ e.m e.m H.e .tosom .pH ova mw sham chum o-m HH-B cane -e Hhuo Ohio one assemHaam .amspfimum gomm mcwccmomm mahxs echo» unmopwm mm.w one am vmpumxo monom prcomapom one “ma mqmee - I|.‘I"I.“-’ I--- "III -I‘ '. i“--1’- ‘ i 0.!" - g 83 highest value, 57.4 pounds, occurred on the 6—11 stairway. For the stairways with 6 and 8 inch risers the lowest value ccurred on the stairway with a 10 inch tread. However, in the set o.‘ stairways with a 7 inch riser the highest value occurred on the stairway with a 13 inch tread. The statistical analysis of the horizontal force for the 140 pound subject indicated significant differences within both t‘:e stairway averages and the percent point averages. The comparisonof the average horizontal force exerted on each of the nine stairways is shown in Figure 33. The average horizontal force for each stairway is also given in Table 1“. Each average contains thirty-six mea suremen ts . The highest average, 3.5 pounds, which occurred on the 9-9 stairway, was significantly different from all the other averages. The lowest average, «3.7 pounds, occurred On the 6-10 stairway. It was significantly different from All Other averages. Six of the nine stairways had a negative ‘q‘fer‘age value. Thus the average horizontal force was directed toward the rear of the tread. The comparison of the average horizontal force at each percfiint point is shown in Figure 34. The average hori- zontal force for each percent point is also given in Table 19' ETach average contains thirty—six measurements. The highest average, 4.3 pounds, occurred at the 6.25 pertht point. However, the average for the 6.25 percent point, Was not sijnificantly different from the average for 84 the 87.5 or the 93.75 percent points. This fact indicates that the initial force exerted by the forefoot is approxi- mately the same as the force exerted by the rearfoot when lsaVing the tread. The lowest average, -8.3 pounds, which occurred at the 25 percent paint, was significantly dif- ferent from all the other averages. Stairways 9 £377: :0) m 9 m <'o Mm}: :ch N' at at J gTJJ 11 l 1 l I I T WT ' I T I\- 0Q ".Q ‘3. Of IQ m' '-' 9 00 O - [0 I I Averages Figure-33: Comparison of the stairway averages for the horizontal force, l40 pound subject ascending the stairways. The statistical analysis of the horizontal force for ‘ths 172 pound subject indicated significant differences vvithin both the stairway averages and the percent point averages. Percent Points a) Q to m 8C? “than a m ' N m m - o: § m now 8 mtixo ‘1 l + l 1 L L 1 L I I I I T I V T I I0 —. Q ‘90? O) ‘0‘": * ‘P I I Averages Figure 34; Comparison of the percent point averages for the horizontal force, 140 pound subject ascending the stairways. 85 .mnH pomfipsm m.m H.u u.m m.~ o.H m.o- o.m- m.ou m.o .moaom -i .DH mua . .mpH . pommnsm m.m n.m m.~ m.m o.H o.m- m.m| H.u- <.¢ .uopom .nH o¢H mm.mo n.5m o.mm m.mo 0.0m m.um o.mm m.uH mm.m mHzHom Hzmomwu .mxmspampm mCHz mnp wcfitcmomm wafiga unfiom pcmopmm noww um cwugwxm woken Hancoufiuom vmmnm>< wne “ma mqmda _ .mnH pownpsm H.o m.m H.m m.o o.H u.m m.m m.ax u.o .moaou .nH mug .mpfi puwfipsm 0.“: m.~ m.m H.o o.H- m.o m.os u.m: o.o .oopom .pa o¢H Harm o”:, mum Hana oflsu m-m Hflwm oflxw m:m - wwdamH¢ one "ma mgm«9 I o' i- DIOII 1%....‘11' 86 A graphical comparison of the average horizontal force‘ ion each stairway is given in Figure 35. The average for each stairway is also given in Table 18. The highest aver~ sage» 5.3 pounds, occurred on the 9-10 stairway. However, ‘this value was not significantly different from the aver- ages of 5.1 and 3.7 pounds which occurred on the 8—0 and 7—9? stairways. The lowest value, -2.9 pounds, was measured cw: the 6-10 stairway. This value was significantly dif- ferwent from all other averages and was the only stairway with a negative average. The comparison of the percent point averages is given irz IFigure 36. The average for each percent point is also Eixreun in Table 19. The highest average, 7.1 pounds, occurred 8t. tdue 37.5 percent point. This average was not signi— ficantly different from the average of 6.2 pounds for the 6-3’5' percent point. The lowest average, 3.0 pounds, occurred Stairway S? ‘ - o a T’ ?E? T ? T7 0, e: as: : e see - - ~09 N N a” Averages I’igure 35: Comparison of the stairway averages for the horizontal force, 172 pound subject ascending the stairways. + 9' the 25' percent point. This average was significantly - different from all other averages. ‘37 Percent Points ID ID N'rs 0's: :0 m N [- N -60 mm 0) V‘- ‘D G l L LL A 1 1 I v 1 v 1 v 1 v I o a: Qm IQ r~ N _ Averages Figure 36: Comparison of the percent point averages for the horizontal force, 172 pound subject ascend- ing the stairways. The horizontal force exerted by the two subjects was compared using a rank correlation analysis. The analysis gave a correlation of R = 0.73. This value indicates a considerable degree of correlation between the two sub- Jects. Thus when the averages for the stairways are ranked from the lowest to the highest the order in which the stairways occur is approximately the same. This fact can be observed by looking at Figures 33 and 35’, starting f'I‘Om the left side and proceeding to the right. Figure 37 shows the average horizontal force exerted by each subject while ascending the stairways. Each per— cent point is an average of the nine stairways. Figure 37 in("icate-s that the horizontal force curve for the two sub- Jects was very much alike. The 140 pound subject exerted a gI‘eater force at the beginning of the step than did the 172 bound subject. However, the 172 pound subject exerted a l’3I‘ger force at the end of the step than did the 140 pound subjec t . 88 .mhmluamam moan on» non owauo>< .oawthuopw one u~m.onsmfih weaocouuo oaunu uncanny» or» one so counono oouon Housemanon any omhuaasoo mmhm NIP no hzuocmu mh Om MN 0 .0 4. o o a? JP O.N_.I by _ VO.QI homemam .3 o! J/ b Ill '03?! \\\\\1\ [11* \l\ a J O a homqamam .0... NF. aa/ . b v ”(N C? a s 1' .Od ON. saunoa ‘3980:l 1V.I.N ozlaon 89 Center of pressure, ascending The force exerted on a stair tread is distributed over some proportion of the shoe sole area. The force applied on the stair tread can be replaced by a concen- trated force, equal in magnitude, acting through the cen» troid of the distributed force. The force plate was de- signed so the point of application of the vertical force could be measured. This point, which is termed the center of pressure, is the centroid of the force applied on the sta 1r tread. . The center of pressure was measured during this in- vestigation to determine whether the dimensions of a stair— way affected the initial point of application of the ver— tical force. Although the center of pressure was meas- ured for the complete step only the measurement at the 6'95 percent point will be analyzed. The center of pressure at the 6.95 percent point is the initial point of applica— tion of the vertical force. If a person is to slip on a st"ii-I‘Way because he is off-balance he will slip when he first places his foot on the tread. Once the person's foot is completely on the step there is very little chance of slip-ping. For this reason only the initial point of appliCation will be analyzed. The center of pressure for each subject while as- tend 111g a stairway with 6 inch risers and 10 inch treads is Sh(mm in Figure 38. The curves in Figure 38 illus- trate the general pattern of the center of pressure while 90 . mac-15.. 9 it .mnmmna saga ad and «Roman Anna 0 spa: hwkafispm a mcflucmoms mags: onsmmona no nopzmo “mm madman 00. othJmIOO “.um u...» no hzwocmn— :3. II """ 1"! hounmam d4 Nb. AWOiiliTllt is... i 1171 \\III \\L1 :4 \\‘ l-I.‘ \ K 406 Dwamam 61.0.! Ck :0.@ Low 'SBHONI lNOle 3HJ. W083 3ONVLS|0 ! '3903 91 ascending the different stairways. The basic differences indicated in Figure 38 can be. accounted for in the way each subject ascended the stair- way. The 140 pound subject placed his complete foot (sole and heel) on the tread when ascending. The second sub- ject ascended the stairway placing only the sole of his shoe on the tread. Figure 38 indicates that the center of pressure moves toward the front edge of the tread during part of the step. When the subject applies pressure. on the tread to lift his body a laraer portion of the shoe sole touches the tread. The vertical force is distributed over a la rrrer area which causes the center of pressure to move toward the front edge of the tread. Figure 38 indicates that at the completion of the ‘ Step the center of pressure for the 140 pound subject was 1Ocated a greater distance from the front edge of the tread . This occurred because the 140 pound subject placed his entire foot on the tread. Therefore, the front of his Shoe was further from the front edge of the tread than Was the\'shoe of the 172 pound subject. The reasons for the sharp increase at the begin- “1.“? 0f the step for the 140 pound subject and the dip near the end of the step for the 172 pound subject are not known. However, these features appear to be character— istic of each subject since these features occurred in “Mt Of the stairways analyzed. rt * 92 - The values of the center of pressure at the 6.25 per- cent point are given in Table 20. The value for each of f four repetitions on each stairway are given. Each value is the distance from the front edge of the tread. A statistical analysis of the values in Table 20 indicated no significant differences between the stairway averages for either subject. A combined analysis indicated no sienificant difference between the two subjects. The statistical test was performed at the 95' percent probabi- li ty’ level . Descending a Stairway The event of descending a stairway can be divided into three basic periods, the "swing", "set" and "support" peri ods. Suppose a person standing at the top of a stairway decides he wants to descend the stairway. The person's f11‘s‘t‘. move would be to lift one foot from the floor and swing it forward. The time interval during which the foot is lfilf‘ted from the floor and moved to a position in front or the body shall be termed the "swine" period. The fore- foo1; shall ‘be defined as the foot which is either stationary or on the lower of any two steps being considered. During the "swing" period the forefoot is the foot which is Stati 0nary. The rearfoot shall be defined as the foot which is either moving or on the higher of any two steps. At the completion of the "swing" period the real-foot 93 Ill .monocw .omom uncut on» Econ mocmpmfia om.m sm.m em.m so.m um.m mo.m mm.m om.m mo.m ouooo>a we.m mH.m mm.m om.m so.m Hm.m em.m He.e .wo.m .¢ ew.m ma.m om.m mm.m oo.m os.m mu.m o¢.m mm.m H m _ ooofinsm mm.m m~.m Hw.o mm.e me.m em.m em.m mm.m oo.m m m .9H mus em.m mo.m mo.m om.m mm.m ms.u mm.~ om.o mm.m ” H o¢.m om.m moflm om.m as.m mo.m H¢.m Ho.m Ho.m a oowoosa ~H.¢ m¢.m ne.o mm.m m.e ma.m Hm.m so.¢ Ho.¢ _ o mo.m me.m om.m un.m so.m m5.m mH.m oo.m hm.m m uoonosw oH.m mm.m mo.m em.e m.m mo.m o¢.m mo.m me.“ a .na oeo Ho.o mm.m mm.m mo.m mm.m mo.m o~.¢ om.e om.~ H Hflxm Oaxm mum Hats oats oxu Harm oauo o-o Howey mweamHeem .mhokhampw moo meoocoomo oases ooooa Hoofiooo> moo oo sodomofiaooa ho oesoo HoHoHcH one "om memes ’i ll 94 13 in front of the body at approximately the same level as the forefoot. The "set" period is the time interval during which the rearfoot is lowered to the next step. When the rearfoot is placed on the lower tread it becomes the fore- foot and the "support" period is started.) The "support" period extends from the instant the rear-foot becomes the forefoot until the time the foot on the upper tread (rear-- foot) is lifted to start the "swing" period. The event of descending a stairway is a continuous repetition of the "swing", "set" and "support" periods. Each of these periods is illustrated in Figure 3‘). Vertical Force, Descending The vertical force exerted by the 140 pound subject while descending a stairway with 6 inch risers and 10 inch treads is shown in Figure 40. F5211”? 43 8130 “1‘15" trates the general pattern of the vertical force while descending a stairway. Figure 40 indicates that while descending a stairway the V8 rtical force has two maximum values. The first maximum occurs near the end of the "support" period when the entire body weight is placed on the forefoot and the reabf‘oot has just been lifted from the upper treado The first maximum value usually occurred at either the 12.5 01‘ the\ 25' percent point. The second maximum value occurred near the end of the "set" period. At this time the entire body weight was still on the forefoot and the body was under .souuaouo a wcavaoomoo mafia: noun oooaoaoo one no uncann>ac cameo one "mm oaswnh Gamma .ananw Qomwm Hum 90me $2.3m 96 .mcmon» non“ 0H one waowfia soda 0 new: aokhawpu a wcfiocoouov oHfink p-onnso canon 03H one an oopnoxo canon Hwofipao> one no: onswdh awhuJQSOO amkm UTE. no hzmomum 00. ms Om 0N ’ L fl 1‘ ‘ :0 b l d 4 «0 » Lwoo .ON. L Om. ‘30303 1VO|183A SONflOd 97 very little upward acceleration due to the completion of the "swing" period. The second maximum value usually occurred near the 75 percent point. Both maximum values were usually greater than body weight. The depression in the curve is believed to be due to an upward acceleration of different parts of the body. The upward acceleration produces an upward force which cancels some of the force due to body weight. The percent of the step taken by each basic period is not clearly designated. The "support" period occupied the first 12.5 to .95 percent and the last 25 percent of the step. The second portion of the "support" period was the time during which the foot was removed from the tread. The "swing" period usually covered the interval from the end of the first "support" period to the 62.5 percent DOint. The "set" period occurred between the 62.5 and 75 Deere ent points. Table 21 gives the value of the vertical force _ exerted on each stairway at the 12.5 and 25 percent points. The values are the calculated values and not necessarily the maximum force which occurred on the step. A larger force may have been exerted between the two points. The maximum calculated force for the 140 pound sub- ‘1th ranged from 141.9 pounds on the 7-lO stairway to 192 .9 pounds on the 8-9 stairway. The forces exerted on the Stairways with 8 inch risers were considerably higher than the forces exerted on the stairways With 6 01‘ 7 inch 98 m.mmm m.mmm e.¢oH m.oom m.aom m.uma e.omm m.HHm m.Hom o.mm n pom new e.HmH m.ona m.oma m.mmH H.00H m.mna m.mma o.mma m.mmH m.mH .pH mma m.moa w.oe~ H.mma H.¢eH m.HeH o.mea H.oma m.mma H.mea o.mu pomnpsm . m.twa 0.0ma o.mma m.mma m.¢HH e.omH m.moa e.oem «.mma m.mH .pa oea aaxw oHum mum Ha-u oa-u a-“ Haim oa-o 9-0 acaoa & m> one ”am mqm¢p 99 risers. The maximum force on the stairways with 6 inch risers ransed from l45.l to 165.5 pounds while a ranve of 141.9 to 156.4 pounds was obtained on the 7 inch stair- ways. However, the stairways with 8 inch risers had maximum forces ranging from 765.7 to 192.9 pounds. There was no relationship between the maximum force and the tread width for the 140 pound subject. The maximum force for the 172 pound subject varied from 197.6 pounds on the 7-9 stairway to 239.4 pounds on the 6-ll stairway. The stairways with 7 inch treads had the lowest forces with a rarae from 187.8 to 236.6 pounds.' Most of the forces on the stairways with 6 and 8 inch risers were above 200 pounds. For the 172 pound subject there seemed to be a relationship between the maximum force and the tread width. For each set of stairways with a constant riser heiaht the maximum force for the set occurred on the stairway with an 11 inch tread. A statistical analysis of the vertical force for the 143 pound subject indicated there were significant differ- ences between the averages of the nine stairways. The aMIYSis also indicated significant differences between the percent point averages. The comparison of the stair- way averages is aiven in Figure 41. The average vertical force exerted on each stairway is given in Table 22. Each a"Page contains thirty-six measurements. The stairway with 8 inch risers and 9 inch treads had the largest average vertical force, 117.6 pounds. The m stairways with 8 inch risers had the highest averages; however, there was no significant difference between these ainerages. The 7-10 stairway had the lowest average, 94.6 pcnunds; however, this average was not significantly dif- ferent from the averages of the 6—9, 6—10 and 7-9 stairways. Stairways C3 - ‘- ‘i’ 53‘? = '7' 9'7 “P N (p (oh “I, :9 00 Q 5 3* h t t *#* t N. to v- : 5 '0"! 3; o ‘2': S ” as - 99 Q Q :2 :1 Averages Figure 41: Comparison of the stairway averages for the vertical force, 140 pound subject ascending the stairways. 'The comparison of the percent point averages is given in Figure 42. The average vertical force exerted at each percenqt point is given in Table 23. Each average contains thirtdh-six measurements. wqqe comparison of percent point averages indicates that true 12.5 percent point had the highPSt average, 156.9 pounds. However, there was no significant difference be- tween-‘tfie average for the 12.5 percent point and the average or 149.J9 pounds for the 75 percent point. The 25 percent point V'ith an average of 146.8 pounds was significantly differenat from the l?.5 percent point but was not signifir cantly different from the 75 Percent point. The lowest average, 25.9 pounds, occurred at the 93.75 percent point 101 and was significantly different from all the other averages. Percent Points «a F: u: g} C? In “? ‘Qciui '0 h- . O N N ID|DN m m» m «n n 0 00k - 1 A 1 5. : : 2: i . ' 1 ‘90205 3 '33 7:33 '3 933: N N h - E " — Averages Figure 42: Comparison of the percent point averages for the vertical force, 140 pound subject descend- ing the stairways. A statistical analysis for the 172 pound subject indicated significant differences within both the stair- way averages and the percent point averages. The compari- son of the stairway averages is given in Figure 43 and the comparison of the percent averages is given in Figure 44. The average vertical force exerted on each stairway is also given in Table 22 and the average vertical force at each percent point is given in Table 23. T Figure 43 indicates the stairway with 6 inch risers and 11 inch treads had the highest average, 136.7 pounds; however, the average for the 6-11 stairway was signifi—‘ cantly different from only the 8-9 and 7-9 stairways. The lowest average, 113.9 pounds, occurred on the 7-9 stairway and was significantly different from the 8-11, 8-10 and 6-11 stairways. A comparison of the percent point averages indicated the 25 percent point had the largest average, 211.9 pounds. .J a x ittga. unease e.mH o.¢e m.pm m.mm 0.0m m.mm o.mmH o.em ¢.om seem «0 & pumfipsm m.om o.mu e.mos o.ssa e.ama e.ooa o.aam m.eea o.ew cocoa .nH msa unmaoa e.ma m.om m.otn m.mo o.mo m.ea m.eoH o.maa o.sm seem co m . poocpsm m.mm m.as m.mea “.mma «.mm m.moH m.o¢~ ¢.oma o.os cocoa .nH sea ms.mm m.em o.mu m.me 0.0m m.am o.mm m.ma mm.e mmzHow Hzmummm .mmmscampm on“: ecu you owmaw>< .mstnampm mcH: on» mcfiocoommc mamas pcfiom unooamm nowm pm cmupmxm Anccaomv moaom Hwofluaw> can ”mm mamea IWI‘ ii i m 1 someone H.¢Ms o.oma s.uaa m.oma s.ema m.m~a s.oma m.ema H.0ma « .9“ me“ “ womfipzm e.ass e.asa 0.5HH o.moH m.em o.msH ¢.moa e.mos u.aoa . .nH oea HHIm OMvm mum Hans Oaum 01h Halw Cato one mw wumum>¢ one «mm mqm< .mzwknaoum on» mcauno-mou mafia: unconnsu on» an nopnouo canon Hmuauao> one aubuJa—aoo awhm Nth no hzwocmm "m: madman 00. v» v ”on MN . r I r ’/ \illllll houfimDm .m... O¢. \ / V\ 171 r/ _ |\ N SIDN— I n \ w {I e‘ a x s I \b i f % ti ow. . POMfimDm .0... Nb. 400m ‘aoaos “wanes A SONflOd 106 .ahmhnumum mafia on» no“ omdao>< .mhaknamnm on» weavaoomoo odds: «oonnso some an caveman .pnmao- moon no cavemen a mo .oonon Haoapno> one «Q: magmas omhmqazou uuhm u...» no hzmocma oo. 2. on mm o I, .\ x _. P L z W aom ’ a I a , soc \ , z a w m :om / homemam.m40¢_ \ I u! gr / on / l/F \\\ I /n\ M I homemam .3 N: I) 7 :8. Do. .lHOISM A009 JO ‘aouOs wouuan 1N30836 107 Horizontal Force, Descending The horizontal force exerted bv each subject while descending a stairway with 6 inah risers and 10 inch treads is shown in Figure 47. The two curves illustrate the general pattern of the horizontal force exerted by each subject while descending the stairways. an The general pattern of the curve for the 140 pound r11, subject indicates that a positive horizontal force (toward the front edge of the tread) was exerted during the first g portion of the step. The maximum value for the l40 pound ' subject occurred between the 12.5 and 25 percent points which was approximatelv the same place as the first maxi- mum value of the vertical force. The horizontal force remained fairly constant during the middle portion on the step. A large negative force was produced when the foot pushed off the tread. The large negative force usually occurred at the 97.5 percent point. For most of the stairways the absolute values of the maximum negative and positive forces weneapproximately the same. The general pattern of the horizontal force for the 172 pound subject was somewhat different than the curve for the 140 pound subject. The 172 pound subject exerted a negative force at the beginning of his step. Apparently the subject's foot was moving toward the rear when it touched the tread. However, the horizontal force changed to the positive direction and reached a maximum value 108 .ooooaa nos“ Ha and encode Anna 0 node adenaopm a wcauauomov mags: «cones» name an umpnoxo canon Hangouanon one ”N: ousmah ONhNJQIOO awhm m1... “.0 hzuocmu 00. on on mm o 4» v m w 11 0.07 :QNr. :odl homfimam .m... 03/ 7; +nw¢u \b’l \ p O I ,, .e. "V \S I” \\~ 410.? I \ 17... 1--.? . II: ‘ «all; sow v homamnm .mJ N~._.\ ...O.N_ “39303 Winozwon SONflOd l09 around the 25 percent point which was approximately the same tine as the first maximum of the vertical force for The 172 pound subject maintained a posi- this subject. On tive force much longer than the l40 pound subject. many of the stairways the horizontal force at the 37.5 percent point was nearly the same value as the force at the 25 percent point. The horizontal force for the 172 Pound subject did not change directions until some time between the 62.5 and 75 percent points. The maximum nega- tive force was exerted at the 87.5 percent point. Table 24 gives the value of the horizontal force at the 12.5 and .25 percent points. The horizontal force / at these points, which is directed toward the front edge or the tread, would be the force which would cause a per— son to slip when descending a stairway. The force given 18 not necessarily the maximum force. A larger force com-"- have occurred between the 12.5 and 25 percent points. A statistical analysis for the 140 pound subject indie”3!:er a significant difference within both the stair- way ‘Ve rages and the percent point averages. The statis- tical Comparison of the. stairway averages is shown in Figure. 49, The stairway averages are also given in Table 29. Each average Contains thirty-51X measurements. For the 140 pound subject the stairway With 8 inch rise PS and 9 inch treads had the highest average hori— zonta 1 force, 3.5 pounds. However, the average for the 6-9 - Stairway was not Significantly different from the 5.5 e.mm. m.un m.m e.HH e.me m.m~ M.“ e.m ntmm eoefinzu m.m o.ea e.m m.m m.m m.m e.m e.e e.e m.ma .LH Nee o.m m.e «nee m.m H.e H.ma 0.0 mnn v.0 o.ma pemmeem no 0.4 m.m o.nH m.e 5.0 m.- e.e m.” m.m m.m~ .ne oea 1L 1. “Hum oH-m elm aaie caue eye aa-e Ogle oae peace e mwa .msmznfiguw on» mcwccmomon maps; venom ucmopmm some pm moppmxo Amrczomv .mouom Amazonahom one ”om mamas fill-g I 3 1 11. a - somassw m..: o.m m.~ s.o e.o m.m m.o- m.m- m.o: .na «ma pownnsm s.ou .m o.¢ 0.0 0.0 m.a a.m 0.0- 0.0 . .pa oaH Hasm ca-m o-o s~-s o~-s o-m Amie 0H-w ox» mW¢RmH< 0:9 "mm mqm< .mhwenadpm use mauvcoomoo odds: poonnsm numb so couaouo oouou Hwaaouaaon 0:9 "mm madman Duthmzoo auhm Nth no hzuocwu 116 00. mn Om 0N QmT 0 a db ’ 1+ w d A ‘ ~ ~- ‘~. \ 1b. W how? a 3m .3 N: A A A .QNT anu 3:? EN. Qw— ‘aouoa auuozlaoa sounoa 117 descending a stairway with 6 inch risers and 10 inch treads is shown in Figure 53. The curves in Figure 53 illustrate the general pattern of the center of pressure while ascending the different stairways. Figure 53 indicates that the characteristics of the center of pressure for the two subjects differed conSiderablv. The basic differences in the two curves can be ac- counted for in the way each subject descended the stair- ways. The 140 pound subject placed his entire foot on the tread while the 172 pound subject descended the stairway on his tip-toes and did not place his heel on the tread. L25 ’When the 140 pound subject descended the stairway he placed his sole on the tread and then gradually set his heel down. This method of descending accounts for the movement of the centroid away from the front edge of the tread. As the 140 pound subject leaves the tread the foot is lifted in a rolling fashion. _Thus the centroid of the force moves toward the front edge. When the 172 pound subject descended the stairway he placed only the sole of his foot on the tread. Because all the body weight is on the sole the center of pressure moves to an equilibrium point and remains nearly constant for a portion of the step. Figure 53 indicates that the center of pressure moved toward the front edge. This characteristic occurs because the foot makes its initial contact with the tread on the rear part of the sole. The 118 .ouooua non“ Ha coo mnomuu nos“ m an“: malnddno a mnavcoomou mafia: poonnsn some non oadmmona mo noucoo "mm enamuh ampusazoo euem m...» ..._o pzuocme oo. 2. on 3 o «in J. Q.\;TLVX. _ _ , w e / homemam d4 we. \ Ifiltl IIIII Q'IIUIOIOAYIIIIII-VII 1! / komfimam .m4 0! 96 saaoul ‘3903 moss 3H1. nous souuslo 119 foot then rolls slightly forward as the body moves forward. The movement of the center of pressure toward the rear edge as the foot left the tread cannot be accounted for. This characteristic is definitely a part of each subject's step since it occurred on nearly all of the stair— ways, Slow motion pictures of a person descending a stair- way would probably be needed to explain the movement. Because this movement does not affect the person's chances of slipping no further attention will be given to it. A statistical analysis of the center of pressure data was performed. However, only the value at the 6.25 per- cent point, which is the initial point of application of the vertical force, was used. If a person is to slip on ‘3 stairway because he is off—balance, he will slip when he first places his foot on the tread. All values 11560 were the distance from the front edge of the tread. The analysis for the 140 pound subject indicated that significant differences did exist between the stair- way averages. A comparison of the averages is shown in Figure 54 while the values for each of the four repeti- tions are given in Table 27. Figure 54 indicates that the 8~11 Stairway had the highest average, 3.64 inches. How- ever, the average of the 9-11 stairway was not signifi— cantly different from the averages of 3.40 and 3.21 inches WhiCh occurred on the '7—11 and 6-10 stairways, respectivelY- Th ' e 7“) stairway, with an average of 2.36 inches, was 120 significantly different from the 7—11 and 8-11 stair- ways. Although the 8-11 stairway had the highest average, 3.64 inches, the other stairways appear to have averages which would eliminate any chance of slipping when off- balanced. The analysis for the 172 pound subfiect also indicated significant differences between the averages for each stairway. A comparison of the averages is shown in Figure 55. The value for each of the four repetitions is given in Table 27. The largest average, 3.61 inches, occurred Stairways m m - QEEG 9 = :: | IT'I' I ' n N w m mh-m w F- m * ewe; —' a s :3 .¢ 3 len ‘9 t in “I N NNNN '0 :0 r0 Averages Figure 54: Comparison of the center of pressure averages, 140 pound subject descending the stairways. on the 8-9 stairway but was not significantly different from the average of 3.33 inches which occurred on the 8-11 stairway. The lowest average, 1.58 inches, occurred on the 7-9 stairway, but was not significantly different from the average of 1.72 inches for the 7—10 stairway. While the highest averages for the 172 pound subject ~_ ‘u‘ —A__._ "v —— — inches. rent Edge, Distance from the F J *7 The Initial Point of Application of the Vertical Force while descending a c7 each Stairwa \ I TABLF 8-10 8-11 IV A 1“] 0 ll ,— r7 YS V 7—10 AIRT qr Trial [\ OJ (MI 121 (I) C u («I (*3 (u' {I} (‘J \J (\1 lb. 140 Subject LR (V \ Ck“ at \Q (‘J m ‘—L C I CK. «r -u- .'-._n-- 4... I I 3,3“--3w .. "2:21": ‘73 .33 i “m -- qn- ‘_—-1 3.64 ..- ‘-n~«—~—. «soc-M ‘~I.“-~ WWW“ ”Mn-“m -..“W m 2.65 *t [\ C) (‘W P ‘~ \C (‘J Average .1 w .0-“ 1‘ C- ‘ O (‘0 o (J [-4 r4 (Vb 2.70 l l!‘\ '3 (‘1 (J 0" \Q o t) ,1) r2) .4“) ,3 (d '5 (\m .4 A C. 3.4 2.62 i U\ l m H I r'\ O I m , m m I at [\ ("J 0 O ('J (’1 0 H L\ A \O O O r'W m C“ \0 (\j .u-d ‘1‘ m 0 N in L\ r4 r4 rx'cc (T\ UN 0 O (D r4 O I H r4 (‘2‘ O O N M OW rfi \l) 0') O O N i m ¢ m.“ --'~--<_ . 122 Stairways a) Q 0 :: — O-— ,L g "3 7 u T 7’. a? CD to (D N mm 0 So (i. «3 J. 1‘ <5 én‘ 3- O -: (0 (D E? 5 3 3 «5 n gun h Averages Figure 55: Comparison of the center of pressure "‘3 averages, 172 pound subject descending the * stairways. # appear safe with regard to slipping the lowest values - are questionable. I. The combined analysis of the data indicated no sigui- Li, fdcant riifference between the two subjects. C ONC LUE’. IONS The following conclusions may be drawn from this investigation: 1) The abrasive strip and the rubber mat showed the best frictional prOperties of the materials studied. The coefficient of friction for these two tread materials was higher than the other tread materials for most all of the sole materials studied. For these two treads, there was little difference between the new and used materials. Wood, varnish and paint generally showed a decrease in the coefficient of friction with use while linoleum increased with use. The ripple sole had the highest average coefficient The 2) Of‘ friction values of the sole materials studied. hi9.!1’1est coefficients of friction for the ripple sole OCCuPred on the smooth surface tread materials. The hiWidest coefficients of friction for the other 50195 occurred on the rough surface tread materials (abrasive and rubber mat). The crepe sole was the only sole for which the new materiaihna a higher coefficient of fric- tion than did the worn material. 3) The vertical force eXerted by a person While eitl1gal, ascending or descending a stairway contained two maximum values. When ascending the stairway the first maximum value occurred near the 25 percent POint and ranged from 100 to 125 percent of body weight. 123 124 When descending the stairways the first maximum value occurred between the 12.5 and 95 percent points and ranged from 100 to 140 percent of body weight. The second maximum value occurred near the 75 percent point for both directions and was approximately equal to the body weizht. The initial rate of application of the vertical force varied linearly with time when ascending or descendine the stairways. 4) The horizontal force exerted by a person while either ascendina or descending a stairway varied con- siderably with different stairways and between subjects. When ascending, a stairway the horizontal force had two maximum values and a minimum value. The maximum values Occurred near the 6.25 and 87.5 percent points. The mini- mum value occurred near the 25? percent point. When descending a stairway the horizontal force had a maximum Value which occurred between the 12.5 and 25 percent points and a minimum value which occurred at the 87.5 percent All maximum values were directed toward the front POT nt . ed qe of the tread, the Minimum values were directed toward the I‘ear edge of the tread. S) The initial point of application of the vertical f‘OI‘Ce was independent of both stairways and subjects when ascending. “Ihen descending the initial point of application was independent of subject but varied some with the Stairways. The initial point of application Oi" the vertical force did not appear to be critical 125 with respect to slippinz for this investigation. 6) The forces exerted by the subjects in this in- vestigation normally were not large enough to Cause a person to slip on a stair tread. However, each subject knew the objective 03 this investigation. because each subject had some knowledge of the investigation it is possible that they were more careful when ascending or ‘" he. descending than they nermallv mu- 7) Alti:i;h ;u2 vertical force tended to increase with an increase in the riser height none of the stair— ways= may be regarded to be critical with respect to slipping under the conditions investigated. :"4. ' ‘ .,'~ n.- ,y ‘3. ~. emu-V SUGGESTIONS FOR FUTURE INVESTIGATIONS The following list contains areas for future investi— eation and suagested changes in experimental procedure. 1) Evaluating the coefficient of friction for dry sole materials on wet tread materials, wet soles on dry treads and wet soles on wet treads. This investigation would determine the effect of surface wetness on the coefficient of friction. 2) Measuring the forces exerted on a stair step when carrying different loads or when movine at different speeds. 3) Measuring the forces exerted on a stair step when people are not aware of the investigation. An investi- gation of this type would give a truer evaluatirn of the ratio of the horizontal and vertical forces. 4) Enclosing the experimental stairways and adding more steps to make them more like a regular stairway. (1) (2) (3) (6) (7) (8) (9) (10) (11) (12) (13) BIBLIOGRAPHY Barnett, 0.3. "The phases of the human gait." Lancet, 1956, No. 2, 6:7-621. Bowden, F.P. and D. Tabor. ‘ and Lubrinntign. John Wiley and Sons, New York, 195 , 150 pages. Cunningham, D.M. and G.W. Brown. "Two devices for measuring the forces acting on the human body." Ezasssflinss 22 the fissisix.£2r.fiznsximsnial fitness Anaixsis- 9: No. 2. 75-90. 1952. Dixon, W.J. and F.J. Nassey, Jr. Intrggnntign 59 S a i Analygig. McGraw-Hill, New York, 1957, 4 0 pages. Eberhart, H.D. and V.T. Imman. ”An evaluation of experimental procedures used in a fundamental study of human locomotion." Hg! 2915 Agnggmy g: nggnge Annals. 51:1213-1228, January, 1951. Federer, V.T. Exngringntnl Design. The Macmillan Company, New York, 1955, 544 pages. Forest $ervice, U.S.D.A. Eggggggmg figgig 9933313;— ti n. Handbook No. 73. Germant, A. Existigngl Engngngnn. Chemical Pub- lishing 00., Brooklyn, 497 pages. Gomer, R. and C.S. Smith. fitrnntnrg and Ergngrjigg finrfnngg. University of Chicago Press, sf §Qlid Chicago, 491 pages. Hunter, R.B. "A method of measuring frictional coefficients of walk-way materials. Bnreau g; §isndsz.so lsurnsi 9f assesses. 5:329-347. July— December, 1930. . Kerritt. F.3- Building ciisn Bandages. McGraw-Hill, New York, 195 . Miller, J.A. "Nature and causes of stairway falls." Unpublished thesis for the degree of Master of Science, Nichigan State University, 1959. Parker, 3., C.M. Gay and J.W. MacGuire, Material: and.nsih2ss sf Architectural gensiznstisn. John Wiley and Sons, New York, 195 , 724 pages. 127 (14) (15) (16) (l7) (18) (19) (20) (2].) 128 Perry, 6.0. and H.R. Lissner. The S n Gage Pzimeg. flcGraw-Hill, New York, 19 . Rehman, 1., P.R. Patek and H. Gregson. "Some of the forces exerted in the normal human gait." Arsgi§§3.2f Buzzissl e .andwfishahilitaiign. 29: 9 ~702, November, 194 . Sigler, P.A., N.N. Geib and T.H. Boone. "Measurement of the slipperiness of walkway surfaces." National 2: fiiandards. lgnraal 9f Research. 40:339-346. January-June, 1942. Steel, R.D., and J.H. Torrie. Princingeg nd gee- gedure e; Statistic . McGraw-Nill, l9 0, 481 pages. Velz, C.J. and F.v. Hemphill. "Environmental Appraisal Appendix B to Home Injuries." University of Nichigan, School of Public Health, Ann Arbor, 1953. Walker, H.N. and J. Lev. Stetistical Inferenee. Holt, New York, 1953, 510 pages. a" l Weaver, E.K. "Physiological Responses of Women at work in the home." Annual report for regional project, NC-9, Ohio Experiment Station. 1959. Weaver, E.K. and Pogue. "A study of housing pre- ferences, activities and opinions regarding the use of stairways by homemakers." Ohio Experiment Station. 1959. APPENDIX I. The strain gage circuit and bridge output for the transducer of the friction measuring machine. =='T _‘ %F : R L lo 20 ‘%‘ n %%C _ggfip‘ ”a” P~€ lb LT 2b bud L n J. g h‘unI-q R ‘ Bar I Bar 2 CIRCUIT Gages a and b are in tension. Gages c and d are in compression. I bar #1 receives 2 amount of the total load, bar 2 #2 will receive PZ-P amount of the total load. The Z reactions at the supports will be: Bar#1 R:2_ B3P#2Rr£§:€ 2Z 22 e :- 1' c where M =- BL ET’ LgPZ-P) 22 For Bar #1 M r EL , for Bar #2 M 22 The indicated strain for each arm of the Wheatstone Bridge is as follows: (Gages connected in series in an arm will average) AI"!!! 1 r. % 22L g y‘ :21. § - A r but - 'U H MI'U N h d 7%: ”W Arm‘2 = ‘E H N'U N 45' H 129 130 APPENDIX I (Continued) Arm 3 a 2 :PEEPEL c ,4 @32ng c] : “>32ng c Arm 4 = —-(PZ—PgL g ,1 —ng-PgL c :- ng-sz _c_ '5 L 22 22 :1 22 ET“ The indicated strain of arms 1 and 3 of the Wheatstone Bridge is positive while the indicated strain of arm 2 and 4 is negative. Therefore the bridge output is the sum of the strain in each arm without respect to their signs. [22m [2ZEI J EI Since c = the distance from the center to the extreme fibers and I = b n3 the above formula can be simplified 12 to the following: .figggNDIX II. Force Plate Design and Operating Circuits. When a person ascends and descends a stairway a force F is exerted on the stair tread. This force is generally three dimensional and can be broken down into three component forces which lie along the coordinate axes. To determine the magnitude of these three components an instrumented stair tread was constructed using strain gages as the sensing element. The top view of the instrumented stair tread is shown in Figure 56. This stair tread is under the influence of a force F. The two horizontal components are shown acting in their respective directions while the vertical force P is shown as a point. The tread is supported at the four corners with supports 2 and 4 being along the front edge. l f 3 L ’$(‘_——'+P “‘dh‘ 1 8' ‘ 2 } H1 7 1 ‘ Figure 56: A Schematic Diagram of the Instrumented Stair Tread. A Top View Showing the Specific Dimensions. Two basic assumptions were made with regard to the design and construction of the stair tread. The first was that the three forces were considered to be concentrated at a point rather than applied over an area. This assumption 131 5’7 f l. ,1. I 132 APPENDIX II. (Continued) makes it easier to compute the forces and strains at the supports. This assumption has no effect on the ac— curacy of the instrument because a series of forces may be replaced by a single force acting through their centroid. The second assumption was that the instrumented tread underwent negligible deflections when it was stepped on. Thus the length L and depth d of the tread remained con— stant. This assumption is valid because the tread was constructed using heavy pieces of angle iron to prevent any deflections. The vertical reactions at each support can be deter— mined by applying the elementary 1aws of statics. The first step is to determine the proportion of P taken by supports 1 and 2 (call this P12 ) and the proportion taken by supports 3 and 4 (call this P34 ). The next step is to determine the proportion of P12 taken by support 1 and the amount that is taken by support 2. The same procedure is followed for supports 3 and 4. The reactions at each support are given by the following formulas. 31p: £3133 R2p— Pe2e4, R3p- Pele3 R4p- Pe2e3 dL d L ciL d L Rnp is the vertical reaction at the support n. Looking at the tread from the top it is possible to apply the laws of statics and determine the pr0portion of Hy taken by supports 1 and 2 and the portion taken by supports 3 and 4. Because supports 1 and 2 are fixed at APPENDIX II. (Continued) one end and a constant distance is maintained between them, where they connect to the tread, each support will receive one-half of the Hy component proportioned to them. The same follows for supports 3 and 4. The reactions due to Hy at each support are: R a R = Hy e4 , R- = H 1y 2? 3y 4y — fly 83 --.w-.— m- 2 2 any is the horizontal reaction at support n due to Hy. The same procedure can be followed for the horizontal component Hx. This force is divided between supports 1 and 3 and supports 2 and 4. The reactions due to Hx at each support are: R1x : R3x ‘ fix 81 . R2x ‘ R4x : Hx 62 2d 2d Rnx is the horizontal reaction at support n due to Hx. Strain Gage Techniques Since strain is the fundamental quantity measured by strain gages the equations for the forces at the reactions must be changed to units of strain. The fundamental for- mula for changing stress to strain is e =.JZL E where 6 equals strain, micro inches/inch. 0'. stress, psi and E 2 modulous of elasticity. For the vertical force 0': Eng and for bending o- . fife where A M : Rny (t) for the Hy force and M 7 Rnx(t) for the Ex force. 134 APPENDIX II. (Continued) t r Distance from the reaction to the strain gages, inches. c : Radius of the support, inches. A : Crossectional area of the supports, sq. inches. I : Moment of inertia of the support, (inches) Perry and Lissner (14) state that the Wheatstone Bridge will be unbalanced only in proportional to the difference of resistance changes in any two adjacent arms, pm?) or in proportional to the sum of the resistance changes A -1 in any two opposite arms. .17: i I." .‘K 0' During this analysis the Wheatstone Bridge will be labeled as shown in Figure 57. The strain in any parti— cular arm will be indicated by the notations.lm where n is one of the arms. Al A2 A4 A3 Figure 57: The Labeling of the Wheatstone Bridge. Since strain is the fundamental quantity measured by strain gages units of strain can be used to determine the amount of unbalance in the Wheatstone Bridge. Using the above statement by Perry and Lissner and starting with arm Al, the unbalance for the Wheatstone Bridge can be written 6B 3 6m " 6A2 " 6A3 where 6B is the strain indicated by the unbalanced "' 6A4 (1) bridge- 135 'APPENDIX II. (Continued) The placement of the strain gages on the supports is shown in Figure 58. The top row of gages was used to determine the vertical force. The middle row was used for determining the coordinate systems. The bottom row was used to determine the horizontal reactions. These gages were placed at the bottom to increase the lever arm thus increasing the sensitivity of the circuit. Circuit No. 1 Strain Cage Circuit for Determining el and e2 . The strain gage circuit and the placement of strain gages for determining e1“ and e2 is given in Figure 59. There are only two forces measured by the gages in this circuit. The strain due to the vertical force and to the horizontal component Hx. The horizontal component Hy is canceled out because of symmetry of the gages. The strain due to the vertical force will be considered negative. The bending stress on the left hand side of the supports will also be considered negative. Assume the horizontal component Hx is acting to the left. Particular combinations of the different quantities appear in all equations derived for each circuit. To make the presentation easier the following substitutions will be made. 0' . S‘T'B’ 5%.— D. +=A* ll 136 A 3 3‘3 r ’ ‘\\ - N ’IA\ : 1 r/ “\ A I I i I ' I b * “f—I ! 1 : : E - : Il : O . | | i : a : . I I V ' i .E .7 +—:;EL.,JL- , Strain gags ‘ mount d B ' “_4H__: in the “Poisson"8 : : position. L: L_L‘ {J z I I: : I. IT 1 3 C : db- *‘TF‘TW" ___IL . I I I H: LL :L. I : I . I l 1 A - Location of the t ng B - Lo 8 rain gages m cation of the strain gages £333.18? . I C I. and 52 . - ocation of th and 65 . 0 strain gages measuring 64 137 APPENDIX II. (Continued) Using these substitutions the following equations can be written for the Wheatstone Bridge. n [T‘*R1p ¢ alxs - A*R3p — R3xs] ll [H 0 6A1 II I... I (D "U .. * .. - *- 5” :3 D [A Rzp 332x A 34p x 34ij - * .. _ * D [RIpA BR1x A R313 ,1 3113)] .. if .. .. * s: .. 6.4 a p [R4pA as4x A 122p ,1 Baa] __1_[e {I d Using equation (1) the bridge output is EdA Using the relationship e1 % e2 = d the following formulas may be solved for. a _ use e1 5%[1 .54.] , e2 a g [1 # AEEJ] Circuit No. 2 Strain Gage Circuit for Determining e3 and e4 . The strain gage circuit and the placement of the strain gages for determining e3 and e4 is given in Figure 59. The strain due to the vertical force and the hori- zontal component Hy are measured by the circuit. The strain due to the horizontal component Hx is canceled '— i 138 . «wuss _w woacaaaoaoo you 3.25.30 owmw mama: one . «w moacaaaoaoo you «Hooufio owmm camupm . .w meaeaanopou Hon aaaonao owwm anmnpm "mm enema“ poems eqq JO oSpG iuozj 139 APPENDIX II. (Continued) of the symmetry of the gages. Assume the horizontal com- ponent Hy is acting toward the front edge of the tread. This puts the front side of the supports in compression thus a negative strain results. The strain due to the vertical force is also negative. The following equations may be written for the f“} Wheatstone Bridge. I 1 : p ~a»a BR — A*R — R B a 1 -é P ; 6A1 I: 1p ’l 1v 2p 2y :l -—-— 4 I 2 E AL i J I— .— Ehz ‘ D,‘“*R3p / BR3y ‘ A*R4p ‘ R4yB£ ‘ _£_ 2.33 ‘ - 2 E AL = D :A*R — sa - A*R BR _‘ = 1 — 5‘ €A3 19 1? 2p g. 2yI .__ e4 - ‘ 2 E AL_J : ...* .. .. * . - 5‘4 DL-A R3p BR3Y I 34p / BR4i] .1. e351 2 E AL Using equation (1) the bridge output is 62 = P(i3 " e4) EAL Using the relationship e3 # e4 = L the following formulas may be solved for. 2 P 2 P 140 APPENDIX II. (Continued) Circuit No. 3 Strain Gage Circuit for Determining the Vertical Force The strain gage circuit and the placement of the strain gages for determining the vertical force P is given in Figure 60. The strain due to the vertical force and the horizontal component Hy are measured by the circuit. The horizontal component Hx is canceled because of the symmetry of the gages. Four of the strain gages; A, B, G and H,'were mounted in the transverse direction of the support. If this had not been done the addition of the strains for the vertical force would have been zero. Assume the horizontal component Hy is acting toward the front edge of the tread. Thus the strains on the front side of the support are negative. The strain due to the vertical force is also negative. The following equations may be written for the Wheatstone Bridge. . - 7 ' Al [% uA 1p % BR1y / uA 81p BR1), 1 uele4P “ E L_A d L '1 _ A2 "' D " “*R2p % BBQ " 5*3 - BR - l -e e I; Y 2 ” [ p 2r“ _ 1 3 E Ld L A e D / uA*R / BR / uR _ : A3 [ 4? 4y 4PA* ' 334;]: l “8293? E A d L L A D - A*R BR - A*R a BB _ Z 7 ‘4 a I: 3:) ’1 By 39 33'] - i e2'34P t1! [__ 3 Q. It?" 1&1 . nw meanneuopoo Hon vasoaao owmm summon one .noapdmoa eooomuome on» cw monsoon one x one o .m .4 momma "om onsmdh paazi sqi JO eBps iUOIJ ——..——_—_—--_.—.__ _.._—._._._ _. . __ ._ ’ .- -i_.——__.s-.-—--- 142 APPENDIX II. (Continued) Using equation (1) the bridge output is 63 a P % (ue1e4)(-e193) / (ue2e3) - (-e2e4)] EAdL Using the relationships e2 = d—e, and e3 2 L-e4 the above equation becomes 63 = P [Eu-l)(2e1e4) # (l~u)(e4d / elL) / udh] EAdL To determine the magnitude of the vertical force P the equations of circuits 1 and 2 were solved in terms of e1 and e and substituted into the above equation. 4 Upon substitution the above equation takes the form aP2 # bP % c v 0 which can be solved by using the quadratic formula. The equation for P becomes , 2_ 1/u 1 AE€€(-1))1 P = ‘3‘63 4( 2 Xx?“ LS" - 2(1)(L‘3) as 2 Circuit No. 4 Strain Gage Circuit for Determining Hy. The strain gage circuit and the placement of the strain gages for determining the horizontal component Hy is given in Figure 61. The strain due to the vertical force and the horizontal component Hy are measured by the circuit while the horizontal force fix is canceled out. Assume the horizontal force Hy is acting toward the front edge. The following equations may be written for the 143 APPENDIX II. (Continued) Wheatstone Bridge. : _ g. _. A* :1 1 "e P Hy €A1 pl} R19 ,1 BRIY R310 ( Bah] __ .l. f... 2 s L d 2 6A2 : ”[4“?le ’ BR2y ’ MR4p " 334% "‘ .i. ":2: ’33? 2 E _ d 2 . - I. .. s I . ‘1 as = DD i ”4p r‘ 334.] a 1 __ 7‘53 2 E _ II 2 = o -A*R — BR — A*R — BR = 1 _Le P -BH 6A4 l: 1p 1y 3p 33] ..._ _1... .3: 2 E d 2 Using equation (1) the bridge output is 6B = Hy t c Hy = E I 53 E I t c Circuit No. 5 Strain Gage Circuit for Determining Hx. The strain gage circuit and the placement of the strain gages for determining the horizontal component Hz is given in Figure 61. The strain due to the vertical force and the horizontal component Hx are measured by the circuit while the horizontal force Hy is canceled. Assume the horizontal force Ex is acting toward the left side of the tread. The following equations may be written for the Wheatstone Bridge. --—.—' ,_ "7 ‘7 141+ mm. on.» cw wcacguopou no“ 0:30.30 0mmm anon: one .ew mcfiofianopoo you pfldoafio ommm :Hmnpm .ow mcacaaaopoo non nasouao owmw camaum "Hm onsmfih J: ‘J((:::;::::}I1D peas: sun 10 eBpa iuoxg 4* 145 APPENDIX II. (Continued) ' H— ‘1 G a — * - — *R - BR = -e P - HxBe A2 .. D[:A 31p BR1x A 3p 332' 1 1 2 E A d d _ w _ a _ "Z W 6“, pl? a?p ,1 BRZX A 34p ,4 3341] - _1...) :23 ,l HXBe2 2 E U A d _ -* BR -A*R BR : :P 3137 6&3 '3 D[A Rip ’1 1x 3:9 % 3X] .3. :L. {_x 81 2 E - A d F" e” - DEVRQP .- 13122x .. “a” — 334x] .. _L “3.2.: .. HxBe2 2 E _ d I d Using Equation (1) the bridge output is 6 : HI t C HX : E I 6 E I t c APPENDIX III. Sole and Tread Naterials. Large Soles New Neoprene Worn Neoprene New Crepe Worn Crepe New Leather Worn Leather New Neolite Worn Neolite New B.F. Goodrich Worn B.P. Goodrich New Ripple Worn Ripple Largg Sole; New Neoprene Worn Neoprene New Crepe Worn Crepe New Leather Worn Leather New Neolite Worn Neolite New B.F. Goodrich Worn B.F. Goodrich New Ripple Worn Ripple Wood New 0.86 0.82 0.65 0.57 0.31 0.37 0.60 0.61 0.48 0.62 1.05 1.05 Worn 0.64 0.56 0.48 0.55 0028 0.34 0.56 0.63 0.45 0.55 0-79 0-97 Abrasive New 8:38 0084 0072 8:5; 0.86 0.76 0.49 0.63 0.91 0.92 Worn 0.86 0.88 0.78 0.74 0.69 008‘ 0.74 0.74 0.54 0.66 0.92 0.95 146 Linoleum New 0.52 0.52 00 O O uaet wo~ F‘O' DC) (DC) C30 0 0o mu.) Own NM 0. 4 H09 \JU'" bum \pxo Worn 0.66 0.60 0.52 0.53 0.32 0.42 0.46 0.58 0.44 0-55 0.84 1.12 The Coefficient of Friction Values for the Varnish New 0.72 0.80 1.6\ mm at HF“ 00 CO 00 OO O 0 HH O\O\ M 0m wk) \10 Worn 0.62 0.58 0.50 0.49 0.31 0-37 0.49 0.63 0.47 0.59 0.84 1.13 Rubber Nat New 0.72 0.74 0.64 0.63 0.67 0.67 0.56 0.53 0.32 5 :2 OO O \035 \1'1 Worn 0.72 0.72 0.68 0.70 823% o \J'lKJ'l \n Owo OK?! 00 .00 OO 00 m \J'l V0 147 APPENDIX III. (Continued) #3 . Wood Linoleum Varnish Small figlgg New Worn New Worn New Worn New Neoprene 0.59 0.54 0.44 0.52 0.60 0.55 Worn Neoprene 0.68 0.71 0.65 0.56 0.76 0.66 New Crepe 0.72 0.60 0.51 0.54 0.80 0.53 Worn Crepe 0.45 0.46 0.30 0.41 0.59 0.39 New Leather 0.21 0.19 0.21 0.21 0.4 0.21 Worn Leather 0.32 0.26 0.26 0.29 0.3 0.25 New Neolite 0.56 0.51 .55 0.47 0.6% 0.54 worn Leolite 0.67 0.56 0.60 0.57 0.8 0.65 New 5.2. Goodrich 0.39 0.41 0.28 0.45 0.52 0.46 Worn B.F. Goodrich 0.70 0.59 0.62 0.61 0.73 0.62 New R1pp1e 1.16 1.03 1.07 1.10 1.24 1.14 Worn Ripple 1.06 1.0 0.99 .1'15 1.17 1.20 Abrasive Paint Rubber Nat Small §_;§§ New' Worn New Worn New Worn New Neoprene 0.g1 0.g3 ‘ 0.54 0.57 0.62 0.62 ‘WOrn Neoprene 0. 0 0. 3 0.69 0.60 0.71 0.70 New Crepe 0.84 0.81 0.63 0.55 0.64 0.70 ‘Norm Crepe 0.70 0.68 0.51 0.42 0.55 0.66 New Leather 0.39 0.46 0.35 0.2 0.36 0.56 ‘Worn Leather 0.49 0.51 0.40 0.2 0.45 0.60 ‘New Neolite 0.74 0.70 0.55 0.57 0.56 0.54 Worn Neolite 0.66 0.66 0.66 0.65 0.53 0.55 New'B.F. Goodrich 0.46 0.54 0.51 0.47 0.88 0.54 Worn B.F. Goodrich 0.69 0.71 0.63 0.65 0. 4 0.63 ‘New Ripple 1.02 1.07 1.12 1.16 0.3% 0.84 Worn Ripple 0.94 1.07 1.08 1.20 0. 0.89 .APPENDIX IV: The Calculation of a Rank Correlation Value. The rank correlation value is a measure of the cor- relation between two people while performing the same task. For this investigation the two subjects were compared by how they ranked the different stairways or percent points with respect to the average force exerted on the stairways or percent points. ' The correlation value will be calculated for the percent points while the two subjects ascended the stairways. The percent points for each subject are ranked from highest to lowest. For this example each subject exerted the largest force at the 25 percent point and the smallest force at the 93.75 percent point. The correlation value is calculated from the following formula: _ sZAZ ~(N‘-I) Ranking of the Percent Points Percent 140 lb. 172 lb. 2 P0 nts Sub ect Subgect .4é. £2L. 6.25 0 0 12.5 5 5 0 0 25.0 1 1 0 0 37.5 3 g 0 0 50.0 7 l 1 62.5 4 4 0 0 $5.0 2 2 0 0 7.5 6 7 l l I 93.75 9 9 o .0... ' 2 For this example the correlation value is 6(2) e I- .1. .- 0.983 R‘ "' 9(sI-I) 6 148 , ____(_ ,—__,* _._ _“H, 7 h,__22 .Ae4—kh.- _ . e ”i . ‘— APPENDIX V: The Magnitude of the Vertical Force, Horizontal Force and the Point of Application of the Vertical Force. Note: The vertical and horizontal forces were not measured at the same time. e (the point of application of the vertical force) is the distance from the front edge of the tread. For the horizontal force, positive values are directed toward the front edge of the tread; negative values toward the rear edge. Each value is an average of four replications. 159 POUND SUBJECT 7-1 In ' J Stairway: 6" risers, 9" treads~ % of Ascending Descending 8 e P g H P e H . 6.25 40.1 3.21 4".1 58.2 2.48 1!; -, 1205 9102 4015 -702 1.2502 2061 60 5- {“1 25.0 139.7 3.40 -9. 145.1 3.81 6.7 2.} 37.5 121.9 3.24 -l.6 105.0 3.91 -0.7 ‘2‘ 50.0 101.9 3.49 1.7 97.3 3.59 -l.6 62.5 111.2 3.70 3.3 127.4 2.71 -1.1 $500 12303 4.75 004' 15403 1060 -201 k 7.5 10209 6021 206 7700 0065 “1109 93.75 30.1 6.77 3.6 26.1 1.59 ~4.0 Stairway: 6" risers, 10" treads % of Ascending Descending Step P e I Hg P e 32. 6025 60.; 3091 207 6301 3021 101 1205 10105 4022 ”130; 14904 3.58 203 25.0 14306 3062 '16. 13505 3o§8 205 3705 11701 3033 ‘704 11007 30 2 -105 5000 990 2 304 -104 10007 30 -206 62.5 112. 2% 3.82 -0.8 130.9 3.02 —2.1 3500 4078 -206 14603 2006 -506 .705 6020 ‘002 7203 1087 -1205 Stairway: 6" risers, ll" treads % of Ascending Descending S e P e H' P e H ‘2'555 4 .9 3.41 “3+7 13172 2:58 7% 1205 10102 4000 "' 08 165.5 3005 707 2500 14405 3038 -1092 15001 3998 900 37.5 125.1 3.22 -2.1 102.1 4.28 2.2 50.0 101. 7 3.34 1.6 90.1 4.22 —0.6 62.5 110. 2 3.51 2.2 118. 8 3.01 -0.8 g5.0 136. 6 5.00 0.8 1.5 .5 1.73 -4.5 705 11.20 2 6057 305 009 O.Z3 -1406 93.75 39.7 6.71 3.1 29.0 1. 3 —2.8 149 ' 150 APPENDIX V. (Continued) Stairway: 7" risers, 9" treads g of Ascending Descending H gen P e By P e .25 4 .2 3.98 2.2 78.5 2. 6 4.8 1205 9 01 3097 “609 156.4 2. 4 1105 2500 14801 3001 ’308 14 .0 2091. 1501 3705 12301 2065 -105 9\ 05 209% 500 50.0 92.3 2.49 3.7 91.5 2.6 3.1 62.5 99.9 2.62 3.1 127. 1.57 2.9 $5.0 135.4 4.04 2.7 142.3 0.74 —1.2 705 1.0105 5.04 4.4 6801 0090 '906 93.75 34.0 5.35 4.2 25.8 2.11 2.7 Stairway: 7" risers, 10" treads % of Ascending H P Descending Ste P e y e H1 "6755 ‘4011 3776 1.9 43.0 2267 2.3 12.5 85.5 4.16 -9.3 114.5 3.2% .7 25.0 139.2 3.20 -9.1 141.9 3.6 6.1 3705 11902 2.79 ”208 10804 4.03 3.2 50.0 920% 2.47 ”105 9003 3029 -003 02.5 1.02. 3016 105 112.9 2.27 ‘002 5500 129.9 4.94 109 13805 1050 "‘206 7.5 91.5 6.10 4.7 74.2 0.72 -10.5 93075 23.0 6085 3.7 2706 2097 -201 Stairway: '7" risers, 11" treads % of Ascending ‘ . Descending Ste P e H P e Hy 6.25 32.0 3.79 2.8 88.6 2.34 2.0 12.5 121.1 4.16 -2.3 .155.5 2.-9 6.3 2500 159.1 3062 " 00 14401 2083 507 37.5 122.1 3.50 -2.1 104.7 2. 3 2.1 50.0 92.0 3.87 0.2 97.2 2.61 0.5 62.5 97.5 4.50 1.2 137.8 2.06 -0.2 ZSOO 141.2 3.58 100 14608 1.55 -205 7.5 102.5 .52. 2.8 56.8 1.70 -6.7 93.75 30.3 7.51 2.3 22.0 2.37 -1.2 151 APPENDIX V. (Continued). Stairway: 8" risers, 9" treads % of Ascending ' Descending §%s£.. __£__ .26. ._fix. .2.. _fl1_ .25 70.4 3. 2 9.5 109.3 2.g4 5.5 12.5 115.0 3.65 —4.5 192.9 2. 9 12.6 2500 14901 2.94 ”502 15301 2.23 14.4 37.5 123.2 2.40 .7 103.0 2. 3 4.6 50.0 94. 2.24 5.6 99.1 2.61 4.2 62., 111.3 2.61 6.8 142.5 2.06 3.3 Z5.0 144.1 4.03 5.5 156.4 1.55 0.1 -7.5 88.2 5.21 6.4 73.7 1.70 -10.7 93.75 22.3 5.99 4.9 27.7 2.37 -2.6 Stairway: 8" risers, 10" treads % of Ascending Descending Ste P e By P e Hz 6.25 38.2 2.92 4.4 104.6 2.65 4.9 12.5 103.1 3.48 -5.3 186.6 3.10 8.2 25.0 145.5 2.71 —7.5 146.8 3.55 7.8 37.5 124.2 2.71 —1.2 93.2 2.89 3.2 50.0 94. 2.58 4.0 9-.7 2.3 2.0 62.5 105. 2.63 6.4 135. 1.7 1.4 75.0 131.3 3.84 6.8 144. 1.34 -°.1 7.5 104.7 5.44 5.0 64.4 1.37 -6.0 93.75 26.7 6 34 4.3 24.5 2.27 -0.6 Stairway: 8" risers, 11" treads ‘% of P Ascending H Descending 8 e e x E H 8.25 28.4 3.46 5. - . 3.64 g.6 12.5 90.7 4.12 -7.2 165.7 3.72 .0 25.0 154.2 3.30 -11. 162.3 4.02 5.0 37.5 134.5 3.05 ~4. 104.4 3.80 0.1 50.0 99.6 3.09 0.6 93.7 3.62 ~0.7 62.5' 105.0 3.31 0.5 134.2 3.12 -2.1 gSOO 137.6 ' 4.79 Ooé 15406 2063 -904 7.5 100.8 5.94 4.3 75.7 2.39 -11.4 93.75' 26.4 6.55 2.7 2 .0 3.11 -0.3 APPENDIX V: ‘0‘ O “1 Ch 6' o o o o o o o 0 \1\J\0\J\O\J\0\J1N \o mamawmr-o wwmwowmm \n r08! 00.... o NH: \)\J\0\’l OU'IO‘J'K \31 \O-WOKJIUJNH \IMNOVUUU w IR 0 h” \‘IWOUIOU'IOU‘ \J‘l , O C O O 0 \ommmwmt-d WQWNOVUIN (Continued) 152 l 122 POUND SUBJECT Stairway: Ascending P g 66.9 3.02 141.5 3.06 195.9 2.60 151.9 2.35 131.4 2.52 149.5 3.07 176.5 3..1 10505 2. 8 33.0 3.14 Stairway: Ascending _§E__ .£_. . 02 3.90 147.9 3.42 192.4 2.86 150.5 2.g2 121.0 2. 3 143.5 3.12 174.2 3.12 9 .7 2.52 2 .6 3021 Stairway: Ascending P 63.2 2688 125.8 2.68 200.0 2.49 182.5 2.36 145. 4 2. 36 146. 5 2. 97 168.13.10 83. 4 2. 7 30.0 3. 2 6" risers, 9" treads Descending H E e H 5. 4 771.0 2.63 —O.6 2.1 132.9 2.29 1.6 -4. 2 201.3 2.41 9.7 1. 4 174.1 2.21 12.1 0. 0 139.6 1.99 5.6 0 .2 151.0 1.71 10.3 101680]. 1059 “505 6.g 98.2 1.72 -15.6 1 3502 3025 -003 6" risers, 10" treads Descending .31. 'g68 ”5676 2§83 71.2 -500 13209 20107 -1100 21102 2001 703 ’80]. 17508 10’ ‘"O 604 —3.9 139.2 1.61 6.4 -3.1 142.8 1.6 -0.7 -2.4 156.2 1. 3 -5.0 2.6 77.7 0. 4 -17.0 2.1 30.5 1. -6.3 6" risers, 11" treads Descending H P _e Hz 8.4 66.0 3.01 2.1 -004 15902 2090 50; -2.7 2 9.4 2.21 13. 0.4 19 6 1.66 10.5 0.4 130. 8 1.64 9.3 1.7 1 6.0 1.5% 3.2 4.5 15. 8 1.5 ‘log 8.2 85.2 0.45 —15. 2.0 32.2 0 76 «1.7 153 APPENDIX v. (Continued) ‘\ Stairway: 7" risers, 9" treads % of Ascending Descending Sggp P e By P 9 H2 .25 74.2 3.03 4.1 53.9 10 -1.0 12.5 1 7.1 2.6. 1.1 10 .2 1.60 3.6 25.0 1 2.8 2.42 0.4 187.8 2.16 13.6 37.5 165.6 2.42 2.7 155.9 2.38 13.4 50.0 136.8 2.62 4.2 130.6 2.44 12.0 62.5 132.4 2.73 4.8 135.1 1.73 6.6 g5u') 157.4 2.9 3.5 155.0 1.44 “3.5 7-5 97.7 3-37 ..1 73-7 1.45 -5.9 93.75 31.0 3.77 2.2 24.7 2.69 1.1 Stairway: 7" risers, 10" treads % of Ascending Descending 8 E H P e _fl 6.25 .9.g 3.28 5.0 80.6 1.72 ~06— 12.5 150. 2.54 0.7 166.1 2.06 3. 25.0 183.7 1.61 —2.6 201.g 1.60 11.7 37.5 137.1 101.7 -105 156. 1064 12.6 5000 11701 1.56 “0.6 121.6 0.72 903 62.5 147.8 2.26 -0.2 142.5 0.75 §.2 g5.0 175. 2.40 1.5 150.2 0.50 -1 .0 7.5 90. 1.26 5.2 74.9 0.61 -13.8 93.75 29.2 1.95 2.1 28.4 1.06 -3.7 Stairway: 7" risers, 11" treads g of Ascending Descending 2 _ Hy _ e Hx_ 6.25 90.3 3664 4.0 48.3 3.16 3.7 1205 15201 3058 -008 122. 2.55 2.3 25.0 200.4 3.37 -2.5 206. 2.30 8.8 37.5 182.4 3.20 -1.6 187.9 2.36 5. 50.0 155.3 3.36 -0.1 159.3 1.96 3.2 62.5 155.9 3.;0 0.3 164. 1.41 —0.1 35.0 143.6 3. 7 1.4 184. 1017 -300 705 54.4 4.85 4.7 75.9 2.92 '1108 93.75 15.4 5.72 5.8 25.7 4 24 —17.2 1511 (Continued) APPENDIX V. F 8" risers, 9" treads Stairway: 057/0 3310 770 £4 01399.. 48 95 111 ... 371017000 972177.: 22 Descending 9225/04.:1984 I _H 418225255 314213130 33222 2334 Ascending e__ 52 0100/4714 001 482 3288 p 83 7 2 7 16 15 2570 9.573 12 35/078 0, . 5 t) o e 000000000 Q. Stairway: 8" risers, 10" treads 2 96 9.1.1088 0 71.57050 2 1211 481517207 2 7311.174 74 C 322221102 93 n 1 d n e 4Jso256fim403 Z. nuzlfixstQZZQu n 7L58432HFOKJQJ 1 000000000 .m 222222223 8 c 3 _A ......... .4fiAd11 .1:)3$111