VARlATIDN 0F RAiNDROP CATCH DUETO AIRFLOW DISTURBANCES AROUND ' A STANDARD RAINGAGE ~ Thesis for the Degree of Ph. D. MlCHlGAN STATE UNIVERSITY CHARLES CARSTEN MUELLER .1969 ‘ T H 5-5" ITY LIBRARIES IIIIIIII :w R I Michigan; State Univet sit)! This is to certifg that the thesis entitled VARIATION OF RAINDROP CATCH DUE TO AIRFLOW DISTURBANCES AROUND A STANDARD RAINGAGE presented by Charles Carsten Mueller has been accepted towards fulfillment of the requirements for Ph.D. degree in Agricultural Engineering Major rofessor gflfi/M 0-169 ":1 675/ @333 3 “2*? 9': "W ABSTRACT VARIATION OF RAINDROP CATCH DUE TO AIRFLOW DISTURBANCES AROUND A STANDARD RAINGAGE By Charles Carsten Mueller The inadequacies of rainfall measurements have been realized for many years, however the need for greater accuracy in precipitation measurements was not appreciated until cloud physics studies by radar techniques were initiated. Runoff forecasting for engineering design pur- poses is also requiring greater accuracy in precipitation measurement as runoff related structures' importance and cost of construction increase. While a raingage's spatial position has an important influence on the gage's performance, the physical presence of the gage itself must be considered a hindrance to its Operation. Obstruction to airflow in the vicinity of the gage, due to the gage's presence, results in disturbances in the local precipitation pattern. This study's objec— tive was to determine the airflow pattern around a U. S. Weather Bureau Standard Raingage, to analyze the airflow's effect on drops approaching the gage's funnel and to obtain a correction curve relating percent of catch to drop size and air velocity past the gage. Charles Carsten Mueller The airflow pattern was determined by measurements with a three sensor hot film anemometer system in a wind tunnel using model gages. This three dimensional flow field description and the known aerodynamic drag charac- teristics of water drops were used in a digital computer to simulate the drops' movements as they approached the gage. The drop paths thus determined were then analyzed to establish the gage's effectiveness in measuring precip- itation. Using drop sizes of l to 5 millimeters in diameter, it was found that the gage caught from 103 to 11 percent of the drops as the free stream airflow velocity increased from 10 to 50 feet per second. In general, the decrease in catch was less pronounced as drop size increased. (Wm. Major Prdfessor Approvedzg;;¢gé§:2%%g 14$ 5522Z%£%;3/ Department Chfiirman VARIATION OF RAINDROP CATCH DUE TO AIRFLOW DISTURBANCES AROUND A STANDARD RAINGAGE By Charles Carsten Mueller A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1969 To Glenda ii ACKNOWLEDGMENTS The author wishes to express his appreciation and thanks to Prof. E. H. Kidder, committee chairman, Prof. M. L. Esmay, Prof. O. Andersland, Prof. R. Hamelink and the Agricultural Engineering Department, for their help and support that aided the completion of this study. I thank you. iii TABLE OF ACKNOWLEDGMENTS LIST OF TABLES. LIST OF FIGURES . INTRODUCTION LITERATURE REVIEW. Gage Errors. . . Gage Shields . Drop Characteristics. EXPERIMENTAL DESIGN General Description Theoretical Approach. CONTENTS Cylinder Drag Characteristics. Falling DrOp Characteristics Tunnel Wall Corrections. Data Collection Points Data Interpolation Drop Catch Area Data Conversion Program TURB Program MAIN Program TRANS Program CORRECTI Program CORRECT2 . Program DROPPATH . APPARATUS Wind Tunnel. . . Anemometer . . . . Analog Computer . . Data Recording. . Raingage Models . Page iii vi vii KOC\LA) UL) l2 l2 13 16 17 18 21 22 25 26 26 27 28 28 28 3O 30 3O 31 32 35 EXPERIMENTAL PROCEDURE Calibration. . Test Routine . DISCUSSION OF RESULTS . CONCLUSIONS. REFERENCES APPENDIX A Field Velocity Data APPENDIX B . . Program TRANS . Program CORRECTI Program CORRECT2 . Program DROPPATH Page 38 38 A0 Al A5 A6 51 51 6A 6A 68 72 75 Al LIST OF TABLES Approximate errors in precipitation measure- ment 0 O I I O I O O O 0 Comparison of various Standard Gages Deviation of unshielded gage catch as com- pared to a gage with Nipher shield . . . Comparison of "sawdust snow" catch in model Standard Gage operating under various wind- shield combinations . . . . . . . Terminal fall velocity of water drops in air I O O D O O I O O O - A12. Field velocity data. . . . . . vi Page 11 51 Figure 10. ll. 12. LIST OF FIGURES Cylindrical coordinate system and simple cylindrical "raingage". . . . Aerodynamic drag characteristic of a truncated cylinder as a function of the Reynolds number . . . . . . . . Wind tunnel correction curve using three data points . . . . . . . . Interpolation pattern to determine unknown velocity ratio at point x. . . . Analog computer circuit for anemometer bridge output conditioning and lineari- zation . . . . . . . . . . . Flow field velocity measurement instrumen- tation system. . . . . Velocity measurement instrumentation Wind tunnel test section Gage models used for wind tunnel tests Anemometer sensor probe, side View. Anemometer sensor probe, front view Percent error of drops caught relative to drop diameter and free stream velocity vii Page IA 16 20 2A 33 3A 36 36 37 37 37 A3 INTRODUCTION As early as “00 BC raingages were in use. It is reported in early Indian writings, translated by Shama- sastry (1915), that: "In (front of) the store houses, a bowl with its mouth as wide as an aratni (2A angulas) shall be set up as a varshamana (raingage). . . ." Typi— cal rainfall quantities are given for various parts of the country. Rainfall predictions were also being made: "A forecast of such rainfall can be made by observing the position, motion and pregnancy of Jupiter, the raise and set motion of Venus and the natural or unnatural aspect of the sun." Just how these factors were used to form conclusions is not discussed, however, the rainfall records were used to determine what crops were to be planted. It is now realized that the accuracy of yesterday's and today's rainfall measurements is often less than desirable and the errors are usually unpredictable. The advent of precipitation measurements and cloud physics studies by radar techniques has pointed this out. How- ever, the inadequacies of raingages in general have been realized for at least 200 years. Heberden (1769) found 1 that similar gages at different heights caught different amounts of rainfall. Many investigators since that time have shown that gage catch tends to decrease as wind velocity increases. This is especially true during periods of snowfall. The precipitation gage is one of the primary instru- ments of observation in meteorology, hydrology and clima- .. l......._ u ..... . 4'1 tology. As a tool for climatological data collection the )L. g.-- .‘ present day raingages have been considered adequate. However, for engineering purposes, such as runnoff fore— casting necessary for design work, and for radar and cloud physics studies, today's gage is often inadequate. While gage exposure plays an important role in the instrument's performance, the gage itself must be con- sidered as a hinderance to accurate measurements due to its own obstruction to airflow in the immediate vicinity of the gage and the resulting disturbance in the local precipitation pattern. This research report concerns itself with the measurement of the disturbed airflow pattern around a gage and evaluating the resulting error on the gage's catch. While the techniques used are time consuming, they are applicable to the evaluation of new or modified gages. The objective of this study was to obtain a correc- tion curve for use with a U. S. Weather Bureau Standard Raingage relating percent of catch to drop size and air velocity past the gage. LITERATURE REVIEW Gage Errors 3 R Several sources of errors are present in most rain- 5. as- h.-......._ --‘_l . a. t . gages and gage installations. Kurtyka (1953) has esti- mated these errors as being: TABLE 1.--Approximate errors in precipitation measurements. % error evaporation -1.0 adhesion - .5 color - .5 inclination - .5 splash +1.0 exposure -5.0 to -80.0 Evaporation losses varied with gage and air temperature. Horton (1919) showed that about 70 percent of the evapo- rative losses occurred during the 12 hour night period. He also found that the water loss due to evaporation over a 7 day period (at 70° F) was equivalent to .01 inch of rain. Painting of gage funnels is not desirable due to the varying effects of aging paint. Differences in gage losses due to gage color have been found to be on the order of one percent, Wild (1873), with a white gage indicating about one percent more than a black gage. Due to most raingage designs, the gage is more apt to receive splash from the surrounding area than to lose it. Gold (1931) found that with a wet surface, drOps 2 mm in diameter could create splash up to A feet high. The errors due to splash are mainly additive. However, other gage errors are nearly always in a negative direction, therefore many investigators Judge a gage on its ability to catch more precipitation than others. Many experimenters have shown the effect of exposure on gage performance. Heberden (1769) conducted an experi- ment that showed a decrease in precipitation with height. His highest gage, 151 feet above ground level, caught A6% less than a gage at ground level. (It was postulated that electricity was concerned with this phenomenon.) A significant experiment carried out by Arnold, and reported by Symons (1871) showed that there was, in fact, no sig- nificant difference in rainfall at ground level and at an elevated station. He used two gages, one at 5 feet, the other at 30 feet, with sloping orifices that always faced into the wind. Over a 5 year period these two gages almost always caught the same amount of rain (.19 inch total difference) and were in good agreement (i0.5%) on a yearly basis. In general the orifice height of gages used through- out the world covers a small range, from 1 foot to 6.6 feet (2 meters). Exceptions are totalizing gages in heavy snowfall areas which may reach 15 to 20 feet in height. TABLE 2.—-Comparison of various Standard Gages. From F Kurtyka (1953). it Orifice Orifice A Country Type Gage Diameter Height (inches) (inches) England M. 0. pattern 8 12 England Snowdon 5 12 Australia 8-inch type 8 12 France Tonnelot 8.88 28.3 Austria Kostlivy 9.93 20.3 United States U.S. Weather Bureau Standard 8 31: France Scientific Assoc. 8.88 39.4 China Board 7.91 39.4 South Africa 5-inch type 5 48 Holland DeBilt 8.88 59.1 Germany Hellmann 6.28 59.1 Sweden Swedish 14.06 59.1 Russia Russian 9.93 78.8 Several conflicting reports have been made concern- ing the effect that orifice size has on precipitation catch. Conover's (1951) experiments with a 3/4 inch orifice gage indicated a higher catch than larger orifice gages. Through a mathematical treatment, Howell (1946) showed that a small gage should be more effective in pre— cipitation measurements. Wild (1885) reported on tests of Calne and Stratfield-Turgis using 8 gages with from l to 24 inch orifices that showed there was little differ- ence with orifices over approximately 4 inches. Smaller orifices indicated less rainfall. No other factor in rain or snow measurement is as important as instrument exposure. A gage site and the air movement over the site area should be representative of the area that the gage readings are supposed to represent. I However, the gage itself presents an obstruction to the general airflow pattern, creating increased velocities over and around the gage, and eddies in its lee and pos— sibly in its funnel. The increased airflow velocity over a gage may carry the smaller and lighter water drops across the gage's orifice instead of allowing them to fall into it. This loss is directly related to wind velocity. That is, as wind velocity increases the losses due to the disturbed airflow pattern increases. Gage Shields Several gage shields have been devised in an effort to reduce the adverse airflow pattern that exists around a gage. None have been completely successful. "The effect of Windshields on raingages is to divert the flow of air down and around the gage so that there is no up— draft in the region of the orifice of the gage to cause a corresponding area of minus precipitation," Kurtyka (1953). An early form of gage shield was developed by Stevenson (1842). His gage's orifice was set at ground level and was protected from splash by a surrounding brush mat. It produced the desirable aerodynamic char- acteristics, and performed well with rain, but snow tended to drift into the orifice. The two best known gage shields are those developed by Alter (1937) and Nipher (1878). Several variations of these shields have also been studied. The Nipher shield is trumpet shaped with the flared end upward and level with the gage orifice. The Alter shield has a similar shape but is formed of movable metal strips spaced in a ring around the gage. These were primarily used with storage gages in snowfall regions. TABLE 3.—-Deviation of unshielded gage catch as compared to a gage with Nipher shield. From Borstein (1884). 45 heavy rains 26 fine rains Wind mph Number of deficit Number of deficit days (%) days (%) 0—1 4 23 1-3 17 6 8 25 4 - 7 13 13 6 18 8 - 13 7 l4 6 46 13 - 18 6 l7 2 52 According to Bernard (1938) the Nipher shield was theoretically correct for sampling snow in windy condi- tions. However, it was found that the rigid horizontal shelf-like portion of the shield funnel collected snow which later blew into the gage. Screens have been used on the horizontal portions of the Nipher shield to effectively reduce splash into the gage. Neiss (1961) studied the variation of snow catch with shielded and unshielded gages with 4 pairs of gages in Michigan. While differences were small during warm months, the mean ratio of unshielded gage to shielded gage snow catch varied from about .9 to .5 as the average wind speed increased from 2 to 14 mph. Warnick (1956) has made extensive studies using a specially constructed wind tunnel, sawdust snow and various photographic techniques to evaluate the effective— ness of several types of gages and shields to measure snowfall. The following table is indicative of Warnick's results. TABLE 4.--Comparison of "sawdust snow" catch in model Standard Gage operating under various wind- shield combinations. ' actual amount of sawdust type of caught in storm period windshield (gms) none 5.8 none 5.2 Nipher 7.6 Nipher 7.9 Original Alter 10.4 Original Alter 11.0 As pointed out by Weiss and Wilson (1958) the range of expected validity of shields must be considered. Nor- mally a gage is subjected to a wide range of turbulent airflow patterns. Eddies on the order of hundreds of feet are created by ridges, large buildings and tree lines. Smaller trees, buildings and brush produce eddies on the order of a few feet. Gage sites that are charac- terized by small turbulent patterns (on a scale of inches) must be rather open with little surrounding obstructions. Only when small turbulence patterns exist can a gage shield be expected to perform well. A shield is princi- pally useful for reducing or eliminating the eddies pro- duced by the gage itself and in reducing the vertical components of the air passing over and around the gage. When evaluating the catch effectiveness of a shielded gage it must also be kept in mind that the standard of comparison itself is subject to uncertainties. The USWB Standard Raingage without shield is usually used as a comparison for rainfall measurements. In snow measurement comparison is often made with the snow depth in the area surrounding the gage site. Drop Characteristics Blanchard (1948) concluded that water drops less than 4.6 mm in diameter are quite stable, that those between 4.6 and 5.4 mm are increasingly unstable, and that those over 5.4 mm in diameter will break up if 10 subjected to a shock. Leonard (1904) concluded that drops over 5.5 mm in diameter cannot exist for more than a few seconds. However, Umback and Lembke (1966), experimenting with drops falling through a 12 foot high section of a wind tunnel, found that 5.5 mm dr0ps did not break up when sub— jected to a 20 fps crosswind. They concluded that "the shock imposed on a drop of this size by this magnitude of wind, and the short fall distance involved, was apparently , . ..._,,_ . -- 2 insufficient to cause breakup." Green (1952) evaluated the data on terminal veloci- ties published by Laws (1941) and derived the following relation: 0.00122 d2°uu K force of air resistance in grams, where K and d drop diameter in millimeters. This relation agreed with Laws' data for drop diameters of 1.17 to 3.92 mm. Gunn and Kinzer (1949) made an extensive study of the terminal fall velocity of drops of 0.07 to 5.7 mm in diameter. Velocities of drops .08 mm and smaller were found to agree with Stoke's law. Drops over 5.76 mm in diameter were found to be unstable. Their results have been used to determine the drag characteristics of drops for this study. Further dis- cussion of this matter will be found in the section on experimental design. Their comments on the effect of 11 density or frequency of falling drops indicated that the change in drag characteristics involved were on the order of a few percent. TABLE 5.--Termina1 fall velocity of water drops in air. From Gunn and Kinzer (1949). drop diameter velocity (cm) (cm/sec) 0.10 403 0.20 649 0.30 806 0.40 883 0.50 909 EXPERIMENT DESIGN General Description The objective of this study was to determine the disturbed airflow pattern in the vicinity of a standard rrrwrrui raingage. And to evaluate its influence on the quantity —& of rainfall measured by the gage. Velocity measurements were made with an anemometer- analog computer system with raingage models in a wind tunnel. Three dimensional flow field velocity components were measured above and upstream of the raingage models. Thus having a flow field description, and knowing the drag characteristics of water drops, the trajectory of drops approaching the gage could be computed, and the pro- portion of drops that were intercepted or those that were deflected from the gage's opening could be determined. The factors influencing the falling drop's path included: the constant force of gravity, the drag forces due to the drop's movement through the air, and the mass momentum of the drop. As the variety of turbulence patterns found at normal raingage sites are numerous, and as they have not been described, the gage was placed in a uniform flow 12 13 field of a wind tunnel to determine the local air disturb- ances created by the raingage itself. The result expected from this experiment was a relation between the proportion of drops intercepted by the gage, the size of the falling drops and the local air- flow velocity. Theoretical Approach A theoretical approach to evaluating and describing the flow field around a raingage could be obtained by applying the Navier-Stokes equations. In the cylindrical coordinate system the three dimensional Navier—Stokes equation set is %%+u%%+%%%+W-§-§-%2--%%§+V[V2u---§2 3%] where V2 = 5%: + %-§%~+ %7 5%; + 5%; , u,v,w = the velocity components along the x, y, and z axis, respectively, r,¢,z = cylindrical coordinates, p = fluid density, t = time, P = pressure, and v fluid viscosity. 14 These equations can be simplified somewhat by assum- ing uniform flow conditions, that is §u__ 8v _ 3w _ 3t 3t at This condition cannot be expected downstream and immedi- ately above the cylinder, where turbulent flow will exist for all but the lowest free stream velocities. If R, the cylinder's radius, can be considered small then it may also be possible to let 3P = 0. Figure 1 illustrates the coordinate system used for this equation set, and a simple cylindrical "raingage." /P (r’g’ Z) l/IZJ Figure l.--Cy1indrica1 coordinate system and simple cylindrical "raingage." 15 The boundary conditions for the Navier-Stokes equations are: u = v = w = 0 when 2 < 0 and r = R, and v + 0, w + 0 and u + Vco as r + m, where V0° is the uniform horizontal flow field velocity. An attempt was not made to solve these equations, because when they were simplified to the point where a 3 solution could be found with today's mathematical tools, they no longer described the problem adequately. [J The possibility of finding a solution by simulation on an analog computer has been considered. As differen- tials must be with respect to time for solution on analog computers, the Navier-Stokes equation set must be con- verted so all partial derivatives are with respect to at 2 2 2 or atz. After multiplying by gt: 3?? gté, collecting like terms and simplifying, the equation set is 2 l zll{¢fl|:uvrt(u_%)_rn(% _ %)-u"(\) +525] +rn¢v [%uv_ $471} = r"¢"(vu"-wu'z'), n n t: _X_1.Y. 2_I V + "' 'X—'—2—-‘ z {0 [v r (u r) r r(ur) v (v-+FT)] r 0 [v r Llr‘ = r"¢"(vv"—wv'z'), z"{¢"[w'r'(u-%)-w"(v-+%%)]i-gw'r"¢'}==r"¢"(VW"-WW'Z'). These equations would require an analog computer having 16 12 integraters, 49 multipliers and at least 60 Opera- tional amplifers, plus auxiliary equipment. Cylinder Drag Characteristics As the coefficient of drag of a truncated cylinder is constant for: 1.5 (10)“ < Reynolds number S 2 (10)5 the flow field description would remain constant for a cylinder (or a simple cylindrical raingage) subjected to a gm flow field of a velocity producing a Reynolds number within this range. For an eight inch standard raingage this is equivalent to a velocity range of approximately: 3 s Velocity (fps) s 50. Thus a relation of catch, drop size and flow field velocity could be obtained over this range by studying the flow field configuration at one velocity within this range. 10 infinite circular cylinder C 1 - ‘\___/:/’“””3L'“—Jfi.“\a finite circular cylinder L/d = 5 102 103 10“ 105' 10b Figure 2. Aerodynamic drag characteristic of a trun- cated cylinder as a function of the Reynolds number. 17 Falling Drop Characteristics Several researchers have investigated the drop size distribution found in various types of rainfall. Most have found that drops of l to 1.5 mm in diameter occur most frequently in all but the more intense thunderstorms. Drops of 3.5 to 4.5 mm have been the largest commonly found. In this report drops of 1, 2, 3 and 5 mm in diame— ter have been considered. The drag coefficient of a drop can be determined by applying the equation: F = % n pa d2V§Cd where F = drag force, pa = air density, d = drop diameter, Vr = relative drop velocity, Cd = coefficient of drag. The drops' weight can be computed from: W = g N d3 g (0w - 0a) where 0w = water density. When a drop is falling at its terminal velocity its weight equals the drag force acting on it. Thus, the two above equations can be equated to obtain: pw - pa 0 4 C :— 3 g a d d \T" r The coefficient of drag was determined by applying the terminal velocity of drops as found by Gunn and Kinzer (1949). I" ll 18 Air density at 20° C, 1 atmosphere pressure and 50 percent relative humidity, and water density at 200 C were used for these calculations. Tunnel Wall Corrections In order to compensate for the constricting effect of the wind tunnel walls, certain corrections must be made on the velocities measured in the tunnel. These corrections are generally termed wall corrections. The principle correction needed for the flow field description is to compensate for the lateral constraint of the flow pattern around the model. This is usually called "solid blocking." The presence of the model in the test section reduces the cross-sectional area through which the air must flow and, by Bernoulli's principle, results in increased velocities around the model which must be compensated for. A second necessary correction is for ”wake block- ing." Any body without boundary layer control creates a wake. This wake has a mean velocity lower than the free stream velocity. To conform to the law of continuity the velocity outside of the wake in a closed tunnel must be greater than the average free stream velocity. This increased velocity in the portion of the stream outside of the wake results in a lowered pressure which in turn produces a pressure gradient and an airflow velocity increase around the model. l9 Streamline curvature is a third error that is created by the constraining influence of the tunnel walls. While this effect is a result of solid blocking, it is usually treated separately in the study of airfoils. Another correction that is commonly made in wind tunnel tests is that for "buoyancy." Most tunnels have a variation of static pressure along the test section due to the thickening of the walls' boundary layers, which results in increased velocities as one traverses the test section's length. This pressure gradient tends to "draw" the model downstream. The tunnel used in this study has a tapered test section to compensate for the boundary layer buildup, thereby minimizing the need for buoyancy corrections. These wall corrections can be experimentally veri- fied by testing several models of different sizes of the same subject at the same Reynolds number. This procedure also provides a second method of evaluating wall correc- tions which encompasses all of the above error terms in one correction. By determining the ratio of the measured velocity at a point to the free stream velocity for each of the two or more models, a dimensionless curve of velocity ratio versus model scale can be made. By extrapo- lating the curve that passes through these points to the ordinate position, where the model scale equals zero, one finds the velocity ratio that would exist with a prototype 20 subject in a nonconstrained flow field. This is illus- trated in Figure 3. That is, the surrounding flow field size to model size ratio approaches infinity, which is the condition found in the normal prototype subject use. Data from two models of different scales can be used similarly, for which a straight line is used in the extrapolation process. Three models create three points on the graph and allow the use of a second order curve which improves the accuracy of this method. This method of correcting the flow field data has been used to correct the data presented in this report. |< / LL. 0 I ‘I + 0 .25 .50 .75 1.00 Model Scale Figure 3.-—Wind tunnel correction curve using three data points. 21 Data Collection Points A three dimensional grid of data collection points was oriented above and upstream from the model. Spacing of all grid points was d/4, where d is the model's top inside diameter. The grid extended to the top of the test section's uniform flow area, horizontally to d/4 beyond the gage edge, and upstream for 25 intervals, or until a nearly uniform flow field was encountered. Thus, the coordinate indices limits were: 1 s x s 4 — horizontally, cross-stream direction, l s y s 15 - vertical direction, 1 s z s 25 - upstream direction. The x = 1 plane passes through the cylinder's verti— cal axis and is parallel to the free stream flow direc- tion. The y = 1 plane is horizontal, d/8 below the cylin- der's top edge, and parallel to the free stream flow direc- tion. The z = 3 plane is normal to the flow field, is vertical, and passes through the vertical axis of the cylinder. Three models of different sizes were used in the wind tunnel tests, which resulted in three different spac- ings of the data collection points. Thus the number of data points along the vertical (y) axis varied with each model. Due to this, the number of points used to find the velocity ratio for various grid points varied. All grid 3‘.— 22 points up to y = 8 above the gage had 3 values for extrapo- lation purposes. When measuring the flow field several diameters up- stream of the model, where the flow field was nearly uni- form, intervals of d/2 were used in the z direction. When the data set collected in the wind tunnel was subsequently used for computations the model's coordinate system was moved 3 intervals in the negative x direction. This allowed sequential numbering of the yz planes when the data values were reflected about the model's center yz plane to obtain a data field for the full width of the gage. Data Interpolation The data values used for drop trajectory computa- tions were in the form of velocity ratios. These ratios being the velocity component parallel to a model axis at a data point divided by the free stream velocity. Thus, any free stream velocity could be considered by using velocity ratios derived from the basic data. To determine the velocity component ratios at posi- tions other than at data collection points it was necessary to interpolate between the known values. This was done in the three dimensional data array by repetitive applica- tion of a one dimensional interpolation procedure. Interpolation was accomplished by using the Newton interpolation formula based on divided differences, Hamming (1962), using data from four grid points, two on each side of the point in question. This procedure, in effect, finds a third order polynomial and evaluates it at that point. To find the unknown velocity ratio at a desired point x (refer to Figure 4) in a three dimensional array of data this procedure was first applied in the y direc- tion for two points above and two points below the X2- plane that point x lies in. This determines the velocity ratios at 16 positions surrounding the point x, on the XZ-plane (points "a" in Figure 4). Interpolation was then carried out in the x direc— tion. Four of the points found in the previous step were used to find the velocity ratios on a line parallel to the z-axis that passes through point x. This was done four times to find four values along this line, two toward the origin and two away from the origin, from point x (points "b" in Figure 3). By interpolating once more along this line, which is parallel to the Z-axis, the velocity ratio at point x was found. When drops approached the edge of the data field it was not possible to use a third order equation based on four data points. When this condition was encountered, that is, when drops approached the bottom or the down stream end of the data field, a procedure similar to that stated above was used, using three data points and second order interpolation. 24 A. a / \\‘ \r 5“\:‘~\\\‘ ‘\\\\\\‘ \:‘~~1 -\ m / I ,5 . ] /Az Z I , ,4, I / // / , I la %, /// data points X a,b,x — data value locations found during interpolation procedure Figure 4.--Interpolation pattern to determine unknown velocity ratio at point x. 25 Drop Catch Area The area defined as the drop catch area is that por— tion of the high shear or boundary layer immediately above the gage's funnel opening. A second velocity data set was collected, using intervals of Ay = d/16 and Ax = Az = d/8, in the immediate vicinity of the gage funnel. By observ- ing the change in velocity between adjacent data collec- tion points it was possible to define the boundary layer's position above the gage's funnel opening. Using this information the boundary layer was simulated by using seg- ments of 17 plane surfaces. The surfaces used, and their limits are defined in function CATCH of program DROPPATH (refer to Appendix B). Velocity measurements below the boundary layer showed that low mean velocity and highly turbulent flow was pre- dominate. Since the drop masses were relatively large as compared to the forces applied to the drops by the turbu- lent air below the boundary layer, and since the drop reac— tion decreases as the frequency of the applied force increases, it was assumed that the drops that passed through the boundary layer were not deflected by the air movements in that region. Thus, once drops had passed through the boundary layer their paths depended primarily on their velocity and movement direction as they passed through the boundary layer. ___- ‘.__p-—" . I 26 Since the boundary layer was a positive distance above the gage's opening (except along the upwind edge) it was possible for a drop to pass through the boundary layer above the cylinder and still miss the gage's funnel if the drop's trajectory was such that it could pass over the edge of the funnel. The possibility of this occurring was allowed for in program DROPPATH. Data Conversion Several FORTRAN computer programs were developed to handle and analyze the data collected in the wind tunnel tests. Program TURB Program TURB is a tape handling routine which trans- fers the three coordinate positions and the three veloci- ties indicated by the anemometer, from paper tape to mag- netic tape in binary form for ease in further processing. Program MAIN Program MAIN was used to convert the binary data on the magnetic tape to the base ten number system and to provide a print out of the basic data. MAIN also punched the six values of each data point along with an identify- ing number onto computer cards for future use. 27 Program TRANS This program served two purposes. From micrOphoto- graphs of the sensor probe, the average angle between each sensor and the plane of the other two sensors was measured. Program TRANS calculated the resulting angles between the sensors and the model coordinate system. Using this information, TRANS then computed the three velocity components parallel to the model axis system at each data collection point from the data obtained from program MAIN. Indicated flow velocity across an anemometer sensor is not directly proportional to the sine of the angle between the flow direction and the sensor's axis. There- fore an additional correction was made to compensate for this crossflow effect by the equation: 2 2 -o2 2 2 Vp = V. (sin a + K cos a) 1 where V = true velocity component perpendicular p to sensor axis, Vi = indicated velocity, u = angle between flow direction and sensor axis, K = correction factor. The value of K was determined for each sensor in the pri- mary instrument calibration procedure. 28 Program CORRECTl Errors in the basic data that were caused by slight misalignment of the anemometer probe were compensated for in this program. Probe misalignment was determined by making velocity measurements at selected points in the wind tunnel after the model had been removed. The veloc- ity components measured in the cross stream and vertical directions were then subtracted from the data taken with the gage in the tunnel. Program CORRECT2 To compensate for the influence of the tunnel walls on the flow field, corresponding flow components collected at each data point for each model tested were used to find the corrected velocity component at that point. The method used is described in the section Tunnel Wall Correc- tions. Program DROPPATH From Gunn and Kinzer's (1949) data, the influence of relative airflow on movement was mathematically described. Combining this force as a function of the local flow field velocity and direction with the influences of gravity and inertial forces, a stepwise progression of a falling drop's trajectory was determined. DROPPATH simulated rainfall using several drop sizes commonly found in rain- fall and several airflow velocities in the 3 to 50 fps range. “.7" 1W: Am». J; 1‘... n. 29 Flow field characteristics between data points were usually determined by third order, three dimensional interpolation. Near the edge of the data field second order interpolation was used. Drop fall starting points were distributed in the y = 14.5 plane at intervals of d/l6 in the x and z direc- tions. The drop was given an initial velocity of the terminal velocity for its size plus the air velocity com- ponents at its starting point. This simulated the drop's travel path as if it had been falling through a uniform flow field similar to that found at its starting point. By comparing the number of drops intercepted by the gage with the number starting in an area of the same size on the y = 14.5 plane the percentage of catch was determined for several common drop sizes. APPARATUS Wind Tunnel The wind tunnel used for model testing is owned and operated by the Mechanical Engineering Department at Michigan State University. This tunnel is of the con- strained suction type with a 25:1 constriction ratio and a test section 2 ft by 2 ft by 10 ft long. The variation of velocity across the test section is less than 2 percent outside of the boundary layer. The test section has a lengthwise taper to compensate for the boundary layer buildup and to minimize the need for bouyancy corrections. The variable pitch fan and motor control system provide excellent control and stability of flow velocities. A Prandtl tube mounted to one side and slightly upstream of the model was used to constantly monitor the tunnel air velocity during tests with the aid of a slop— ing tube water manometer. A mercury column barometer and thermometer in the laboratory provided data to correct the manometer readings for atmospheric changes. Anemometer A three channel constant temperature hot film anemometer system was used for three dimensional flow 30 31 field measurements. The sensing probe held the three hot film sensors in a pyramid formation. The angles between the sensors were approximately 100 degrees. Three temper- ature compensating probes were placed in the downstream end of the tunnel's test section to provide automatic anemometer compensation for air temperature changes. Two rack and pinion gear driven hook gages with scales were modified to manipulate the probe in the hori- zontal (cross stream) and vertical directions. The base holding these gages was moved along the tunnel test sec- tion to obtain a longitudinal placement. Probe placement accuracy was t .006 inch (.0005 ft). Analog Computer The three bridge voltages from the anemometer modules were fed to an analog computer. This computer provided signal conditioning, conversion of anemometer bridge vol- tage to the related velocity (linearization), and real time integration to obtain mean velocities normal to each sensor element. From each bridge voltage, a voltage equal to the bridge output at zero velocity was subtracted. The result- ing signal was multiplied by a constant to obtain a 10 volt signal when an anemometer sensor was normal to a 100 fps flow field. This conditioned signal was fed to a 32 variable diode function generator (VDFG) which converted the O to 10 volt range such that: E5 = 0.100 x Velocity (fps). The VDFG was adjusted with the anemometer calibra- tion data obtained from the instrument's primary cali- bration to allow for variations in individual bridge and sensor characteristics. This voltage (E5 - a function of velocity) was divided by 10 and then summed by an analog integrator over a 10 second period to obtain a mean velocity value. Three of these circuits were used to convert the three anemometer bridge voltages. An independent square wave generator operating at 0.0500 Hz was used to control the time period of integra- tor operation. Data Recording Three variable voltage sources were used to provide probe position data. These were adjusted to correspond to the anemometer probe's position. These three voltages, along with the three analog output voltages were fed to an analog-digital converter and paper tape punch. Thus, the probe's coordinate positions, X, Y and Z, and the anemo— meter's indicated velocities, V1, V2 and V3, were recorded on the paper tape when the converter's remote start scan switch was actuated. 33 .COApmNHhmmCHH use wQHCOHqucoo pseudo mwpflpn AmmeoEmcm how pflzopflo amDSQEoo moamc psopso omo> I mm pmmeOHpccpoo I m Hmcwfim mcpoEoEmcm cmNHammcHH I om nonmawmpcfi I H cmmpao> mwpfipn pcmeOEmcm I ppm meMLMQEoo I o Ampmpccmm coauoczw mp0fic manmfihm> I oma> pmamaaqem Hmcoaummcao I < 120mm omIJ nonmamcmw Hmcwam Eopw chasm wcHEHp m>m3 opedvm < ¢ omo> 34 .Empmzm coapmpcmeshpmca pcoEmASmwms szOOHo> camfim sonII.m oaswfim monoao mocha swommOwwzm sunfish wcfiummcmdsoo mpfiooam> p p mmecQOIcHonlpomma mhdpmncoscu Acmcmm m cpoEcp mpoEmp pseudo comp Amoco fl Pr.— concede house was» Loewe moDSQEoo mowcfimn a amphc>coo Q\¢ woamcm memEoEmcm l_ E a mmfiaaozm owwpao> wchHOAUcfi coapfimoa chose hoEHu acumpwmpca 35 Raingage Models Three models of the USWB Standard Raingage with the steel tripod stand were constructed for tests to be con- ducted in the wind tunnel. Their linear scales, relative to a prototype standard gage, were .704, .490 and .227. As the full height of the largest model could not be facilitated in the wind tunnel due to the tunnel's size limitation, its lower end was truncated such that the top centers of the models were positioned at the vertical and horizontal center point of the tunnel test section. As the smallest model's height was less than the tunnel floor to center point distance, a ground plane was constructed to maintain a normal gage to ground surface relation and bring the model's top to the tunnel's center point. This allowed the use of a complete model gage with stand. The ground plane, in effect, raised the floor of the tunnel to its height. The model cylinders were machined from cast acrylic plastic, to a tolerance of i 0.001 inch. The gage stands were fabricated from cold rolled steel of the pr0per scale size to a tolerance of t 0.002 inch. Figure 7.—-Velocity measurement instrumentation. Left to right: the analog—digital converter with paper tape punch, digital voltmeter, analog computer, anemometer with the analog timer below it. Figure 8.—-Wind tunnel test section. Along the top of the test section, from left to right: the three temperature compensating probes, the three probe position indicating voltage sources, the remote switches controlling the com- puter and A/D converter, the probe manipulator with sensor probe. Within the test section the smallest model is shown mounted on its ground plane. 37 '.<:y, 0! ‘3’? M4 'Jool‘. "mm "0 lt‘ltvv a!“ Figure 9.—-Gage models used for wind tunnel tests. Model scales, from left to right, are: .704, .490 and .227. Figure 10.-—Anemometer Figure ll.-—Anemometer sensor probe, front view. sensor probe, side View. EXPERIMENTAL PROCEDURE Calibration The initial calibration of the anemometer system was made with a one inch free jet. Curves of bridge voltage versus velocity and indicated velocity versus angle of flow over the sensors were determined for each anemometer bridge-sensor combination. The bridge voltage versus velocity data was used to adjust the VDFGs in the analog computer to obtain auto— matic linearized bridge voltage to velocity conversion. The velocity versus angle of flow curve was used to evalu— ate the correction factor (K) used in computer program TRANS which compensated for angled flow across the anemo- meter sensors. The three sensor probe was mounted in the probe manipulator and placed in the empty wind tunnel. With a moderate flow velocity in the tunnel the probe was oriented so that all sensors indicated the same velocity to insure that the sensors were symetrically oriented to the uniform flow field. Next the signal conditioning por- tion of the analog computer circuit was adjusted so that the VDFG's output voltage was zero at zero flow 38 39 velocity, and was 10.000 times the sine of the sensor- flow direction angle at 100 fps. The external square wave signal generator for the timing circuit was adjusted so that the integrator output voltage equaled ten times its input voltage. Following the initial instrumentation calibration the desired model was mounted in the tunnel and the probe was adjusted to a known reference point, that is, a data collection grid point relative to the model. The tunnel operating velocity was monitored with a Prandtl tube and a sloping tube water manometer. The desired dynamic—static pressure head differences was com— puted periodically and velocity adjustments were made if needed. The desired pressure head difference was com- puted from the ambient air temperature, barometric pres- sure and the desired Reynolds number. All tests were run at Re = 7 (10)“. After velocity measurements were made at all data collection points the model was removed from the tunnel and velocity measurements were repeated on the z = l, 12 and 25 planes as a check for proper probe orientation and flow uniformity. Any deviations found were corrected for in computer program CORRECTl with this information. 40 Test Routine After mounting the desired model in the wind tunnel, the probe was positioned at a reference point and the desired operating velocity was established. The normal sequence for data collection was: 1. position probe at desired x, y and z coordinate, :3 I 2. place analog computer in Operate mode allowing timer to operate integrators for 10 second period, \ 7 ,7. \Tifl-ITMFI—v 4.0.”, :. ‘ 3. adjust variable voltage sources for proper x, y and 2 values to be recorded, 4. At end of timer cycle initiate scan cycle of A/D converter and paper tape punch to record the three coordinate values and the three velocities measured with the anemometer, 5. reset the analog integrators to zero, 6. repeat the above steps at the next data collec- tion point. DISCUSSION OF RESULTS To make use of this study's results the accuracy of the procedures used must be considered. A precise analysis of the errors involved in this study was precluded by the presence of several unknown possible errors in many of the procedures used. However, the major source of error is probably in the basic veloc- ity measurements made. An estimate of the errors involved in the velocity measurements can be obtained by considering past experi- ences by researchers using basically the same instruments and techniques under similar conditions. In the area of fluid mechanics, mean velocity measurements using hot wire anemometers are generally considered to be within 10 per- cent of the actual flow velocities. The use of check pro- cedures, such as the probe alignment correction made by program CORRECTl, will reduce this error. However, by combining several instruments to handle the data, such as the analog computer and analog—digital converter used in this study, the maximum error probably remains in the vicinity of 10 percent. 41 42 The largest error source in the computations using the velocity data would be in the iteration portion of program DROPPATH that determines the path that a drop follows due to the influence of its surrounding velocity field. This error source was minimized by running test programs using several drop sizes and free stream veloci— ties and by varying the time interval (DT in program DROP- A'J PATH) of the iteration process. It was found that a DT g smaller than 0.002 second made negligible difference in :9” the dr0ps' path descriptions. Thus, a time interval of E 0.002 second was used. Considering these factors and the confidence in the procedures used it is estimated that the results of this study (Figure 12) are not in error by more than 15 to 18 percent. A comparison of the drop paths showed a tendency for drops that were caught by the gage to be carried further from the upstream edge of the gage as the free stream velocity increased and as the drop size decreased. This trend was expected. However, this trend of being dis- placed downstream was also evident with drops falling to the level of the gage's top but slightly in front of and to one side of the gage funnel. This tendency can increase the gage's catch. This is the direct result of the gage's obstruction to airflow in its vicinity due to the physical presence of the gage itself. While the quantity of drops 43 +207- 0* -20‘- g -40-~ -60» 9 1 mm drop dia. .A 2 mm drOp dia. '80 ‘” V 3 mm drop dia. I 5 mm drop dia. -100 t i I t i O 10 2O 3O 4O 50 Free Stream Velocity - fps Figure l2.--Percent error of drops caught relative to drop diameter and free stream velocity. 44 influenced by this trend is small, it is probably respon- sible for the small increase in catch of the larger drops at free stream velocities in the neighborhood of 20 to 40 fps. As drop size decreases to 1 mm, this trend resulted in most drops being caught in the downstream side of the gage. As free stream velocities increase beyond 20 fps most of these smaller drops were carried beyond the gage funnel before they fell to the level of the gage's t0p, resulting in a sharp decrease in the quantity of drops caught. This effect is very pronounced for 1 mm diameter drops in the 30 to 50 fps range as shown in Figure 12. As drops in the l to 2 mm size range occur most frequently in normal precipitation, and as they account for a large portion of the total volume of rain falling, the error created can be large if the free stream veloci- ties are above 25 fps. To use this data one needs to know the drop size distribution of the rainfall, and to measure the free stream velocity in the gage's vicinity during the rainfall period. The portion of drops of each size falling is then adjusted with the values found in Figure 12 to find the corrected portion of each drop size. Summing the volume of the adjusted amount of each drop size will then deter- mine the corrected precipitation quantity. CONCLUSIONS The results of program DROPPATH showed that rain- fall measurements made with a U. S. Weather Bureau Stand— ard Raingage indicate less rainfall than actually fell as the dr0p diameter decreases and as the free stream air velocity in the gage's vicinity increases. At velocities over 30 fps the amount of 1 mm di- ameter drops caught was in error by over 40%. At 40 fps the 1 mm diameter drops measured were in error by 80% and 2 mm diameter dr0ps were in error by approximately 20%. As a large portion of the drops in a typical rainfall is usually within this size range, rather large errors should be expected in the amount of rainfall indicated by a Standard Raingage if wind velocities are over 30 feet per second. While the results of this study could be applied to rainfall data that has been collected it should also be considered as an indicator of the need for development of an improved precipitation measurement system. 45 ‘EEE%" REFERENCES REFERENCES Alter, J. C. (1937). Shielded storage precipitation gages. Monthly Weather Review 65: 262-265. Bernard, M. (1938). The expanded program of the U. S. Wea. Bu. in snow-work. Trans. Amer. Geo. U., Regional meeting, January. Blanchard, D. C. (1948). Observations on the behavior of water dr0ps at terminal velocity in the air. Occasional Rept. No. 7, Project No. 7, Project Cirrus, G. E. Res. Lab., Schenectady, N. Y. Borstein, R. (1884). Ueber der von Nipher vorgeschlagenen Schutztrichter fuer Regenmesser. (Concerning the protecting funnel suggested by Nipher for rain- gages). Meteorologische Zeitschrift Band I Berlin 1: 381-392. Conover, J. H., and T. G. Nastos (1951). Tests of Steward and Victor precipitation gages. Blue Hill Report, Harvard University. July. Gold, E. (1931). The splashing of rain. Meteorological Magazine 63(746): 39-40. Green, Robert L. (1952). Evaluation of air resistance to freely falling drops of water. Agricultural Engi- neering 33: 28, 286. Gunn, Ross and G. D. Kinzer (1949). The terminal velocity of fall for water drops in stagnant air. Meteoro- logy 6: 243-248. Hamming, R. W. (1962). Numerical Methods for Scientists and Engineers. McGraw-Hill, Inc., New York. 409 pp. Heberden, W. (1769). Of the different quantities of rain, which appear to fall at different heights, over the same spot of ground. Philosophical Trans. 59: 359-362. 47 ' L" l " \ ”‘1‘... ..' _._~ _". “'V. 48 Horton, R. E. (1919). The measurement of rainfall and snow. New England Water Works Assoc. 33(1): 14— 72. Howell, W. E. (1946). Blue Hill Report, Harvard Uni- versity. Kurtyka, John C. (1953). Precipitation measurements study. Illinois State Water Survey Div., Report of Investigation No. 20. Laws, J. Otis (1941). Measurements of the fall velocity of water drops and rain drops. Trans. Amer. Geo. Union 20: 709-721. Leonard, P. (1904). Ueber Reger. (Concerning Rain.) Meteorologische Zeitschrift 21: 249-262. Nipher, F. E. (1878). On the determination of the true rainfall by elevated gages. Amer. Assoc. for the Adv. of Science 27: 103-108. Shamasastry, R., translated by. (1915). Arthasastra. (321-296 B.C.) Government Oriental Library Services, Bibliotheca Sanskrit. Stevenson, T. (1842). On the defects of raingages with description of an improved form. Edinburgh New Philosophical Journal 33: 12-21. Symons, G. J. (1871). Notes on foregoing papers. British Rainfall: 56-57. Umback, C. R., and W. D. Lembke (1966). Effects of wind on falling drops. Trans. of ASAE 6: 805-808. Warnick, C. C. (1956). Influence of wind on precipitation measurements at high altitudes. Univ. of Idaho, Engineering Expt. Sta. Bull. No. 10. Weiss, Leonard L., and W. T. Wilson (1958). Precipitation gage shields. Int'l. Union of Geodesy and Geo- physics 1: 462-484. Weiss, Leonard L. (1961). Relative catches of snow in shielded and unshielded gages at different wind speeds. Monthly Weather Review, October: 397-400. Wild, H. (1873). Yearbook of the Physical Central Observa- tory_in St. Petersbugg. 3‘. .w-nma :- whon“ . .u. w "( ° 1"; l l 49 Wild, H. (1885). Einfluss der qualitaet und aufstellung auf die angeben der Regenmesser. (Influence of the quality and exposure on the data from rain gages.) Repertorium fuer Meteorologie, St. Petersburg Com- missionare der Kaislerlichen Akademie der Wissen Schaften 9 (9): 1—23. . I. .1. .. .9. lhl.w_£¢flgm~.§ “I! APPENDIX A 51 “— 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 no.0 00.0 no.0 00.0 00.0 00.0 00.0 mn 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 no.0 no.0 00.0 00.0 no.0 an 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 00.0 00.0 00.0 00.0 on 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 00.0 no.0 no.0 no.0 no.0 no.0 no.0 on 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0: no.0- no.0- 00.0 00.0 00.0 no.0 ~o.0 no.0 no.0 ~o.0 No.0 No.0 No.0 No.0 nn 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 00.0 00.0 00.0 no.0 no.0 no.0 no.0 no.0 ~o.o No.0 No.0 ~o.o No.0 no.0 ~0.0 No.0 on 00.0 no.0 «0.0 no.0 no.0 no.0 no.0 no.0 mo.o m0.o no.0 no.0 mo.o mo.o 00.0 00.0 00.0 00.0 m0.0 no.0 no.0 00.0 00.0 20.0 «0.0 o ~o.0 No.0 «0.0 «0.0 ~0.o «0.0 00.0 «0.0 ~0.0 no.0 No.0 no.0 No.0 No.0 no.0 no.0 30.0 00.0 00.0 00.0 no.0 No.0 50.0 00.0 0o.o 0 no.0 no.0 no.0 no.0 No.0 No.0 ~0.o 00.0 No.0 00.0 00.0 no.0 no.0 00.0 no.0 no.0 30.0 50.0 00.0 mo.0 00.0 nn.o 00.0 50.0 50.0 A 00.0 no.0 No.0 «0.0 No.0 no.0 No.0 00.0 «0.0 00.0 no.0 no.0 no.0 no.0 No.0 No.0 no.0 no.0 30.0 50.0 00.0 00.0 00.0 00.0 00.0 0 no.0 no.0 no.0 no.0 no.0 no.0 no.0 00.0 no.0 00.0 no.0 00.0 00.0 no.0 no.0 m0.0 so.o 50.0 00.0 00.0 mn.o on.o mn.o 00.0 00.0 m no.0 no.0 No.0 no.0 No.0 No.0 no.0 00.0 no.0 00.0 no.0- No.0- no.0- 00.0 no.0 no.0 no.0 m0.o 00.0 on.o on.o No.0 0n.o 00.0 ~n.0 . no.0 no.0 No.0 no.0 no.0 no.0 00.0 no.0- no.0 00.0 no.0- 00.0. «0.0- no.0- 00.0 00.0 no.0 no.0 no.0 0n.o nm.o a~.0 mo.o mn.0 00.0 m no.0 no.0 No.0 No.0 no.0 no.0 00.0 00.0 no.0- «0.0- No.0- No.0- no.0- no.0- 00.0 no.0- no.0- no.0- no.0- 00.0 mn.0 non.0I0 nwm.0-0 Amn.0I. Amo.oI0 N «0.0 no.0 no.0 no.0 no.0 no.0 00.0 00.0 no.0- 00.0 no.0 No.0- nw.c- no.0- no.0- mo.o- no.0- no.0- No.0- n ma an mm no no on on en en on mn an mn Nn nn 0n 0 m a 0 m a m m n uncanvnoou N .Loaan apocaon no» nowaw 0:0 annun: and nononpcohaa an aoanu> .ocann : I u on» co canuoouno x on» an nOnuuu aun00n0> K eavutpaoog .0000 noncono> onunmun.n< mnm .ocena m n x 020 :0 cOnuovnnv x on» an nonoan zunoOno> .nuav aun00n0> ununLII.NI< me

.0000 han00n0> vnOnmIt.n< Nam<9 54 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 mm 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 tn 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 MH 00.0 no.0I no.0: 00.0 no.0: 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 00.0 «0.0 . 00.0 Nn 00.0 n0.0I no.0I no.0I No.0I no.0I no.0I no.0: no.0I no.00 n0.0I no.0: n0.0l no.0I 00.0 00.0 00.0 00.0 00.0 no.0 no.0 no.0 n0.0 an 00.0 no.0I no.ot no.0I no.0I 00.0 00.0 no.0! 00.0 no.0I 00.0 no.0: 00.0 00.0 00.0 00.0 no.0 00.0 00.0 no.0 no.0 «0.0 no.0 0n 00.0 00.0 00.0 no.0 no.0I 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 00.0 no.0 no.0 no.0 no.0 no.0 No.0 N0.0 N0.0 O 0A nu No.0 No.0 No.0 no.0 00.0 No.0 No.0 no.0 00.0 00.0 no.0 no.0 00.0 ~0.0 no.0 No.0 No.0 80.0 No.0 .0.0 m0.0 no.0 M0.0 D W m No.0 No.0 no.0 No.0 no.0 No.0 no.0 mo.o no.0 no.0 no.0 no.0 no.0 no.0 no.0 00.0 m0.0 50.0 30.0 00.0 50.0 50.0 .0.0 5 W .0. No.0 50.0 50.0 No.0 no.0 no.0 no.0 no.0 no.0 00.0 00.0 no.0 no.0 m0.0 no.0 30.0 30.0 m0.0 80.0 m0.0 m0.0 50.0 m0.0 w no.0 no.0 no.0 no.0 no.0 no.0 no.0 no.0 no.0 no.0 00.0 no.0 no.0 no.0 No.0 {0.0 50.0 m0.0 0n.0 nn.0 00.0 Hn.0 00.0 m No.0 no.0 no.0 00.0 00.0 no.0 00.0 no.0 no.0I no.0I m0.0I no.0I 00.0 n0.0I n0.0| n0.0| no.0 10.0 00.0 0n.0 Nn.0 00.0 50.0 1 No.0 no.0 no.0 no.0 no.0 na.0 nc.o no.0 03.0 no.0 no.0 00.0 No.0I no.0 no.0! no.0 no.0 no.0 0n.0 0n.0 0n.0 Mn.0 nn.0 M 00.0 no.0 no.0 no.0 no.0 no.0 no.0 00.0 00.0 00.0 no.0: no.0I N0.0I no.0I m0.0I 00.0 no.0 no.0 0n.0 mn.0 0n.0 HN.0 an.0 N No.0 no.0 no.0 no.0 no.0 nc.o 0.0 00.0 03.0 no.0I no.0I no.0I m0.0I m0.0I m0.0I no.0 no.0 A mm mm nm on wn on 5n 0n mn an mn mn nn On a m 5 0 m t M N n 000Cnonoou N .vcann 5 I u use co conuounnu x on» an nonunh hunoono> .aalu hanoono> Ononnll..< mna .ocmno : u A an» no conuomunu A on» an nonusp msnuones .asso munoonw> onsnauu.m< mqm .0550 m a n 23 co conuoouno » on» 5 non»: hogan; .au-v 5unoOn0> enunMII.o< 04055 57 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 no.0 n0.o n0.o n0.o n0.o no.0 n0.o no.0 no.0 n0.o no.0 n0.o n0.o n0.o no.0 mn 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 no.0 no.0 no.0 n0.o n0.o n0.o no.0 n0.o no.0 No.0 no.0 no.0 no.0 no.0 n0.o no.0 an 00.0 00.0 00.0 00.0 00.0 00.0 n0.o n0.o n0.o n0.o no.0 n0.o no.0 n0.o No.0 No.0 no.0 no.0 no.0 no.0 no.0 n0.o no.0 n0.o no.0 mn 00.0 00.0 00.0 00.0 00.0 00.0 no.0 no.0 n0.o n0.o n0.o No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 n0.o no.0 no.0 no.0 Nn no.0 no.0 n0.o n0.o no.0 no.0 No.0 No.0 No.0 no.0 no.0 m0.0 m0.o m0.o mo.o no.0 no.0 :0.0 00.0 =0.o 00.0 no.0 no.0 No.0 No.0 nn No.0 No.0 No.0 No.0 No.0 No.0 No.0 m0.0 no.0 m0.o m0.0 no.0 30.0 no.0 00.0 20.0 00.0 20.0 00.0 00.0 00.0 no.0 no.0 M0.0 No.0 0n no.0 no.0 No.0 No.0 No.0 No.0 m0.0 no.0 no.0 m0.0 m0.0 no.0 m0.0 mo.0 00.0 20.0 m0.o m0.0 m0.0 mo.0 00.0 m0.0 No.0 No.0 no.0 0 .A 0 No.0 No.0 No.0 no.0 No.0 No.0 no.0 No.0 no.0 m0.0 m0.0 m0.0 No.0 m0.0 n0.o No.0 m0.0 No.0 No.0 No.0 m0.0 n0.o: 00.0 n0.o N0.0I w w m no.0 No.0 No.0 No.0 n0.o No.0 m0.0 No.0 mo.0 No.0 No.0 m0.0 No.0 No.0 n0.o m0.0 n0.o No.0 No.0 m0.0 No.0 00.0 no.0: no.0I n0.o: 5 W n no.0 no.0 no.0 no.0 No.0 no.0 No.0 No.0 No.0 No.0 No.0 mo.o No.0 mo.0 mo.0 No.0 No.0 No.0 00.0 50.0 no.0 No.0 00.0 no.0 m0.0I 0 00.0 no.0 No.0 No.0 No.0 no.0 n0.o no.0 no.0 no.0 n0.o no.0 No.0 m0.0 m0.0 No.0 no.0 no.0 50.0 00.0 m0.0 no.0 no.0 no.0I Nn.0I m 00.0 no.0 n0.o no.0 No.0 n0.o n0.o n0.o no.0 no.0 No.0 n0.o No.0 no.0 No.0 no.0 30.0 mo.0 50.0 50.0 50.0 m0.0 30.0 mn.0I 0N.0I n 00.0 00.0 no.0 no.0 n0.o no.0 no.0 no.0 mo.0 n0.o no.0 00.0 mo.0 No.0 mo.0 No.0 no.0 mo.o 00.0 00.0 00.0 00.0 m0.0I 0N.0I mN.0I m 00.0 no.0 no.0 n0.o n0.o no.0 no.0 No.0 No.0 no.0 n0.o No.0 no.0 no.0 No.0 No.0 50.0 50.0 no.0 on.o nn.o 00.0 Mn.0I 5m.0I mn.0I N 00.0 00.0 00.0 00.0 00.0 00.0 n0.o n0.o .00.0 00.0 no.0 No.0 no.0 m0.o no.0 30.0 50.0 00.0 mn.0 n mN 3N MN NN nm 0N an on 5n 0n mn an mn Nn nH on m w 5 m m a m N H Oulfiavhooo N .0930 0 n x on» an canuuouno » on» an 0030b aun00n0> .0000 hun00n0> vnonmtl.5< mam<fi 58 00.0 00.0 00.0 00.0 00.0 00.0 00.0 n0.o n0.o n0.o n0.o n0.o no.0 no.0 n0.o n0.o n0.o n0.o no.0 no.0 no.0 no.0 no.0 n0.o no.0 mn 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 no.0 n0.o no.0 no.0 no.0 n0.o no.0 no.0 n0.o n0.o no.0 no.0 n0.o n0.o n0.o no.0 no.0 an 00.0 00.0 00.0 00.0 00.0 00.0 00.0 n0.o n0.o n0.o n0.o n0.o No.0 no.0 no.0 n0.o no.0 no.0 no.0 n0.o no.0 no.0 n0.o no.0 no.0 Mn 00.0 00.0 00.0 00.0 00.0 00.0 no.0 n0.o n0.o no.0 No.0 No.0 No.0 n0.o No.0 No.0 no.0 no.0 No.0 No.0 No.0 no.0 no.0 no.0 no.0 Nn 00.0 n0.o 00.0 00.0 00.0 00.0 no.0 n0.o no.0 no.0 No.0 n0.o No.0 No.0 No.0 No.0 n0.o No.0 No.0 No.0 No.0 No.0 No.0 n0.o no.0 nn no.0 n0.o 00.0 00.0 00.0 00.0 n0.o No.0 no.0 n0.o No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 m0.o no.0 no.0 no.0 n0.o no.0 0n no.0 n0.o no.0 00.0 00.0 00.0 n0.o n0.o n0.o no.0 no.0 No.0 No.0 No.0 m0.0 No.0 No.0 m0.0 No.0 No.0 No.0 No.0 No.0 no.0 no.0 0 K 3 no.0 no.0 00.0 00.0 00.0 00.0 no.0 n0.o n0.o n0.o no.0 n0.o No.0 No.0 No.0I No.0 No.0 No.0 No.0 n0.o No.0 00.0 no.0! n0.0l n0.0I 0 W m n0.o 00.0 no.0 No.0 No.0 n0.o m0.0 no.0 no.0 No.0 No.0 mo.0 m0.0 00.0 No.0 no.0 no.0 no.0 mo.0 No.0 no.0 No.0 no.0 N0.0I No.0! 5 W a u No.0 No.0 No.0 No.0 No.0 00.0 No.0 no.0 No.0 no.0 no.0 m0.0 No.0 no.0 m0.0 No.0 No.0 30.0 m0.0 m0.0 m0.0 n0.o n0.o 00.0 00.0 0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 No.0 no.0 n0.o 00.0 No.0 m0.0 No.0 m0.0 no.0 00.0 mo.0 30.0 «0.0 m0.0 no.0 00.0 N0.0I m 00.0 n0.o no.0 no.0 n0.o 00.0 n0.o no.0 no.0 no.0 no.0 00.0 m0.0 No.0 m0.0 00.0 n0.o «0.0 no.0 00.0 m0.0 m0.0 n0.o 00.0I mn.0I n 00.0 n0.o no.0 n0.o 00.0 n0.o No.0 n0.o n0.o no.0 00.0 m0.0 no.0 No.0 00.0 m).0 20.0 50.0 50.0 no.0 no.0 No.0 No.0I Nn.0l on.0I m 00.0 n0.o no.0 no.0 n0.o 00.0 no.0 no.0 n0.o 00.0 00.0 No.0 n0.o No.0 No.0 mc.0 No.0 50.0 m0.o 00.0 00.0 m0.00 00.0 mn.0I MN.01 N 00.0 00.0 00.0 00.0 00.0 no.0I n0.0I no.0 00.0 no.0I no.0I 00.0 n0.o no.0I no.0 m0.0 m0.0 50.0 00.0 n an .N mN NN nN ON 0— 0n 5n on mn an mn mn nn 0n 0 m 5 o m z m N n Ouncludhoonu N .ocana 5 I x on» :0 cenuoonno m an» an menu-n apnoono> .0000 hunoono> vnunhol.m< qu .eCAna : u x new at canuuwnnn n esnpmwmu on» an nonuan hunoonob .0000 hunuono> 0no-LII.o< 00005 »| 60 01.0 mm.o mm.o :m.o co.“ oo.a oo.H oo.~ oo.H oo.a oo.H oo.~ oo.a oo.H Ho.a a0.“ Ho.H flo.H Ho.H no.“ no.a Ho.a Ho.a ao.H “o.H mm mm.o m~.o 1%.0 ma.o ma.o oo.H oo.~ 00.n oo.H oo.m oo.a oo.a oo.H oo.H 00.n oo.d co.” oo.H oo.H oo.H flo.a ao.a Ho.H Ho.a Ho.H aa mm.o ma.o om.o :a.o oo.o cm.o co.m oo.a oo.H co.” oo.~ oo.H oo.fl oo.H oo.a oo.~ 00.n uo.H oo.fl 00.n oo.~ oo.fl Ho.a Ho.H Ho.H ma om.o mm.o mp.o mm.o no.0 mm.o am.o mm.o oo.H mo.o mm.o 00.n mm.o no.0 oo.H oo.H oo.H oo.H oo.a oo.H oo.H oo.H Ho.H Ho.~ Ho.H NH mm.o mm.o wa.o wm.o m¢.o mo.o om.o no.0 mo.o mm.o mm.o m®.o ma.o No.0 mm.o mm.o mm.o mm.o mm.o mm.o mm.o oo.H oo.d Ho.H mo.H OH nm.o om.o mm.o no.0 om.o ma.o $0.0 mo.o mm.o $0.0 mo.o 50.0 No.0 No.0 mm.o mm.o mm.o mm.o mm.o mm.o oo.H oo.a 00.n mo.H ao.H m 0A Q $0.0 hm.o hm.o wa.o mo.o no.0 ¢m.o $0.0 no.0 59.0 $0.0 oo.o mm.o no.0 5m.o 5m.o 5m.o mm.o 5m.o oo.H oo.« oo.m oo.H no.” mo.H m w J p Y: m@.o mm.c no.0 mm.o o¢.o co.” oo.~ aa.o mo.o ao.o no.0 mm.o 50.0 5m.o mm.o wo.o mm.o mo.o no.0 oo.H Ho.H Ho.H mo.H mo.a ho.n h w 1 3 no.0 om.o wa.o no.0 mo.o mm.o mm.o 5a.o no.0 no.0 No.0 om.o om.o wm.o m¢.o mm.o mo.o mm.o 5m.o Ho.m Ho.H HO.H mo.a mo.a no.H c No.0 mm.o >m.o no.0 ¢o.o wa.o mm.o sa.o 5¢.o ~m.o 5a.o no.0 mm.o om.o wo.o No.0 No.0 nm.o No.0 00.n oo.H Ho.~ mo.a 50.H o~.~ m oa.o ma.o 09.0 no.0 ma.o ma.o no.0 No.0 No.0 50.0 50.0 no.0 no.0 om.o 09.0 00.0 oa.o mm.o mm.o mm.o do.” mo.H No.H mo.~ HH.H a >0.o om.o cm.o no.0 no.0 so.o $9.0 no.0 wo.o so.o 00.0 00.0 mm.o mm.o ma.o mm.o mm.o No.0 Hm.o om.o mo.H mo." mm.a ma.” NH.H m na.o wa.o no.0 no.9 ma.o no.0 no.0 No.0 ha.o >a.o 00.0 o¢.o no.0 03.0 mo.o mm.o No.0 mm.o mm.o om.o mo.H nam.omg Afim.~ v nom.wav fio.a N 00.0 00.0 00.0 00.0 00.0 00.0 00.0 00.0 3.0 :10 no.0 3.0 00.0 3.0 mo..0 3.0 $0 00.0 0.0.0 H mm aw mm NN Am on 0~ ma 5a a" m" 45 ma NH AH 0a m m n m m a m m a buncunpoou u .Lohmfl mnficnon no» muwmm any sang“: nun monocuccnan c“ nosaa> .ocmflu m I x on» :0 :Oapooufin n o>uummvc o.» c" mOHuaL huwoofion .aumv kudooHo> vfioumul.oa< mqmm.o om.o mm.o mm.o oo.H mo.~ mo.~ do.H mo.H mo.~ o ma.o pm.o hm.o ~o.o no.0 oa.o mo.o mo.o so.o mm.o mm.o ma.o em.o em.o mo.o om.o No.0 om.o no.0 oo.fl co.“ mo.fi Ho.H ao.H mo.“ m hm.o ~m.o sa.o No.0 no.0 mm.o mm.o mw.o om.o hm.o No.0 mm.o mm.o om.o m¢.o mm.o 09.0 mm.o om.o mo.o Ho.H Ho.fl mo.~ so.~ HH.H a no.o hm.o om.o so.o mm.o mm.o »@.o ~o.o wo.o >¢.o No.0 mo.o mm.o m¢.o no.0 ma.o mm.o mm.o No.0 om.o mo.H so.H mo.H 0H.H m~.a m sm.o ~m.o hm.o mm.o mm.o mm.o mm.o mo.o ~m.o No.0 ~m.o ma.o mo.o no.0 m¢.o ma.o mm.o on.o oa.o 09.0 mo.H mH.H mm.fi mm." mH.H m mm.o Fm.o hm.o mm.o wm.o mo.o mm.o mm.o cm.o em.a 01.0 mo.o m¢.o ma.o mw.o fim.g ga.o Ho.a :o.H H mm an mm «N am on ”d ma 5H ca ma 2H MH mH fifl OH p m N n m a m m H ouacfinuoou u .acafiu o u x on» :0 Cnuuueuuv n o>aummou 02» c“ weapon huaoofio> .uuaw auauoflo> aflowman.HH< mgm0.0 00.0 09.0 m9.o m0.o mo.o mo.o ma.o «3.0 w».o mc.o no.H mo.H :0.H 0H.~ ~H.H N 00.0 50.0 00.0 50.0 00.0 $0.0 50.0 50.0 00.0 $0.0 90.0 m3.o «9.0 no.0 mm.o no.0 no.0 no.0 0H.H H mm «m mm mm MN on an ma hm ma ca zfi Ma m~ fig 0“ m m w o m z m m H opacficpooo a .ocaaa 5 I x mcu co :ouuoeuun n e>Hummoc ecu Ca moans; huaooHo> .32. 3322, gainim: ”Sm: APPENDIX B nnn 100 50 51 I PROGRAM TRANS TO CONVERT ANEMONETER BRIDGE VOLTAGES FROM A THREE SENSOR PROBE TO VELOCITY COMPONENTS ALONG THE MODEL AXIS SYSTEM DIMFNSION VAXI4015025IQ VAY(4015925)9 VAZ(40159?5)9 IVAX(4015925)9 57 02957795 301415926: 3HVXI 3HVY2 3HV73 RAD PIE NA] NAZ NAB IVAY(4.15025)0 IVAZI4915025) SURSENSOR TO MODEL AXIS ANGLES AXXPP AXYPP AXZPP AYXPP AYYPP AYZPP AZXPP AZYPP SINXXPP $INXYPP