ARABISIS OI'THI LINE LKIOUT, CABLE AND SHEAVE REQUIREMENTS, AND FDUNh DhTIONB 0! A 8000 IT. T-BAR SKI-LIFT. A thesis submitted to The faculty of MICHIGAN STATE COLLEGE of AGRICULTURE AND APPLIED fiCIENCE by Emery Carlson \- Candidate for the degree of Bachelor of Science June, 1148 THESIS AOKNOWEEDGMENT The writer wishes to take thie opportunity to expreee hie eineere appreciation to Mr. Blair Bird- eell, Ale't Chief Engineer. Bridge Division or the John A Roebling'e Sons Company; and to Mr. John R. Herr, Aeo't Superintendent of American Steel. end Wire Company for their kind consideration and advice. It was through the information they furnished that this paper Wee made possible. In addition, I would like to thank Professor Cede or the Michigan State College faculty for hie advice throughout the project. 33537:?! 1.0 3.0331011118135333? The writer wishes to take this opportunity to exproce hie sincere appreciation to Mr. Blair Bird~ cell. nee't Chief Engineer, Bridge Division or the John A Roebling's Sane Company; and to ur. John R. Herr. Aeo't Superintendent or American Steel and Wire Company for their kind coneideretion and advice. It was through the information they furnished that this paper was made possible. In addition, I would like to thank Professor Cede or the Michigan State College faculty for his advice throughout the project. EH72? 0 runs or commas PIOIaIO. e e e e e e e e e e e e e e e e e e e e Introduction 1. Evolution of ski-lifts from commercial 8. 3. tramwayS................................ Discussion of the different type lifts.. Description of the Tobe: list ayetan.... Design Methods 1 O 2. 3 4. 5 Objectives of this paper..............5 General Procedure....................... Limiting Requirements................... Eeeential preliminary date.............. Assumptions made..-..........-.......... Computations l. 2 3. 4. 5. 6. 7. Forces acting on main hauling rope...... Derivation of an original formula....... Computing sag and tension along the line Selection of rooa..,f................... Clearances in each span................. Sheave loade..:......................... Foundation loads and design............. B1b11°8rnthQ one e e e e e e e e e e e e e e e Page 1 2 2 & 7 5 0 m 15 a (J! 36 41 45 50 PHIIAGE I have chosen to analyse the design of s ski-lift for several reasons: first, being an ardent ski enthusiast. I IIVC an intense interest in the subject and have had the opportunity to use and observe several different types of ski lifts while in operation. Secondly, since the sport of skiing has become popular in the United States only in the lest ten years, it is a relatively new subject. The need for more and better skiing facilities is apparent to anyone who becomes well acquainted with the sport. I have chosen to analyze a T—bar lift because they seem to be the most practical in both the economic and engineering sense for the majority of slepes that are available in this section of the country. Since there are probably less than half a dozen companies in the whole United States that specialize in this type of work, the available material concerning the design of lifts is very limited. If the material presented here in any way helps further the efforts of those interested in the subject, the work I have put forth will have been well worth while. w T. "- 'ul _ 1 ll-' IRTRODUCTION “the engineering background for this type of structure is not new at all. For many years numerous companies have been designing and building this type structure for trans- porting freight of various types. The common name applied to these structures is "aerial ropeuay". or "aerial tramway." rinse tramays have been long used by mining companies to carry ore or coal over mountainous terrain over distances up to 72 miles. They have been built and successfully used to transport such articles as sand, gravel, cement, rock, bananas, fish, and even optical instruments. Their use as a mode of transportation has been made economically feasible in instances where the ordinary methods proved too expensive or unhandy. The mining industry has by and large made the greatest use of the aerial tramway, though in recent years it has been used in the construction of several of the larger dams. Boulder Dam is a good example of where an aerial tramway was used to overcome especially difficult transportation coalitions. Development of aerial tramways for passenger conveyances was first developed to high degree by the Europeans. It was not until 1938 that the first aerial tramway was built in the United States. This was built on Cannon Mountain for the State of New Hampshire by the American Steel and Wire Company. Since that time, the sport of skiing and the facilities offered mushroomed until today there are an In: ”tinted oseothsusend lifts of every variety. including lope tows. By applying the known and proves engineering knowledge used in building freight aerial tramwaye, conversion to passenger type structures was relatively easy. The prin~ ciple problem lay in the field of safety. An economical, yet absolutely safe, structure was needed: one that required no physical alertness or agility on the part of the rider to safely use the lift. Commercial tramways consist of four basically different types of structure: bi-cabla tramway, twin-cable tramway, reversible tramway, and the mono-cable tramway. Since the fastest, most economical method was desired with no exces- sive weight requirements, a mono-cable or bi-cable type was chosen as most practical for a ski-lift. Of these two types, the mono~cable type has been most extensively used. Breaking the mono-cable types down into further classes, we find a chair 11:12. a T-bar lift, and a J-bar lift. The- least expensive lifts, most simply constructed, are the T-bar and J-bar lifts. These types are of mono-cable variety and constructed so that the skier remains on the ground and is pulled up the hill. Since this type is better suited to general use than the most expensive chair types used for long steep hauls, I have chosen to analyze one of this type. A waar lift needs to be of heavier construction than the J-bar, but is used because of the increased capacity obtained. The system consists of a row of towers supporting an endless wire rope which is constantly moving while the skiers get on and off the lift. Each towing outfit consists of a (3 VI (1 ': _,.".' (‘5' c“ ‘ . .5". \ t ' I.’ .=. . ,3 , ' . ' , y . :7 .4 '10 Mill unsound-«mo horns-Mao 1.113. Ill: '; r: | .J. r. 1 . r Hus-i | .I' ' ”.c ._ .5 s .s 'b I I .As .evio: sec-1 “I iii-'11:," 1,4113 133139.533'5? 'r- dorm a a. ' "1C)."- . .i‘ J. '._', .I t I. .- 'J l " 4 I ' 1' 4' ‘7 .i - .i I t E lope pip attaching the outfit to the healing rope, a hanger menus down from this sup, n so~cellsd spring box on Mlle take-up attached to the bottom of this hnser and a wooden fo-stick which dangles from this spring box. The upper end of the rustick is attached to a piece of small wire rope which is wound on a drum inside of the spring box. In the ease of the hydraulic type takeoup, the wire is shortened by the hydraulic cylinder device. Both are teine successfully used at ths present tins. ' is a skier mounts the lift, this rope is pulled out and is extended to its full length thmughout. the uphill travel of the skier. The passenger's skis remain on the ground and he is literally pushed uphill by means of the crossbar of the T-stick which rests against his hips. In normal operation tn passengers are cerred by each T-sti ck, although one may comfortably ride using a small degree of balance. As the skier lets loose the T-stick it is pulled up and out of reach of the skiers. At the low er and of the structure an anchorage tower is situated and the power is applied at this point. At the upper end a tension tannins]. is located where the counter-weight is suspended, acting against the frame which contains the tension sheave. By controlling the weight of this counter~weight and having the tension frame free to ride on a truss of the tension structure, a known and uniform tension is imparted to the traction rope at all times, under all conditions of loading-«no load to full load. As the wire rope wears and stretches, the counterweight lowers and the tension frame moves back. The power is applied to the hope by a large horizontal ..- n I -l I o s‘ ': ‘U u! " I"‘ \e .\ if 21— u.- " .‘n' 4.2;." '7‘ 'I'cq: ." t "' .'l Us. {-5.34 -- “'1' flf; r”. i 'L 1.. : .. U: '3 ‘5‘. .+ I . “-5 - ‘ - l. | ' l 1 f -. a ' I i: i U.‘ I: l 3 ‘ r '1. . , . . .. .{d‘ :-,.:".t:..')§--.:-.:: with 91:01 an 1' Mains t. 1‘15" 351.“; “i 32:. ‘e'ii minus; I s- d.- ' U ' -' ill-1:41....) - t1 1'. :" JO O"! E" ' .I ' : - . ' :'9‘ll‘u‘s-“ i sheave located in the anchorage terminal. The power is trans- ferred to this suave by means of. a set or Level gears, s richt angle speed reducer. and a U—belt drive. or some can-- binstion or them. The power unit may be either a gasoline engine. diesel engine, or electric motor. The gasoline or diesel engine are used where electricity is not available, but the electric motor is better suited for most units. The ground under the rope must be relatively smooth and level perpendicular to the line to keep the skiers from sliding of: the tow trail. When in operation, three or tour operators are required. One should be at the controls or the power unit at all times. Another operator is needed to pull down the T-stick and aid the skiers in getting started. Also, one operator should be stationed at the upper end or the tow as a safety precaution“ the skier doesn't leave the stick at the upper end he would have a free pathway to con- tinue around the tension sheave. This point of the system presmts the only point or danger and this is very remote. It a skier falls off the T~sti ck or becomes fouled in his skis on the tow path he merely lets go the T~sti ck and maneuvers himself off the path. The great advantage or this type lift is the simplicity by which it operates plus the large capacity it has. It can be used for any reasonable slope with relative comfort to the skier. d .- ‘9 3' “Li '2. .f" -- .Jl' ,.-" s n. .-.;~'. :.I.'..'! n]. fist-1.1304 91193.53 '12' - 1"... nut-3 -.-. ~ I" In. I l‘. a ‘- f ‘e. s- ! s P .sl e 332-}: a: barn an“? " " 3 f: . - i'tu .15.: " - :L. '§":‘.."Ir.*s- .':')'-"."33 4.! 3.51:; iiifiti'fl' e .3 Ir" .. 0 s. d ‘ .- 1 . I t I O ‘ J - I J o s. I I .L — § .( o - 3- " I i a «I J \ ' I . s . d. . a - I O 1 I I It I v I ' . ‘ t . _ Q . ’ \ O | I 0-. I I u ' i O . i u - s g l i r . ‘O ‘ K I I a 1 s, . I . l O .5. .In tide paper. I will analyze a list being installed at Jilin: Peek. Hancock, Massachusetts, by the John A. Enabling Eons company. Since a complete analysis of all the fixtures eating up the lift Iould require more time than is available and would entail many problems outside the field or the Civil Engineer, I sill confine my analysis to the following items: 1. risding the tension of the Cable throughout the entire line on both the uphill(loeded) side and the downhill finnpty)side. 8. Finding the maximum tension and size of rope required. 8. Finding the resultant forces on the towers. 4. Finding the number of sheaves required at each tower. 5. checking the distance between the rope and the ground at all points for all conditions or loading. 6. Checking the design or the foundations against sliding, overturning, and excessive soil pressure. In the usual procedure of designing a lift. the engineer sould have to first make several essunptions based on his past experience and then clack then and who the necessary corrections to finally arrive at workable solution. Taking the profile or the proposed lift and the capacity that is expected the designer proceeds along this line. First, he establishes the position or the towers. The tension and anchorage terminals are first put in at each end or the line. Next. a tower is put at every sharp break in the profile, sometimes spacing several relatively close it the break is very pronounced. Intermediate towers are then spaced between those needed at critical points. The length S: -_-:'l: ' I o \- I. .J . . - C . I .. . ' -': 3111 Eli.- .J'i'! L1." 1.1 it? I. .“t-cu‘; k1} - 3M3 n; = rfrna ..r inf-‘13?" l..- .I L . I. s .-.' l I . ‘ 1—1-1 aloe-cu. .J'lueil vnlmi-T. ‘L ills-:1. -4' s mama-"J mic-s: ..' '12.! EH1. -’.."i _ve-'s.i'_‘[- :5 \ I“ . I . I \ J. .. - ‘ .. P'l -' 's 1.1.... "' e.- I- . L. . , ‘ . . o .1 ‘I I.I..- C II 'I. F C d - . -.I I . l U I I . IO" It In“ Int be adjusted such that the sea of tin sable Ill not be so great as to require unreasonably high towers. A good rough rule to use when picking the length of span is to seems the see to be five percent of the span. i‘hs hei slit of tower used in ski lifts may vary free so to 80 feet. but should keep within these limits. Knowing the approximate tower height to be used and clearances rec quired of the cable, the distance between towers can be estimated. Once the tower sites have been selected the designer chooses a likely rope size and, using the sea pre- viously allowed for, and the maximum expected load, will calculate the cable tension along the entire line. If the cable strength is sufficient to resist the maximum tension times the given safety factor the rope selected is used. If not, another trial is made. After the tension at each toner has been calculated, the towers my be designed and the number of sheaves deter- mined. When the maximum tension has been determined a counterweight is selected to keep a constant tension in the cable at the upper end. The anchorage terminal must be ' designed to accommodate the drive sheave and power plant and suitable frame structure and foundation to resist the tension of the cable. The tension terminal must be de- signed to contain a tower for suspending the counterweight and for the tension franc to ride freely upon. Speed of the rope must be such that the skier will have sufficient time to get mounted and this time usually detemines the capacity 01' the lift . ‘- .J 1 v .. .- . - . 1 e - E; l ‘ " I I u, . y -: fi 1. I . 1" {<1 -.~.;ir.' I: work will consist or showing the method the designer v‘nlp e'un use to check his first asampticns. 1 will use the plans and “to give: in the completes. lift and shot how they fall within the specification. The whole design will he conducted with the following end results in nine: 1. I1'11th the hw have a capacity or see skiers per hour. 8. That the sexism: vertical distance between the rope and ground at any point on the ascending side or the line he 86 toot. 3. That tin minim vertical distance between the rope and ground at any point he 16 feet. \‘l -'.‘IJ M m MORE «(I N 5 PER DAY! . . . thanks to the Patented Constam Ski Lift “W" ”Y ROEBLING It’s FASTER: The twin seating on this lift means more skiers are on the way up at one time, therefore less wait— ing between runs. It’s more congenial, too. . . gives you a chance to compare notes, have more fun. "'5 EASIER: Even novices find it simple to engage the stick or to leave the lift at any level spot. The ride is smooth, pleasant. ..with just enough effort needed to prevent getting chilled. "IS SAFER: Your skis are on the snow through the whole trip up. And these lifts are engineered and built by Roebling . . . the builder of the world's great suspen- sion bridges. RESORT OWNERS: Facts prove that Roebling—built Constam Ski Lifts attract new crowds. And now is the time to get the facts about building a lift for the 1948-49 season. Write John A. Roebling’s Sons Company, Trenton 2, New Jersey—exclusive licensee for the Patented Constam Ski Lift in the United States east of the 100th meridian. IO) W Estonian: whether the i istaace between the rope and snow is within allowable linits at all points. m .. (Distances) 1. Average snow depth « s it. ' I. Dictate between snow :14 contact point between Tastick and skier - 2 rt. 5. Contracted or minimum length of towing outfit .. 6'-8". 4. Extended or maximum length of towing outfit .- sane". lots: In both 5 md i the lengths stated represent the distance from the center line of rope at the rope grip to the cross bar or the T-ctick measured along the towing outfit. The tow outfit is connected to the 31:11) by means or a swiveling Joint so that this distance can always be considered to be a straight line. ‘ 5. Minimum distance between rope and ground at any point-u- 16 i‘t. (full load condition) 6. Maximum distance between rope and ground at any point -- 36 rt. (single skier) 'I. Towers are ideal-vane 36 ft. high. . coefficient of: friction between skis and snow-4.0%. (Weights) Total weight of towing outfit -- 68 lbs. 1 8 3 4. Two skiers ride on each T—stiok. Average weight of skier -- 165 lbs. Weight of rope -- .9 lbs/ ft. é...e.s:_-.~..*1.E....§W ' In 0 .3: b '93:“: 155...! cur-J grim-919%. -43 i. ii -‘.£t.;.':.'.¢ '1 .1: “in? 1T! ’65? ..: .1 --— hit-hi; ma. ogmcev. .i' -i. -- L. 7 '2'..'- .i- ..I . '--')'."‘.' .. 1-,: 'Ii'I-Z’. i-::Jl)"“i.".-5'- ">Dn'"'EC-'r'i’-. .- ...'i . -- 'i J22“; 5r. . . , . } . - - III. . . .1 - l v I. . . 'J - . I a. e . 1- --- -J.. .2 .' 'u . H m: '." . e. e ‘ . El I. n -' - . 'l' x w ' ' \ f ’- e. \ \J . .1. l . .. _ . . I' | .‘ . l ._ . J . .. , . _ . . ..— ‘1, I, I n . I I O _ -.. . w \ - ‘ . \ ‘ \ x I I lo I. here date - &' dineter cable. 47.400 lbs. (max. strength) 6. Safety factor on maximum tension .. 5 7. Speeing of tee outfits along rope .. 96A feet. ‘The data given above is required to make the initial ”auntie”. Inediately, the followim condition presents a pmblen where the first assumption must be made. It concerns the the angle that the tow outfit when with the vertical as the skier prodeeds up the slepe between the towers. I have shown this as angle (a) in the sketch labeled Figure 1. Since the tow outfit is extended to its full length all the time the skier is being pulled, the angle between the tow outfit and the vertical would vary as the distance between the ground and the main cable changed. This would cause the components of force exerted on the main cable to vary accordingly. This problem was solved by using the following assumptions: 1. Use an average slaps for the entire lift. 8. Use an average rope height above ground for the entire length of the lift. Figurgfz shows angle (a) with assumptions made. With these two assumptions the following set vertical em horizontal forces were found to act upon the hauling rape. Figure 3 gives a sketch showing the forces and how they act. Figure 4 shows the angles used and distances used in oonput ing the forces. The reaction at the main hauling rope is broken down into a component of tension along the -'.’("‘ s l to {Hi u- .r.... .‘_‘I'_ e” ‘ Mai” (/1: average 597‘ \ ' \ (05¢ dyer-0y: .s/o/oe) Mf.‘ of Jklier' F72 are '4 /r/ ”/79 all _1__2_ Iais'hanlisg reps and a vertical amount. 'i'he coupons“ of tusion divided by the spacing of the towing outfits results in an average loss of tension per foot of rope length. Bmlarly, the vertical reaction plus the weight of tb towing outfit divided by the spacing of the towing outfit result in an average vertisel load per foot of rope length. This added to the unit weight of the rope gives the total load per foot of rope length for the uphill (loaded) side. The downhill (empty) side loading is simply the weight of the towing outfits and the rope. Since the loss of tension per foot of cable along the span is than the tension at either and of a span can be calculated knowing one end. From this an average horizontal tension is computed and the mllowing formulas for a uni- formly loaded span applied. '3 1": '. L. :1 D ,l. 59J.Iu-"."'a '5. 5:19! 3' m :“tll'fid amp ‘x_ LJN- ' 15') ”Wig-13:? ‘21P.- -':;.' 12 '1 .. : ..-;.T I ' . ' ' J' -' ."1' '- ' 3112' i: i. 53 331.; 3'3": nun .. ... . 1.}. '2. - a- , .L'f .. :r'i “ . ~:' . .31. - .; .san:ol.'{."ivl; . .r;- a", . " 'J r l “.l. e . L L f . . . '. ‘ ‘1 ‘ ' ‘ ‘ J; . ' 1' - I .12 O'IIIIAIIOEI 90 11!)11:]:gggMHIELOPIlAIDAMHEMfli 8310!! ‘ roses nope Ground Differ-soc Wm... . - M no.0 no.0 14.0 i ism (i‘é‘im 13.3 a some 179.? 21.9 s 293.7 no.5 sea a some 391.5 35.9 e «on: 439.5 27.: s 634.4 no.5 30.9 7 some «4.9 25.9 °3:313:11”). 738.6 914.. 24.1 TOtIl 30‘.3 Avgrsgs EELEEE 0; none .- 2232' Total elevation Difference 738.5 of rope l B.% Total elevation Difference 714.‘ of slope l 6 ‘ Average elevation Difference -- 603.5 tan of angle (b) in Figure 4 - .3079 Horizontal length of too ~- 1960’ A re s s e -- 307 ~‘J— .— . _ . nu}... m _ | . “49.1.9 -‘*‘ 3&- -v-- - -- l ....1 I I I‘ D e n e a e I e I e . I I IU‘E‘I £4"? Dim the figuree and dimmione shown in Figure 4. mile: b, e, and d were tonal by the following method: I .. previously round equal to 17°09! e .- 90°; 17°ovv 8 107°ov' I‘D. O 3 [£111 1030071‘333202 : .7587 e .. 48°55¢ a - 90-b-e 2 85°66' hon Analyti 0e]. Mechanics P 3 I sin b 11 one D - 350 2943 .1 .9557 g . loose7usineS " .6 ._ . .758 M Using the Sine Law 01' Tri angles: Vertical Coupons” V = 128.67 (sin 48°55” - .7537 128.39 .. W" L‘T‘Lé'fir‘im ' All—:11. Horizontal Component 3: 128.67 (sin 83°58' : 188.67 .4062 - L’THTWT‘Lan 07 2 W3 7 “5"“ mom “Hm OH TE 1811‘ ammo m” i. new“ Side-- .1. vertical Componente 101.91 lbe. one to weight or ekier ‘gggog " due to weight or to! outfit 169.91 lbe. Note: Horizontal spacing at tow outfits equals spacing alone rope times cosine of angle (b) of Figure 0-- (96.£)(.9557) 2 98.15 feet. 3, Weisht per Horizontal Foot $%%f%% ; 1.85 lbs. Weight per Horizontal Foot due to Cable= (.9)(.9557)86" Total —- 5.7T lbs. per horizontal foot 0. Component along the Hope : 5‘e98 to '"—TE3 92. - .596 loo/Horizontal Foot 95,40 3 .570 lbe./toot of rope 3. Deeoenling Side-- A. Vertifial O°mP°n°nt‘ -—§%3 ' 74 lbs due to wei - , . ght or 92' tow outfit .86 lbs. due to weight of Total weight per 0 le horizontal root ~~-~ 1.60 lbs. I. leis“ per Housemate]. fact an (lJOHein b) (1.0o)(.sue) t .470 inn/toot 3. Component elong the Rope -- (.Woitooe b) (470M050!) : .«o lbeJroot or my. 8. ‘i'otel Pull on Cable (assuming no neg) ‘ieceneing - (2065”.5697) : 1170.9 lbe. Descendinc - (2055)(.449) = 920.7 lbe. The problem of figuring the deflection, tension, angles et eupporte etc. presented a special case not covered by the ordinary females for suspended cables. The case or the fiber lii't consisted of a counterweighted span and loads I having both vertical and horizontal lcnponente. There are ‘ numerous equati one for vertically suspended loade upon a ‘ oounterweighted span based on ei ther the oatenory or parabolie curves. Upon studying the derivation of formulas presented ‘ by 1". G. Gonetanp‘nen in an article published in the A.S.C.E. ' ; Proceedings, I attempted to derive a formula for this special case using thesme general methods. The i‘ormula is based upon a counterweighted span having any number of evenly spaced loads. It applies to any position the loads may assume along the span and is set up for the case where the supports are at derferent elevations. It is presented as follows 3 .é ' ¢:-. --.'.'-_ “4111‘ Nomenclature of guentitiee y - ert ca Def ectlon from Upper support to Point xy H h- T - so :0 0'5 l l Ge- Go- f- m l t. Vertical Difference in elevation of supports Horizontal Tension of Cable at Lower Support Horizontal Tension of Cable at Upper Support Vertical Tension or Cable at LoWer Lupport Vertical Tension of Cable at Upper bupport Horizontal Spacing at loads Horizontal distance from left support to first load Number of concentrate- loads Horizontal 00mponent of the Concentrated load i Vertical Component of the Concentrated load AnEle between the Horizontal ana a chore between supports Horizontal dlstance between aupports HOrizoatal distance to the left of the point under consideration ”Eight of Cable per foot of horizontal span ‘ . 4| '. . fl; .5 H011zon*31 component a“ Iable *rn510n .r-Mee locate the left at the ram “fie-1n: Hun-2.1 Hang in 8 a Ian 1 In the derivation the cable 1: treated on a tree body. I; a g 1' '49, Mg‘ Q," 94/ 95- )(sin flr‘l‘; 3 0 1.5.3 ' {3‘} sz-(n G can 1% n) = o a! 2 g 32' = (a-n)G Aa—m—emo/(s-m-aa)GcAa-m-nemo} was ,l '13.}: I Gun tan fl} Gala/omen r) ,4 enumézo) tan 1') l G. ((m’M) tan t)eooooooo Lot tan 1' 3 z A R ~nooo¥g- nn;GeaJ{%;/1i_gyl[nmca.tant7 K nSn-lla Ga ten g 23 HbBo yt=xR ~15; -Pxes—pnos,l[p_(_g_ggao] lineman? [’PLEEJ. 5163128117 y 2 - - PxGl - Em Ga 11 1312—11 a SEX—[pin Gs ten '17 g_ at t t at T 'filfiifla Gs tan £7 Substituting R in the equation for y. ngfiGo-chj-fi bGoA [waxiTsthxZ—nm___g_____: gang] .3 a t a {IFGsatanE—iewx?’ ~21Gq-pmG3/oeas . ’c' ,e E? t t t —[om Gs tan f] «[2; Gs tan f t t Z ' l .nsu 5" 1L n J:- 3' ,5 K... J . 'V it a i I. l r. “ ..“ .' r 3 al.- cut-“Ulr- U .- Inl- '- I... t“ 13.] k 5.. ' ‘efi; - e7 * 1%?- * e27*[~e-—ae-l][~n7 a§[§f p 57%;; why-[firm (way A lice ion to 8 a a 8 500 Go =(laa.ev)(.9153) 117.? x 2 150 Go 3(128.67)(.4062.) 53.2 c = 188.67 2 =3 p: 1 ,1 : 85 58' r = 17 04' b 3 £551 3 tan r 2 .3070 o : lgl-M o n 2 58.42 I : .86 loin/root a 2 91.58 11:92.1 r=t=esea ' tatavzcevz Y 3 WM [fig-531558.422 - 5‘91. .581]; giggelisooz ,1 geeegozogoangl ,1 150 (117. '7 6L._30'7)][(58. 42 ,4 (31591. .45e)]:: - 61:50 “reopen ,t 117. :37 [117. '7 (58. .42)] Obviously. the shove female. is such too cumbersome e‘ for too precise to be poetical for the design of e m. lift of this type more cone idereble leave: is per- melt]... Ho ettenpt he been made to derive a. simplified fem covering the special eases of one or two loads centered on the span. although they could be derived by the some methods. Checking the deflection in Span 3 by this formula. I find the deflection at the center to be 47.54. feet. Using the approximate method used by the J. H. Roeblins Company, I run the deflection at the center to be 50.61. Although there appears to be considerable discrepancy in the results the approximate method gives a larger result and would be more toward the safe side in this case than- were the reverse true. It is my belief that the derived fomuls SIVBS the more accurate results since no assumptions are used in its derivation, while the approximate method requires using an average of values and assumes a uniform load which is not the case. Since my derived formula is too unwieldy in its present state and since time is too limited to further investigate. I will use the approximate method in my calculations. Using the estimated value of 8000 lbs. as the tension at the lower end of the ascending side of the Cable, I worked out the tension along the line toward the top. I found the tension at the top would exceed the strength of the cable I had chosen after applying the safety factor. A more practical method is to start mm the upper end !"" arc. .r -. .-.' -o -. 3i ".5 .'..'. arr-z. 2.... die-.mlniu -; L1. " .. L. -:.'- 1'1. L-‘rf'l' -'.‘n- f-.' Tina-3'“! (TN? 'ICTMB ; 1”,: he --..".. ' -- .' Z:.- 1.:"- J. L'- 3'1' -' "'I.‘ '5. If .-: .. __ m.- .. :u- .. ....:..J u o.‘ .ei..:-.'u;-. -. . - _ ... _'.. . . -. . .. .. - .. .im-nv‘t l .-' I . ' ' .- .._.- -.J.:. =.. " - .: ::.' vied oh- :4 1.. .' a 51' e e - -J- " in. .' . . . u'- I _. e . ' _ ‘ = \ Ln- ff. . . C \ l . , . fibre the tension is known and kept constant by the counter. vein“. min as one worn down along the open the only 1113‘ 11-13135 the design is the amount of sea. It the tneion because so low at the lower end of the cable as to allow excessive sec. allfln’zer' cable and higher initial tension at tb upper and would have to be used. an my second trial I worked from the upper end and found the sea to be within limits of the specifications so only ten trials were necessary. I calculated the descending line in the same matter from the upper and down. l .eeiu... II . 1‘ $.&,_, (Cub/e) 5; $5. (/ower' 5v/aloar7') m ”MING NWGLATURI AND FORM WERE USED IN THE DESI“ 01TH! GARE. y w Vertical deflection mu upper support to point xy I - Borisontel distance between airports h ... Vertical Difference in elevati one 01‘ supports v - leig‘ht per foot or horizontal length or span 2 - ensle between tin horizontal and a chord between supports 3,-— Anele between the horizontal and a tangent to a cable curve at the upper support 32» Angle between the horizontal and a tangent to cable curve at the lower support tL-m Horizontal component of cable tension at lower support t: uflaximun cable tension at lover support two Vertical component of cable tension at lower support tn - Horizontal component of cable tension at upper support tuv- Vertical component of cable tension at upper support ti, - Maximum cable tension at upper support “11- Ararage horizontal component of cable tension in the span Cable ten eion approaching and leaving, each tower is equal making t:/ of one open equal to 13,; of the next higher span. Since the horizontal component of tension in the case or this ski lift is not the same throughout the open an average value of the horizontal component at either end will be used instead. Y :s wsz ,l h a?“ ‘2‘ 8,: we / tan. r 'é't' "I f" I": i no?!“ '13“- -tant to 3 (t: or next high” span) (Cosine B ) tau:= to .. (length 0; spa) (Tension Difference per Horizontal root t1. 3 tu ~ (length of apanHteneion difference per horizontal ~ root) fly 8 tn see 3, I '31. H tL .00 B 7’ - tb I111 BI E I tn 3 3L sin 3; Since the mnxinnm deflection is all that is required it is necessary to calculate the deflection only at the center of the span. Because of the large slope angle B; will be round to be an angle above tie horizontal exerting an upward pull at the toner which in the case of towers l and 5 exceeds the down- Ward pull of the cable in the adjacent span. This condition requires the use of depressor sheaves. TERMINAL glaze rm” OF 30" ——.- \) T a c 06 fl Paws-a 51/54 v: TENS/01V J'flt‘A vs: Tension at Point '1‘ is equal to the weight of the counter weight. Increased tension in cable cue to bending over sheaves applied at either side of tension she-eve (a 6:. b) and is .35% of maximum rope tension 3 (.0033)(9480)= £51,; Tension at C may be roughly estimtec as follows: assume tension at b = 9200 c ' 9200-451-1'700 3 80005“ SPIN l a. lit TRIAL I 8 3.91 lbs./root Assume: ti 2 8000# B; ' 8°54' from angle 1 Trial: :1. 3 (BOOOHCoslne 3054'): (sooo)(.9ee)t 7904 to = (7904) / (150)(.695) = 7993 tau 3 7949 tan Ba 3 {3.71“}.50z - (.1566) 2: 7028' 2 7949 tL = (8000)(9915) . 9932 tu = (793:) ¢ (89) = 8021 tau = v97? ten 3; = 8.71 .0547 160 - (.1566) = .1310 Be : 7031' 1'“Ti&%7§‘VTLL"‘L tan B, = (.0247) g (.1566) = .1815 B, = 10°17. t2 = (t )(seo B ) = (7904)91.ooev) : 7972 t2; ‘ (tu)(seo s ) = (7993)(1.01es) = 8120 tuv = (tu)(sin s ) = (s120)(.1794) = 1457# f y . (2.71)(15q12 / 11.75 = 12.71 s ‘7949 L ._ e... L. 2.... a“: .9... up? we? was. emu? ow Engage when my 5. we”. Haw-fl. 3. «s an: em up 3.. «. .34 x «r; w 32. Sou ease «one. u . u «8» easy 33 «cup. Sex... e3» :8 w coca come some Some. m 38 a a «3.» 88. .23 Some. Ease. .,, been mtb $8 5»... .. u some see» my: $93. h muse a)». u 3.3 mag qoaq whom» .595. m *3. mwmu. ”mum No.5 v «we» anew was» $03. .W seem a u 8.3 ones mace Kata 805. 85 we; moon mesa w meow meow meme Eco? _ 83 a a See some 88 508. Sean. neon move 53 not. a. 3.8 one. o8.» 305. . 33 o u 3.3 83 3.3 swag. was»? . 3% £8 seen was» m e o. 33 we: owe» Sees. . some H u save on: 33 Sees. 503.” . “babe some $8 «mac 0 w 83 .58.. Some .905. . .._. u 33 SE Sou... hrwere. Kai. .. 3.5» 8.3 one» See Ina-II .- I. II V... .|\ .n.-llll.l I .I r wacHus n} v 4 fr ‘1: lil l I.l. l.l . 5., 1.... s I -\ .'. 41-“- .- _-. . y. . up . Q w. l M. q. 3.. M. he: ~ -_-.' 11...: {ill- \- ..\ s12.” r[ . r . . . makes... Snakes. . .55 .55 u .5 8. was we on the .55 L95 .83 a :08 “8 mo ‘0 Ppowa ...l .. 080° ”“0”” Cg“ .w M .38 .93» m . a 3.3 «8 v.3 mo Goes. .. _ .. .83 3.8 .88 .88 _. _... .uqo» . were .1. , o . o w. u .38 3.3 L38. have 3.2. cafe :3 am we as. .. . . a m :83 .33 H w n of.» 39a we» or Kane. 2.. . meme up. 8 . no.3 . ”to .. . . .83 .39». . i! d C O 0 O 3.8 «no we» we... face. . .. ten we on some «may m m .33 .83 a o .u. . .uumu 3.8 .2...» .uoee 8.3 . Sn 8... a» we m». n h .. .83 .53 .o . . o no.»- spc use 3.. use m. u... m .ueee no.3 .35 L52. r. BFAH B - and TRIAL It 14°so' frow.lst Trial 9200 # mun: B, ti 3! tu (9200)(Cos B.) = (9200)(.9680) = (8906) tL = 8906 - 125 = 8781 tau 8 8905 - 63 = 8845 > tan 8, = 2.7;.84219; ,1 (.2262) = .2584: B, = 14°59. sum: B, 3 14°59! tu (9800)(.966) “ 8887 tL 3 (8887 ~ 135) = 8762 M I tau = (8887 ~ 53) t 8884 ten B, = 2.71 210 # (.2262) : .2584 B, : 14°59! 2 2845 tan 3; = (.2262) - (.0522) = .1940 B1 = 10°59' .5 n (tu}(seo 3 ) a (8906)(l.0552) = 9219# Maximum 12 : (t )(sin B ) = (8781)(l.0187)= 8945# t“. : (tu )(sin B ) = (9219)(.2585) a 2383 tn 2 (t )(sin B ) = (8945)(.1905r $1704 y s gnaw?)2 { 25.75 = 25_44 1.. . k... 57.2... ...._ , v I.- .I 2... \fi waning—DH so. no. «a u «as up we 34 .n 4 w w 2.3 2...» 808. a «So one» 2.8 Soto. «com. 55 sum w «are 2.4» Koo». u... u 8.5 as»... :3 Zoo». wees. See 3% 53 K»... a w 33. some moons. 58¢ u So... 38 32.. meow». Game. 33 $8 $8 58 o u. 3.: 3e... moose. .33 a «you 38 com... moose. $05.. sumo , swam we we Sam a u. .38 «no... Some. 88 . u 32. 38 .38 Seem. to»... mono 3mm meme 5% o w .3»... 32. means. moo. , a 38 33 3S $05. moose. mono mouo gm 8% e a. neon menu Sosa. 8‘ u 2: can. seem poops. $98. 8.- 88 38 £3 a w 38 menu 85 Kama. £8 a once o3» ecu» Knee. Some. a»: 88 meme So» ‘ a “.2" 3 . 8n 3 .i,_ an w -.r -.- | fi' an vi _ a a .. w . 8 u u . . ., n . _ t i _.._ _ r u _ - .rn. . .- 1 . _ .. v t. m“ .o c .. . c n . .... ‘ .u .I .u-H- . an”; .ltl..(1uu .........:..LI... .u .. .. ..... E .L 4 M. . mil. H.255» 9H Sun. nu wannabe _ no. N n25 mango—5.. u no... . «up mp «on an . u Hanwn poops. . w . 5.3 So an mom. a.» L58 5.2. . .58.. .58 W wuooo. .u.. M @. a up.a« was ac whommwg . .maao mu.uu .mmeo .mm’m moooo. .. a . 8.3 «cc :5 . 500.3. M. .88 2:8 .33 kg» 8on8. _ o 3.3 aura we... Gamma. . .38 «Fun .33 .5»... wqouo. o .33 “3.9.. .83 .83 «.38 as... 5 team: . . . $08. . W . o . o _ 13...» 8.3 .38 .89. g. . 82:. «.3 amp "3 89, . _ . . ”coco. _ w . . .33 3.8 .38 .nopo 3.3 :5 S... 503.. . m A 0 a 8.3 nun :8 Exit 9 o LB l'_ r 4' f‘. . ! '_. —_.._‘ , . no. no. as n «as up an E. a 4 u .33. «“8 «on... .. 7 v u flaw «84 «man was . wove. .22....” u 32.... yuan. you» w «ace .58 Earn. .58. _. u a «84 ammo «wan Son... 598. 3a... .7 «Be 83 58 m u. .29.. «man. Boa. «may a o o . «no... mum... moo» a «on... .38.. «was 5 .5. 5 3. .32. _ . p .38 32. Sup». 9 3.5 3% $0... 8.3 .u .33 .83 3a... 5 we. 5 3. 2.3 w 88 moan 50$. 9: «Eu wave Sac u u 88 33 mean 59$. 50%. 25 . w .38 «m3 macaw. mag . at... am? «5a a u 33 .38 8.3 «mama. «~05. 83 u 83 83 Boa. com. .82. 83 mac... 4 a 88 , 2.8 8.»... San... Soc... 8.... . u 35 map 593. 98. . .. .. .88 8.8 $3 7 ... u a. . 8a. 8a.. 88 508. toga. a; ... ".' . LT’HT: - "J 9 30 n! It! . I. I ’2'!" .2; u. .1; ~_.' . 4 mail mun: bun». nu >358» y .. 4. 5 w. 3— no. N hon—mg mow. eons. u Hon. H3 u an: up. n m panpapu upooo. .wnso .wpow 5.8. Go a. mo”... 0 pm oo. mu.uu .wqmm .maou ”You . :8 3 town. has wwooo. no.0u .uawm .mqa. .a.ao moo pip wqoo». .mcqo waozo. um.uu .wuoo .mme» 8.5 aura pg Sou». .23. goco. £000 .800 ONNQU mo.pa m¢o.q ma ppcmu. .mmao . u ..oow W N308. mmomu Armm or: «2.. .5... $08. .3... o mm.uo .uamc .uomo pm mo. . o. . Boo... BELM'E 0! OF ROPE Since the litt he: been designed tor a maxim tension of 9200} em a safety rector of 5 in required. the mun-mu tape was selected: 6 x 19 Standard Hoisting Rope 3 4 inch diameter 0! Monitor Steel and a breaking strength or 4.7.600 lbe., end weight or .90 lbe./root. Thin conforms with the weight used in the design and agree. with the rope selected by the Roebling Company. A standard hauling rope was selected instead of the locked coil typo usually used on tramway: because a 51:1 11:1: would not wear the rope nearly as severely and a great saving in rope cost could be had. PM“! mm 331’! IUD BIO! ”an ( Y 1 Clearance on clearance abate = -. - Mandi on Deni I i ie.e¢ 11.37 11.86 13.43 ”b‘e.14 a 86.73 83.91 15.: 17.03 1.e e 60.61 48.50 24.1 26.: t11l.o e 57.59 55.83 30.5 25.0 Hone e 37.89 so.¢7 23.5 84.? none 6 90.11 87.48 19.8 80.5 None 9 ae.ee 22.91 32.2 32.7 none 6 no.¢4 24.94 13.2 13.9 °ute Note: maxim allowable clearance = 88' Minimum allowable ole arenoe = 18' . .. -——r-.-....--o-vn ’vw “"' ii! '._'\¢ ' I300 .900. 6 4 x / 79K? /5 % .. :1; SPAN-l . 150‘ ' i *‘ .. - -.._vq. . - _«- ' '_ .' \g' _. ;v- . p -.- ‘- t - ‘ ‘“ 13:17 .1'. sfffiulifis g--—— Era-u: Caf’é fcéf --""Z_// Cut’lé I Ia. 94 //6 (N0 60/- or‘ F'// Rafa/red) 69-3 ‘ 37/.5 JPAN‘G 375 ’ ~ —.—_——— ——__._.—..——_ 634.4- 6/35 /67.7 466. 7 \____ (It/0 Cai“ or/‘7'// Reyu/reo’) 4.3.9. 5 \ .‘ .>.//\\ _664.9 /I/ ’ . pr... . . . I . ..- fill! . . . . .II' n . . . . . . s. .I r . ... .. ..\. .1 n. s.. \_ ... . .. . . . . ... . I _ . . . . ..1 r a . II ..I . u. . . .. ..tL... .. \..(.. . 1. 1 \ .u .14.}... .. x . “1.. ... . u .... . MY! mm 0] m KEANE “EB 11'! non MIR ~— ———.. ~——- w lleendin; Bile Mounting an. .-.-1 . I V0.1. 11. .1 _ -.. V11 ; -... 1.35.3 .n‘fl" I u 133 134. 133 137 I 4.70 '5' 370 293 ’4. 18 13 ‘fi— -—-b- 381 703 737 185 307 310 ~b— ' 337 1130 1210 W 774 014 133 3171 34.3 367 807 I on: --- " 000 1321 1030 W 1:72 1370 “... 3:1 1:33 1300 39 1033 1100 Each sheave tdeo one-half the reeultent load which in no one 01000“ the following up oirioationox Maxim allowable prelim-e on each support sheave alone tb line -- 700 lbs. minim allowable preeeure on each hold down or depress 3110an along the line -- 685 lbs. Minimum allowable pressure on any sheave --- 200 lbs. . I .1. _. __ -.- _. .— _ ...—..— .-¢u-.--—ou~-~u J --.' 3-; ' ~-':.-'rln’. _ ,. :- ' - ' 1 - '- . j I . . . .n u. I L. -r _. . . . . . - — -. . ' fl .- -_- bar‘- I 'I ' . . e - — u t 1 - -‘ . '- . .' ._ — | --+- . ' 5 ‘1 4' |'. DATA COMBINING ME ram Tb total weiats or the various towers on be “sued to be as follows: _ l. 10 ft. tower -.-.- 4,850 lbs. applied along e vertical line l’d' uphill from the center line or downhill enehor bolt group. 2. ll rt. tower - 4.500 lbs. applied along a vertical line 3'0” uphill from the center line 01' downhill anchor bolt gmup. 3. 86 ft. tower -- 6.100 lbs. applied along a vertical line 2'4" uphill from the center line or downhill anchor bolt. The forces acting through the sheaves can be assumed to act through the center line or the tower and at the mpe elevation. jrhe weight 01' the concrete foundations were figured using 140 lbs. per cubic foot and are as follows: 1. 13 ft. tower -- 8,660 lbs. 2. 21 ft. tower «10,000 lbs. 3. 23 rt. tower --11.3oo lbs. Resisting force or the soil against sliding is taking 1000 lbs. per square foot as recommended by Peele's Handbook of Mining Engineering. Soil pressure figured by Formula to 3 E (l ,1 Go) A ( - ) "5 " . 3 On :31- Ubfib umbinO mhfiman ufioaow thsze o, (Wt of fcwe r) (Verfrcd/ Sheen/e Pre-SSV’E) (W* of Fauhddf/bfi) .33 --*——— lenyffi - "0' “ (oucrfurn/nj wmatrusnr") 0600* 0‘ 771/3 case opp/lo: 7‘0 founder/”ion: d‘f +ower: 2,356,; \ fl II 75PoF Bot 73p or CONCRET’ ____,________ NT' To Fm. l W A'J‘ TOP OF CONCRETL' '\ _\ m \ //«= ) [1 al- / \ // \ K (/ \\\. NFaec/Aré Bod ~ Del/.1. f Gnauf /’o" in E0: Ic (BEND frfaP) tor/NG— ROCK TYPE 375— ' SH; X 55M/- FuwsH£ 0 NUTflg-QOJ 3:0"MIM/flyk 45510” 5047‘ (F-B.o,) Hwy/£0 TH FOOT’NG SHALL Fewer/2.475 ;—*__1 sarcasm Engineeucws Record (May 30, 1989) by l. P. moi-rises, Tramway Engineer at the Marina Steel no. lire company. WW 1' con-'6 0 on Eagles:- h i T. ,by r. c. Gerstorphon, II. in. Sec. 0.3., o , pp. 8108, LS. 0.3. Proceedings. aretorpen, o . 83 of Am. .Soc. of C. E. Transactions. p. 1383. lo 000 aerial T w , by F. G. Garstcrphen. Vol. lea (August, chfifigineers and Miners Journal, p. 110. Handbook of Mining mgeery. by Peeles, Vol. 2. Wire Rope Engineering Handbook by American Steel and Wire onpnny. ' by Seely and Ensign. Mechanical Engineer's Handbook (Fourth Edition) by Lionel e Markl. Anal ticel Mechanics for I-‘ ineers ..-.--. W1! : w. macaw. - Amflrwmm' Y 082 6 ”WWII!!! 3 .Lflflmlilfl'm