Contents - Home | US Forest Service€¦ · Desc~pdion of "Fi Figure 2.-Log geometry. The load-cawing capability of a cable logging system de- pends not only on the size and strength

Contents

. . . . . . . . . . . . . . . . . . DESCRIPTION OF VARIABLES 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LIVE SKYLINE 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gable gesmetr~; 4

Log geometv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . hscedure - 4

Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion - 6

. . . . . . . . . . . . . . . . . . . . . . . . . RUNNING SKYLINE 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cable geometry 6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . Log geometv -6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roeedure 6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion 8

. . . . . . . . . . . . . . . . . . . . . . . . . STANDING SKYLINE 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cable gecmetqi 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Log geometq 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pvocedure 9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion I1

. . . . . . . . . VARIATIONS IN YARDING CONDITIONS 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . Yarder position 11

. . . . . . . . . . . . . . . . . . . . . . Direction of movement 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example 12

LITERATURE CITED . . . . . . . . . . . . . . . . . . . . . . . . 13 APPENDIX I-STANDING SKYLINE-LENGTH AND LOAD PATH . . . . . . . . . . . . . . . . . . . . . . . . . . 14

hogram descdption . . . . . . . . . . . . . . . . . . . . . . . . 14 User instruction . . . . . . . . . . . . . . . . . . . . . . . . . '16

APPEND1 X 2-PARTIAL SUSPENSION LOAD FACTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 8

Program description . . . . . . . . . . . . . . . . . . . . . . . . 18 User instmetion . . . . . . . . . . . . . . . . . . . . . . . . . . 19

APPENDIX 3-PARTIAL SUSPENSION PAYLOAD III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Program description . . . . . . . . . . . . . . . . . . . . . . . . 21 User instruction . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Live skyfine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Running skyline . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Standing skyline . . . . . . . . . . . . . . . . . . . . . . . . . . 26

APPENDIX 4-EQUATIONS . . . . . . . . . . . . . . . . . . . . 28 Cable geometrgi. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Log geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Payload calculations . . . . . . . . . . . . . . . . . . . . . . . . 29

Several tools are available for predicting the payload capability of cable logging systems. Hmdheld calculator pro- g ~ m s (Binkley and Sessions, undated) are among the tools that are capable of yielding the most reliable results with less effort thm other hand methods. However, no systematic approach or procedure has been documented for using these progrms, which can be followed with relative ease by some- one unfmiliar with cable systems mechmics, as there has been for the chain and board method (Lysons and Mann, 1967). Therefore, hand-held calculator programs to determine payload capability are not effec~vely used by field pevsonnel,

Fur&hemom, existing progams are based on the assumption that the logs are fully suspended, while actual yarding conditions usually involve partid suspension. The traditional way to account for the effect of partid suspension is to in- erear;e the fully suspended payload by a "consewative'350 percent (Binkley and Sessions, undated). The actual ratio of a partially suspended payload capability to a fully suspended payload capability can range from about 0.5 to 3 -5. mere are methods to calculate an approximate ratio when the amount of suspension is known, but because the amount of suspension is a function of severai va~ables and not easily determined, these methods of predicting payload capability are not as realistic as they should be, nor are they always consem-ative a

T h i s paper presents a systematic p r o c e d u ~ for predicting the payload capability for the most common skyline yarding systems, by the use of three hand-held calculator programs, that include effect of partial suspension. Because the procedures for predicting the payload capability can be confusing, whether or not piutial suspension i s considered, the basic p~nciples are also expalined. As a result, the u s r can better understand the purpose s f each step of the procedure and increase the effectiveness of this as well as other methods of predicting payload capability.

mese programs use mathematical fomulas based on assumptions that are similar to the soedled %@d ctink9"Carson 1976). mese fomulas have been simplified and extended so that the effects of pavtial suspension may be included directly. Appendix 4 lists the simplifying assumptions made and the equations used in each of the progams. &cause it is not always easy to know when a mainline or haulback is required when partial suspension is considered, the option of a haulback line on live and standing skylines is included. The yarder is assumed to be positioned on the left with stationing increasing toward the right. In addition, the carriage is assumed to be the type in which the mainline is used either to bring the turn to the carriage or to maintain carriage position while the load is brought into position for inhaul.

Desc~pdion of "Fi Figure 2.-Log geometry.

The load-cawing capability of a cable logging system depends not only on the size and strength of the cables, but dso on the angles at which the cable tensions act at the carriage, These angles depend on the system geometry-, which may be thought of as consisting of two parts: the cable geometry which accounts for the deflection, and the log geometry which accounts for the m o u n t of suspension. Re- gardless of the systems being analyzed, the system geometry must be specified before the payload capability can be determined.

The cable geometv (Fig. 1) is described in two ways. Nor- mally, it is described by the locations of the yarder, tailhold and carriage in terms of X and U coordinates, and their appropriate heights. These are reduced to the variables L, E, d , and y for the actual calculations. However, when L, E, d, and y are known they may be used directly.

Figure 1.--CabIe geometry.

T

XY,YY = X B Y coordinates of yarder spar X T , Y ~ = XEir Y cmrdrnotes of larlhold XL,Y,= X 8 Y coordinates of rood point hyFTpi=He~ghts of yarder, tailhold,& load clearance L = Hor~zontal distance-- yarder 15 to~lhold E = Verticoi drstance--yarder to tallhold d = Horirontol dtstance--yorder to iood pornt y = Vertical distance--yorder to load pornt

The log geometrgi (Fig. 2) is specified by the friction coefficient, the log and choker lengths, the ground slope, and the carriage clearance. These five variables are used to calculate the partial suspension load factors, v and h , which express the proportion of log weight that is transferred to the carriage as vertical and horizontal force components. For full suspension, v equals 1 and h equals 0.

These diagrams show that as the position of the carriage changes, the cable and the log geometry also change. This results in a different payload capability for each carriage position. In other words, the cable tensions resulting from a

P = Friction coefficient 1 , = Length of log Ic = Length of choker @ = Ground slope

= Car"age clearance v = Vertical load factor h = Horizontal load factor

given size and weight log will vary- as the carriage is moved along the skyline. Generally, the skyline tension is @eater when the load is in the middle of the s p a , and the mainline or haulback tension is greater when the load is near one end of the span. Because this is a general statement, the payload capability for each line should be calculated for several carriage positions.

The payload capability for a particular carriage position is determined by the analysis of a free-body diagram of the cw- riage. Figure 3 shows a typical free body for a skyline system with a mainline. The actual forces that act at the carriage depend on the system being andyzed and whether a mainline or haulback is needed to maintain log stabiliw.

The ma~or difficulty in the analyses and the programs that follow is undemtanding the geometry. When i t is known how the cable geometry changes for the different systems and how this affects the log geometr~; and associated load factors, the analyses become straightfornard. As an aid to under- standing this concept, each major skyline system (live, running, and standing) in the text is discussed separately and in order of increasing complexity, even though there are simi- larities among them. After these systems are discussed and

exmples are given, methods of using these programs for The reader should become familiar with these concepts by other yovding configurations are presented. working the exmple problems in the appendices before pro-

ceeding to the example problems for the different systems.

Figure 3.-Free body of carriage. Live Skywe

Figure 4 depicts a typical live skyline. For convenience, the system is shown with only a mainline although a haulback may be required. The program considers either case. As discussed here, a live skyline is one in which the length of the skyline is actually varied as the log turn is brougbt toward the landing. If the skyline length is not varied, then, even though it i s traditionally classified as a live skyline, it should be analyzed as a standing skyline. This distinction is important because it determines the cable geometry.

TI = Tension in skyline Ts = Tension in mainline

= Line of ae l~sn of skyiine to left of carriage a!3 = L ~ n e of oc t~on of mainline 61 = Line of action of skyline .to right of carriage

Wc = Carriage weight v W n = Vertical component due to net paytoad h W n = Horizontal component due to net payload

Figure $.--Live skyline configuration.

Cable Geometq

Since the skyline length varies as the load is brought toward the landing, the load clearance (hL) is considered to be held constant for each camiage position. Figure 5 traces the cardage at each point along the skyline eouridor, The geometry is descdbed by specifying the coordinates and heights of the yarder spar and tailbold, and then specifying each Load point in terms of its coordinates m d the constant load clearance.

h g Geometvy Since the load clearance, hL, of the cable geometu~i remains constant, the carriage height, y,, also remains constant. For most carriages these two clearances e m be taken as the same (faL = y,), and this assumption is made throughout these dis- cussions and in the proeams. However, for very large ear- riages, the more exact relationship given by equation 1 may be used.

where d, = distance separating the skyline and the mainline (or choker) at the carriage, For the live skyline then, the only fog geometry gavameter that chimgex sipificantly from one load point to another is the ground slope.

Procedure The assumption that the earfiage clearance is eonstant makes the procedure for detemining gaigrload capability vevy straightfornard, The two main steps me :

1- Use the ""Ptial Suspension Load Factors" popm (Ap- pendix 2) do detemine the partial suspension load hetow for each load point for which capability is to be detemined.

2. Use the ""Partial Susgensisn Payload (Ill)" "program (Ap-

Figure 5.-Load path sf a live or running skyline.

pendix 3) to detemine the allowable payloads Eor each load point for which capability is to be determined,

The least of these payloads is the one taken to be the maximum load that the system can c a w without exceeding any of the allowable tensions.

Exmpfe Tke profile data of Figure 6A and the data that folIow illustrate the procedure.

Yarder location: Terrain point (T.P.) 3, h, = 50 ft Tailhold location: T.P. 10, hT = 20 ft Minimum load clearance: hL = y, = 12 ft

Step 1. Use the ""Ptial Suspension Load Factors" WouogPam (Appendix 2) to determine the load factors.

1. Input ,u = 0.6 (Key A) 2, Input PI! = 40 and

1, = 16 (Key B) 3. For each load point, enter the ground slope (Key C), and then enter the carriage elearmee and compute the vdue for v and h (Key D). The results are:

Terra in goin l

Figure 6.-Profile data in standard form for garder above tailhold (A) and below tailhold (B).

TERRAIN POINT

PROFILE DATA 9

SLOPE DISTANCE % SLOPE X COORDINATE Y COORDINATE

125 0.60 568.0 4968.2 125 0.40 675.2 4903.9 150 0.20 79 1.2 4857.5 135 0.40 938.3 4828.0 I50 0.25 1 063.7 4 777.9 140 0.40 1 209.2 4741.5 130 - 0.40 1339.2 4689.5

1459.9 4737.8

9 PROFILE DATA

TERRAIN POINT

10 9 8 7 6 5 4 3

SLOPE DISTANCE % SLOPE X COORDINATE Y COORDINATE

Step 2. Use the ""Prtial Suspension Payload 111" "program (Appendix 3) do determine the allowable payload.

1, Input T3 = 13700 w3 = 0.72 T, = 8900 and w, = 0.46 (Key A)

2. Input f .= 3. W, = 750 TI = 34500 and o, = 1.85 (Key B)

3. Input Xu = 568.0 U, = 4968.2 and h, = 50 (Key fA)

4, Input ]I, = 1459.9 U, = 4737.8 and h, = 20 (Key fB)

5. For each load point, enter the coordinates and ca~ iage clearance (Key fC), and then ues Key E to enter the load factors and calculate the allowable payloads based on the allowable skyline tension. Use Key fE3 to ealcuIate the payload based on allowable mainline tension. The results are:

By these calculations, the system capability is 18512.13 Zb, which is 2*03 times the payload that is found by wsuming full suspension.

The major difference between detemining payload capability by this method and traditional methods is the calculation of the load factors. T h i s also is the most timeconsum- ing part of the procedure. The procedure can be simplified significantly by using one or more load factors calculated on the basis of one or more "average9' s o u n d slopes. The results will still reflect the effects of partial suspension without much more effort than tradition& methods.

A typical running skyline (Fig. 7) bas one fine that sewes both as a skyline and a haulback line. This line is usually edled the baufback fine.

Gable Geometry

Since the leng"ch of the haulback line vaGes as the turn is moved toward the landing, the load clearance (hL) i s eon- s i d e ~ d to be eonstant for determination of payload capability. The path of the carriage under these conditions is also shown in Figure 5. The cable geometvy is then desc~bed by first specifying the coordinates and heights of the yarder spar and tailhold, and then specifying each load point in terns of its coordinates and the constant load clearance.

Since the Ioad clearmce remains eonstant, the caruiage clearance, y,, does too. For running skyline cauriages, it is assumed that y, = h, without significant emor, Therefore, the only log geometvy parameter that will change significantly from one load point to another is the gound slope.

Procedure

The assumption that the cadage cleavarnce is constant makes the procedure for determining payload capabifie for a running skyline essentially the s m e as for the live skyline. The inputs are only slightly different. Two m ~ n steps are:

1. Use the ""Partial Suspension Laad Factors9' wo@am (Appendix 2) to determine the partid suspension load fae- tors for each tenain point for which capability is to be de- demined.

2, Use the ""ntial Suspension Payload (111)" p o s a m (Appendix 3) to deternine the allowable payloads for each tem&n point for which capability is to be detemined,

The least 06 these payloads is the one taken to be the mlaxi- mum load that the system e m e;arw without exceeding any of the &lowable tensions,

The profile data of Figure 6A and the data that hllow illustrate the procedure.

Yarder location: T.P 3, h, - 50' Tailhold location: T.P. 10, h, = 20' Load clearance: hL = 12'

Figure 7 .-Running skyline configuration.

Step 1. Use the ""Prtial Suspension Load Factor" program (Appendix 2) to detersnine the load factors.

I. Input 1.1 = Q,68 (Key A)

2. Input lQ = 40 and

I, = 16 (Key B)

3. For each telrrain point, enter the ground slope (Key C), and then enter the emiage clearmee (Key I)). the values of v and h will be displayed. The result is:

Inp u t Output Ternin point 8 Ye u Tz

Step 2. Use the ""Prtial Suspension Payload (111) program (Appendix 3) to determine the payload capability

1. Input T3 = 34500 u, = 3.70 T, = 1 and a4 = I (Key A)

2. Tnput f = 2 W, = 750 TI = 34500 and w, = 1.85 (Key B)

3. Input Xy = 568.0 Yy = 4968.2 h, - 50 (Key fA)

4. Input X, = 1459.9 U, = 4737.8 h, = 20 (Key fB)

5, For each terrain point. enter the load point coordinates and the load dearance (Key fC), and then enter the load factors, v and h, and calculate the payload based on allowable haulback tension (Key E). Use Key flE: to calculate the payload based on allowable mainline tension. The results are :

Inpu ts Outputs The amount of accuracy sacrificed depends on the variation Terrain in ground slope. However, the results will still reflect the point X , Y , h , v h &(Ti) U.',(T,) effects of partial suspension without much more efforts than traditional methods.

On the basis of these results, the net allowable system payload is 22110.78 Ib and is mainline limited. This payload is 1.40 times the payload determined with a full suspension analysis,.

Discussion

There is essentially no difference in procedure for payload determinations for the running skyline and live skyline except for the inputs on one of the programs. Different input is needed because different forces act at the carriage for a running skyline and a live skyline.

The major difference between determining payload capability by this method and traditional methods is the calculation of the load factors. This also is the most time-consuming part of the procedure. The procedure can be simplified significantly by using one or more ""average9' ground slopes.

Note that some running skylines, because they operate on an essentially constant haulback tension regardless of load, de- viate from the conditions described. The constant haulback tension causes a cable geometry with a varying, rather than a constant, load clearance. However, the maximum payload for these conditions can be calculated in the way described without a significant decrease in accuracy.

Standing Skyline

A typical standing skyline configuration is shown in Figure 8. If the skyline length is not varied as the carriage is moved along it, the system is analyzed as a standing skyline. This distinction is important because it determines the cable geometry.

Cable Geometry

Since the skyline is essentially constant, the path that the carriage takes is elliptical (Fig. 9). This path can be described mathematically once the skyline length is known. Hence, the system geometry can be determined.

Figure 10 illustrates that for each point on a given profile there is an associated skyline length (L,) that allows passage

Figure 8.-Standing skyline configuration.

of the carriage at exactly the required clearance. Since these along the skyline. This means that the amount of suspension lengths vary, as illustrated, there is only one length that will can vary considerably for a standing skyline, and the load allow the cavriage to pass each temain point within the factors can vary considerably also. tzlilowable clearance, which is obviously the shortest of all possible lengths. The shorLest skyline length is found by Procedure calculating the length required to pass the carriage at exactly

Payload capability analysis of the standing skyline is more the required clearance for several terrain points until it is

involved than the live or running skyline systems because of certain that a shortest one has been found. By using the the fixed skyline length. The three primary steps are: shortest skyline length, So, the system geometry is specified

by finding the deaection, y, at any distance, d, with the 1. Use the ""Sanding Skyline Length and Load Path" pro- mathematical expression describing the elliptical load path. gram (Appendix 1) to determine the skyline length, So, then

deternine the cable geometry parameters, L and E, for the system, and then determine the geometry parameters d, y ,

Lctg geometry and y, for each load point.

Because of the elliptical load path, the load clearance, hL, 2. Use the "Partial Suspension Load Factors'' program (Ap- and the cardage clearance, ye, vary as the carriage moves pendix 2) to determine the partial suspension load factors for

each load point.

Figure 9,-Elliptical load path of a standing skyline.

Figure 10,-Skyline lengths.

3. Use the "Partial Suspension Payload (111)" program (Ap- nrrain lnpu t Output Input Outipul pendix 3) to determine the allowable payloads. point

d The least of the payloads is the one taken to be the maximum

Y YL Ye

load the system can support without exceeding any of the 4 107.2 80.13 4903.9 34.1'7 ailowable tensions. 5 223.2 128.00 4857.5 32.70

Example 6 370.3 178.18 1828.0 12.02 7 495.7 214.54 4777.9 25.76

The profile data of Figure 6A and the data that follow illus- 8 641.2 249.54 4741.5 27.16 trate the procedure. 9 711.2 271.91 4689.5 56.79

G;I = 1.85 lbift TI = 34500 Ib f i = 0.60 u g = 0.72 lbift T3 =: 13700 Ib 19 = 40 ft

= 0.46 Ibift TTq = 8900 Ib 1, = 16 ft Step 2. Use the ""Partial Suspension Load Factors" program W, = '750 Ib (Appendix 2) to determine the load factors for each load

Yarder location: T.P. 3, h, - 50 ft Tailhold location: T.P. 10, hT = 20 ft Load clearance : hL = 12 ft

point.

1. Input p - 0.60 (Key A)

2. I n p ~ t l y = 40 and

Step 1. Use the "'Standing Skyline-Length and Load Path" 1, = 16 (Key B) program (Appendix 1 ) t o determine the skyline length, So, 3. For each load point enter the ground slope (Key C) and the cable geometry parameters, L and E, for the system, and then the carriage clearance (Key D). The calculator will dis- then cable geometry parameters, d and y, and the carriage play the load factors, The results are: clearance, ye, for each load point.

X, = 3968.2 (Key fA)

2. Input ITT = 1459.9

V, = 4'735.8 (Key fB)

3. Input ky = 50

h, - 0

= 112 (Key fD)

4. For each terrain point that seems as if it might Iirnit the skyline length, enter the coordinates (Key fC) and then calcrafate the length, L,, and the distance, d. The results are:

Terrain Inp u ts Outputs

point XT ="-L Ls d

Terrain Inpu l Output

point 0 Yc L' h

Step 3. Use the ""Partial Suspension Payload (Ill)" program (Appendix 3) to determine the payloads based on the appropriate line tensions.

I. Input T3 = 13700

5 791.2 4857.5 946.16 223.2 = 0.72 6 938.3 4828.0 938.98 370.3 T4 = 8900 and 7 1063.7 4771.9 943.24 495.1 8 1209.2 3741.5 944.43 641.2 u4 = 0.4 6 (Key A)

9 1339.2 4689.5 966.88 771.2 2. Input f = I W, = 750

The limiting skyline length, So, according to these calculations isXo = 9338.98 T~ = 34500

5 . Determine the cable geometvy parameters, L and E, for w , = 1.85 (Key B)

the system {Key E). 3. Input L = 891.9 and

These are L = 891.9 ft , and E = 260.4 ft. E = 260.4 (Key 6)

6. Input So = 938.98 (Key A) then determine the cable 4. For each load point enter d and y [Key D), and then enter geometry parameters, d and y, and the cavriage clearance, v and h and calculate W, (T, ) f Key E). Calculate M;, (TJ ) y,, for each load point. The results are: (Key fEj. The results are:

On the basis of these results, the limiting payload is 15145.13 lb which is 1.10 times the payload determined with a full suspension analysis.

Discussion

The analysis of a standing skyline is more complex than the analysis of the live or running skyline, because Step 1 must be used to determine skyline length and load path. The remainil~g two steps are identical, as far as the mechanics are concerned.

Traditionally, the only load point that is examined for a standing skyline analysis is at midspan. However, the determination of the cable geometry and load factors can be critical because the payload capability at any load point is as sensitive to the amount of suspension as it is to the amount s f deflection, and because the amount of suspension can vary from full suspension to no suspension quite easily, depending on the topography, there is no assurance that the limiting load will be at midspan. Therefore, the payload for several terrain points should be determined to be certain which one limits the capability of the system. Payload predictions, based on the payload at midspan only, can easily be 50 percent off, and it is not unusual for them to be 80 percent off.

For typical yarders with typical line sizes, a live skyline anal- psis will nearly always yield a payload capability at least as large as a standing skyline analysis will yieid. Therefore, it may be convenient to andyze a profile for a live skyline first. If a satisfactou3: payload capability is not obtained, there is no point in analyzing the profile for a standing skyline. As experience is gained in using the programs, it will be easier to identify the "critical9' terrain points as well as to estimate how much less a standing skyline will carry than that of a Live skyline on a given profile.

Variations in Yarding Conditions

The programs used in these analyses are based on the assumption that the yarder is higher in elevation than the tailhold and that the logs moved toward the yarder. However, variations in yarding circumstances can and do occur. For example, it may be desirable to move the log away from the yarder, and some systems are designed with the yarder lower in elevation than the tailhold. The programs can be used to

predict payloads for each of these vaviations if the proper inputs are made.

Varder Position

If the top of the yarder spar is higher than the top of the tailhold (elevation difference, E>O), then no modifications for yarder position are required. If the reverse is true (E<O), then the allowable tensions should be reduced because the tension in any cable (for a given load at a given location) is maximum at its highest point in the system. The algorithms in the programs use the tensions at the yarder spar because that is assumed to be the highest point. If the yarder is lower than the tailhold, the maximum skyline and haulback tensions are at the tailhold. To account for this, the allowable tensions should be reduced by the prodnct of the line's weight and the elevation difference between the top of the yarder spar and the top of the tailhold. The relationship is expressed by equation 2.

T ; ~ ~ = T + WE

where

'TBli - allowable tension with yarder lower than tailhold

Td, = allowable tension with yarder higher than tailhold

w = cable weightlfoot

E = elekfation difference, feet

Since the elevation difference, E, is negative when the yarder is lower than the tailhold, the allowable tensions will be reduced accordingly. The tensions in all lines should be reduced, even though that may yield results that could be slightly conservative if the payload is limited by mainline tension.

Direction of Movement

The direction of log movement, whether toward or a%vay from the yarder, is another variation that may require rnodi- fieation to the inputs. Consider the free body diagram of Figure 3. In particular note that the horizontal component of force due to drag resistance, the '%hW," force, is toward the right. ?'his is true if the turn is to be moved toward the yarder which Is assumed to be on the left. But, if the turn is to be moved away from the yarder, this ""bW," force would be toward the left. This discrepancy is corrected by simply reversing the sign of the horizontal load factor, h. The load factors are calculated first as they would be normally (give careful attention to which ground slope is specified as well as the sign of the ground slope); then the sign of the horizontal factor, h7 is reversed only if the load is to be moved away from the yarder.

The modifications are simple, but because they are some- times contrary to traditional thinking, they can be confusing.

For this reason, the following chart summarizes the required modifications and the following examples illustrate them:

Log movement

'Y'arder position Towardyarder Awayfromyarder

Above (Elevation difference E>O) No modifications Reverse sign of h

Below (Elevation Reduce tensions difference E<O) Reduce tensions Reverse sign of h

Example

To illustrate the modifications for the variations in yarding conditions, consider the profile data of Figure 6A and 6B, both of which are in standard form for having the yarder on the left. These profiles are the same; one is merely the reverse of the other. Note that the beginning coordinates are completely arbitrary. In addition, consider that a live skyline will be used with the same specifications as listed on page 4. It should also be noted that the modifieations are the same for running and standing skylines.

Yurder position betow. If the yarder is at T.P. 10 and the tailtree at T.P. 3, then the profile would be specified as shown in Figure 6B, to be in standard form. Because the yarder is lower than the tailhold (E<O), the allowable tensions should be reduced by the product of the cable's weight and the elevation difference, E. In this case: E = -200.40 ft and the appropriate reductions are:

These reduced tensions are entered as the allowable tensions, and the payloads are determined as before. If the turns were to be brought toward the yarder, the load factors would be calculated normally and not reversed. The results for the load factors and payloads are:

Load factors Pay loads Terrain point 8 u h iJ,(T,! WniT,) U",(Ts)

Yarderposition aboue. With the yarder at T.P. 3 and the 4 -0.60 0.50 0.00 31247.58 44503.18

tailhold at T*P. 10, use the profile data of Figure 6A. If the logs were to be moved toward T.P. 3, no modifications These results show that a payload of 31247.58 Ib is possible would be required to the inputs. without exceeding the allowable tensions. This is 3.68 times

the payload determined with a full suspension analysis.. If however, the turns were brought toward T.P. 10 (away from the yarder), the load factors will be different, because If the log was moved away from the yarder, then the load a different ground slope is specified. Then the sign of each factors will be different, because of the difference in spec- factor, h, will need to be reversed after it has been calculated. ified ground slope. In addition, the sign of the load factor, The change in sign of h is the only modification required. h, would need to be reversed. The results for both the load The results are: factors and payloads are :

Load factors Pay loads "remb'n point 0 v h Wn(Tld wn(T3f wn('41

These results show that the system can carry a load of 32554.14 lb without exceeding the allowable tensions. These results indicate that a payload capability of 13002.63 This is 3.56 times the payload determined by full suspension Ib. can be expected, which is 1.53 times the payload found analysis. Note that the system is haulback limited. with a full suspension analysis.

Ljterature Cited

Binkley , Virgil W., and John Sessions. Carson, Ward W. (n.d.1. Chain and board handbook for skyline tension 1976. Determination of skyline load capability with a and deflection. USDA For. Sew., Pae. Northwest Reg. programmable pocket calculator. USDA For. Serv. Res. Portland, Oreg., 191 p. Pap. PNW-205. 11 p.

Carson, Ward W. Lysons, Hilton H., and Charles N. Mann. 1975. Analysis of running skyline with drag. USDA For. 1967. Skyline tension and deflection handbook. USDA Serv. Res. Pap. PNW-193. 8 p. For. Serv. Res. Pap. PNW-39. 41 p.

Appendix. 1 Standing Skyline -- Length and Load Path

- - - - -- -

Conltibulor's Name D- F@k--- _ - -- Dgce: Sgpt-. 1979

Address Fogest Engineering Researek, NE - - - - - - - -- -- --- - - -

- -

inputs more consistent with field data, to calcuPate a skyline length without the

u s e of a secondary progrm, and to provide outputs that allow f o r payload analyses - -

that include t he e f f e c t o f partial s u s p e n s i o n . - -- -- - - - -

- a - -

X T ~ YT = X and U coordinates of tailhold (ft) - - - -

XL, Yl, = X and '9 c o o r d i n a t e s of load paint ift)

Operating Limits and Warnings

- - - - --

- - -

--- - --

- - -- - -

--- - - -

-- --

-- - - - - - - -- - -- - - - - - -

Cclnlriilaulor% Hame - - -- -- - - - - - . - - - --

Adr(9w - -- -- -- --- - - -- -

L, = s k y l i n e length with hL as J-ozid clearance (ft)

d = horizontal distance, yarder - to - load p o i n t (ft)

yc = load clearance with So as skyline l e n g t h ift) - - - - -- - - - - - - -- -- - -

a1 = skyline weight -- ( I b / f t ) - - -- - - --

T3 = skyline allowable tension - (Jb) - -

So = ~ " s t r e t c h e d skyline length (ft)

-- - --

-- - --

- - -- -- -- - -- - - -A - - - - -- - --

- - - - - - - --

- - - -- -- -- -- - - - - --

- -- - - - - - --

- - -- -- -- - - - - -- -- --

- - - - - - - -- -- - - - - - - -

- - - - - - - -

Operaflng Limits and Warnings - - - - - - - - - - - -

- - -- - - -- -- -- - - -- -- --

- - - - - - - -- -- -

-- --- - - - - - - - - - - - -- -- - ---.

-- - - - - -- -- - - -- - p~

- - -- - - ---

ST,DING SKYLINE--,,,, AND LOAD PATH

in Yy arid store Xy and Y,

and store XL and YL -- - - -

- -- tep LO for each "suspected"t terra in point - - --- - - - - - -

u r t i l satisfied that t h e shcr tes t

s been found (Each Ls and d ca lcu la te - -- - - - -

wr~tten down E 3 r l a t e r use.)

y in YL ane calculate yc - -- - - -- --

Coztlnue to repeat steps 12 and 13 u n t i -- -- - - - - - - - - - -. arid j7 have k e n foucd for cach der , i r -- --

i e r ra rn ~ O I L ~ , (Each of trese -\-i-alires ' -- -- - - - - -- - --- --A

a l s o be rziritter: down for later JW,) -- - -- - - - -- --

eters, for use in the "

-s~ension ;;ayToac? 111" program,) -

The program is illustrated by determining the geometry parameten for a standing skyline for the following profile: a 55-foot yarder spar at T.P. 1, a 10-foot tailtree at T.P. 7, and a 12-foot minimum Load clearance,

P"errain point X Coord Y Coord

The first step is to determine L, for each load point that may limit the skyline length. Teurain points 2 to 6, inclusive will be examined to illustrate the procedure.

Key in Xy = 0.0 and Enter f Key in PI, =. 5000.0 and fA Key in X, = 1093.2 and Enter ?' Key in UT = 4784.2 and fB k y in XL = 156.2 and Enter ?; Key in UL = 4875.1 and fC Key in hy = 55 and Enter f Key in h, = 10 and Enter ?' b y in hL = el2 and fD Key fE. The calculator should Bash E, = 1170.92, and then display d = 156.20. 'Tkese are the s7alues at T.P. 2 since the input values of XL and YL were for that tenain point.

The values of L, and d are found for the remaining terrain points by inputting XL and YL for each termin point (Key fC) and calculating the desired parameters (Key -f@) as folIows : Key XL = 357.4 and Enter 1' Key YL = 4774.4 and f 6 Key fE. The crtlcuiator should flash L, = 1182.92, and then display d = 351.40, These are the values for T.P. 3.

The procedure is repeated for each terrain point that may limit the skyline length. The values for the remaining temain points, along with the appropriate inputs, are:

Terrain Inp u ts Outpub

point XL YL s d

Since the shortest L, is 1170.92, input that value as 3,. After it is input calculate the cable geometry. Key in% = 1170.92 and A. Key in d = 156.20 and B. The cafculator should display y = 167.91. Key in Uy = 4875.10 and 6. The calculator should display Y, = 11.99. These are the values of y and U, for T,P. 2 since the input values of d and Uy were the values for the ternrain point. Note that the actual-clearance should have been 12.00. The difference is a result of rounding emor,

The values of y and y, are found for the remaining terrain points by inputting d and calculating y (Key B) and then inputting YL and calculating y,fKey 6) as follows: Key d -- 357.40 and B. The calculator should display y = 247.99. Key 'UL = 4774.40 and 6. The calculator should display y, = 32.61. These are the values for T.P. 3. Note: If the distance parameter, d, was not detemined previously, it can be determined manually by d = XL - X y ., It will then be in the X register ready to be input (Key B) as above.

The procedure is repeated for each terpain point for which payload capability is to be determined. The values for the remaining tevrain points, along with the approp~ate inputs, are :

Terrain point d Y y~ y~

In addition to detemining the cable geometv parameters above, the distance and height parameter, L and E, can also be detemined any time after the first trial L, value has been determined. This is dope by keying Key E. Key E. The calculator should first flash L = 10931.20 and then display E = 260.80.

Also, it may be desired to know the unstretehed skyline Key wl = 1.85 and Enter 7" length, So, given the allowable tension and line weight. I f Key TI = 34500 and I). The calculator should display the allowable tension (TI J is 34500 Ib and the weight (ul ) S, = 1164.76. i s 1.85, then So is found as follows:

Append& 2 &"&id Suspension Load Factors

ontrlbutor's Name Gary '. Fa'k Date: Sept. _ 1979

the effects of partial suspension, It nay also be used to deternine the required

carriage-to-ground clearance for a specified leg-to-ground clearance.

The ~;arm~eters are :

t = frictional coe f f i c i en t

1% = log length (ftl - measured from choker to end of log

LC = choker Length (ft) exc lud ing m o u n t to go around Log

yc = carriage clearanze (ft)

- - -

PARTIAL SUSPENSION LOAD FAGIV)IIS

The grogvam is illustrated by finding the partial suspension Key in B = 0.30 and C. load factors for terrain points 2 t o 6, inclusive, of the foEollow- Key in yc = 32.61 and D. The calculator should flash v = ing profile: friction coefficient, p = 0.60, Iog length, l g = 0.81 and then display h = 0.21. These are the factors for 33 f t , and a choker length, 1, = 1 2 ft. T.P. 3 .

The procedure is repeated for each load point for which the load factors are to be determined. The load factors for the remaining terrain points, along with the appropriate inputs, are given below :

Inp u ls Te n-r~ l n Ou t p u f s

point 0 Y e L' h

5

it should be emphasized that the ground slope t o be specified for a particular load point is in the direction opposik that in which the log turn is do be moved. Also, the ground slope is positive if id is moved uphill, negative if it is moved downhill. For example, if T.P. 3 is t o be examined, a ground slope of +830 should be specified if the turn is brought toward T.P, 1. However, a ground slope of -0.50 would be specified i f the turn is brought toward T.P. 7 .

The first step is t o input the parameters tbat are common to all terrain points as follows:

Key in p = 0.60 and A

It is desirable t o view the load factors again without spellding the time necessary t o recalculate khem, simply Key fE. and the calculator will redisplay them.

Key fE. The calculator should first flash v = 0.50 and then display h = 0.02. These are the load factors for T.P. 6, which is the last terrain point examined.

This program also calculates the required carriage clearance for any combination of log and choker lengths, ground slopes, friction coefficients, and log-to-ground clearance. For example, t o determine what carriage clearance is required t o achieve a log-to-ground clearance of 1.5 ft for a log 40 ft long with a choker 1 6 ft long on a 25 percent ground slope, with a friction coefficient of 0.60--

Key in ,u = 0.60 and A

Key in lk = 35 and Enter Key in 1q = 40 and Enter 1' Key in 1, = 12 and B. The calculator is now ready t o cal- Key in l, = I 6 and B eulate the load f a e l o ~ .

Key in S - 0.25 and C.

T-P. 2 is the first to be examined. The inputs which follow Key in h , = 1.5 and E. The calculator should flash ye =

are for that terrain point. 12.81 and then flash v = 0.61 and then display h - 0.39.

Key in 6' = 0.50 and C.

Key in y, = 11.99 and D. The caiculator should flash v =

0.75 and then display h = 0.39. The iterative routine used to calculate v and h will normally take about 1. minute to complete. It may be somewhat shorter or longer depending on the inputs.

The Ioad factors for each successive terrain point is calculated by inputting 0 (Key C) and then inputting ye and calculating the Load factors (Key D) as follows:

For a ground slope of 50 percent

Key in f3 = 0.50 and C.

Key in h , = 1.5 and E. The calculator should flash yc =

11.32 and then flash v = 0.73 and then display h = 0.42.

It should be emphasized that h , is the vertical clearance to the grou~ld, and that the sign convention for the ground slope is positive for a log moving uphill and negative for a long rnoving downhill.

For negative ground slopes that are larger in magnitude than result. If the factors for a situation such as this are desired, the friction coefficient, negative values of h will result. If enter a vdue s f ground slope just slightly lilrger in magnitude the friction coefficient is equal in magnitude to the negative than the friction eoeffieient and this will allow the load fae- slope, division by zero will be attempted and an enor will tors to be determined.

Mpendix 3 Padid Suspension Payload III

- -

Contributor'sHame Gary D, Fa lk Address F o r e s t Engineer ing &sea rch , NE

s k y l i n e systems f o r maximum payload c a p a b i l i t y based on s p e c i f i e d allowable Line

t e n s i o n s . Also, hecause it includes t h e e f f e c t s of e i t h e r a mainline or haulback -

t h i s one program i n c l u d i n g downhi l l yard ing s i t u a t i o n s , Although it was p r i m a r i l y

a n a l y s e s can be done wi th it.

?he i n p u t parameters a r e desc r ibed as follows: (See accompanying f i g u r e ]

T3 = a l lowab le ma in l ine t e n s i o n a t yarder

w3 = main l ine w e i g h t p e r u n i t l e n g t h

(mainl ine + s l a c k p u l l i n g l i n e weight fo r running skylines)

Tk = a l lowab le haulback t e n s i o n ( l i v e and standing s k y l i n e s )

u 4 = h a u l h c k weight Per u n i t length ( l i v e and s t a r t d ing skylines)

f = 1 f o r f i v e and s t and ing s k y l i n e s

2 f o r running s k y l i n e s

W, = c a r r i a g e weight

T t = a l lowab le s k y l i n e t e n s i o n a t yarder

Operating Limits and warnings The ya rde r 1s assumed to be on t h e l e f t with i n c r e a s i n g

s t a t i o n i n g t o t h e r i g h t whether uphill o r downhill. yard ing . Increased payloads

by us ing both t h e ma in l ine and haulback s imu l t aneous ly i s not considered, I f

e i t h e r a ma in l ine o r a haulback i s n o t used on t h e system being analyzed, "dumy"

Program Bescriptism, Ecgualions, Variables

X Y F ~ y , hy = X and Y coordinates of yarder l oca t ion and yarder spar height .

X T t - Y T ~ hT = X and Y coordinates of t a i l h o l d location and height .

XL, YLF h~ = X and Y coordinates of load po in t and load clearance.

L = hor izonta l distance, yardex t o tailhold

d = horizontal distance, yarder to Load po in t

y = vertical distance, top of yarder t o load p o i n t

v = vertical p a r t i a l suspension load factor -

h = horizontal partial suspension Load factor

Operating Limits and Warnings -- - - . -

- - - - a -- - --

A

- - -

- -

Xy +Yy thy X T + U ~ + . ~ ~ X L f U L f h ~ "TW, (TI 1 *n (T3 ,,)

pARTI;4i SUSPENSION PAYLOAD (LIT)

in w3 and E n t e r ?

--

in Wc and E n t e r t - -

" L and Enter + - - - -- - - - - -- --

3. Calcuia I 6

ser t h a t a haulback is r

rrnined by s tep 15. -- step 14, the dz

n t h i s ease Step 15 is skipped.

nst ruct ions

in ul- and B. --

and E n t e r 4

I f A '

Calculate WE IT2) or Wn ( T ~ ) -----

steps 19, 20, and 21, are s u b s t i t u t e d for - - - - ------

, L 5 , and L6. -- ---

The program is illustrated by calculating the payload capability for t e ~ a i n points 2 to 6, inclusive, of the fallowing profile for a running, live, and standing skyline. Et should be mentioned that in order to illustrate the use of the program in as. short example, the profile data used result in values that are wmewhat atypical

Terrain point X Goord Y Coord

Live Skyline

The foL10wing yarder speeificatisns are given.

T3 = 13706 1b f = I ~ 3 3 = 0,72 BbIEt W, - 100 1b T4 =: None TI - 34580 1b u4 = None w E = 135 lib!ft 'dai-der location: T.P, l9 la, - 55 %t Tailhold location: T.P. 7 , hT - 10 f d Minimum load clearance: hL - 12 R

Option 2 is normally the more efficient option to use for both the live and running skyline because it uses the reduced profile data directly. The first step is to input the yarder speciicreatisns, and use ""dmmy" values for the missing haulback line.

Key in T3 =. 13700 and Enter "r Key in a 3 = 0.12 and Enter 1' Key in T4 - l and Enter f Key in = I and A Key in if = I. and Enter t Key in W, = '700 and Enter Z' Key in TI =: 34500 and Enter 1' Key in wl = "P85 and B.

The yarder and d ~ l h o l d Iseations and heights are input after the yarder specifications.

Key in Xy =I 0"0 and Enter t Key in Yy = 5080-0 and Enter 1' Key in k, = 55 and 68 Key in XT = 1093-2 and Enter ? Key in Y,, = 4784.2 and Enter f Key in hT - 10 and $Be The cable geometry parameters3 L and E, are caleuhated and stored in the correct registers, They can be recalled from storage registers B and 2, respectively,

The calculator is now ready to begin to calculate the slow- able payloads for each desired terrain point, 'k-Pa 2 will be examined firsst. The inputs which follow are the values for that terrain point.

Key in XL = 156.2 and Enter "r Key in YL = 4875.1 and Enter ?

Key in h, - E2and EC

Key in v -- 0.75 and Enter "1'

Key in h = 0.313 and E, The ealeu%ator should display W,(TI ) - 94433.148

Key fE, The calculator should display W,bT3 1 = 18108.71. These are the mmimum payloads at this point based on the allowable tensions in the respective cables.

The payloads for the remaining terrain paints are caleu&aked by inputting the X and Y coordinates of the load point and the load clearance (Key fC), then inputting the load factcars and calculating W,(Tl ) (Key E) (or Key f D , as ilius"krated later), and then calculating W,(T3), {or FV,(T4 i, as shown later) (Key fE). This is shown for 3 as follow:

Key in XL = 357,4 and Enter?

Key in YL -- 4774.4 and Enter ":

Key in hL - P2and f@

Key in v - 0.66 and Enter "r

Key in h - 0,38 and E, The caleuBator should display W = 63994,5%.

Key fE, The calculator should display W, (T3 ) - 221 80.32- The procedure is repeated for each load point for which capability is to be determined. The values for the remaining terrain points, along with the appropriate inputs are shown as follows:

lnpu ts Terrain OU $ M OS

point XL YL kL h WnjT1.? Fnji;"si

Running Skyline

The running skyline procedure is essentially the same as the live skyline procedure. The differences are in the yarder specification inputs and, of course, the outputs. The following yarder specifications are given:

Ti = 34500 1b f = 2 ~3 = 3-70 IbiEt Wc = '700 1b Ts = Kone TI = 34500 Lb ci;,; = None mi = 1.85 ib,'ft Uarder location: T.P. 1, h , = 55 f t Tailhold location: T.P. 7, hT - 1 0 f t Minimum load clearance: h L = 1 2 ft

As stated hefore, option 2 is the more efficient option to use for the running skyline. The first step is to input the yarder specifications, and be certain to input "dummy9' values far the missing line.

Key in T3 = 34500 and Enter ': Key in w3 = 3.70 and Enter '! Key in T4 - 1 and Enter 2' Key in u4 = I and A Key in f = 2 and Enter ? Key in W, = 700 and Enter t Key in Ti = 34500 and Enter 4' Key in u,.; - 1.85 and B,

The yarder and tailbold locations and heights are input after the yarder speeif"ications.

Key in X, = 0.0 and Enter ? Key in Y, = 5000.0 and Enter f Key in I?, = 55 and fA Key in Xr, - 1093.2 and Enter ? Key in Y,, = 4784.2 and Enter ? Key in hT = 10 and fB. The cable geometry parameters, L and E, are eaieulated and stored in the correct registers. They may be viewed by recalling them from registers 1 and 2, respectively.

The calculator is now ready to begin to calculate the allowable payloads for each desired terrain point. T.P. 2 svill be examined first. The inputs which follow are for that terrain point.

Key in XI, = 156.2 and Enter 1" Key in UL = 4875.1 and Enter ?

Key in hL = 12 and EC.

Key in v = 0.75 and Enter f Key and h = 13.39 and E. The calculator should display Wn (TI ) = 190838.15.

Keq' fE. The calcuIator should display Wn(T3 j = 36370.36. These are the maximum payloads at T.P.2 based on the allowable tensions in the respective cables.

The payloads for the remaining terrain points are calculated by inputting the X and Y coordinates of the load point and the load clearance (fC), then inputting the load factors and calculating %(TI (Key E), and then calcuiating W,/T3 ) (Key fE). This is shown for T.P. 3 as follows:

Key in XL = 351.4 and Enter T

Key in UL = 4774.4 and Enter ?

Key in h, = 12 and fC.

Key in v = 0.66 and Enter ?

Key in h = 0.38 and E. The calculator should display

W n ( ~ j ) = 129609.04.

Key in fE. The calculator should display ( T I ) = 37930.77.

The procedure is repeated for each load point for which capability is to be determined. The values for the remaining tenain points, along with the appropriate inputs are shown as follows:

lnpu ts Outputs Terra in point

XI, YL 4' L" h wn{Tl) WnC7"3)

Standing Skyline

The same yarder specifications as those used for the live skyline example will be used for this example. In addition, a haulback line will be specified.

T3 = 13700 1b W, = 500 1b b j 3 = 0.12 lbift TI = 34500 1b T4 = 8900 1b w , = 1.85 1b/ft ws ' 0.46 1b;ft Uarder Iocation : T.P. I , h = 55 ft Tailhold location: T.P. 7. hT = 10 ft

In addition to the above data, the following inputs will be used because they have been previously determined with the ""Sanding Skyline-Length and Load Path 'bnd 'Tartial Suspension Load Factors '~rograms.

Because the cable geometry parameters L, E, d, and y have been previously determined, option 1 is the more convenient option to use for the standing skyline. m e first step is to input the yarder specifications.

Key in T3 = 13100 and Enter l' Key in w3 = 0.72 and Enter Key in T4 = 8900 and Enter l' Key in w4 = 0.46 and A Key in f = 1 and Enter f Key in W, = 700 and Enter 1' Key in TI = 34500 and Enter t Key in wl = 1.85 and B.

The cable geornetq parameters L and E are input next,

Key in L = 1093.20 and Enter 1' Key in E = 260.80 and C . The calculator is now ready to begin calculating payloads.

me payload at T.P. 6 is calculated first because it illustrates what happens when a haufback is required. The inputs which f01167w are the values for that terrain point.

Key in d = 917.90 and Enter f

Key in y - 339-62 and E)..

Key in v = 0.50 and Enter ?

Key in h = 0.02 and E. The calculator should display W,(T1 ) = 0.00. This means that a hauiback is required at this load point to maintain cadage stabifity. To calculate w, (TI):

Key f E). The calculator skould display W, (TI ) = 48028.95.

Key fE. The calculator should display W,(T4) = 3866150.98 It should be emphasized that the only time it is necessary to key fD to determine W,(TI ) is when the display from Key E is 0.00. The display from Key fE is W,(T4 ) when the 0.00 is displayed.

The basis for using this procedure is that it is often difficult to determine whether a mainline or haulback is necessary, especially for ""dwnhill" "rding under partial-suspension conditions. Payloads calculated by assuming that a mainline is used when a haulback is required are not valid and vice versa. This way the user not only has valid payloads, but also knows whether a mainline or haulback, or both, are required on a part;icular profile.

The payload for each load point for which capability is to be detemined is found by inputting d and y (Key D), then inputting the load factors and cdculating W,(TI ) (Key E) (or Key fd, as appropriate), and then calculating W,(T3 ) or W,(T4 ) (Key fE). This is shown for T.P. 5 as follows:

Key in d = 753.80 and Enter I'

Key in p = 332.75 and B.

Key in v - 1.00 and Enter Z' Key in h = 0.00 and E. The ctllculator should display W,(TI ) = 19625.66.

Key in fE. The calculator should display W, JT3 ) =

131099.13.

The procedure is repeated for each load point for which capability is t o be determined. The values for the remaining t e r r ~ n points are shown below:

Terrain point

ln the previous examples it was assumed that the user started out without ha.ping previously input any of the parameters. If previous correct values were input, it is not neeessam to re-enter them. This is particularly useful when going on to analyze another profile or changing the position of the yarder or tailhold or heights without changing yarder specifications. However, when at least one value, which is input with a particular key, is to be changed, all the values input with that key must be entered whether they change or not, For example, to increase the tailtree height to 20 feet without changing the Iocation, it would be necessary to reenter the location along with the changed height, If they aren" re-entered, erxoraeous values will be entered for its location, After changing any values, the load point (Key D or fG, whichever is appropriate) must be reentered as well, even if it does nod change. The load factors must always be input before Key E is used to calculate W,(T1 ).

Note, also, that the inputs with Keys A and B can be? made after the inputs with Keys fA and fB. This is so that E can be determined and adjustments made to the ailowable tensions of the yarder when it is below the tailhold. All other inputs should be made in the specified order or erroneous answers will result.

Appendix 4 Equations

Cable Geometry

Lice and running skyline. Given the coordinates and heights of the yarder, tailtree, and Isad point (Fig. I ) the cable geometry parameters L, E, d, and y are determined by the foilowin g equations:

L =a, x,) Qn.~,o) E = my + ky) --- (+l(cT + !IT) (1.a.o)

d '(Xr--XL) (1.3,O)

Standing skyline. The skyline Length that allows passage sf the carriage at exactly the required clearance at any tdal load point is:

where L, E, d, and p, are given by equation 1.1.0 through 4-4.0, respectively. The difference between y and y,, which are both giren by equation 1,4.0, i s that y, is only a ''trial'9 value for a standing skyline, The actual value of y is determined after the limiting skyline length (%) i s determined.

The skyline length given by equation 1-5-0 is the sum sf two straight line cable segments. The difference between this length and the more accurate catenary length is insignificant for cables tensioned to about one-third of their breaking strength, As a result of this simplifying assumption, the error is less than the emor that is introduced as a resultof temperature differentials*

The limiting skyline length, so, i s determined by using equation 1-5.0 $0 calculate L, for several points, and the shortest of these i s q. After the limiting skyline length is determined the following system of equations is used to solve for the cable geometry parameter, y,

V

where { = ( L ~ 4- E~

The sign of the radical in equation 1.6.2 is the same as the s ign of the elevation difference, E,

The log geomety is speciged for the sole purpose of determining the pa~ia l ; suspension load factors, which are given by the following equations:

sin0 + pease h = (2.2.0)

(eosB -psino) + kana (sin@ + pess0)

Before equations 2.1,a) and 2.2.6) can be solved the angle from the horizontal to the choker, a, must be known. This is done with an iterative procedure for the simultaneous solution sf equations 2,3,0 and 2-4-0.

eosB - y sin@ a = tan" [%an (8+@ + I (2.3.0)

sin0 -i- pcosB

Equation 2.3.0 is valid only if the ground-to-log angle, P, is greater than zero (Carson 1915). For yarding situations where this angle is zero, the choker angle can be determined directly from equation 2.5.6).

-1 Y G a = sin j-cos8 ) + 8 1,

The carriage clearance, yc, used in equations 2.4.8 and 2.5.0 for the live and mnning skyline is the same as the minimum required load clearance, hL. For the standing skyline, y, is taken to be equal to the variable load clearance, hL&given by equation 2-6.9).

h L f = (Y, +h, ) - (YL + y) jZh6.0)

where y is from equation 1.6.0.

The equations giving the load hetors, v and h, were gen- erated by assuming a homogenous, cylindrical column of negligible diameter to length ratio. The error intrsdueed is minimal compared to the uncertainty of the log" weight d i s t~bu t i sn , the leading end, the choker placement, and scale allowance for log length.

Payload Cdeulations

The payloads that will cause the tensions to reach the allowable finnit are given by the following systems of equations for running skylines and for live and standing skylines when a mainline is needed for carriage control.

Y W3

( v ~ + fv2 -a (H, - fH, ) W , z w,(T1) = (3.1.0)

Y [ V - (;) h l

The following expressions yield the payloads when a haulback is needed on live and standing skylines.

The value for the variable f is I for l ive and standing skylines, 2 for running skylines. Some of these equations are based on certain simplifying assumptions similar to the ""uigid link" analyses (Carson 19761, However, the errors involved for the vertical and horizontal forces are considerably less and the expressions are much easier to work with. The greatest error is introduced by equations 3.2.0 and 3.4.0 because they assume that the supporting line tension is at the speciEed allowable tension, but the supporting line "censisn may be considerably more or less. However, because only the angles at which they act are involved, the eursr is usually less than about 2 percent.

U.S. G O V E R I V M E N I P R i N T l N G OFFICE: 1981-703-01 1 / 7

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Contents - Home | US Forest Service€¦ · Desc~pdion of "Fi Figure 2.-Log geometry. The load-cawing capability of a cable logging system de- pends not only on the size and strength