cofe 2001 sessions chung

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2001 Council on Forest Engineering (COFE) Conference Proceedings: Appalachian Hardwoods: Managing Change

Snowshoe, July 15-18, 2001

Effect of Load Distribution and Trailer Geometry on the Gradeability of Short Log Tractor-

Trailer Combinations

John Sessions and Woodam Chung

Professor and Graduate Research Assistant, respectively, Department of Forest Engineering,

Oregon State University, 215 Peavy Hall, Corvallis, OR 97331

ABSTRACT - The use of cut-to-length systems has increased the use of short log tractor and trailers in the western United

States and elsewhere. The equations for uphill gradeability for a loaded short log tractor and trailer are derived and compared

to a loaded long log pole trailer. A sensitivity analysis shows the gradeability of the short log tractor and trailer is highly

affected by the load distribution and is also affected by the angle of the reach between the tractor and trailer.

INTRODUCTION

Roads in the western United States are often in mountainous

terrain. The road systems have been developed considering

the log truck with pole trailer. The use of cut-to-lengthsystems has increased the use of short log tractor and trailers

in the western United States and elsewhere. In this paper,

equations for uphill gradeability of a short log tractor and

trailer in loaded configurations are derived. The purpose of

these equations is to allow the user to analyze the limits of

truck performance under a variety of loading and road

conditions.

MODEL

The basic model for developing the gradeability equations is

the short log tractor and trailer combination. The short logtractor and trailer is a log truck that has a straight front bunk

for loading short logs and a trailer attached by a hitch point

(Figure 1). When performance of the loaded short log

tractor and trailer is evaluated, the reach from the trailer is

assumed to function as transferring tangential (parallel to

the road) and normal (perpendicular to the road) forces

depending upon angle of the reach. Connections between

the tractor and trailer are assumed pinned.

Figure 1. Configuration of a short log tractor and trailer

Maximum Gradeability

The following equations were derived to predict maximum

gradeability (P) for loaded log trucks in tractor-trailer

configurations:

where, P is the percent slope, representing the limit of

gradeability and other terms are as defined in Table 1.

Table 1. Nomenclature for a short log tractor and trailer

geometry and load distribution as used in Figure 2 and thegradeability equations, with sample values.

Symbol DescriptionSampleValue

W Weight of tractor plus short log load 35,000 lb

L Weight of trailer plus log load 45,000 lb

X1Distance from front axle to center ofgravity of tractor plus short log load

15.0 ft

X2 Distance from front axle to end of stinger 30.0 ft

X3 Wheel-base of tractor 22.0 ft

X4Distance between center of trailer tandemand center of gravity of the trailer pluslog load

10.0 ft

X5Distance between center of trailer tandemand reach

30.0 ft

X6 Wheel-base of trailer 20.0 ft

Y1Height to center of gravity of tractor plus

short log load3.5 ft

Y'2 Height to stinger or front bunk 4.0 ft

Y2Height to attached point of reach attrailer

4.0 ft

Y4Height to center of gravity of loaded

trailer7.0 ft

NF,ND,NTF,NTR

are the respective normal components ofthe axle loads

1223

3122

)tan'(tan1

)(

)()tan'(

tan1tan

yWxyLLWx

LWxxWxyL

tan100P [Eq.1]

[Eq.2]

19.8ft 4.3ft 4.3ft 4.3ft13.7ft 15.7ft


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TV,THare the normal and parallel forcestransferred to the tractor from the trailer

f coefficient of rolling resistance 0.02

coefficient of traction 0.4 is angle of the reach from the trailer 0

Figure 2. Geometry of a tractor with a straight front bunk

(part I) and trailer (part II) for sample

calculations. Nomenclature is defined in Table 1.

This function was derived by summing forces normal and

parallel to the road surface and summing moments. The

sums were then set equal to zero (Eq.3,4,6,7). For the trailer,

the moments were summed about the rear tandem (Eq.5).

For the tractor, the moments were summed about the front

wheels (Eq.8). Maximum usable thrust was calculated as theweight on the drive axles multiplied by the coefficient of

traction (Eq.9). Force parallel to the road surface, TH, was

assumed to be transmitted to the tractor through the reach

from the trailer and force normal to the road surface, TV,

was assumed to determined by the relation of TH and the

angle of the reach (Eq.10). This provided eight equations

with eight unknowns. This system of equations was solved

simultaneously to yield the equations listed above.

For the trailer,

For the tractor,

For the boundary conditions,

Once we know the gradeability of a log truck, we can alsoestimate normal forces at each axle (Eq. 13,14,15,16) as

well as normal and parallel forces transferred to the tractor

from the trailer (Eq.11,12).

APPLICATIONS

Given the vehicle illustrated in Figure 2, and the associated

data in Table 1, the equations presented in this paper can be

used to determine the maximum hill climbing ability of

loaded log trucks. For the example in which the coefficient

of traction is assumed to be 0.4 and the coefficient of rollingresistance is assumed to be 0.02, the maximum grade is

10.8%, when the reach from the trailer is parallel to the

ground.

Figure 3 illustrates the effect of different values of the

coefficient of traction on gradeability for the loaded truck

and trailer noted above. Figure 3 also illustrates some

observed ranges for coefficients of traction for three

surfaces that might be encountered on log hauling roads.

Figure 4 shows the change of gradeability with respect to W

0sincosL;0

sin;0

cos;0

64524

xNyLxTyTxM

NfNfLTF

NNLTF

TFVHa

TFTRHX

TFTRVY

0cossin';0

sin;0

cos;0

11223

xWyWyTxTxNM

WNfNfTTF

WNNTF

HVDb

TFTRHX

FDVY

H

V

D

T

T

NT

tan

f

LNfTN

x

xTyLyTxLN

NTwheref

WTNfTN

fTWTWfN

TT

f

LfLT

TFHTR

VHTF

DHD

F

VHD

HV

H

sin

sincos

,sin

sincos

tan

1tan

sincos

6

5424

TH

RTR

NTR

X6

X4

X5

TV

Y2Lsin

Lcos

RTF

NTF

Y4

Part II

a

Part I

RD

RF

ND

NF

X2

X1X3

TH

TVY'2

Wsin

Wcos

Y1

T

b

[Eq.3]

[Eq.4]

[Eq.5]

[Eq.6]

[Eq.7]

[Eq.8]

[Eq.9]

[Eq.10]

[Eq.11]

[Eq.12]

[Eq.13]

[Eq.14]

[Eq.15]

[Eq.16]


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and L, weights of tractor plus short log load and trailer plus

its log load, respectively.

Figure 3. Change of gradeability with respect to coefficient

of traction for the short log truck and trailer with

sample values

Figure 4. Change of gradeability with respect to weight oftractor and trailer with loads for the example truck

with = 0.4

Figure 5 illustrates the gradeability of a log truck is

proportional to the angle of the reach from the trailer. It

illustrates the effect of the angle of the reach on a normal

force at the drive axles, which in turn affects the amount of

potential thrust of the tractor. A negative value of the angle

in Figure 5 means the location of the trailer hitch point is

lower than that of the trailer reach, which has negative effect

on gradeability.

The results were compared with the estimated gradeability

of a log truck with a pole trailer. The equations derived by

Sessions et al.(1986) were used. Figure 6 describes the

gradeability of a short log tractor and trailer is less than that

of a log truck with a pole trailer because of a lower

proportion of the total weight on the driving axles.

Figure 5. Effect of the reach angle on gradeability for the

short log truck and trailer with sample values ( =0.4)

Figure 6. Comparison of gradeability between a typical log

truck with a pole trailer and a short log tractor and

trailer with sample values ( = 0.4)

CONCLUDING COMMENTS

The equations presented can be useful in predicting shortlog tractor and trailer uphill gradeability in nonturning

motion under conditions of constant velocity. Similar

relationships can be derived the down hill gradeability

considering maximum gradeability limited by engine brakes

for sustained grades (powered axles) or a combination of

engine brakes and service brakes.

REFERENCES

Clark, M. 1986. Cost and productivity of a dual load

quadaxle trailer. FERIC. TR-70. 18p.

Dykstra, D.P. and J.J. Garland. 1978. Log Trucking inOregon - a Survey. The Transactions of the American

Society of Agricultural Engineers. 21(4): 628-632p.

Sessions, J and et al. 1986. Calculating the Maximum grade

a log truck can climb. The western journal of applied

forestry. 1(2): 43-45p.

Sessions, J. and John Balcom. 1989. Determining maximum

allowable weights for highway vehicles. Forest

Products Journal. 39(2): 49-52p.

10000

20000

30000

40000

50000

60000

70000

10000

25000

40000

55000

70000

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

22%

24%

Gradeability

L (lb)

W (lb)

9.0%

9.5%

10.0%

10.5%

11.0%

11.5%

12.0%

12.5%

13.0%

Gradeability

0%

5%

10%

15%

20%

25%

30%

0.2 0.3 0.4 0.5 0.6

Coefficient of Traction

Gra

deability

A short log tractor and trailer

A log truck with a pole trailer

cofe 2001 sessions chung

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