January 18, 1999
Problem Set 2: Curve Widening
Objective:
1. Find (using formula from USFS Road Design Handbook and Curve Widening Program) the required curve widening for the following vehicle type:
Tractor/Lowboy with standard D8L-Cat.
Tractor/Lowboy with Cat 245 Excavator.
Self-propelled Skagit T-90 yarder.
Log truck with 15 foot stinger carrying 90 foot poles.
Calculate the length of reach to distribute weight of the poles (total load) evenly over axles. Use large end diameter = 36 inches, small end diameter = 27 inches (truncated cone).
2. Find required cut-slope ratio needed to let vehicles pass on switchback.
Equations:
From the USFS Road Design Handbook, the following equations where obtained necessary for calculating the required curve widening:
(Eq. 1)
Where:
CW = Curve Widening (ft).
R = Centerline radius (ft).
I = Central angle (degrees).
L = Length of tractor plus trailor (ft).
For a lowboy or standard tractor trailer:
(Eq. 2)
Where:
L1 = Wheel base of the tractor (ft).
L2 = Distance from the fifth wheel to the middle of the rear duals for the first trailer (ft).
L3 = Distance from the fifth wheel to the middle of the rear duals for the second trailer (ft).
For a stinger type log truck:
(Eq. 3)
Where:
L1 = Wheel base of the tractor (ft).
L2 = Length of the stinger measured from the middle of the tractor rear duals to the end of the stinger (ft).
L3 = Bunk to bunk distance minus the length of the stinger (ft).
For cut-slope ratio of any vehicle type:
(Eq. 4)
Where:
CS = Cut-slope ratio
Run = Horizontal overhang (can be either in front or rear of vehicle).
Rise = Vertical distance from ground to top of object of overhang.
Determination of the center of gravity for the specified log being hauled by the logging truck was found using the following equation:
(Eq. 5)
Basic statics equations:
(Eq. 6)
(Eq. 7)
(Eq.8)
Procedure/Results:
Before any calculations could be performed, vehicle specifications were researched (see Table1).
Table 1
|
Vehicle |
Wt. (lbs.) |
Truck/Trailer |
L1 |
L2 |
L3 |
|
D8L – Cat |
82 243 |
Lowboy (7 axle) |
17 |
16.83 |
48.74 |
|
245 Excavator – Cat |
144 941 |
Lowboy (9 axle) |
17 |
16.83 |
48.74 |
|
T-90 Yarder – Skagit |
126 800 |
Lowboy (9 axle) |
14 |
0 |
0 |
|
Log Truck w/stinger |
30 000 |
Standard (5 axle) |
15 |
15 |
55 |
From the data listed in Table 1, the amount of curve widening could be determined. Calculations were made using a spreadsheet created in Microsoft Excel. Table 2 illustrates a summary of the curve widening results based on the data listed in Table 1 for a curve radius of 55 feet and a central angle of 50 degrees.
Table 2: R=55 ft and I=50 degrees
|
Vehicle |
L (ft) |
CW (ft) |
MLW (ft) |
|
D8L – Cat |
54.29 |
19.38 |
31.38 |
|
245 Excavator – Cat |
54.29 |
19.38 |
31.38 |
|
T-90 Yarder – Skagit |
14.00 |
1.72 |
13.72 |
|
Log Truck w/stinger |
55.00 |
22.76 |
34.76 |
Table 3 illustrates a summary of the curve widening results based on the data listed in Table 1 for a curve radius of 60 feet and a central angle of 180 degrees (switchback type curve).
Table 3: R=60 and I=180 degrees
|
Vehicle |
L (ft) |
CW (ft) |
MLW (ft) |
|
D8L – Cat |
54.29 |
32.30 |
44.30 |
|
245 Excavator – Cat |
54.29 |
32.30 |
44.30 |
|
T-90 Yarder – Skagit |
14.00 |
1.66 |
13.66 |
|
Log Truck w/stinger |
55.00 |
33.67 |
45.67 |
In order to determine the required cut-slope ratio needed to let vehicles pass on the switchback, the amount of overhang (OH) and the height (HT) from the ground to the object that is in front or behind the vehicle had to first be researched. Table 4 lists the overhang for a log truck with 90 foot poles and the amount of overhang for the yarder due to its boom geometry. The reason why the bulldozer and excavator are not listed in Table 4 is because they both sit on a trailer with no overhang.
Table 4
|
Vehicle |
OH (ft) |
HT (ft) |
|
T-90 Yarder – Skagit |
32 |
14 |
|
Log Truck w/stinger |
18 |
5 |
With the data in Table 4 and the Microsoft Excel spreadsheet, the cut-slope ratio required for safe passage could be determined (see Table 5).
Table 5: R=60 and I=180 degrees
|
Vehicle |
Cut-slope Ratio (Run : Rise) |
|
T-90 Yarder – Skagit |
1 : ½ |
|
Log Truck w/stinger |
1 : 2/7 |
In order to determine L3 for the logging truck, the dimensions of the logs being hauled were given, and axle loads and the weight of the logs being hauled were found using required highway specifications. Table 6 lists the data used in determining the center of gravity for the load of logs and the axle loads.
Table 6
|
Description |
Specification |
|
Max. on Highway Weight |
80 000 lbs |
|
Weight of truck/trailer |
30 000 lbs |
|
Weight of logs |
50 000 lbs |
|
Diameter of log at butt end |
36 in |
|
Diameter of log at tip |
27 in |
|
Log length |
90 ft |
Next, a free body diagram was drawn for the truck and trailer (see Figure 1).
Flog
R1 R2
With the free body diagram and the use of equations 5 through 8, L3 was calculated to be 47 feet. From L3, the amount of overhang was determined to be 18 feet.
References:
US Forest Service: Road Preconstruction Handbook
Caterpillar Performance Handbook: Edition 28
Download the Excel file used for calculations: PS2.xls