Chapter 9

Mobile Equipment Power Requirement

9.1. Estimating Equipment Travel Time

In calculating the time required for a haul unit to make one complete cycle, it is customary to break the
cycle down into fixed time and variable time.

cycle time = fixed time + variable time

Where:
 Fixed time represents those components of cycle time other than travel time. It includes spot time
(moving the unit into position to begin loading), load time, maneuver time, and dump time.
 Variable time represents the travel time required for a unit to haul material to the unloading site and
return.

9.2. Factors Affecting Travel Time

 Vehicle’s weight and power
 Condition of the haul road
 Grades encountered
 Altitude above sea level

9.3. Required Power

Required power is the power needed to overcome resisting forces and cause machine motion. The
magnitude of resisting forces establishes this power requirement.

 Forces resisting the movement of mobile

a) Rolling Resistance
Rolling resistance is the resistance of the equipment operating surface to the forward or reverse
movement of a piece of wheeled equipment. It is primarily due internal friction of the wheel bearing,
tire flexing and penetration of the travel surface due to the pressure of the tires.

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 rolling resistance factor = 20 + 6  penetration  Where:

Frr =  weight of vehicle  rolling resistance factor  Penetration is in cm

Rolling resistance factor is in kg/metric ton
Weight of vehicle is in metric ton
Frr = resisting force cause by rolling
resistance in kg

Typical values of rolling resistance factor

Type of Surface Rolling Resistance Factor (kg/t)
Concrete or asphalt 20 (15)*
Firm, smooth, flexing slightlyunder load 32 (26)*
Rutted dirt roadway, 1-2 in. penetration 50
Soft, rutted dirt, 3-4 in. penetration 75
Loose sand or gravel 100
Soft, muddy, deeply rutted 150-200
*Values in parentheses are for radial tires

Note:
 Crawler tractors are usually considered to have no rolling resistance when calculating vehicle
resistance and performance since crawler tractors may be thought of as traveling over a road
created by their own tracks.
 Although a crawler tractor is considered to have no rolling resistance, when it tows a wheeled
vehicle (such as a scraper or compactor), the rolling resistance of the towed vehicle must be
considered in calculating the total resistance of the combination.

b) Grade Resistance
Grade resistance is the force due to gravity that a piece of equipment must overcome when
moving up a grade. It represents that component of vehicle weight which acts parallel to an inclined
surface. When the equipment moves down a grade, the force of gravity that assists the movement is
called grade assistance.

grade resistance factor  kg t  = 10  grade in % Where:

Fgr =  weight of vehicle  grade resistance factor  grade resistance factor is in

kg/metric ton
Fgr =  vehicle weight in kg  grade in decimal  Weight of vehicle is in metric ton
resisting force cause by grade
resistance in kg
Note:
 When the vehicle is traveling up a grade, grade resistance is positive
 When the vehicle is traveling downhill, grade resistance is negative

To determine the maximum speed of a vehicle in a specific situation, it is necessary to determine the
total force resistance to movement of the vehicle. The resistance that a vehicle encounters in traveling over
a surface are the rolling resistance and grade resistance. The required power is the power necessary to
overcome the total resistance to vehicle movement, which is the of rolling and grade resistance.

Fr = Frr + Fgr

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9.4. Effective Grade
The total resistance to movement of a vehicle (the sum of its rolling resistance and grade resistance)
expressed as a grade (%), which would have a grade resistance equivalent to the total resistance actually
encountered.

effective grade  %  = grade in % 

 rolling resistance factor in kg t 
10

9. 5. Effect of Altitude
All internal combustion engines lose power as their elevation above sea level increase because of the
decrease in density of air at higher elevations. Manufacturers use a derating factor to express percentage
of reduction in rated vehicle power at various altitudes. However, when derating tables are not available,
the derating factor obtained by the use of the equation below is sufficiently accurate for estimating the
performance of naturally aspirated engines.

derating factor  %  =
 altitude in meter   915
102
rated power available  % = 100 - derating factor

9.6. Effect of Traction

Rimpull refers to the pull available at the rim of the driving wheels under rated conditions to move the
wheel vehicle and its load. It also refers to the power available at the surface of the tires.
Drawbar pull is the power available at the hitch of a crawler tractor operating under standard
conditions.
Another factor limiting the usable power of a vehicle is the maximum traction that can be developed
between the driving wheels or tracks and the road surface. Traction depends on the coefficient of traction
and the weight on the drivers. This represents the maximum pull that a vehicle can develop, regardless of
vehicle horsepower.

maximun usable pull =  coefficient of traction  gross vehicle weight 

Typical values of coefficient of traction

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 Type of Surface Rubber Tires Tracks
Concrete, dry 0.90 0.45
Concrete, wet 0.80 0.45
Earth or clay loam, dry 0.60 0.90
Earth or clay loam, wet 0.45 0.70
Gravel, loose 0.35 0.50
Quarry pit 0.65 0.55
Sand, dry, loose 0.25 0.30
Sand, wet 0.40 0.50
Snow, packed 0.20 0.25
Ice 0.10 0.15

9.7. Use of Performance and Retarder Curves

Crawler tractors may be equipped with direct-drive (manual gearshift) transmissions. The drawbar pull
and travel speed of this type of transmission are determined by the gear selected. For other types of
transmissions, manufacturers usually present the speed versus pull characteristics of their equipment in the
form of performance and retarder charts.

 A performance chart indicates the maximum speed that a vehicle can maintain under rated
conditions while overcoming a specified total resistance.
 A retarder chart indicates the maximum speed at which a vehicle can descend a slope when the total
resistance is negative without using brakes.

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Steps in using the chart:
1. Calculate the required pull or total resistance of the vehicle and its load in kilogram.
2. Enter the chart on the vertical scale with the required pull and move horizontally until you intersect one
or more gear performance curves.
3. Drop vertically from the point of intersection to the horizontal scale. The value found represents the
maximum speed that the vehicle can maintain while developing the specified pull.

Note: When the horizontal line of required pull intersects two or more curves for different gears, use the
point farthest to the right, because this represents the maximum speed of the vehicle under the given
conditions.

Figure below represents a more complex performance curve of the type frequently used by the
manufacturers of the tractor-scrapers, and wagons. In addition to curves of speed versus pull, this type of
chart provides a graphical method for calculating the required pull (total resistance).

Steps:
1. Enter the top scale at the actual weight of the vehicle (empty or loaded as applicable).
2. Drop vertically until you intersect the diagonal line corresponding to the percent total resistance (or
effective grade), interpolating as necessary.
3. From this point, move horizontally until you intersect one or more performance curves. From the
point of intersection, drop vertically to find the maximum vehicle speed.

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When the altitude adjustment is required, the procedure is modified slightly.
1. Start with the gross weight on the top scale and drop vertically until you intersect the total resistance
curve.
2. Move horizontally all the way to the left scale to read the required pull corresponding to vehicle
weight and effective grade.
3. Divide the required pull by the quantity “1-derating factor” to obtain an adjusted required pull.
4. From the adjusted value of required pull on the left scale move horizontally to intersect one or more
gear curves and drop vertically to find the maximum vehicle speed.

The retarder curve (figure shown below) is read in the same manner similar to the performance curve.
Remember however that in this case, the vertical scale represents negative total resistance. After finding
the intersection of the vehicle weight with effective grade, move horizontally until you intersect the retarder
curve. Drop vertically from this point to find the maximum speed at which the vehicle should be operated.

9.9. Methods of Estimating Travel Time

 One method which accounts for acceleration and deceleration is to multiply the maximum vehicle
speed by an average speed factor to obtain an average vehicle speed for the section. Travel time
for the section is then found by dividing the section length by the average vehicle speed. When a
section of the haul route involves both starting from rest and coming to a stop, the average speed
factor from the first column of the table should be applied twice (i.e., use the square of the table
value) for that section.
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  A second method for estimating travel time over a section of haul route is to use the travel-time
curves provided by some manufacturer’s. Separate travel-time curves are prepared for loaded
(rated payload) and empty conditions. Travel time for a section of the haul route may be read
directly from the graph given section length and effective grade. However, travel-time curves
cannot be used when the effective grade is negative. In this case, the average speed method must
be used along with the vehicle retarded curve. To adjust for altitude, deration when using travel-
time curves, multiply the time obtained from the curve by the quantity “1 + derating factor” to obtain
the adjusted travel time.

Average speed factors

Increasing Decreasing
Length of
Starting from 0 or Maximum Speed Maximum Speed
Haul Section
Coming to a Stop from Previous from Previous
(m)
Section Section
46 0.42 0.72 1.60
61 0.51 0.76 1.51
92 0.57 0.80 1.39
122 0.63 0.82 1.33
153 0.65 0.84 1.29
214 0.70 0.86 1.24
305 0.74 0.89 1.19
610 0.86 0.93 1.12
915 0.90 0.95 1.08
1220 0.93 0.96 1.05
1525 0.95 0.97 1.04

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Problem Set for Chapter 9:
1. A wheel tractor-scraper weighing 91 tons is being operated on a haul road with a tire penetration of 5
cm. what is the total resistance and effective grade when
a) The scraper is ascending a slope of 5%
b) The scraper is descending a slope of 5%
2. A crawler tractor weighing 36 tons is towing a rubber-tires scraper weighing 45.5 tons up a grade of 4%.
What is the total resistance of the combination if the rolling resistance factor is 50 kg/t?
3. A four-wheel-drive tractor weighs 20 000 kg and produces a maximum Rimpull of 18 160 kg at sea level.
The tractor is being operated at an altitude of 3 050 m on wet earth. A pull of 10 000 kg is required to
move the tractor and its load. Can the tractor perform under these conditions?
4. Using the crawler tractor performance curve, determine the maximum speed of the tractor when the
required pull (total resistance) is 27 240 kg.
5. Using the wheel scraper performance curve, determine the maximum speed of the vehicle if its gross
weight is 68 000 kg, the total resistance is 10%, and the altitude derating factor is 25%.

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