2. Mobile Equipment Power
Requirements
The constructor must select the proper equipment to
relocate and/or process materials economically.
The analysis procedure for matching the best possible
machine to the project task requires inquiry into amachine to the project task requires inquiry into a
machine’s mechanical capability.
The engineer must first calculate the power required to
propel the machine and its load.
This power requirement is established by two factors:
1. Rolling Resistance
2. Grade Resistance
3. Mobile Equipment Power
Requirements
Equipment manufacturers publish performance charts
for individual machine models.
These charts enable the equipment planner to analyze
a machine’s ability to perform under a given set of joba machine’s ability to perform under a given set of job
and load conditions.
4. Payload
The payload capacity of construction excavation and
hauling equipment can be expressed either
volumetrically or gravimetrically.
Volumetric capacity can be stated as struck or heaped Volumetric capacity can be stated as struck or heaped
volume and either volume can be expressed in terms of
loose cubic yard, bank cubic yard, or compacted cubic
yard.
The payload capacity of excavation buckets and
hauling units is often stated by the manufacturer in
terms of the volume of loose material, assuming that
the material is heaped at a specified angle of repose
5. Machine Performance
Cycle time and payload determine a machine’s
production rate, and machine travel speed directly
affects cycle time.
The three power questions:
1. Required Power
2. Available Power
3. Usable Power
6. Required Power
Power required is the power needed to overcome
resisting forces and cause machine motion.
The forces resisting the movement of mobile The forces resisting the movement of mobile
equipment are:
1. Rolling Resistance
2. Grade Resistance
9. Total Resistance
Therefore, power required is the power necessary to
overcome the total resistance to machine movement,
which is the sum of rolling and grade resistance.
Total Resistance(TR) = Rolling Resistance(RR)+Grade
Resistance(GR)
13. Rolling Resistance
The maintenance of low-rolling resistance haul roads is
one of the best financial investments an earthmoving
contractor can make. The cost of having a grader to
maintain the haul road is repaid in increasedmaintain the haul road is repaid in increased
production.
14. Rolling Resistance
The rolling resistance in pounds per gross ton is . . .
R = P (lbs.)
W (tons)W (tons)
Where:
R = Rolling resistance in pounds per ton
P = Total tension in tow cable in pounds
W = Gross weight of mobile vehicle in tons
15. Rolling Resistance
When tire penetration is known, an approximate
rolling resistance value for a wheeled vehicle can be
calculated . . .
RR = [40 + (30 * TP)] * GVW
Where:
RR = Rolling resistance in pounds
TP = Tire penetration in inches
GVW = Gross vehicle weight in tons
17. Grade Resistance/Assistance
The force-opposing movement of a machine up a
frictionless slope is known as grade resistance.
It acts against the total weight of the machine, whether
track type or wheel type.track type or wheel type.
When a machine moves up an adverse slope, the power
required to keep it moving increases approximately in
proportion to the slope of the road.
If a machine moves down a sloping road, the power
required to keep it moving is reduced in proportion to
the slope of the road. This is known as grade
assistance.
18. Grade Resistance
The most common method of expressing a slope is by
gradient in percent.
A 1% slope is one where the surface rises or drops 1 ft.
vertically in a horizontal distance of 100 ft.vertically in a horizontal distance of 100 ft.
If the slope is 5%, the surface rises or drops 5 ft. per 100
ft. of horizontal distance.
If the surface rises, the slope is defined as plus,
whereas if it drops, the slope is defined as minus.
20. Frictionless Slope-Force
Relationships
F = W sin α
N = W cos α
For angles less than 10°, sin α ≈ tan α (the small –angleFor angles less than 10°, sin α ≈ tan α (the small –angle
assumption); with that substitution:
F = W tan α
tan α = V = G%
H 100
21. Frictionless Slope-Force
Relationships
F = W * G%
100
If we substitute W = 2,000 lb/ton, the formula reducesIf we substitute W = 2,000 lb/ton, the formula reduces
to:
F = 20 lb/ton * G%
This formula is valid for a G up to about 10%, that is,
the small angle assumption (sin α ≈ tan α).
22. Total Resistance
Total resistance equals rolling resistance plus grade
resistance or rolling resistance minus grade assistance.
It can also be expressed as an effective grade.
Rolling resistance expressed in lb/ton = G%
20 lb/ton
24. Available Power
Internal combustion engines power most construction
equipment.
Because diesel engines perform better under heavy-
duty applications than gasoline engines, dieselduty applications than gasoline engines, diesel
powered machines are the workhorses of the
construction industry.
Diesel engines have longer service lives and lower fuel
consumption.
Diesel fuel presents less of a fire hazard.
25. Work and Power
Work is defined as force through distance.
Work = Force * Distance
26. Torque
An internal combustion engine by the combustion of
fuel in a piston develops a mechanical force that acts
on a crankshaft having a radius r.
The crankshaft in turn drives the flywheel and gears The crankshaft in turn drives the flywheel and gears
that power the other components of the machine.
The force from a rotating object, such as crankshafts (a
“twisting” force), is termed torque.
27. The Relationship Between
Horsepower and Torque
Horsepower (hp) = 6.2832 * rpm * Torque = rpm *Torque
33,000 5,25233,000 5,252
Conversely, to calculate torque . . .
Torque = 5,252 * hp
rpm
28. Horsepower Rating
Manufacturers rate machine horsepower as either
gross or flywheel (sometimes listed as net horsepower)
Gross horsepower is the actual power generated by the
engine prior to load losses for auxiliary systems, suchengine prior to load losses for auxiliary systems, such
as the alternator, air conditioner compressors, and
water pump.
Flywheel horsepower (fwhp) can be considered as
usable horsepower.
It is the power available to operate a machine-power
the driveline-after deducting for power losses in the
engine.
29. Rim pull
Rim pull is a term that is used to designate the tractive
force between the tires of machine’s driving wheels
and the surface on which they travel.
If the coefficient of traction is sufficiently high there If the coefficient of traction is sufficiently high there
will be no tire slippage, in which case maximum rim
pull is a function of the power of the engine and the
gear ratios between the engine and the driving wheels.
If the driving wheels slip on the supporting surface,
the maximum effective rim pull will be equal to the
total pressure the tires exert on the surface multiplied
by the coefficient of traction.
30. Coefficient of Traction
The factor that determines the maximum possible
tractive force between the powered running gear of a
machine and the surface on which it travels.
31. Rim Pull Equation
Rim Pull = 375 * hp * efficiency (lb)
speed (mph)
The efficiency of most tractors and trucks will range
from 0.80 to 0.85 (use 0.85 if efficiency is not known).
32. Drawbar Pull
The towing force a crawler tractor can exert on a load is
referred to as drawbar pull.
Drawbar pull is typically expressed in pounds.
To determine the drawbar pull available for towing a To determine the drawbar pull available for towing a
load it is necessary to subtract from the total pulling
force available at the engine the force required to
overcome the total resistance imposed by the haul
conditions.
If a crawler tractor tows a load up a slope, its drawbar
pull will be reduced by 20 lb for each ton of weight of
the tractor for each 1% slope.
33. Usable Power
Usable power depends on project conditions:
primarily, haul-road surface condition, altitude, and
temperature.
Usable force = Coefficient of traction * Weight on
powered running gear
34. Performance Charts
Equipment manufacturers publish performance
charts for individual machine models.
These charts enable the equipment estimator/planner
to analyze a machine’s ability to perform under a givento analyze a machine’s ability to perform under a given
set of project-imposed load conditions.
The performance chart is a graphical representation of
the power and corresponding speed the engine and
transmission can deliver.
The load condition is stated as either rim pull or
drawbar pull.
35.
36. Rim Pull Performance Charts
Required Power Total Resistance
1. Estimate the rim pull (power) required – total
resistance (rolling resistance plus grade resistance) –
based on the probable job conditions.based on the probable job conditions.
2. Locate the power requirement value on the left
vertical scale and project a line horizontally to the
right intersecting a gear curve.
3. From the point at which the horizontal line
intersects the gear curve, project a line vertically to
the bottom x axes, which indicates the speed in mph.
37.
38. Rim Pull Performance Charts
Effective Grade Total Resistance
1. Determine the machine weight both when the
machine is empty and loaded. These two weights,
empty and loaded, are often referred to as the netempty and loaded, are often referred to as the net
vehicle weight and gross vehicle weight.
2. Calculate a total resistance (the sum of rolling plus
grade resistance both expressed as percent grade).
3. Project a line horizontally from the intersection
point of the vertical vehicle-weight projection and
the appropriate total-resistance diagonal.
39. Rim Pull Performance Charts
From the point at which the horizontal line
intersects the gear range curve, project a line
vertically to the bottom x axes, which indicates the
machine speed in mph.machine speed in mph.
40. Retarder Chart
A graphical presentation that identifies the controlled
speed of a machine descending a slope when the
magnitude of the grade assistance is greater than the
rolling resistance.rolling resistance.
