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Gradability Equation and Calculator

Power Transmission Design and Engineering
Engineering and Design Applications

Gradability and Traction Equation and Calculator

Gradeability is dependent on:

• Tractive force (see Tire Traction Force Equation and Calculator)
• Overall combined mass, including overall mass of the trailer or semi-trailer
• Rolling resistance
• Adhesion (friction)
• Gradability can be viewed as the maximum uphill or downhill grade (angle) which there will be tire traction to continue forward movement.

 

The gradeability determined using the equation given below which calculates the vehicle's gradeability based on its

• Engine torque
• Transmission, transfer case, final drive and tyre ratio and
• Overall combined mass

Properties. Here only the vehicle’s ability to tackle a specific gradient based on its properties is considered. Not taken into consideration is the actual adhesion between wheels and road which, in poor conditions (e.g. wet roads) can reduce propulsion so that hill-climbing performance is far below the value calculated here.

Gradability Equation

Where:
p = Gradeability, in %
G_z = Overall combined mass, in kg
f_R = Coefficient of rolling resistance, see Table 1
F_z = Tractive force in N - calculated in accordance with Tire Traction Force Equation and Calculator
Required for F_z calculations:
i_G = Transmission ratio
i_A = Driven axle ratio
i_V = Transfer case ratio
M_Mot = Engine torque, in Nm
U = Tire rolling circumference, in m
η = Overall efficiency in the drive train, see Table 2

Table 1: Coefficients of Rolling Resistance

Road surface	Coefficient fR
Good asphalt road	0.007
Wet asphalt road	0.015
Good concrete road	0.008
Rough concrete road	0.011
Block paving	0.017
Poor road	0.032
Dirt track	0.15...0.94
Loose sand	0.15...0.30

Table 2: Overall Efficiency in the Drive Train

Number of driven axles	η
One driven axle	0.95
Two driven axle	0.90
Three driven axle	0.85
Four driven axle	0.80