If a driver wants to keep its speed constant, he needs to have equivalent engine power to the running resistance but needs more power for acceleration to overcome the acceleration resistance. In the case of deceleration of the vehicle, the inertia energy of the vehicle can be restored by the inertia energy recovery system of the vehicle. The engine power required for driving changes at all the time due to the variation of moving condition on a road.

In here, the mathematical equations of the resistance terms are introduced to make the governing equation of the power train system of a vehicle. In general, the running resistance terms on a moving vehicle consist of:

  • Rolling resistance
  • Aerodynamic resistance
  • Gradient resistance

A general form of total running resistance force of a vehicle can be expressed as the summation of above terms as given below:

Rt = RA + RR + RG (1)

With the change of driving condition, the general equation Eq. (1) should be modified.

  1. Rolling resistance

The friction resistance between road and tire surface is defined as rolling resistance of a vehicle. It is clearly affected to the surface roughness of road but not to the vehicle speed. From the principle of physics, the rolling resistance of a running vehicle can be obtained from Eq. (2):

RR = K x W (2)

Where, K – constant of rolling resistance, depends on the nature of road = 0.015 for loose unpaved road.                                     W – Weight of the vehicle = 250 x 9.81 = 2452.5N (Let)

Therefore, RR = 36.79N

Where W is gross weight of a vehicle and W is the induced lift or down force on a running vehicle.

The rolling resistance coefficient (K ) depends on surface condition of road, material and tread pattern of tires and its charged air pressure and vehicle speed etc. Thus the multiple factors affecting rolling resistance cannot be taken into account at a time. In here, the most commonly used coefficient varied with road surface condition is incorporated in this study table.


Road surface Rolling resistance coefficient Fr
Firm Road condition 0.010 – 0.035
Unmade road surface 0.045 to 0.300
ATV 0.3
  1. Aerodynamics Resistance

As a vehicle runs on a road, the relative air movement occurs opposite to the driving direction of the vehicle even with no wind in air. Because of this air flow, the vehicle experiences aerodynamic force such as drag and lift on the body. The aerodynamic drag force generated on the frontal and rear side of the body acts on the vehicle as a driving resistance.

From the analytical equation in Eq. (3), the aerodynamic drag force can be estimated.

RA = (1/2)ρAf Cd(V/3.6)2 (3)

ρ – Density of air            Af – Projected frontal area    Cd coefficient of aerodynamics resistance                                     V– Velocity of the vehicle

As a vehicle goes up or down the hill, it experiences gravitational resistance due to its weight and it is called gradient resistance of the vehicle.

The gradient resistant is calculated by Eq. (4):

RG = W sinθ (4)

Where θ is gradient angle of road.

The vehicle is desired to be able to climb a 30 degree slope while carrying the heaviest of the team’s drivers.

Hence θ = 30°

Velocity of Vehicle, Power of propulsion, Tractive effort, road performance and gearbox selection ………. coming soon

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