Aerodynamic Forces and Moments acting on the Vehicle Body

In order to analyse the various aerodynamic forces and moments acting on the vehicle body, consider the vehicle as a mass having six degrees of freedom. Now the various aerodynamic forces acting on the vehicle body can be summarized as follows:

P_x – Force of air drag in the direction of motion with wind angle along the longitudinal axis

P_y – Cross wind force

P_z – Aerodynamic lift

Longitudinal Air Drag to measure Aerodynamic Forces

The longitudinal component of the resultant of pressure distribution is called as “Longitudinal Air Drag”. The magnitude of this component can be represented by,

P_x = C_x ρ A V² / 2

where,

C_x – Longitudinal wind force dimensionless coefficient

ρ – Air density in kg/m³

V – Velocity of wind in m/s

A – Cross sectional area of the vehicle viewed from the front in m²

Cross Wind Force to measure aerodynamic forces

Cross wind force is formed by the asymmetric flow of air around the vehicle body when the wind angle is not equal to zero. The cross wind force can be given as

P_y = C_y ρ A V² / 2

where,

C_y – Cross wind force dimensionless co-efficient

Aerodynamic Lift to measure aerodynamic forces

Aerodynamic lift is the vertical component of the resultant of the pressure distribution over the vehicle body due to flow of air around it. The aerodynamic lift can be represented as

P_z = C_z ρ A V² / 2

where,

C_z – Lift co-efficient

The lift will tend to reduce the pressure between the wheels and the ground, which causes losses of steering on the front axle and the loss of friction on the rear axle. The magnitude of this lift and its distribution over the front and rear is a function of ground clearance, the contours of the body and the underbody and the angle of attack of the air on the vehicle body.

Since these factors are not acting at the centre of gravity (C.G) of the vehicle body but at the centre of pressure, they create the following three aerodynamic moments:

M_x – Rolling moment

M_y – Pitching moment

M_z – Yawing moment

Rolling Moment to calculate Aerodynamic Forces

This movement is caused by the cross wind force P_y about the longitudinal axis. The magnitude of this rolling moment is given by

M_x = P_y a = C_mx ρ A L V² / 2

where,

a – Height of centre of thrust above CG

C_mx – Rolling moment coefficient

L – Reference length

The rolling moment affects the weight distribution on the wheels. This effect is dangerous for tall vanes where the side force acts much above the CG. The only near solution to reduce rolling moment is to increase the wheel track.

Pitching Moment

Pitching moment is caused about y axis by cross wind force P_y or the longitudinal force P_x. The pitching moment M_y is given by

M_y = P_x b = C_my ρ A L V² / 2

where,

b – Distance between CG and CP

C_my – Pitching moment coefficient

L – Reference length of the wheel base

The pitching moment is usually negative I.e. nose down and this moves. The rear axle lifts off the ground and further reduces the available traction.

Yawing Moment

Yawing Moment is caused about z axis by cross wind force Py. The yawing moment M_z is given by

M_z = P_y c = C_mz ρ A L V² / 2

where,

c – Distance between CG and CP

C_mz – Yawing moment coefficient

L – Reference length

These moments adversely affects the directional stability of the vehicle at high speed. The use of stabilizer fins at the rear of the vehicle gives a very good reduction in yawing moment.

Note:

Centre of Gravity is the point where the whole mass of a system is assumed to be act

Centre of Pressure (CP) is the point where the total pressure acts on the system.