Directional stability
Directional stability is frequently called "weather vaning" because a directionally stable vehicle free to rotate about its center of mass is similar to a weather vane rotating about its (vertical) pivot.
At high angles of attack, drag forces may become excessive, the vehicle may be impossible to control, or may even experience structural failure.
In general, land, sea, air and underwater vehicles are designed to have a natural tendency to point in the direction of motion.
A road vehicle does not have elements specifically designed to maintain stability, but relies primarily on the distribution of mass.
The first stage of studying the stability of a road vehicle is the derivation of a reasonable approximation to the equations of motion.
The diagram illustrates a four-wheel vehicle, in which the front axle is located a distance
The tyre treads at the region of contact point in the direction of travel, but the hubs are aligned with the vehicle body, with the steering held central.
The tyres distort as they rotate to accommodate this mis-alignment, and generate side forces as a consequence.
We assume that the tyre force is directly proportional to the slip angle (
This is made up of the slip of the vehicle as a whole modified by the angular velocity of the body.
: This is called a second-order linear homogeneous equation, and its properties form the basis of much of control theory.
We do not need to solve the equation of motion explicitly to decide whether the solution diverges indefinitely or converges to zero following an initial perturbation.
If for some reason (incorrect inflation pressure, worn tread) the tyres on one axle are incapable of generating significant lateral force, the stability will obviously be affected.
Assume to begin with that the rear tyres are faulty, what is the effect on stability?
Also, locking the rear wheels by applying the handbrake, renders the vehicle directionally unstable, causing it to spin.
Since the vehicle is not under control during the spin, the 'handbrake turn' is usually illegal on public roads.
Deflecting the steering changes the slip angle of the front tyres, generating a sideforce.
When the speed is low, the slip is negative and the body points out of the corner (it understeers).
As an example: Evidently moving the centre of gravity forwards increases this speed, giving the vehicle a tendency to understeer.
Even worse is the installation of an oversized power unit into a rear engined production vehicle without corresponding modification of suspension or mass distribution, as the result will be directionally unstable at high speed.
Engine torque likewise re-distributes the load between front and rear tyres.
The complete analysis is essential for the design of high performance road vehicles, but is beyond the scope of this article.
This is primarily achieved by the area of the vertical stabilizer and the sides of the fuselage aft of the center of gravity.
