Directional stability

Directional stability is stability of a moving body or vehicle about an axis which is perpendicular to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation to the oncoming medium (water, air, road surface, etc.) when disturbed (rotated) away from that original direction. If a vehicle is directionally stable, a restoring moment is produced which is in a direction opposite to the rotational disturbance. This "pushes" the vehicle (in rotation) so as to return it to the original orientation, thus tending to keep the vehicle oriented in the original direction.

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.

With the exception of spacecraft, vehicles generally have a recognisable front and rear and are designed so that the front points more or less in the direction of motion. Without this stability, they may tumble end over end, spin or orient themselves at a high angle of attack, even broadside on to the direction of motion. 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.

Arrows, darts, rockets, and airships have tail surfaces to achieve stability. A road vehicle does not have elements specifically designed to maintain stability, but relies primarily on the distribution of mass.

These points are best illustrated with an example which is familiar to most readers - the humble motor car.

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 metres ahead of the centre of gravity and the rear axle is b metres aft of the cg. The body of the car is pointing in a direction ${\displaystyle \theta }$ (theta) whilst it is travelling in a direction ${\displaystyle \psi }$ (psi). In general, these are not the same. 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.

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