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Castor angle is the angular measure from the vertical of the suspension of a steered wheel in a car or other vehicle, measured in the longitudinal direction.
The pivot points of the steering are angled such that a line drawn through them intersects the road surface alightly ahead of the contact point of the wheel. The purpose of this is to provide a degree of self-centring for the steering - the wheel castors around so as to trail behind the axis of steering. This makes a car easier to drive and improves its straight line stability (tendency to wander). Excessive castor angle will make the steering heavier and less responsive, so performance cars often have only very small castor angles.
>>Edit: In racing large castor angles are used to improve camber gain in cornering. Castor angles over 10 degrees with radial tires are common. Power steering is usually necessary to overcome the jacking effect from the high castor angle.
Note that the steering axis (the dotted line in the diagram below) does not have to pass through the centre of the wheel, this allows the Castor to be set independently of the mechanical trail, which is the distance between where the steering axis hits the ground, in side view, and the point directly below the axle. The interaction between castor angle and trail is complex, roughly speaking they both aid steering , castor tends to add damping, while trail adds 'feel', and returnability. In the extreme case of the shopping wheel trolley the system is undamped, but stable, as the wheel oscillates around the 'correct' path. The shopping trolley setup has a great deal of trail, but no castor. Complicating this still further is that the lateral forces at the tyre do not act at the centre of the contact patch, but at a distance behind the nominal contact patch. This distance is called the pneumatic trail and varies with speed, load, steer angle, surface, tyre type, tyre pressure and time. A good starting point for this is 30 mm behind the nominal contact patch.