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Theta = Phi - Alpha - R = T/2 - SAL*Sin( SAA) - TR - TR/2 - MD,
SAA = ArcTan( (T/2 - MD)/ Wheelbase )
Alpha = ArcCos( ( SAL^2 + b^2 - R^2 ) / (2*SAL*b) )
R = T/2 - SAL*Sin(SAA) - TR - TR/2 - MD
b = root( (TR + R + SAL*Sin(SAA) )^2 + ( SAL*Cos(SAA) )^2 )
Therefore,
Theta = ArcTan( ( TR + R + SAL*Sin(SAA) ) / ( SAL*Cos(SAA) ) ) - ArcCos( ( SAL^2 + b^2 - R^2 ) / (2*SAL*b) ) - ArcTan( (T/2 - MD)/ Wheelbase )
where R = Tie Rod Length, T = Track, SAL = Steering Arm Length, SAA = Steering arm angle, TR = Rack Travel, MD = Steering arm mounting distance from wheel, Theta = Steering Angle, Phi & Alpha are angles found through geometry, and b is a length found through geometry.
A further explanation of this derivation can be explained by asking Robin Pearce (rsgpearce@gmail.com).The Steering arm angle will be set to between 15.5 and 16.6 degrees. This is found by creating a triangle that runs from the steering arm through the centre of the rear axle and then finding the angle between the hypotenuse and the centre line of the car. The greatest steering angle will be 26 degrees and will provide a turning radius of 6.2 m. The steering arm length, tie rod lengths and rack travel will all depend on the rack chosen.
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