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To determine our steering arm angle we use perfect Ackerman principles and draw a line directly from the mounting point of our steering arm on the front axle to the centre point of our rear axle, this is represented by the formula: ArcTan( ((Track/2) - Mounting distance from wheel) / Wheelbase ), where Mounting distance = the distance between the wheel and the steering arm mounting point = 80 mm, wheelbase = 2600 mm and Track = 1600 mm. Therefore our steering arm angle is 15.47 degrees.

The below sketch was used to determine a series of steering geometry equations:

Image Added

To determine our steering arm length, tie rod length, and maximum rack travel we derived a series of equations using the physical geometry of our car. These equations are as follows:

     Phi = Theta + Alpha + SAA

     Phi = ArcTan( (

Mathinline
body\Phi = \Theta + \alpha + SAA

Mathinline
body\Phi = arctan(\frac{TR + R + SAL
*Sin
\cdot sin(SAA)
) / ( SAL*Cos
}{SAL\cdot cos(SAA)})
)

     Theta = Phi - Alpha - SAA

     SAA = ArcTan( (T/2 - MD)/ Wheelbase )

     Alpha = ArcCos( ( SAL^2 + b^2 - R^2 ) / (2*SAL*b) )

     R = T/2 - SAL*Sin

Mathinline
body\Theta = \Phi - \alpha - SAA

Mathinline
bodySAA = arctan(\frac {\frac {T}{2}-MD}{Wheelbase})

Mathinline
body\alpha = arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL \cdot b})

Mathinline
bodyR = \frac {T}{2} - SAL\cdot sin(SAA) - TR - \frac{TR
/
}{2} - MD
     b = root(

Mathinline
bodyb = \sqrt{(TR+R+SAL
*Sin
\cdot sin(SAA))
^2
^{2}+(SAL
*Cos
\cdot cos(SAA))
^2 )
^{2}}


Therefore,     Theta = ArcTan( (

Mathinline
body\Theta = arctan(\frac{TR + R + SAL
*Sin
\cdot sin(SAA)
) / ( SAL*Cos
}{SAL\cdot cos(SAA)})
)
-
 ArcCos( ( SAL^2 + b^2 - R^2 ) / (2*SAL*b) ) - ArcTan( (T/2 - MD)/ Wheelbase )Since SAL, SAA, R, b, MD, T and Wheelbase are constants we know have Theta as a function of rack travel.   
arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL\cdot b}) - arctan(\frac {\frac {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 = Inner Wheel Steering Angle, Phi & Alpha are angles found through geometry, and b is a length found through geometry.

    Since SAL, SAA, R, b, MD, T and Wheelbase are constants we know have Rack travel as a function of Theta (inner steering angle).   

A further explanation of this derivation can be explained by asking Robin Pearce (rsgpearce@gmail.com).


The following spreadsheet does the following calculations and takes input as steering arm length, total rack travel and total rack length.

View file
nameSteering Geometry Spread Sheet.xlsx
height250

Component Selection

Google drive sheets
urlhttps://docs.google.com/spreadsheets/d/1HWLhJIZaHs1ThZESJGmf2ntnilZFSSpStdOptPTek7U/edit#gid=0

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