Geometry
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. maximum angle of our tires (steering angle) is determined using our desired steering radius, 6.2 meters. This radius was chosen because FSGP & WSC require that our car perform an 8 m radius u-turn where all portions of our car less than 200 mm from the ground must remain within the 8 m radius. To ensure we meet this requirement we have set our outer turning radius to be 7 m and therefore our turning radius and inner turning radius to be 6.2 m and 5.4 m respectively. Using this radius we can use geometry to derive that our largest steering angle will be at the inner wheel and will be: Theta = ArcTan( Wheelbase / (radius - track/2)), where wheelbase = 2600 mm, track = 1600 mm and radius = 6.2 m. From this we find our largest steering angle must be 25.71 degrees.
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:
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| body | \Phi = \Theta + \alpha + SAA |
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| body | \Phi = arctan(\frac{TR + R + SAL\cdot sin(SAA)}{SAL\cdot cos(SAA)}) |
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| body | \Theta = \Phi - \alpha - SAA |
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| body | SAA = arctan(\frac {\frac {T}{2}-MD}{Wheelbase}) |
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| body | \alpha = arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL \cdot b}) |
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| body | R = \frac {T}{2} - SAL\cdot sin(SAA) - TR - \frac{TR}{2} - MD |
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| body | b = \sqrt{(TR+R+SAL\cdot sin(SAA))^{2}+(SAL\cdot cos(SAA))^{2}} |
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Therefore,
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| body | \Theta = arctan(\frac{TR + R + SAL\cdot sin(SAA)}{SAL\cdot cos(SAA)})-arccos(\frac {SAL^{2}+b^{2}-R^{2}}{2\cdot SAL\cdot b}) - arctan(\frac {\frac {T}{2} - MD}{Wheelbase}) |
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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.
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| name | Steering Geometry Spread Sheet.xlsx |
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| height | 250 |
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Component Selection
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| url | https://docs.google.com/spreadsheets/d/1HWLhJIZaHs1ThZESJGmf2ntnilZFSSpStdOptPTek7U/edit#gid=0 |
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