ASC Paper Notes
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The distance of the NSP from the front axle is determined by the following equation   Assuming the tires in the front and back are the same model, and thus the cornering stiffness values are the same, the equation simplifies down to 1/3WB. |
The location of the CG relative to the NSP determines the characteristic of the yaw response. This can be summarized in variables known as the static margin and the understeer coefficient
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The Static Margin (SM) is defined as “the distance from the CG rearward to the NSP divided by the wheelbase wheelbase” and is expressed with the following equation (somehow…?). It is the distance from the front axle to the NSP as defined earlier, minus the distance from the front axle to the CG (denoted as LG), all divided by WB. Notice that for the first term since WB is in the definition, dividing by WB cancels it out.  In our case, with 3 wheels of the same cornering stiffness, this can be simplified down to  |
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When turning, the side load from before becomes the centrifugal force. With this model, the steering angle can be described with the following equation
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This, using lateral force vs slip angle data such as figure 3 (in the first expandable section), this equation can be re-written as Re-writing this equation by replacing slip angles alpha yields the following equation.
where W_f is the weight on the front axle and W_r is on the rear. This can be further simplified by introducing the understeer gradient and simplifying the lateral acceleration.
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For ASC regulations, the car must be able to withstand a 45-degree tipping table. This gives us an Fc of at least 1.
This is the equation for a 4 wheeler
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Braking Weight Transfer
Under braking, the following side view model can be used. In this scenario, the car may have 3 or 4 wheels.
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Using this model, the following equation can be found.
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F_t, which is ambiguously described in the paper, is the target % of weight transfer. That is to say, the percentage of the total weight on the rear axle that would be desired to leave the rear axle under braking. UMinnesota used F_t of 30%, which indicated that 30% of the default rear weight was transferred to the front axle.
F_b is the prescribed max braking deceleration, which in our case, is 1g minimum.
Glossary
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Note: Underlined terms have definitions in expandable sections above. WB - Wheelbase, the distance between the rear and front axle CG - Center of Gravity HG - The height of the CG TR - Track, the distance between the tires on the same axle NSP - Neutral Steer Point, the point at which a lateral load can be applied to the vehicle without inducing rotation (yaw) SM - Static Margin, the distance from the CG rearward to the NSP divided by the wheelbase K - Understeer gradient, performance indicator indicating under and oversteer. LG - Distance rearward from the front axle to the CG LNSP - Distance rearward from the front axle to the NSP C_f - Front TIRE cornering stiffness C_r - Rear TIRE cornering stiffness C_f bar - Sum of C_f for all tires on the axle C_r bar - Sum of C_r for all tires on the axle W_f - Weight on the front axle WF_i - Weight on front inside wheel WF_o - Weight on the front outside wheel W_r - Weight on the rear axle a_y - Lateral acceleration; can be present through an applied force OR the centrifugal force δ - Delta, steering angle Slip_F - front tire slip angle; the angular difference between the front tire’s direction and the actual velocity Slip_R - rear tire slip angle; the angular difference between the rear tire’s direction and the actual velocity |
Reading List
https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.633.5587&rep=rep1&type=pdf
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