Longitudinal load transfer and Pitch compensation

AIM:

1. Calculate the following parameters:

(i) Front end deflection under load

(ii) Rear end deflection under load

(iii) Pitch angle

(iv) Pitch gradient

2. Use the IC location information to calculate the following:

(i) Front anti-lift angle

(ii) Rear anti-squat angle

(iii) Front swing arm angle for 100% anti-lift

(iv) Rear swing arm angle for 100% anti-squat

(v) Front anti-lift %

(vi) Rear anti-lift %

3. To eliminate the pitch angle (theoretically), keep the rear swing arm height fixed at 16 inches from the contact patch. Calculate the following:

(i) Front anti-lift % and rear anti-squat % for zero pitch angle

(ii) Front end deflection under load, accounting for the new anti characteristics

(iii) Rear end deflection under load, accounting for the new anti characteristics

(iv) Pitch angle, accounting for the new anti characteristics (verify that it is indeed zero)

GIVEN DATA:

SOLUTION:

Formulae:

Load transfer = (Total weight * Throttle acceleration * CG height) / (Wheel Base * Acceleration due to gravity)

Front axle weight (after load transfer) = Front axle weight (static) - Load transfer

Rear axle weight (after load transfer) = Rear axle weight (static) + Load transfer ... (Rear Wheel Drive)

Front wheel rate = Front spring rate * (Front spring motion ratio)^2

Rear wheel rate = Rear spring rate * (Rear spring motion ratio)^2

Without compensation:

Front end deflection under load = (Load transfer * 0.5) / Front wheel rate

Rear end deflection under load = (Load transfer * 0.5) / Rear wheel rate

Pitch angle = arctan[(Front end deflection + Rear end deflection) / Wheel base]

Pitch gradient = Pitch angle / Throttle acceleration (g)

Throttle acceleration (g) = Throttle acceleration / Acceleration due to gravity

Front anti-lift angle = arctan[(Front IC vertical distance - Tire radius) / Front IC horizontal distance]

Rear anti-squat angle = arctan[(Rear IC vertical distance - Tire radius) / Rear IC horizontal distance]

Front swing arm angle = arctan(CG height / Wheel base)

Rear swing arm angle = arctan(CG height / Wheel base)

Front anti-lift % = (Front anti-lift angle * Drive Ratio) / Front swing arm angle ... (% front Drive ratio was given)

Rear anti-squat % = [Rear anti-squat angle * (100 - Drive ratio)] / Rear swing arm angle

With compensation:

Front end deflection under load = Front end deflection under load (w/o pitch compensation) x (100 - Front anti-lift %) / 100

Rear end deflection under load = Rear end deflection under load (w/o pitch compensation) x (100 - Rear anti-squat %) / 100

Pitch angle = arctan[(Front end deflection + Rear end deflection) / Wheel base]

Pitch gradient = Pitch angle / Throttle acceleration (g)

Pitch compensation % = [Pitch angle (w/o pitch compensation) - Pitch angle (with compensation)] * 100 / Pitch angle (w/o pitch compensation)

1.

Parameter	Value	Unit
Front end deflection under load	0.6315124444	in
Rear end deflection under load	0.1879504378	in
Pitch angle	0.4790263613	deg
Pitch gradient	0.9492091591	deg/g

2.

Parameter	Value	Unit
Front anti-lift angle	3.453213858	deg
Rear anti-squat angle	6.043308572	deg
Front swing arm angle for 100% anti-lift	9.8398559	deg
Rear swing arm angle for 100% anti-squat	9.8398559	deg
Front anti-lift %	0	-
Rear anti-squat %	61.41663693	-

3. Keeping the rear swing arm height fixed at 16 inches from the contact patch

Parameter	Value	Unit
Front anti-lift %	0	-
Rear anti-squat %	229.4680637	-
Front end deflection under load	0.6315124444	in
Rear end deflection under load	-0.6306754337	in
Pitch angle	0.0004892955191	deg

Excel Output:

After eliminating the pitch angle:

Excel Link: https://docs.google.com/spreadsheets/d/1LLaK5ZVLWOuC-UOAXJtml8U3WcvA7vq6LW6XHbqLoBY/edit#gid=979414198