Problem set 2 -week 3 challenge : Anti-Characteristics

https://docs.google.com/spreadsheets/d/135kM0sGFzjKKAiGNfrrOPY1kUnT5vOJ9CzK-bQTGfbI/edit?usp=sharing

FORMULAE given in the HELP SESSION:

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 = 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

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

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

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

the loads w.r.t the load transfer is calculated

Load transfer	lbs	328.2854291
load on front wheel	lbs	2062.5
load on rear wheel	lbs	1687.5
Front axle load(after load transfer)	lbs	1734.214571
Rear axle load(after load transfer)	lbs	1359.214571

The wheel rate is calculated using the motion ratio given for both the front and rear suspension

Front wheel rate	lb/in	259.92
Rear wheel rate	lb/in	336.96

Then the deflection and the pitch angle due to the load transfer is calculated (without any compensation)

Without Compensation
Front end deflection	in	0.6315124444
Rear end deflection	in	0.4871281889
Pitch angle	deg	0.6539857511
Pitch gradient	deg/g	0.04024527699

the pitch angle is 0.653 deg

Then the ANTI LIFT and the ANTI SQUAT angle found with respect to the IC positions mentioned in the question

Front IC vert. distance from contact patch	in	13.22
Front IC hori. distance from contact patch	in	28.5
Rear IC vert. distance from contact patch	in	16
Rear IC hor. distance from contact patch	in	42.5

then the ideal swing arm angle calculated.

Front Swing arm angle	deg	9.84113176
Rear Swing arm angle	deg	9.84113176

then the Percentage anti squat and anti lift is calculated

Front anti Lift angle	deg	3.45366161
Rear anti Squat angle	deg	6.044092162

Front anti Lift %		0
Rear anti Squat %		61.41663693
Front end deflection	in	0.6315124444
Rear end deflection	in	0.1879504378
Pitch angle	deg	0.479088473
Pitch gradient	deg/g	0.02948236757

Compensaation % of pitch

26.74328573

the pitch angle is 0.479

the percentage pitch compensation is 26.74%

NOW

we need to make the pitch zero by keeping the RICV = 16in , therefore we can onlly change the RICH value

so that we can achieve 100 percent pitch compensation.

Front IC vert. distance from contact patch	in	13.22
Front IC hori. distance from contact patch	in	28.5
Rear IC vert. distance from contact patch	in	16
Rear IC hor. distance from contact patch	in	10.85
we can change the value of RICH for zero pitch angle

the anti angles are found to be

Front anti Lift angle	deg	3.45366161
Rear anti Squat angle	deg	22.52606055
Front Swing arm angle	deg	9.84113176
Rear Swing arm angle	deg	9.84113176
Front anti Lift %		0
Rear anti Squat %		228.8970527
Front end deflection	in	0.6315124444
Rear end deflection	in	-0.6278938782

the corresponding pitch and percentage compensation is found to be

Pitch angle	deg	0.002115597629
Pitch gradient	deg/g	0.0001301906233
Compensaation % of pitch		99.67650708

the RICH for the zero pitch angle and for the 100%pitch compensation is 10.85inches .