Making the ride comfortable by analysing & increasing the pitch compensation using Excel

https://drive.google.com/file/d/10recHUYKZvkoV1FhfjXVZbAFdU9k2yND/view?usp=sharing

Aim

1. To calculate pitch compensation and reduce the pitch angle to zero
2. To calculate the updated anti characteristics and verify the pitch angle is actually zero .

Software Used

Excel

Flow of Calculation & Concepts Used

Preliminary Calculations

• Convert the given values to SI units .
• Find the wheel rate

Wheel rate = Spring rate*(Motion Ratio)^2

• Find Load Transfer ( Due to acceleration )

Load Transfer = (Total Weight * Throttle Acceleration * CG Height )/(Wheel Base *Acceleration due to gravity )

• Add the load transfer to the rear axle and subtract it from the front axle

Front Axle Weight (after the load transfer )= Front Axle Weight ( Static ) - Load Transfer

Rear Axle Weight (after the load transfer ) = Rear Axle Weight ( Static ) + Load Transfer

• Now we have to find wheel rate

Front Wheel Rate =Front Spring Rate *(Front Spring Motion Ratio )^2

Rear Wheel Rate = Rear Spring Rate *(Rear Spring Motion Ratio )^2

• Now we have to find the front and rear deflections of vehicle before we do the process of pitch 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

• Now we have to calculate the pitch angle ( in degrees )

Pitch Angle = ArcTan(((Front End Deflection + Rear End Deflection )*(180/Pi))/Wheel Base )

• Now we have to calculate pitch gradient

Pitch Gradient = Pitch angle /(Throttle Acceleration/Acceleration due to gravity )

• We will caluculate anti-lift angle , anti-squat angle , front swing arm angle , rear swing arm angle

Front Anti lift angle = arctan(((Front IC vertical distance - Tire Radius )*(180/Pi))/(Front IC Horizontal Distance))

Rear Anti squat angle = arctan(((Rear IC Vertical distance -Tire Radius )*(180/Pi))/(Rear IC Horizontal Distance ))

Front Swing Arm angle = arctan((CG Height /WB )*(180/Pi))

Rear Swing Arm angle = arctan((CG Height /WB)*(180/Pi))

• Calculate anti lift , anti squat percentage using drive ratio given

Front Anti Lift % = (Front Anti Lift * Drive Ratio )/( Front Swing Arm Angle )

Rear Anti Squat % = ((Rear Anti Squat Angle*(100-Drive Ratio ))/Rear Swing Arm Angle)

With Compensation

So after keeping the Rear IC vertical distance fixed from contact patch , we have to tweak the value of Rear horizontal distance from the contact patch to reduce the pitch angle and increase the pitch compemsation as close to 100 % , to increase the comfort of ride .

• New front end deflection under load = (Front End Deflection load)*((100-Front Anti Lift % )/100)
• New Rear end deflection under load = (Rear end deflection under load )*((100-Rear Anti Squat%)/100)

Now calculate the new pitch angle and pitch compensation

• Pitch Compensation %=((Pitch angle _old - Pitch angle_new )*100)/Pitch Angle_old

Observation & Calculation

Result

Hence , the pitch angle was reduced to 5.46217E-06 which is similar to zero , pitch compensation came close to 99.99916997 , very close to 100 % at the Rear IC distance of 10.8111 inches . Hence , there will be less (or negligible )deflections during the ride and the ride will be comfortable .