Calculation of the forces acting on a vehicle.

Aim: To calculate the forces acting on a vehicle for the given set of questions.

1)What should be the maximum speed of the motor used in an electric scooter capable to run at 90 kmph, if the fixed gear ratio is 7 and tire size is 90/100 R10 53J? How to read a tire?

Given:

• Gear ratio=7
• Speed=90kmph=25m/s
• Tyre spec=90/100 R10 53J
• Rim radius=5inches=0.127m

angular speed, ω=(vr).G

radius of wheel, r=rim radius+height of sidewall

height of sidewall=sectional width of tyre=0.09m

∴r=0.127+0.09=0.217m

ω=(250.217)⋅7=806.45rad/s*9.54=7693.54rpm @ const.speed of 90kmph

• If tyre code is 90/90 R18 51P, then

rim radius r=9inches=0.2286m

height of sidewall=0.9*90=81mm=0.081m

∴r=0.2286+0.081=0.3096

ω= (250.3096)⋅7=565.24rad/s*9.54=5392.44rpm @ const.speed of 90kmph

2)Prepare a simple excel calculator to identify vehicle propulsion power based on given inputs and outputs. 

Inputs: Kerb Weight (kg), Payload (kg), Coefficient of rolling resistance, Air density (kg/m3), Width (m), Height (m), Drag coefficient, Speed

Output: Total power in kW 

What are the limitations of this calculation?

The limitations are:

• The calculations are made for a particular input value which can be varied.
• The vehicle is moving at a const.speed.

3)Assuming that tire pressure reduction by 15% results in an increase of rolling resistance effect by two times, how much will be the difference in total traction power keeping all other parameters the same? 

The rolling resistance coefficient is a function of tyre inflation pressure, the value of rolling resistance coefficient increases when tyre inflation pressure decreases.

∴Froll=μmg=2⋅0.02⋅800⋅9.81=313.92N

Proll=Froll⋅velocity=6.796−3.488=3.488kW

So, the rolling power is increased by 100%

4)See the video of the Range rover sport dragon challenge. How much is the gradeability? What was the average speed? Which are the forces acting on the car?  

Link to the video: https://www.youtube.com/watch?v=EUwzWHD3Htg

`Gradeability=rise/run, in this case it's 45deg= 1/1=100% gradeability

Average speed=diatance/time

• From the link: https://www.landrover.com/explore-land-rover/onelife/adventure/dragon-challenge.html

Distance=11.3km

Time=22min41sec=0.37hrs

∴average speed=30.54km/hr

The forces acting on the car assuming const.speed:

• Aerodynamic drag force= 0.5⋅Cd⋅p⋅A⋅V^2
• Rolling resistance force= mg⋅cosθ
• Hill climbing force= mg⋅sinθ

Conclusion: Thus, the forces acting on a vehicle for the given set of questions are calculated successfully.