Forces Acting on a Vehicle

1a) 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? Assume the following arrangement from motor to wheel:

From 90/100 R10 53J, it is deducible that the wheel diameter is:

(100% of 90)x2 + 10in*25.4 = 434mm

Wheel radius is therefore 217mm = 0.217m

Using GV = rw:

where linear velocity V = 90kmph = 25m/s, G = 7, and r = 0.217m, angular velocity w of the wheel and thus the motor is:

w = 7(25)/0.217 = 806.45 rad/sec or 7701.05 rpm

1b) Recalculate the same value if tire code is 90/90 R18 51P

(90% of 90)x2 + 18in*25.4 = 619.2mm

Wheel radius is therefore 309.6mm = 0.3096m

Using GV = rw:

where linear velocity V = 90kmph = 25m/s, G = 7, and r = 0.3096m, angular velocity w of the wheel and thus the motor is:

w = 7(25)/0.3096 = 565.25 rad/sec or 5397.70 rpm

2a) Prepare a simple excel calculator to identify vehicle propulsion power

• Inputs have been assumed as is evident, and outputs such as rolling resistance force, air drag force, hill climbing force, and power have been calculated using relevant formulae.
• Two vehicles have been compared

b) What are the limitations of this calculation?

• The limitations mainly exist with the constants i.e. coefficient of rolling resistance, drag coefficient, and air density.
• Rolling resistance depends on tire pressure and road surface, which constantly vary. Therefore, assuming a fixed value of coefficient of rolling resistance only calculates rolling resistance force at some point in time.
• Drag coefficient depends on aerodynamic factors, which could change depending on the amount of fluid flow around the vehicle, so a fixed value does not always provide a precise answer.
• Air density changes with temperature and pressure of the air, so a fixed value cannot always provide an accurate answer
• Vehicle propulsion power has been calculated at a single speed, however speed is always changing.

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

• Coefficient of rolling resistance was doubled to show for comparison
• The effect in total power will be about 1.4-1.5x when all other parameters are kept the same, as is highlighted in red.

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

• The gradeability is 100%, since the slope angle is 45 degrees to climb the 999 steps
• Whole journey was 11.2km and it took 22min 41sec, so average speed was about 30kmph
• Forces acting on the car include aerodynamic drag, hill climbing, rolling resistance, and acceleration.