Forces Acting on a Vehicle

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? Assume the following arrangement from motor to wheel.

Refer to below image to read a tire.

Recalculate the same value if tire code is 90/90 R18 51P.

2. Prepare a simple excel calculator to identify vehicle propulsion power based on given inputs and outputs. Implement formulas in cells.

Inputs: Kerb Weight (kg), Payload (kg), Coefficient of rolling resistance, Air density (kg/m3), Width (m), Height (m), Drag coefficient, Acceleration (0 to top speed in specified seconds), Hill climbing angle, Speed

Output: Total power in kW

What are the limitations of this calculation?

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 keeping all other parameters same?

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?

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

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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? Assume the following arrangement from motor to wheel.

Formula for speed of the motor ω = G*v\r

where, G- Gear Ratio

v-Velocity

r-Radius of the Tyre

We have known the values for G and V.

To convert velocity into m/s

1Kmph = 1000m\36000s = 5/18m/s

Then for 90Kmph, 90*5/18 = 25m/s

Velocity v= 25m/s.

We have to find the radius of the Tyre,

Tyre Specifications are

To convert the Rim diameter(d) into mm

1 inch =25.4mm

Then for 10 inch = 25.4*10 = 254mm

Rim diameter d = 254mm.

To calculate the Tyre Diameter (D)

D = 2W (AR/100)+ d

where, W- Section Width,

AR- Aspect Ratio

d- Rim diameter.

D= 2*90(100/100)+254

= 180+254

= 434mm

Diameter of Tyre (D) = 434mm

Radius of Tyre (r) = 217mm = 0.217m

Formula for speed of the motor ω = (G*v)/r

= (7*25)/0.217

ω = 806.45 rad/s

To convert into rpm

ω = 806.45*60/2π = 7704.94 rpm

Therefore the maximum speed of the motor is 7704.94rpm.

For Tyre code 90/90 R18 51P.

Gear ratio and velocity are same, only the radius of the tyre will change

To convert the Rim diameter(d) into mm

1 inch =25.4mm

Then for 18 inch = 25.4*18 = 457.2mm

Rim diameter d = 457.2mm.

To calculate the Tyre Diameter (D)

D = 2W (AR/100)+ d

where, W- Section Width,

AR- Aspect Ratio

d- Rim diameter.

D= 2*90(90/100)+457.2

= 162+457.2

= 619.2mm

Diameter of Tyre (D) = 619.2mm

Radius of Tyre (r) = D/2 = 309.6mm = 0.3096m

Formula for speed of the motor ω = (G*v)/r

= (7*25)/0.3096

ω = 565.245 rad/s

To convert into rpm

ω = 806.45*60/2π = 5400.43 rpm

Therefore the maximum speed of the motor is 5400.43rpm.

2. Prepare a simple excel calculator to identify vehicle propulsion power based on given inputs and outputs. Implement formulas in cells.

Inputs: Kerb Weight (kg), Payload (kg), Coefficient of rolling resistance, Air density (kg/m3), Width (m), Height (m), Drag coefficient, Acceleration (0 to top speed in specified seconds), Hill climbing angle, Speed

Output: Total power in kW

What are the limitations of this calculation?

The screenshot of the excel calculator

The Limitations of the above calculation is,

It is difficult to use for large data, because we have to enter the values manually.

We have to repeat the same data multiple times to get the power requirement for various speeds instantaneously.

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 keeping all other parameters same?

In vehicle1, the total power is increased by 21%.

In vehicle2, the total power is increased by 29%.

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?

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

Gradeability:

Gradeability is defined as the highest grade a vehicle can go up maintaining a particular speed.

In the above case, the gradeability is 45deg

In percentage tan(45)=100

So the gradeability is 100%

The chart shows 45 degrees =100% and having 1:1 gradient ratio.

Average speed of the car (in the above case)= Distance/time =11.26km/0.368h = 29.7Kmph

The average speed of the car = 29.7kmph.

Forces acting on the Range rover car:

1. Rolling resistance force
2. Aerodynamic drag force
3. Hill climbing force
4. Acceleration force

Filname	Size	Action
Vehicle…ion.xlsx	17.57 KB