To Calculate Forces Acting on a Vehicle.

OBJECTIVE :

1. To calculate the power of Motor in terms of angular velocity by using tyre data.
2. To prepare excel calculator and calculation of power in Kw also limitations of this excel calculator.
3. To calculate traction power at the rate of 15 % tyre pressure reduction.
4. To Find the gradeability, average speed and forces acting on Range Rover Sports dragon Challenge.

Solution 1 : -

Numerical calculation

• 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 Tyre size is 90/100 R10 53J ? How to read a Tyre ?
• Recalculate the same value if Tyre code is 90/90 R18 51P ?

SPEED RATING OF TIRE TABLE :

LOOD CARING CAPACITY CAPACITY FOR TIRES :

Given data for electric scooter

For Calculation 1 (90/100 R10 53J) (To find Max Speed of Motor)

Velocity = 90 kmph

Gear Ratio = 7

Tyre size = 90/100 R10 53J

Step 1: - converting km/hr to m/sec, so for that we will proceed with following calculation :-

Then for 90 km/hr
= 90 * 1000/3600 (m/sec)
= 100/4
= 25 m/s

Now we have to calculate Tyre Diameter “90/100 R10”
Here
90 is Width of Tyre
100 is Aspect Ratio
R10 is Rim diameter in inch

So Here 1 we have to convert Rim diameter into mm

D(mm) = ('d') * 25.4
= 10 * 25.4
= 254 mm

Now for calculating Tyre Diameter we will use given formula

D = 2w (AR/100) + d

Where,

W = width of Tyre
AR = Aspect ratio
d = Rim dia

So,

Tyre Diameter (D) = 2w (AR/100) + d
= 2 * 90 (100/100) + 254
= 180(1) + 254
= 434 mm

Now for Tyre Radius

Radius = Diameter (D) / 2
= 434 /2
= 217 mm

= 217 * 10^(-3)m
= 0.217 m

Another step is to calculate speed of motor angular velocity

ω = G * V / r
= 7 * 25 / 0.217
= 806.451 Rad/s

Now Converting Rad / s to RPM

= Rad / s * 60 / 2 π
= 806.45 * 60 / 2 * 3.14
= 806.45 * 60 / 6.28
= 806.45 * 9.55
= 7701.59 RPM

Therefore, the maximum speed of the motor is 7701.59 RPM or 806.451 Rad/s for 90/100 R10 53J used by electric scooter

For Calculation 2 (90/90 R18 51P) (To find Max Speed of Motor )

Velocity = 90 kmph

Gear Ratio = 7

Tyre size = 90/90 R18 51P

Step 1: - converting km/hr to m/sec, so for that we will proceed with following calculation :-

Then for 90 km/hr
= 90 * 1000/3600 (m/sec)
= 100/4
= 25 m/s

Now we have to calculate Tyre Diameter “90/90 R18”
Here
90 is Width of Tyre
90 is Aspect Ratio
R18 is Rim diameter in inch

So Here 1 we have to convert Rim diameter into mm

D(mm) = ('d') * 25.4
= 18 * 25.4
= 457.2 mm

Now for calculating Tyre Diameter we will use given formula

D = 2w (AR/100) + d

Where,

W = width of Tyre
AR = Aspect ratio
d = Rim dia

So,

Tyre Diameter (D) = 2w (AR/100) + d
= 2 * 90 (90/100) + 457.2
= 180(0.9) + 457.2
= 162 + 457.2
= 619.2 mm

Now for Tyre Radius

Radius = Diameter (D) / 2
= 619.2 /2
= 309.6 mm

= 309.6 * 10^(-3)m
= 0.3096 m

Another step is to calculate speed of motor angular velocity

ω = G * V / r
= 7 * 25 / 0.3096
= 565.245 Rad/s

Now Converting Rad / s to RPM
= Rad / s * 60 / 2 π
= 565.245 * 60 / 2 * 3.14
= 565.245 * 60 / 6.28
= 565.245 * 9.55
= 5398.08 RPM

Therefore, the maximum speed of motor is 5398.08 RPM or 565.245 Rad/s for 90/90 R18 51P used by electric scooter

Solution 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 ?

Formula used

• Rolling Resistance (Frr) = μrr * Total Weight
  μrr = Coefficient of rolling resistance
• Aerodynamic Drag = ½ * rho * A * V^2 *Cd
• Total Power = ((Frr + Fad) *Velocity/1000

VEHICLE PROPULSION POWER BASED :

• Rolling Resistance Force (N) (Frr) = Vehicle 1 is 39.24 N

= Vehicle 2 is 73.575 N

• Aerodynamic Drag (N) (Fad) = Vehicle 1 is 105.55 N

= Vehicle 1 is 105.55 N

• Total Power = Vehicle 1 is 3.21 Kw

= Vehicle 2 is 3.98 Kw

Limitations of this calculation

• We cannot use this the excel calculator for lengthy calculation.
• Always we have to be aware of units.
• We cannot get the exact value because there is a limitation of reading or calculating complicated force power interactions.
• The large calculation is not possible to solve due to inputting each value manually.

Vehicle Propulsion Power at Different Velocity :

Solution 3 : -

• Assuming that Tyre 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 same ?

For calculating 15% reduction of tyre pressure I multiplied Coefficient of rolling resistance (μrr)*2 and Rolling Resistance Force (Frr)*2.

The following results calculated.

• Total Tractive Force (N) (Fte)

Vehicle 1 = 184.035 N
Vehicle 2 = 252.705 N

• Total Power (Kw)

Vehicle 1 = 4.089 N
Vehicle 2 = 5.615 N

• Power Difference (Kw)

Vehicle 1 = 0.872 Kw
Vehicle 2 = 1.635 Kw

• Difference Power Output (Kw) = 0.763 Kw

15% Decrease in Tyre Pressure :

• Traction Power calculated and the total power difference is 0.763 kW.

Traction Power Difference :

Solution 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 ?

Video Link of Range Rover Sports Dragon Challenge :

The challenge consisted of climbing 999 steps at a 45 degrees angle. It began at the bottom of the Tianmen Mountain Road, which has a stairway and 99 dizzying turns. The Range Rover Sport has a 300PS Ingenium petrol engine as well as a 116PS electric motor. Together they produce 404bhp and 500Nm of torque. It took Range Rover Sports 22 minutes 41 second to cover 11 km (7 mi) road with 99 bends and 999 Steps to complete and reaches the top of the mountain Tianmen cave, a natural arch in the mountain of a height of 131.5 m (431.4 ft).

Gradeability

Gradeability is well-defined as the highest grade a vehicle can go up maintaining a particular speed. Gradeability is dependent on:

• Tractive force
• Rolling resistance
• Adhesion (friction)
• Engine torque
• Transmission, transfer case, final drive and tyre ratio
• Overall combined mass properties

To convert, use this angle degrees to the percentage of slope formula:

Percentage = [ Tan ( Degrees ) ] x 100

For Range Rover Hill Riding an angle of 45 degrees would be:

Percentage of Slope = [ Tan ( 45 ) ] x 100

Calculated out this gives a slope percentage of 100.00 %

This show the gradeability chart was 45 degrees = 100 % and having 1:1 Gradient ratio.

GRADEABILITY CHART :

AVERAGE SPEED OF RANGE ROVER SPORTS :

Speed = Distance / Time

Average Speed of Range Rover Sports = 30.25 Kmph

Forces Acting on Range Rover Sports During Challenges

1. Tractive force F : - Created between the wheel and steps on which Range rover is moving uphill condition. Depending upon the wheel, torque and power.
2. Gradeability Effort : - Distance travelled on the uphill direction at 45 degrees.
3. Aerodynamic Force D : - Here vehicle is 30.25kmph but drag may occur due to density of air because atmospheric pressure is changing due to the vehicle is moving upward about 431.4 ft from the ground.
4. Rolling resistance R : - It created due to rolling of the tyre and here it will be more due to stairs on which Range rover have to move upward direction.
5. Vertical & Longitudinal Force :- R & R acting rear side of the car and above the car when moving upward.

Forces Acting on Range Rover :

Excel Calculator Google Drive Link :-

1. VEHICLE PROPULSION POWER BASED

2. VEHICLE PROPULSION POWER AT DIFFERENT VELOCITY

3. 15% DECREASE IN TYRE PRESSURE

4. TRACTION POWER DIFFERENCE

5. AVERAGE SPEED OF RANGE ROVER SPORTS

https://drive.google.com/file/d/1wgFLF3mGgi6XRYE9pFbP8yF9FVLbg6Ri/view?usp=sharing