Vehicle Propulsion Power Excel Calculator and Study of Range Rover Sport Dragon Challenge

Objective

1. To find the maximum speed of the motor used in an electric scooter capable to run at 90 km/h, if the fixed gear ratio is 7 and tire size is Case 1: 90/100 R10 53J and Case 2: 90/90 R18 51P?

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

3. To find the power difference if the tire pressure is reduced by 15% increasing the rolling resistance by two times.

4. To find the gradability and average speed of the car in Ranger Rover Sport Dragon Challenge.

Methodology

1. Maximum Speed of the motor

Given:

V= 90km/h = 90*5/18 = 25m/s

Gear Ratio, G = 7

To find:

Motor Speed

Solutions:

Case 1: Tire Code: 90/100 R10 53J

Tire Nomenclature:

Section Width, SW = 90mm

Aspect Ratio, AR = 100%

Construction = R (Radial)

Rim Dia = 10in

Load Index = 53 = 206 Kg (from Fig 1)

Speed Sumbol = J = 100 km/h (from Fig 2)

Fig 1 (Ref:https://www.tyresizecalculator.com/charts/tire-load-index-chart)

Fig 2 (Ref: https://www.tiresplus.com/tires/tire-buying-guide/tire-speed-rating/)

AR = Section Height(SH)/Section Width(SW)

SH = SW * AR

= 90 * 100/100 = 90mm

Rim Dia = 10in =254mm

Dia of tyre, D = Rim Dia + (2*SH)

= 254 + (90*2)

= 434mm

Hence R = D/2 = 217mm = 0.217m

Angular Velocity of the motor, ω = V/r * G

= (25/0.217) * 7

= 806.45 rad/s

= 806.45 * 60/2π

= 7701.03 = 7701rpm

Case 2: Tire Code: 90/90 R18 51P

Tire Nomenclature:

Section Width, SW = 90mm

Aspect Ratio, AR = 90%

Construction = R (Radial)

Rim Dia = 18in

Load Index = 51 = 195 Kg (from Fig 1)

Speed Sumbol = P = 150 km/h (from Fig 2)

AR = Section Height(SH)/Section Width(SW)

SH = SW * AR

= 90 * 90/100 =90 * 0.9 =81mm

Rim Dia = 18in =457.2mm

Dia of tyre, D = Rim Dia + (2*SH)

= 457.2 + (81*2)

= 619.2mm =0.6192m

Hence R = D/2 = 0.3096m

Angular Velocity of the motor, ω = V/r * G

= (25/0.3096) * 7

= 565.245 rad/s

= 565.245 * 60/2π

= 5397.69 = 5398rpm

2. Vehicle Propulsion Power Excel Calculator

Inputs: Kerb Weight (kg), Payload (kg), Coefficient of rolling resistance μ">μμ, Air density ρ">ρρ (kg/m3), Width (m), Height (m), Drag coefficient Cd, Acceleration Final Speed Vf, Acceleration time t, Hill climbing angle ψ">ψψ, Speed V, Speed while climbing Vc

Formulas Used:

Gross Weight, m = Kerb Weight + Pay Load

Frontal Area, A = 0.85 * Width * Height

Rolling Resistance Force, Frr = μ* m * g

Aerodynamic Drag Force, Fad = 1/2 * ρ * A * Cd * V^2

Tractice Force, Fte = Frr + Fad

Tractive Power, Pte = Fte * V

Hil Climbing Force, Fhc = m * g * sinψ

Hill Climbing Power, Phc = Fhc * Vc

Acceleration Power, Pac = 1/2 * (m * Vf^2)/t

Total Propulsion Power, P = Pte + Phc + Pac

Results:

Vehicle Propulsion power = 84.15368 KW

Spreadsheet link: Power Calculation.xlsx

Screenshot:

3. Power Difference when tire pressure reduced by 15% increasing the rolling resistance by 2 times

Results:

Vehicle Propulsion Power = 89.51648

Power Difference = 89.51648 - 84.15368 =5.3628

Spreadsheet link: Power Calculation.xlsx

Screenshot:

4. Range Rover Sport Dragon Challenge

Information known from:

Dragon Challenge Details

https://www.youtube.com/watch?v=EUwzWHD3Htg

Slope angle = 45deg

Distance = 7miles = 11.2654km = 11265.4m

time taken = 22min 41 seconds = 1361sec

To find:

a) Gradeability

b) Average speed of the vehicle

Solution:

From the below given figure, for a slope of 45def, the gradeability percentage shown is 100%

Average Speed of the vehicle = Distance/time taken = 11265.4/1361 = 8.28m/s = 8.28 * 18/5

= 29.808km/h

Forces Acting:

1. Rolling Resistance force

2. Aerodynamic Drag Force

3. Hill Climbing Force

4. Acceleration Force

Conclusion

1. Motor Speed at Case 1 for tire code 90/100 R10 53J is 7701rpm

2. Motor Speed at Case 2 for tire code 90/90 R18 51P is 5398rpm

3. Excel Calculator Prepared ( Power Calculation.xlsx )

4. Power Difference due to doubling the rolling resistance is 5.3628

5. Gradeability of range rover sport is 100% and the average speed in covering 7 miles was 29.808km/h

References

1. https://en.wikipedia.org/wiki/Rolling_resistance#:~:text=%22Rolling%20resistance%20coefficient%20(RRC),measure%20the%20RRC%20of%20tires.&text=)%20equal%20to%20the%20value%20of,divided%20by%20the%20wheel%20load

2. https://study.com/academy/answer/the-frontal-area-a-represents-the-frontal-projection-of-the-car-s-area-and-could-be-approximated-simply-by-multiplying-0-85-times-the-width-and-the-height-of-a-rectangle-that-outlines-the-front-of-a-c.html#:~:text=Question%3A-,The%20frontal%20area%20A%20represents%20the%20frontal%20projection%20of%20the,normal%20to%20the%20front%20grills.

3. https://www.tyresizecalculator.com/charts/tire-load-index-chart

4. https://www.tiresplus.com/tires/tire-buying-guide/tire-speed-rating/

5. https://www.sellanycar.com/cars-related/range-rover-sport-completes-dragon-challenge-set-new-world-record/#:~:text=Details%20of%20the%20Breathtaking%20Dragon%20Challenge%20Record&text=To%20begin%20with%2C%20the%20driver,that%20had%2099%20hairpin%20turns.