Aim- To analyse and access forces acting on a vehicle

Objectives-

1. To calculate 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 & 90/90 R18 51P.
2. To develop a simple excel calculator to identify vehicle propulsion power based on given inputs and outputs.
3. To find the difference in total tractive power of a vehicle if the tire pressure reduction by 15% results in increase of rolling resistance effect by two times, keeping all other parameters same.
4. To find the gradeability, average speed the forces acting on RANGE ROVER SPORT on the Dragon Challenge.

Introduction-

Tyre Nomenclature-

Source: Bridgestone Tyres

Governing Equations-

`D_t=D_r+2.S_h`

`A_R=S_h/S_w`

`ω=υ/r.G_r`

`F_"RR"=μ_"RR"+m.g`

`F_(aero)=1/2 ρc_d Av^2`

`F_(Hill)=m.g.sin⁡(θ)`

`F_(la)=m.a`

`F_(ωa)=I.(G_r)^2/r^2.a`

`F_(Tractive)=F_"RR"+F_(aero)+F_(Hill)+F_(la)+F_(ωa)`

`Power=F_(Tractive).υ`

where,

`D_t="Tire Diameter"`

`D_r="Rim Diameter"`

`S_h="Section height"`

`S_w="Section width"`

`A_R="Aspect ratio"`

`G_r="Gear ratio"`

`ω="Angular velocity"`

`μ_"RR"="Coefficient of rolling resistance"`

`m=mass`

`C_d="Drag coefficient"`

`A="Frontal area"`

`v="vehicle velocity"`

`θ="Inclination angle"`

`I="moment of inertia of motor rotor"`

`"r=radius of tyre"`

`a="acceleration of vehicle"`

For 90/100 R10 53J-

`S_w=90 mm=0.09m`

`A_R=100%`

`"Construction type"=radial`

`D_r=10 "inches"=0.254m`

`"Load index"=53 (206 kg)`

`"Speed index"= J (100kmph)`

`D_t=D_r+2.S_h`

`D_t=0.254+2*0.09=0.434m`

`r_1=0.217m`

For 90/90 R18 51P-

`S_w=90 mm=0.09m`

`A_R=90%`

`"Construction type"=radial`

`D_r=18 "inches"=0.4572m`

`"Load index"=51 (195 kg)`

`"Speed index"= P (150kmph)`

`D_t=D_r+2.S_h`

`S_h=A_R*S_w`

`S_h=0.9*0.09= 0.081m`

`D_t=0.4572+2*0.081=0.6192m`

`r_2=0.3096m`

`"Scooter top speed" (v)=90 kmph=25"m/s"`

`G_R=7`

`ω_1=υ/r_1.G_r`

`ω_1=25/0.217.7=806.4516 " rad/s"= 7701.045 " RPM"`

`ω_2=υ/r_2.G_r`

`ω_2=25/0.3096.7=565.5454 " rad/s"= 5400.560 " RPM"`

Hence the maximum speed of the motor to be used for the electric scooter are-

`ω_1=7701.045 " RPM"`

`ω_2=5400.560 " RPM"`

Excel® Calculator for power requirement-

Excel Calculator

Tyre Pressure Reduction-

We can clearly see from the spredsheet that reduction in tyre pressure by 15% results in increasing the propulsive power by a resonable amount of 31 kW.

Range Rover Dragon Challenge-

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

Gradeability-

Gradeability is the ability of a vehicle to negotiate a grade in Gross Vehicle Weight condition and it can vary from 0 to 45 degree (maximum).For the dragon challenge the gradebility was 100% , 45 degree angle with 99 turns and 999 steep steps completed in 22min 41 sec by Range Rover Sport PHEV.

Forces Acting on Range Rover Sport-

Hill climb force

Aerodynamic resistance force

Rolling resistance force

Acceleration force

Average Speed-

`"distance covered"=11.3" km"`

`"time taken"=22.41 " min"=0.3735 " hrs"`

`speed=11.3/0.3735 =30.25 " kmph"`

So the average speed was around 30 to 35 kmph.

References-

1. Dragon Challenge - Adventure Travel - Land Rover. (n.d.). Www.Landrover.com. Retrieved November 23, 2020, from https://www.landrover.com/explore-land-rover/onelife/adventure/dragon-challenge.html
2. Davis, K., & Hayes, J. G. (2016). Analysis of electric vehicle powertrain simulators for fuel consumption calculations. 2016 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC). https://doi.org/10.1109/esars-itec.2016.7841414
3. x-engineer.org. (n.d.). EV design – energy consumption – x-engineer.org. Retrieved November 23, 2020, from https://x-engineer.org/automotive-engineering/vehicle/electric-vehicles/ev-design-energy-consumption/
4. Lowry, J., & Larminie, J. (2012). Electric vehicle technology explained. Wiley.
5. Tire Speed Rating Chart. (n.d.). Www.Tyresizecalculator.com. Retrieved November 23, 2020, from https://www.tyresizecalculator.com/charts/tire-speed-rating-chart
6. Murali, S. (n.d.). Gradeability of Commercial Vehicles. Skill Lync. https://skill-lync.freshdesk.com/support/solutions/articles/43000572450-gradeability-of-commercial-vehicles

7. How to read your tyre size. (n.d.). Bridgestone NZ. Retrieved November 23, 2020, from https://www.bridgestonetyres.co.nz/how-to-read-your-tyre-size

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