Forces acting on a vehicle

Objective -

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? How 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.

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?

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

Solution

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? How to read a tire?

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

--Tyre is having a designated code printed on it which is in this case 90/100 R10 53J.

This designation of tyre can be described as

90 – is the width of tyre in mm

100 – aspect ratio is given in percentage

R – Radial construction

10 – Rim diameter in inches

53- load capacity of Tyre

J – velocity (speed) rating

Image for the symbol

Speed rating of tyre table

Load carrying capacity for Tyres

90/100 R10 53J

SPeed rating for tyre is 100 Km/h

and Load carrying capacity is 206 kg.

Now the speed of motor for 90/100 R10 53J can be calculated by

ɯ (omega)= G (v/r)

where

ɯ = angular velocity (speed)

G = gear ratio = 7

v = linear velocity in m/s 90 Kmph or 25 m/s

r = radius of the wheel in m

so to find the radius of the wheel formula is

diameter of wheel = 2(width X aspect ratio) + rim diameter

= 2 (90 X (100/100)) + 254

= 434 mm or 0.434 m

Radius is D/2 so r = 0.217 m

Now v = is given as 90 KMph which is 25 m/s

Thus ɯ = G(25/0.217)

= 806.451 rad/s

= 7(806.451 X 30)/2

= 7701 RPM.

Now for the tyre 90/90 R18 51P with all the other values remaining the same

diameter of wheel = 2(width X aspect ratio) + rim diameter

= 2 (90 X (90/100)) + 18 X 25.4

= 619.2 mm or 0.6192 m

Radius is D/2 so r = 0.3096 m

Now v = is given as 90 KMph which is 25 m/s

Thus ɯ = G(25/0.217)

= 565.24rad/s

= (565.24 X 30)/2

= 5398 RPM.

Thus speed of motor is 7701 RPM for 90/100 R10 53J

And 5398 RPM for 90/90 R18 51P

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?

-Total tractive Forces = Rolling resistance force + Aerodynamic Drag force + Hill climbing Force + Acceleration Force

In this case we are considering that the vehicle is moving at constant velocity so acceleration forces gets cancelled.

Rolling Resistance force = It is also know as Rolling friction of Rolling Drag force resisting motion of Body when a body rolls on a surface. The coefficient of rolling resistance varies from surface to surface.

Typical values of rolling resistance coefficient

Frr = μrr x m x g

Where μrr = rolling resistance coefficient

M = mass of vehicle in Kg

g =9.81 m/s

Aerodynamic Drag Force – It is the drag to the motion of body caused by the Fluid surrounding the body. When a car is moving forward the air is the fluid and resistance to motion by air is called aerodynamic drag resistance.

Coefficient of Drag for air 1.25 kg/m^3

Typical values of Drag coefficient

Fad = ½ xρ"> ρ.A.Cd.v^2

Where A = Front area

Cd = drag coefficient

v = velocity of vehicle

ρ = density of fluid

Hill climbing Force = As the name suggests the force acting on the vehicle when the vehicle is climbing a slope or hill. The angle of slope determines the force acting on the vehicle

Formula for Fhc = m.g. sinØ

Whrer Ø = slope angle in radians.

m = mass of vehicle in Kg

g =9.81 m/s

Thus Total Tractive force acting on the vehicle is given by

Fte = Frr+Fad.+Fhc

In this case we are considering that the vehicle is moving at a constant speed of 90 Kmph.

The Drag coefficient is assumed along with Rolling resistance coefficient. It can change depending on the surrounding conditions and the road conditions.

Vehicle 1 has different total weight then vehicle 2 and 3.

Power required for motor to overcome all the forces acting on vehicle can be given as

Pt = (Frr + Fad +Fhc) * v

where Frr= Rolling resistance force

Fad = Aerodynamic drag force

Fhc = Hill climbing force

v = velocity in m/s

the angle for slope is assumed to be 8 deg.

For vehicle 3 the tire pressure is reduced by 15% thus causing the coefficient of rolling resistance to be double then in for vehicle 2.

Total traction power is 17.777 Kw for vehicle 2 and 21.3088 Kw for vehicle 3

Thus the difference is 3.5311 Kw.

EXCEL sheet attached

What are limitations for the calculations?

You can change the assumed conditions such as constant speed as they may change due to surrounding factors.

As we are assuming the values of drag coefficient and rolling resistance coefficient the results may differ then the actual results.

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?

Grade Ability of vehicle is ability of a vehicle to climb a slope or a hill at ag given constant speed.

Method 1 = Image

As the angle is 45 deg the grade ability is 100.

Method 2 = grade ability of vehicle can be given by tan^-1 Ø X 100

Ø = slope angle

In this case the angle of slope is 45 deg

So tan^-1 (45) X100 = 1 X100 = 100

Thus in this case grade ability is 100.

Forces acting on the car are Hill Climbing Force ,Rolling Resistance force , Aerodynamic drag force.

Car has travelled 7 miles which is 11.26km in 22 minutes and 42 seconds, where the average of 30 kmph.by using

speed = distance/time = 29.7764kmph = 30kmph.

RESULT : Hence the gradeability of of Range rover sport dragon challenge is 100, the average speed is 30kmph and the forces acting on the vehicle are listed.

Speed of Motor is calculated.

And Power required to over come tractive forces is also calculated using Microsoft Excel.

Excel sheet Link - https://drive.google.com/file/d/1IX4yQFnJWSBdKCZzusMl4grxGq7pBv7U/view?usp=sharing