forces acting on the vehicle

Q.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 & tyre size is 90/100 R10 53J? Also recalculate the value if the code is 90/90/ R18 53P ?

Example -

Fig.1 - Tyre Reading Chart

Defination-

Tyre is the typical inflated rubber covering that is surrounded by the inflated rubber tube, placed round a wheel to form soft contact with the road or we can say that, A ring shaped component that surround the round wheel’s rim to transfer the vehicle’s load from axle through the wheel to the ground and to provide traction on the surface travelled over.

How to read tyre size?

Tyre size is 90/ 100/ R10

1.Width-

this indicates the section width of the tyres in millimetres. So if the three digit code is 195 then then width of the tyre is 195 mm. this code will be found on left most side of the tyre. And this width is referred as sectional width. It is necessary that tread width is generally smaller then the actual width of the tyre & overall width can be measured from one side of the tyre to the other side in fact kerbing ribs, extra sidewalls and raised letters are also taken into consideration as well. To have more accuracy in the tyre width calculation it is always preferred that sidewalls of the tyres are also taken into consideration.

2. Aspect Ratio or Profile-

It is the height from the base of the tread of the rim and this number represents a percentage of tread width and the low profiles tyre have smaller aspect ratio percentages. For example 55 is the tyre aspect ratio and we can say that the height of the tyre is 55% of its width. It is also known as profile and the profile is basically height of the sidewall. It is generally referred as the ratio between section width of the tyre and the sidewall. Smaller aspect ratio tyres are also available for sports cars and they are generally used for more precise handling and sharp corners capabilities but the disadvantage is they don’t offer comfortable and cushioned ride.

3. Tyre construction-

R means the tyre is radial ply construction meaning the way in which it has constructed radially and this is the most preferred in manufacturing and you will rarely fond the tyre without R on its specifications.

4.Rim-

Rim or Rim Size is the measurements of tyre inner diameter combined with the wheel’s outer diameter and 16 indicates the diameter of the rim and if you want to buy the wheels for existing tyres you will require this size.

5.Load index-

87 is the number indicates maximum load capacity of the tyre.

6.Speed Symbol-

V is the letter which indicates the speed at which the tyre can be safely operated, subject to the tyre being is sound condition, with the recommended pressure and correctly fitted.

Data given & Solution-

Width(W) = 90mm.

Aspect Ratio (AR) = 100%

Aspect Ratio is converted into height- H = AR*W/100 (100*90/100)

Height = 90mm. (Total Height = 2*90)

Rim Size = 10 inches (254 mm)

Diameter (D) = wd = D + 2 * H = 254 + 2 * 90 = 434 mm.

Wd = wheel diameter.

Radius (R) = 217MM = 0.217 m.

Gear Ration (G) = 7

Speed/ Velocity (V) = 90 kmph = 25 m/s.

Angular velocity = G*V/r = 7*25 /0.217 = 806.45 Rad/sec = 806.45*60/2 = 7701.03 RPM.

Therefore, Angular Velocity () = 7701.03 RPM.

Recalculate the same value if the code is 90/90 R18 50P

Width(W) = 90mm.

Aspect Ratio (AR) = 90%

Aspect Ratio is converted into height- H = AR*W/100 (90*90/100)

Height = 81 mm. (Total Height = 2*81)

Rim Size = 18 inches (457.2 mm)

Diameter (D) = wd = D + 2 * H = 457.2+ 2 * 81 = 619.2 mm.

Wd = wheel diameter.

Radius (R) = 309.6 mm = 0.3096 m.

Gear Ration (G) = 7

Speed/ Velocity (V) = 90 kmph = 25 m/s.

Angular velocity = G*V/r = 7*25 /0.3096 = 565.24 Rad/sec = 565.24*60/2 = 5396.69 RPM.

Therefore, Angular Velocity () = 5396.69 RPM

Q.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 Resistence .

Air Density (Kg/m³).

Width (m).

Height (m).

Drag Coefficient.

Speed (m/s).

Total power in KW.

Formulaes Used-

Rolling Resistence

Where, = coefficient of rolling resistance.

m = Total mass of the vehicle (kerb weight + payload).

g = gravitational acceleration.

Aerodynamic Drag Force

C_d = Coefficient of drag.

A = Projected front area.

= Density of Air.

V = Speed.

Goggle Drive link- Forces acting on a vehicle

The limitations of the above calculation is –

1. It is not suitable for lengthy calculation.
2. We have to neglect power loss due to internal forces.
3. The vehicle is running on flat surface hence we can ignore the effect of gradient and hill climbing force which leads to total tractive force of the vehicle
4. We can ignore the acceleration forces because in this case the acceleration is zero as the vehicle is moving at constant speed.

Q.3 Assuming the tire pressure reduction by 15% results in increase of rolling resistance effect by 2 times, how much will be the difference between the total traction power keeping all other parameters same?

From above table assuming that rolling resistance force doubled due to 15% decrease in pressure it is concluded that the total tractive power is increased by 8.1%.

	clear all 
close all
	clc 
	
	load=500; 
	wt=1000; 
	u=0.03; 
	p=1.225; 
	d=1.5; 
	h=1.5; 
	cd=0.2; 
	
	speed=linspace(0,100,100); 
	
	%total weight 
	w=(load+wt)*9.81; 
	a=h*d; 
	
	v=speed.*(5/18); 
	
	fdrag=0.5.*p.*a.*(v.^2).*cd; 
	frr=u*w; 
	
	power=((frr+fdrag).*v)/1000; 
	%rolling resistance is doubled due to tyre pressure reduction 
	power2=(((2*frr)+fdrag).*v)/1000; 
	
	plot(speed,power,speed,power2) 
	xlabel('Speed(kmph)'); 
	ylabel('Total power(kW)'); 
	legend('tyre fully inflated','15% reduction in tyre pressure'); 
	title('effect of increase of rolling resistance by two times'); 
	saveas(gcf,'2.jpg');

Q.4 See the Range Rover Sports Dragon Challenge, How much is the Gradebility? What was the average speed? Which of the forces acting on the car?

Range Rover Sports Dragon Challenge

The grade also called (slope, incline, gradient , rainfall, Pitch or rise) of a physical feature, constructed line refers to the tangent of the angle of that surface to the horizontal. Gradeability is the ability of the vehicle to climb an elevation or slope a given constant speed.

From the above reference we can calculate the percentage of Gradeability which is defined by (RISE/RUN)*100. In this case 45 degrees slope is equal to 1/1 ratio of RISE/RUN which is 100% Geadeability.

Average spped driven by the professional is 40 KMPH.

Forces acting on a vehicle are-

Average speed of the car = Distance/ Time

From this article –

Range Rover Article

Total Distance = 11.3 KM.

Time = 22 Minutes 41 Seconds = 0.37 hrs.

Average Speed = 11.3/ 0.37 = 30.54 km/hr.

CONCLUSION –

From this article it is concluded that rolling resistance increases as soon as tyre pressure decreases and hence power required to overcome those forces increases. Air resistance force, gradient resistance, Traction force, Rolling resistance will act on a car while Gradeabilty.also, as elevation angle goes on increasing Gradeability goes on increasing.