Forces acting on vehicle-Electric Scooter

Q1. What should be the maximum speed of the motor used in an electric scooter capable to run at 90kmph? If the fixed gear ratio is 7 and tire size is 90/100 R10 53J?

An Electric scooter with the below data

Total load, m(kg)=87kg(data taken from tyre spec)

Air density,`rho`=1.25kg/m^3

Drag coefficient,`Cd`=0.75

Frontal Area,A =0.6 `m^2`

Rolling resistance coefficient, `murr`=0.007

Reduction Gear Ratio, G=7

Wheel radius, r=0.3m (radius =Rim Radius +Height of the tyre;

From Tyre Spec, Rim Diameter=16inches=0.4062m

Rim radius=0.2m

Height of tyre=50%of width of tyre=195/2

=97.5mm (width of tyre=195mm)

=0.0975m

Wheel radius=0.2+0.0975=0.2975m

Motor characteristic, TorqueT=153-1.16w (below critical speed)

T=153-1.16Gw/r (above critical speed)

Moment of inertia, I =m.r^2=87*0.3^2=7.83 kg-m^2

Velocity of the vehicle=90km/hr=25m/s

`G/r*T=murr*m*g+0.625*A*Cd*v^2+(m+(I*G^2)/(etag*r^2))*dv/dt`

7/0.3*0.98* (153-1.16*w) = 0.007*87*9.8+0.625*0.6*0.75*25^2 + (87+7.83*7^2/98*0.3^2) dv/dt

22.8(153-1.16*w) =5.96+175.78+157* dv/dt ----------------EQ1

dv/dt --- acceleration

To find acceleration, we use Matlab program

t=linspace(0,50,501);
vel=zeros(1,501);
d=zeros(1,501);
dt=0.1;
t=t+1;
for n=1:500
    if vel(n)<10.8
        vel(n+1)=vel(n)+dt*(0.17-(0.000063*(vel(n)^2)));
    elseif vel(n)>=10.8
        vel(n+1)=vel(n)+dt*(0.78-(0.46*vel(n))-(0.000063*(vel(n)^2)));
    end
    d(n+1)-d(n) | 0.1*vel(n)
end
     vel==vel.*36
     plot(t,vel);   
     xlabel('time/seconds');
     ylabel('velocity/kmph');

after executing above code ,we get acceleration value a=0.018m/s^2

Substitute in EQ1, we get the angular velocity of the motor w=125m/s^2

This should be the maximum speed of the motor to attain a vehicle speed of 90km/hr.

For tyre 90/90 R18 51P, the specification details of the tyre are as follows

90 - width in millimeter of the tyres across

90 - the aspect ratio,it is the ratio of the sidewall height to the cross-section width.

R - radial construction

18 - dimension in inches, stands for the diameter of the wheel that the tyre is designed to fit

51 – the load index i.e., the maximum weight each tyre can carry at full speed

P -- the speed rating .e., the maximum speed for the tyre at full speed.

An Electric scooter with below data:

Total load,m=51kg(data taken from tyre spec)

Air density,`rho`=1.25kg/m^3

Drag coefficient, `Cd`=0.75

Frontal Area,A=0.6m^2

Rolling resistance coefficient,`murr`=0.007

Reduction Gear Ratio,G=7

Wheel radius,r=0.3m (radius =Rim Radius +Height of the tyre;

From Tyre Spec, Rim Diameter=18inches=0.4572m

Rim radius=0.23m

Height of tyre=50%of width of tyre=90/2

=45mm (width of tyre=90mm)

=0.045m

Wheel radius=0.23+0.045=0.275m

Motor characteristic, T=153-1.16w (below critical speed)

T=153-1.16Gw/r (above critical speed)

Moment of inertia, I =m.r^2=51*0.275^2=3.85 kg-m^2

Velocity of the vehicle=90km/hr=25m/s

`G/r*T=murr*m*g+0.625*A*Cd*v^2+(m+(I*G^2)/(etag*r^2))*dv/dt`

(7/0.23)*0.98* (153-1.16*w) =0.007*51*9.8+0.625*0.6*0.75*25^2+(51+(3.85*7^2)/(.98^2*0.23^2)dv/dt

29.82(153-1.16*w) =3.5+175.78+88.13*dv/dt ----------------EQ1

dv/dt------acceleration

To find acceleration, we use Matlab program

t=linspace(0,50,501);
vel=zeros(1,501);
d=zeros(1,501);
dt=0.1;
t=t+1;
for n=1:500
    if vel(n)<10.8
        vel(n+1)=vel(n)+dt*(0.29-(0.000074*(vel(n)^2)));
    elseif vel(n)>=10.8
        vel(n+1)=vel(n)+dt*(1.2-(0.04*vel(n))-(0.000074*(vel(n)^2)));
    end
    d(n+1)-d(n) | 0.1*vel(n)
end
     vel==vel.*36
     plot(t,vel);   
     xlabel('time/seconds');
     ylabel('velocity/kmph');

2. Prepare a simple excel calculator to identify vehicle propulsion power based on given inputs and outputs, implement formulas in cells.

Inputs: Kerb Weight (kg), payload(kg), Coefficient of rolling resistance, Air density(kg/m^3),Width(m), Height(m), Drag Coefficient, Acceleration(0 to top speed in specified seconds),Hill climbing angle, Speed.

What are the limitations of this calculation?

1. In electrical vehicles ,both mechanical and electrical systems are designed to provide optimal range and performance. The model is used to define the required vehicle output power demand in comparison with the actual data . the forces required to propel a vehicle while cruising consist of rolling resistance,aerodynamic resistance and hill-climbing resistance.

Where `Frr` is the rolling resistance force, Fad is aerodynamic force, Fhc is the hill-climbing force, µrr is the rolling coefficient of the tyre, m is the total vehicle mass, is the drag area,Cd is the drag coefficient and v is the velocity.

Excel calculator for calculating Power output of the Electric scooter:

The limitations of this calculation are, the hill-climbing angle and speed of the vehicle.

3. Assuming that tire pressure reduction by15%results in the increase of rolling resistance effect by two times. How much will be the difference in total traction power keeping all other parameters the same?

1. When the tyre pressure reduction takes place,it directly affects the rolling resistance force of the vehicle and reduces the tractive force. That is because of tyre characteristic that is made from rubber. When the vehicle speed was low, the frequency of tyre deformation was also low and resulted in high energy losses. So the high rolling resistance force was generated, when the vehicle speed is high, the frequency of tyre deformation increased and made the molecule of the rubber vibrate more than low vehicle speed. These effects made the tyre stiffer than low frequency and resulted in decreasing the rolling resistance force.

4. See the video of Range over sport dragon challenge. How much is the gradeability? What was the average speed? What are forces acing on cars?

1. Gradeability is the steepest gradient a machine can climb, compared to the Operating Angle which is the steepest gradient a machine will operate on.

Th gradeability is 45degrees. The average speed is 40Kmph.

The forces acting on car are Rolling Resistance force, Hill climbing Force and Aerodynamic force.