Calculating the forces Acting on a vehicle
1) Given data:- Tyre 1 : 90/100 R10 53J
Tyre 2 : 90/90 R18 51P
Gear Ratio (`G`) = `7`
Speed (`v`) = `90` kmph = `25` m/sec
To find:- Maximum speed of the motor used in an electric scooter.
Solution:-
The tyre diameter is calculated using the following formula:
`Total Diameter = (Section Width * Aspect Ratio * 2) + Wheel Diameter`
`Radius of tyre 1 = (10*25.4)+(90*1*2)`=`434/2 = 0.217 m`
`Radius of tyre 2 = (18*25.4)+(90*0.9*2)`=`619.2/2 =0.3096 m`
Now, the maximum speed of the motor can be calculated using the following formula:
`omega = v/R * G` (in rad/sec)
`N = 60*omega/(2pi)` (in rpm)
Therefore, `omega_1 = 25/0.217*7 =806.45` rad/sec
`omega_2 = 25/0.3096*7 = 565.2` rad/sec
Now, `N_1 = omega_1*60/(2pi) = 806.45*60/(2*pi) = 7701.03` rpm
`N_2 = omega_2*60/(2pi) = 565.24*60/(2*pi) = 5397.64` rpm
2) Finding Propulsion Power:-
The Drag Force,Rolling Resistance Force,Hill Climbing force is calculated using the following formula:-
`F_(drag = 1/2 *C_d*rho*A*v^2`
`F_(roll) = mumg`
`F_(hill) = mgsinpsi`
`F_(tractive) = F_(drag) + F_(roll) + F_(hill)`
`P_(drag) = F_(drag) *v`
`P_(roll) = F_(roll) *v`
`P_(hill) = F_(hill) *v`
`P_(tractive) = F_(tractive) *v`
The limitations of this calculations are that the power is calculated only for a particular speed, also it depends on the designer to choose the values of air density,drag coefficient,rolling resistance coefficient.
3) Assuming that tire pressure reduces by 15% which results in increase of rolling resistance effect by two times,difference in total traction power :
Since rolling resistance coefficient is a function of tyre inflation pressure, value of rolling resistance coefficient increases when tyre inflation pressure decreases.
`therefore F_(roll) = mumg = 2*0.02*800*9.81 = 313.92 ` N
`therefore P_(roll) = F_(roll)*velocity = 6.976` kW
Difference in Rolling Power = `6.976-3.488 = 3.488`kW
Hence, the rolling power has increased by 100 %
4)The gradeability of the hill was 45 degrees and the average speed during the 99 turns was around 93 kmph and during the 999 steps was 38 kmph.
The forces acting on the car were:-
Rolling resistance force, Tractive Force, Drag Force, Hill Climbing Force, Linear Acceleration force and Angular Acceleration force.
Link of excel file:-
https://drive.google.com/file/d/11__P5qJKWHA5FSiKM70A2Iyg43U4BYbv/view?usp=sharing