Forces acting on a Vehicle
AIM: To learn about all the forces acting on the vehicle and to calculate the power needed for the vehicle to overcome all the opposing forces.
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? Assume the following arrangement from the motor to the wheel.
90/100 R10 53J
Referring to the above tire specs,
Section Width: 90 mm
Aspect Ratio: 100%
Therefore, the height of the tire sidewall = 100100⋅90100100⋅90 mm
Rim diameter: 10 inches
Load index: 53
Excel sheet:
| Speed(kmph) | 90 |
| Speed(mps) | 25 |
| Gear ratio | 7 |
| Tyre specs | 90/100 R10 53J |
| Section width | 90 |
| Aspect ratio | 100 |
| Rim diameter(inches) | 10 |
| Rim Diameter(mm) | 254 |
| Load index | 53 |
| Tyre height(mm) | 90 |
| Tyre radius(m) | 0.217 |
| Motor Calculation | |
| Max speed of the motor(rad/s) | 806.4516129 |
| Angular velocity(rpm) | 7697.947564 |
Therefore, the maximum speed of the motor used in an electric scooter capable to run at 90 kmph is 806.4516 rad/s.
For 90/90 R18 51P,
| Tyre specs | 90/90 R18 51P |
| Section width | 90 |
| Aspect ratio | 90 |
| Rim diameter(inches) | 18 |
| Rim Diameter(mm) | 457.2 |
| Load index | 51 |
| Tyre height(mm) | 81 |
| Tyre radius(m) | 0.3096 |
| Motor Calculation | |
| Motor Torque, T(Nm) | 34.66703367 |
| Max speed of the motor(rad/s) | 565.245478 |
| Angular velocity(rpm) | 5395.525263 |
Therefore, the maximum speed of the motor used in an electric scooter capable to run at 90 kmph is 565.2454 rad/s.
Hence, as tyre radius increases, the electric motor can run at lower speed for the same input parameters.
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, Acceleration (0 to top speed in specified seconds), Hill climbing angle, Speed.
Vehicle Propulsion:
Propulsion is a means of creating force leading to movement.
A propulsion system has a source of mechanical power (some type of engine or motor, muscles), and some means of using this power to generate force, such as wheel and axles, propellers, a propulsive nozzle, wings, fins, or legs. Other components such as clutches, gearboxes, and so forth may be needed to connect the power source to the force-generating component. The term propulsion is derived from two Latin words: pro meaning before or forwards and pellere meaning to drive.
FORMULAE:
Rolling Resistance Force, N
Frr=μrr⋅m⋅gFrr=μrr⋅m⋅g
where,
μrrμrr is the coefficient of rolling resistance
mm is net weight, kgkg
gg is the acceleration due to gravity, ms2ms2
Air Drag Force, N
Fad=12⋅ρ⋅A⋅v2⋅CdFad=12⋅ρ⋅A⋅v2⋅Cd
where,
AA is the frontal area, m2m2
vv is vehicle speed, msms
CdCd is coefficient of drag
Hill Climbing Force, N
Fhc=m⋅g⋅sinψFhc=m⋅g⋅sinψ
where,
ψψ is the hill-climbing angle, radiansradians
Excel sheet:
| Rolling Resistance Calculation | |
| Kerb Weight(kg) | 110 |
| Payload(kg) | 300 |
| Coefficient of rolling resistance | 0.005 |
| Rolling Resistance Force, Frr(N) | 20.1105 |
| Air Drag Calculation | |
| Air density(kg/m3) | 1.25 |
| Width(m) | 0.7 |
| Height(m) | 1.2 |
| Frontal area(m2) | 0.84 |
| Drag Coefficient | 0.2 |
| Speed(kmph) | 90 |
| Speed(mps) | 25 |
| Air Drag Force, Fad(N) | 65.625 |
| Fte = Frr + Fad, (N) | 85.7355 |
| Pte = Fte*v, (kW) | 2.1433875 |
| Hill Climbing Calculation | |
| Angle(degrees) | 10 |
| Speed during hill climbing | 35 |
| Hill climbing Force, Fhc (N) | 698.0798608 |
| Gear ratio | 7 |
| Fte = Frr + Fad + Fhc, (N) | 783.8153608 |
| Pte = Fte*v, (kW) | 19.59538402 |
Hence, the total power is 2.1433 kW and the total power(including the Hill climbing force) is 19.5953 kW.
LIMITATIONS:
- Formulae must be entered manually.
- Time-consuming.
- Plotting the graphs is hectic.
- Cannot copy-paste the formulae if formulating new vehicle data.
3. Assuming that tire pressure reduction by 15% results in an increase of rolling resistance effect by two times, how much will be the difference in total traction power keeping all other parameters the same?
| Rolling Resistance Calculation | |
| Kerb Weight(kg) | 110 |
| Payload(kg) | 300 |
| Coefficient of rolling resistance | 0.005 |
| Rolling Resistance Force, Frr(N) | 20.1105 |
| Air Drag Calculation | |
| Air density(kg/m3) | 1.25 |
| Width(m) | 0.7 |
| Height(m) | 1.2 |
| Frontal area(m2) | 0.84 |
| Drag Coefficient | 0.2 |
| Speed(kmph) | 90 |
| Speed(mps) | 25 |
| Air Drag Force, Fad(N) | 65.625 |
| Fte = Frr + Fad, (N) | 85.7355 |
| Pte = Fte*v, (kW) | 2.1433875 |
| Tyre pressure reduction by 15%, doubles the rolling resistance | |
| New Rolling Resistance Force, Frr(N) | 40.221 |
| New Fte(N) | 105.846 |
| New Pte(kW) | 2.64615 |
| Difference between tractive powers(kW) | 0.5027625 |
DIFFERENCE BETWEEN OLD AND NEW TRACTIVE POWER:
Therefore, on doubling the rolling resistance the tractive power is increased by 23%.
4. See the video of the Range rover sport dragon challenge. How much is the gradeability? What was the average speed? Which are the forces acting on car?
Gradeability:
A car's gradability is its ability to climb slopes. Gradability is measured either in degrees or percentages. Gradability is dependent on engine power, drivetrain type, gear ratio, weight, weight distribution, car's center of gravity, and traction.
Mathematically,
Gradeability = riserun⋅100riserun⋅100 = δhdδhd
where
δhδh = rise
dd = run
αα = inclination
- The gradeability of the Heaven’s Gate on Tianmen Mountain, China is 100%. As the inclination of the mountain is 45 degrees.
- The average speed of the Range rover sport was 40 kmph.
There are three forces acting on the car, Those are,
- FrrFrr = Rolling Resistance Froce
- FadFad = Aerodynamic Force
- FhcFhc = Hill Climbing Force
Technically, even Acceleration Force is added to the total tractive effort. Since the average speed is considered the acceleration force on the net effort is neglected. Although there is some angular acceleration acting on the net effort.
CONCLUSION:
- The maximum speed of the motor used in an electric scooter capable to run at 90 kmph was calculated.
- Excel calculator to identify vehicle propulsion power based on given inputs is drafted.
- By changing the rolling resistance values, the difference in total power s calculated.