Forces Acting on a Vehicle
Aim- To understand the different forces acting on the vehicle.
To find 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.
Same calculation with tire 90/90 R18 51P
Prepare a simple excel calculator to identify vehicle propulsion power based on given inputs.
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.
Finally to evaluate Gradability, Avg Speed & Forces acting on Range Rover.
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Types of forces acting on a vehicle are-
- Rolling Resistance Force
- Aerodynamic Drag Force
- Acceleration Force
- Hill Climbing Force
Introduction about tire code-
Automobile tires are described by an alphanumeric tire code also called as ISO Metric tire code, mandated by the U.S. Department of Transportation (DOT) but used worldwide.
P215/65R15 95H
- First initial optional letter (or letters) indicates vehicle class of tire
P: Passenger car
LT: Light truck
ST: Special trailer
T: Temporary
2. 3-digit number: Nominal section width of the tire in millimeters
3. 2 or 3-digit number: Aspect ratio of sidewall height as a percentage of the nominal section width of the tire.
4. The second optional letter indicates the construction of the fabric of the tire
B: Bias belt
D: Diagonal
R: Radial
5. 1 or 2-digit number: Rim diameter in inches of a wheel.
6. 2- or 3-digit number: Load index indicates the maximum weight limit per tire.
7. 1 or 22-digit/letter combo: Speed rating indicates the maximum speed for the tire at full load.
The figure to decode the speed rating and load index of the tire.
Now for the given tire 90/100 R10 53J
Rim diameter = 10inches=254mm
tire height = (aspect ratio*tire width)/100=(100*90)/100=90mm.
tire radius=254/2+90=217mm.
speed of scooter V given as 90kmph converting to m/s= 25m/s.
The angular velocity of tire=linear velocity/radius of tire
= 25/0.217
=115.20 rad/sec
=1100 rpm
Gear ratio=7
angular velocity of motor=1100*7=7700rpm=806.34rad/sec.
Tyre Data 2-90/90 R18 51P
Tyre Width = 90mm
Aspect Ratio=90%
Tire height=(90*90)/100=81mm
Rim diameter =18in=457mm
Load Index =51
speed rating P=150kmph
tire radius=Rim radius/2+tire height
=(457/2)+81=310mm
speed of scooter V given as 90kmph converting to m/s= 25m/s.
The angular velocity of tire=linear velocity/radius of tire
= 25/0.31
=80.75rad/sec
=771rpm
Gear ratio=7
angular velocity of motor=771*7=5397rpm=565.172518rad/sec.
The maximum speed of the motor when 90/100 R10 53J tire is 806.34rad/sec and
tire 90/90 R18 51P is 565.172518rad/sec.
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Excel Calculator on Vehicle propulsion power based on inputs-
Result-The total tractive force for vehicle-1 is 243.74N and Total Power is 6.77KW.
Vehicle-2 tractive force is 209.406N and total power is 5.81KW.
Limitations of Excel calculation-
1. The calculation only at peak Power operation does not vary with time.
2. Aerodynamic force calculations do not Include Protrusions, skin friction, or shape change.
3.coefficent of rolling Resistance is given constant.
4.Air density changes with Temperature.
5. Large and lengthy calculations cannot be performed entering each value for Inputs.
6. Road conditions are considered uniform, flat for calculation.
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Assuming that tire pressure reduction by 15% results in an increase of rolling resistance effect by two times.
The difference in tire Pressure value of coeff.of rolling resistance increases thus the power value which has to overcome the resistance also increases.
The rolling resistance is increased by 100%
percentage increase in total power is 30.13% if tire pressure is reduced by 15%.
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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 the car?
Answer-
the forces acting on the car were- Tractive force, drag force, hill climbing force, acceleration force, centripetal force.
the gradeability of hill os 45 degrees. there are 99 turns and 999 steps and the gradability of range rover sport is 45degrees.Gradient ratio of 1:1.
average speed for 11.3km in 22 min 41 sec is 30.25kmph.
Excel file for vehicle power calculation-
https://docs.google.com/spreadsheets/d/1J47wWbhTvpejvBDbbKRVGneawafXb-1dbQCC58DnevI/edit?usp=sharing