...

• In order to determine the required torque of the motor to pass the hill test, we need to see how much it needs while going the minimum speed on the highest incline road

  • The minimum speed the car can go is 32.2 km/h

    • Regulation 12.24

  • The highest incline road in the US 37% incline Canton street in Pittsburgh

    • §  https://en.wikipedia.org/wiki/Grade_(slope)

• all variable values for drag were acquired from Michael Hanley, Aero team lead

  • Cross sectional area of the car 1.5m^2

  • Coefficient of drag 0.15

  • Michael also said we are safe to assume that the center of pressure CP is in approximately the same spot as the center of gravity CG

• A few values had to be inferred by Jens and Malcolm

  • total mass 200kg

  • coefficient of rolling resistance for each wheel 0.0055

    • Jens will be calling Bridgestone to confirm the exact coefficient value sometime soon

    • this assumption is from “The Winning Solar Car” page 18

  • wheel base 2m

  • track 1m

  • center of gravity and center of percussion pressure located at middle 1m in from the front wheel (center of the wheel base) and half of the tracks distance above the ground (1m and 0.5m respectively0.5m up from the ground (half the distance of the track)

  • coefficient of static friction 0.3.7

    • http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/frictire.html#:~:text=Jones%20and%20Childers%20report%20coefficients,an%20%22all%20weather%22%20compromise.

    • assuming perfect rolling on dry roads

• all other values are fixed known values

  • acceleration due to gravity

  • density of air

  • tire radius

...

• using this information, its possible to make free body diagrams and derive an equation for the required torque on the back wheel, assuming that's the only wheel with motors on it

  • full derivation and calculations can be found here: Malcolm @ University of Waterloo

• a spreadsheet was made to test different variable values and to solve the equation

  • found here: Motor Calculation V2 Public.xlsx

• using all the preliminary information, the required torque is ~203.29 Nm

  • Image RemovedImage Added

  • Image Added

Analysis/Adjustments

• From the mitsuba motor’s documentation, the highest achievable torque is 62.8 Nm

  • Motor Documentation on the 131V (LO) ECO graph

  • Even with 2 motors, its not able to hit 200 Nm of torque

• checking values, it seems that MSXIV MSXII used a max incline gradient of 15%

  • Motor Requirements

  • we will change the gradient from 37% to 15%, as its more likely we will be driving on a road of similar incline to 15%

...

• After keeping everything the same, but reducing the incline angle down to 15%, we get a required torque of ~95 Nm

  • Image RemovedImage Added

Conclusion

• The torque is now low enough that it is attainable

• the car must have 2 motors to attain this value

  • It is important to note that this assumption is based on a few assumptions

    • The motor torque only acts at the back wheel

    • the highest attainable torque is 62.8 Nm at ~55 km/h