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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
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
https://scientificgems.wordpress.com/2019/10/11/world-solar-challenge-car-weights/
it is not known at the time whether this includes driver weight or not
if not, the mass increases to 280kg, and that causes an issue because the torque is then outside specified ranges
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 pressure located at 1m in from the front wheel (center of the wheel base) and 0.5m up from the ground (half the distance of the track)
coefficient of static friction 0.7
all other values are fixed known values
acceleration due to gravity
density of air
tire radius
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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
Analysis/Adjustments
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