The goal of this project is to determine the optimal gear ratios for a vehicle containing a four-speed transmission. This vehicle is required to reach a speed of 30 m/s in the minimum time possible. Equations for the velocity at each shift point were found. An equation for the total time that the vehicle took to reach 30 m/s was then derived and equations for the times spent in each gear were found through integration of the provided formula for acceleration. The optimal gear ratios were then found by taking the partial derivatives of the total time equation with respect to each gear ratio. These equations were set equal to zero and solved by the method of substitution to obtain the optimum value for each gear ratio. These results would provide engineers with the information required to efficiently develop transmissions to reach particular speeds in a minimum amount of time.
"Optimum Gear Ratios for an Electric Vehicle,"
Undergraduate Journal of Mathematical Modeling: One + Two:
1, Article 4.
Available at: http://scholarcommons.usf.edu/ujmm/vol7/iss1/4
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Kanaka Nallamshetty, Mathematics and Statistics
Jonathan Burns, Mathematics and Statistics
Scott Campbell, Chemical and Biomedical Engineering