Mathematical modelling to optimize mobile performance on downhill ramps
DOI:
https://doi.org/10.35819/remat2021v7i2id4800Keywords:
Ramp Mobiles, Gravity Car Race, Dynamic Equation, Mass Influence, Performance OptimizationAbstract
The present study analyses mobiles, with or without traction force, that descend an inclined ramp under the action of gravity, subject to drag forces and kinetic friction. From the dynamic equation and the obtainment of the speed and position equations, the effect of the mobile mass on their performance in an eventual competition was investigated, understanding by performance the distance travelled by the mobiles in a fixed interval of time, previously stipulated. It was possible to conclude that, when the mobiles are not motorized, the performance grows continuously with the mass. For this reason, it is necessary to standardize the mass value of competing vehicles to guarantee isonomy. When vehicles are equipped with constant traction force, there may be a mass value capable of maximizing performance. Therefore, it is interesting to leave it up to competing teams to determine the most advantageous mass value for their vehicles. The conditions under which the performance is supposed to be optimized were evaluated and an analytical expression for determining the mass that maximizes the performance was obtained.
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