# Homework Help: Model car formula

1. May 13, 2004

### jacko88

hi, at uni theres a track about 6 or 7 metres long, and we have been assigned a task to create a car that has the fastest time possible. I have found these equations....

mph = (rpm x tire diameter) / (gear ratio x 336)
rpm = (mph x gear ratio x 336) / tire daimeter
gear ratio = (rpm x tire diameter) / (mph x 336)

obviously if the track was 200m long, the gear ratio would have to be geared up for speed, and on a 2m track the car would needs alot of acceleration, but how can i use a forumula to create the perfect gear ratio? I realise that gear ratio = (rpm x tire diameter) / (mph x 336) would work, but how do i find the maximum mph? please help

2. May 13, 2004

### krab

Your first formula suggests that the lower the gear ratio, the higher the speed. You know that this is not true. Take your typical 24-speed bicycle, drive it on a flat road, and see if you can get most speed out of the highest gear. You cannot, no matter how long the track is. You mentioned acceleration and that lower gearing is required because of inertia. The missing component is of course the dissipative forces (rolling resistance, air drag). After getting up to speed, optimum gearing is simply where maximum available power is going completely into these forces. So what you do is calculate the top speed from the max power plus formulas for drag, note what rpm is required for that max power, and calculate the gearing.