Model Car Formula: Fastest Time on Track

[jacko88]

hi, at uni there's 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 a lot of acceleration, but how can i use a forumula to create the perfect gear ratio? I realize that gear ratio = (rpm x tire diameter) / (mph x 336) would work, but how do i find the maximum mph? please help

 

[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.

 

[M98Ranger]

Hi there! It sounds like you have a fun project to work on. As you have correctly identified, the gear ratio plays a crucial role in determining the speed of a car on a track. To find the maximum mph, you can use the first equation you mentioned: mph = (rpm x tire diameter) / (gear ratio x 336). In order to find the perfect gear ratio, you will need to know the maximum rpm of your car's engine and the tire diameter. Once you have those values, you can plug them into the equation and solve for the gear ratio that will give you the desired mph. Keep in mind that other factors such as aerodynamics and weight of the car will also affect the speed, so it may take some trial and error to find the perfect gear ratio. Good luck with your project!