Motor RPM given car speed, gear and wheel radius

Question

Reading about Tesla cars I found that they can achieve 16000 RPM, single gear ratio 9.73:1 and differential ratio around 8.28:1, but... if I try to get RPM from car speed (max 200 km/h): RPM = car speed/(wheel radius) x differential ratio x gear ratio x (60/(2 x PI))

car speed: 200 km/h = 55.55 m/s wheel radius = 0.34 m differential ratio = 9.73 gear ratio = 8.28 conversion rad/s to rpm:(60/(2 x PI))

I get: RPM = (55.55/0.35) * 9.73 * 8.28 * (60/(2 x PI)) RPM = 122104.193095

which does not make sense

Am I missing something?

Answer 1

First, let's convert the speed to m/s:

200 km/h = 55.55 m/s, that's correct.

Then rotational speed:

55.55/(2*pi*0.34) = 26 rotations per second

After ratios: 26*9.73*8.28 = 2094.7 rotations per second

Per minute this is 125680 RPM.

I think what you're missing are the gear ratios. If you include only one of those, say 9.73, you would get 15179 RPM. This sounds about correct.

Perhaps the single gear ratio includes the differential ratio already and you're including it therefore twice.