Car Gear Ratios (Calculate Wheel RPMs, Torque at Wheels, and Force at Wheels)

Lets talk about car gear ratios. In this video we will be going over how to calculate the number of revolutions the wheels will turn for a given engine RPM, what the torque multiplication will be after going through the driveline, and what force will reach the outside edge of the wheels.
Now in most cars there is an engine that supplies torque and rpms in the system. This is marked all the way to the left as 2 pistons. A transmission that is marked with a purple box around it which consists of multiple gears that can be changed depending on speed of vehicle, this changes torque and rpms reaching the wheels. Once you get going at higher speeds you don’t need as much torque to keep going. So the transmission switches to a higher gear larger gear number this higher gear has a smaller gear ratio. So there is less torque at higher rpms reaching the wheel at a higher gear. Finally there is an axle which has a fixed gear ratio also known as axle ratio. This turns higher rpms and lower torque at the input into lower rpms at higher torque at the output or wheel.
So I have listed out the gear ratios of the transmission and the axle for my vehicle. We need to collect the engine RPM and speed at the desired gear in this case 1st gear to find how many times the wheel will spin around. In this case we have an engine RPM of 2400 RPM at 20 mph in first gear.
Now we need to find the radius of the wheel. As you can see from the picture it is 15 inches. (sorry to those who think in metric however the logic of this problem should still apply)
So now let’s list out all of our givens and first solve for the theoretical wheel rotations per minute
First we need to find the wheel circumference in miles. This can be done by taking 2 pi times the wheel radius times the conversion of inches to miles.
The next step is to find how many miles per minute the car is traveling. This can be completed by converting the speed in miles per hour by 60 minutes.
Finally we can take the miles per minute and divide by the tire circumference in miles to get the theoretical wheel rpms. The theoretical wheel RPM’s is 224
Recall that for every one revolution of the driven gear the driver gear or where the torque and motion is coming from rotates the number of times listed in the gear ratio.
So now let’s solve for the experimental wheel rpms we can take the engine RPM’s and divide by the transmission gear ratio and then divide by the axle ratio.
Now lets calculate how much torque is reaching the wheels. Recall that for gear trains we can multiply the gear ratios together to get an equivalent gear ratio. We can take the input torque and multiply times the transmission gear ratio and the axle ratio. We get that with an input torque of 100 ft pounds we get around ten times the torque our about 1059 ft-lbs at the wheels. This is assuming 100% efficiency if you want to get a realistic value you will have to figure out what the efficiency of the driveline is.
Now to finish off this video lets take the output torque and divide by the wheel radius to get the force applied to the ground by the wheels. In this case the wheels are applying a force of 847.5 lbs.

Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.

[VAM_Physics_and_Engineering]

Note you will have less torque reaching the wheels due to inefficiency in the driveline. You will need to multiply times a driveline efficiency factor to get a closer real world approximation. The example was assuming 100% driveline efficiency.

[MrSam]

Dude, you come off like that middle school science teacher who simply can't keep his audience interested. Lighten up!

[clintonikechukwu]

How to calculate engine rpm before and after shifting gears. Having a transmission ratio of 2.4, 1.47, 1, 0.67 respectively and if its engine rotational speed during gear shifting is 3000

[johncoyle]

Does the torque converter need to be added in the torque formula?

[ronnieCNL]

Quick question. For the final answer of force applied to the ground from the wheels. Is that 847.5 lbs per wheel or in total?

[anettelira]

how did you solve each of the gear ratio to the highest gear ratio

[dragan]

Can someone please tell me is it 1059 divided by 15 inches???? As it doesn't equal that amount? Im doing something wrong? Cheers

[phalanx]

the final drive to wheel torque does not work for metric e.g my Land Cruiser has 5, 195Nm on the axle in first gear the wheel radius is 40cm 5, 195/40=129Nm that's less then my engine or i do it in meters 5, 195/0.40=12, 987Nm witch seams too much.

[dragan]

1059 ÷15 inch is not 847? Please explain??? As im new to this an not sure what im doing wrong

[jimchance]

How would I find top speed in a gear given the gear ratio, wheel size, and engine specs?

[Xjaje]

It would be nice if you could use metric system units for better understanding, smh.

[hopolo]

I had to stop the video when you said "rpms". Learn English

[nepalgamingleauge]

🥹i just want my car to be fast in a game and here i go