*Question by Mother G*: I’m working on a “toy” car for 8th grade science (physics) What gear ratio would be the most ideal?

I tried 5:1, 25:1, 75:1 and others. NOW I JUST WANT SOME DAMN HELP SO I CAN GET A GOOD GRADE ON THIS PROJECT lol. okay…how does she expect us to learn what ratio works when there are like 400,000,000 to try. It would be nice if someone could just tell me what’s best for a ratio and why, isnt that all that really matters. I mean gosh…

**Best answer:**

*Answer by huippi*

There is no universal “best ratio”. You have to use different ratios for different projects. If your motor has high rotation speed but it doesn’t have much torque (it has more torque if it harder to stop using hands) you could use higher ratios likes 50:1 (when motor rotates 50 times wheels rotate only once), but if your motor has high torque but low speed you could use lower ratios, even 1:1 over 0.5:1.

You could also measure speed of your car and then grade few ratios or measure how fast your can climb steep hill and then rate all ratios. The last test would maybe produce more useful gear ratio for general use but it always depends how you will use your car.

I am confident that if you will make both tests, plot your measurements and then make your choice based on those measurements you will get good grade.

**Know better? Leave your own answer in the comments!**

I can’t answer the question directly, but I can help you with some ideas on where to start.

There’s going to be a number of trade-offs.

Looking at the characteristic curve for a DC motor, torque increases as speed decreases. This makes sense. Torque is proportional to current, current is inversely related to back-emf, and back-emf is directly related to speed.

The motor faceplate will say how fast the motor turns at full speed. It’ll also tell you the torque.

The first thing you’ll have to design for is overcoming the force of static friction, where everything actually starts to move. You can figure out this by testing it. Place the fully loaded car on a flat surface, and apply an increasing amount of force until the car moves. That measurement is the amount of force you’ll need to get the car moving. It’s always going to be more force to first move the car than to keep it going.

Once you know the force required to get the car moving, you can now choose a gearbox based on getting the car rolling with the motor you’ve got.

The torque at the wheel will be:

Wheel Torque = radius of the wheel * Force

Torque from the gearbox will be

Gearbox torque = Motor torque * gear ratio

Your motor probably doesn’t give enough torque at stall to get the vehicle moving. What you can do is, now that you know your force of static friction, shoot for getting about twice that from your motor.

Let’s say it takes 100N of force to move your car, and the wheel is 1m radius.

The torque required will be 100N * 1m = 100N-m

The motor will usually say the stall torque right on it’s faceplate. Take this, and figure out what gear ratio will give you enough torque at start to get the car moving.

let’s say we’ve got a 50N-m motor. If we use a 1:2 gearbox, we’ll end up with 100N-m of torque, which will apply 100N of force to the wheels, which will move the car.

The other factor to take into account is top speed. A motor typically turns pretty quickly. You can get into the thousands of RPMs. If you attached that 1:1 to the wheel, you’d have a wheel that takes forever to reach a ridiculous speed (assuming it doesn’t just reach a steady state because the toruqe is inadequete to push the vehicle any faster).

If you’ve got a top speed in mind, that can help you determine your gear ratio too. let’s say you’ve got a motor that turns at 600RPM, and a wheel of .02m. 600RPM is 63 Radians per second(Rev/min * 2pi/60 = rad/s), and going by v = w * r, you’d be moving at 1.25m/s, which is about a slow walking speed. The same 1:2 gearbox which increased the force from 50N-m to 100N-m will now decrease your 600RPM to 300RPM. 300rpm is about 31 rad/s, which would be very very slow.

As you can see, you want to find the right combination of speed and torque to allow you to get past startup forces, accelerate at the rate you want, and reach a speed you want.