# Gear Ratios and Constant Power/Torque: find max velocity?

• jzmaster
In summary: So at some point, the power available to the output gear will be less than what the engine can deliver, and the motor will stall.
jzmaster
I'm trying to determine how exactly gear ratio limits velocity. I know that a high torque configuration is generally regarded as low speed, but my calculations do not seem to support that.

Basically, I've written a small problem where we have an input gear with constant torque and an output gear with a load on it. If I apply a gear ratio of 1, I get a lower angular acceleration than if I do a gear ratio of 10 (output has 10 times the teeth) -- this makes sense.

When calculating maximum angular velocity though (assuming about 0.3*<omega> on the output gear), I get a maximum velocity that is much larger than with a lower gear ratio. The torque is the same, the power required is very large (orders of magnitude difference). I am assuming 100% transmission efficiency.

So, if we have a motor which can produce constant torque regardless of RPM (possibly in excess of 22000) while being able to provide the necessary power, is it reasonable to say that the output gear would be driven at a faster speed than if the gear ratio was 1? Attached is a quick sketch of my problem.

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• Geerz.png
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Rate of energy flow = Power = Torque * RPM.

Simply put, the speed ratio of the output gear to the motor gear is the inverse of the output gear diameter / motor gear diameter, i.e for a 1/3 gear ratio the output gear rpm will 3 times the motor rpm. This speed ratio totally independent of the motor power or the output gear loading.

If you assume constant motor torque regardless of its speed, you are essentially allowing it to produce limitless power as its speed increases. Your best acceleration is with an extremely high amount of gear reduction, and the torque multiplication that comes with it. But your motor speed would be extremely high, and since power = torque times angular velocity, your power would have to be huge.
In real motors, torque will drop with higher speed, batteries are limited in how much power they can supply, and air flow restriction into an engine limits its power.

## 1. How do gear ratios affect the maximum velocity of a vehicle?

The gear ratio is the ratio between the number of teeth on the driving gear and the number of teeth on the driven gear. In a vehicle, the gear ratio determines how many times the engine rotates for each rotation of the wheels. A higher gear ratio results in a lower maximum velocity, while a lower gear ratio allows for a higher maximum velocity.

## 2. Why is constant power/torque important in determining the maximum velocity?

Constant power/torque is important because it ensures that the engine is able to produce enough power to overcome the resistance of the vehicle and maintain a constant speed. Without constant power/torque, the vehicle would not be able to reach its maximum velocity.

## 3. How do you calculate the maximum velocity using gear ratios and constant power/torque?

The maximum velocity can be calculated by dividing the constant power/torque by the resistance of the vehicle, which is influenced by the gear ratios. This calculation takes into account the engine power and the vehicle's weight, aerodynamics, and other factors that affect resistance.

## 4. What is the relationship between gear ratios and torque?

The gear ratio and torque have an inverse relationship. This means that as the gear ratio increases, the torque decreases and vice versa. This is because a higher gear ratio allows the engine to rotate more times for each rotation of the wheels, resulting in a lower torque output.

## 5. How does changing gear ratios affect the acceleration and top speed of a vehicle?

Changing the gear ratios can affect both the acceleration and top speed of a vehicle. A lower gear ratio will provide faster acceleration, but a lower top speed. A higher gear ratio will result in slower acceleration, but a higher top speed. This is why vehicles have multiple gears to allow for optimal performance at different speeds.

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