Is horsepower related to torque in electric motors? [closed]

Is torque related to size or power at all in electric motors? And what about gas motors too?

I have a go kart that is 2.5hp and it's 50cc and its about 1ft x 2ft x 1ft in size. I also see online there are .21 cubic inch gas motors for R/C cars that are also 2.5hp, the difference being that the R/C motor spins at 32k rpm while the go-kart motor spins at 12k rpm. If I were to put a gear reduction on the R/C motor, would it preform more or less the same as the go kart motor? Why is there a size difference?

Same for electric motors. I can buy an RC car electric motor that's 10hp and the size of a pop can. The CNC machine at work has a 10hp motor the size of a 5 gal bucket. Again, the only difference is the RPM.

If I were to reduce both setups so they spun at the same RPM, would they preform the same?

The only reasons I could think of is 1. Cooling and 2. RPM control (For PID loops and sensors)

What is horsepower?

Horsepower is a measure of power (work done in a specific period of time - the higher power, the more work done), just like watts or kilowatts. $1 hp \approx 0.75 kW$ In case of mechanical power it is torque multiplied by rotational speed.

Relation between power and torque

The more power a motor can produce the more torque you can get from it, at the same rotational speed. However, you can change ratio of torque to speed using gears, so you can have high power motor that will give less torque than appropriately geared weaker motor.

Relation between size and power/torque

Generally the bigger motor, the more power it can produce. However, there are many different types of motors: BLDC will usually have higher power from the same size than regular DC motor.

Motors with integrated gears will be bigger than those without them, but will produce the same power, but different torque and different speed. Motors that are intended to run for years in the industrial environment will be bigger than its hobby counterparts - the bigger size allows them to be less stressed and better cooled.

Torque is the amount of "rotational force" available at the output shaft of the motor. You can increase or decrease torque using gears. Torque has nothing to do with how fast the rotational force can be applied to do work (gearing will change the required motor shaft rotational speed to achieve the desired output shaft rotational speed, but that is still just an increase or a reduction in torque).

Horsepower is a measure of power - work done in a specific period of time. So a higher hp motor can produce its torque in less time than a lower hp motor can.

Horsepower is torque multiplied by angular velocity.

If you have an electric motor that has constant torque throughout its speed range, then the horsepower will increase proportionally with speed, and the maximum horsepower will be at the maximum speed. The faster it can spin, the more horsepower it can produce.

An internal combustion engine's torque is never constant with speed, so it is harder to know at what speed you will have maximum horsepower (and some electric motors have the same issue). It is usually near the top RPM, just above the peak in the torque curve. If you can move the torque curve up on the RPM, by improve breathing or by super/turbo-charging, then you will increase the horsepower without needing to increase torque.

Horsepower will remain constant through a gear-train, except for frictional losses. Reducing the speed will increase the torque proportionally. So if you you use a 5:1 gear reduction, you divide the speed by 5, but muliply the torque by 5, giving you the same horsepower.

• Mark, what type of electric motor do you refer when you say about constant torque? Brushed DC motor torque is inversly proportional to rotational speed. Jul 22, 2016 at 8:35
• The torque of DC motor is only indirectly related to rotational speed. Torque is directly proportional to current, regardless of speed. The effect that you are citing is: If you don't control current, then increased speed creates increased BEMF, which causes a decrease in available voltage, which causes decreased current, which causes decreased torque. When a manufacturer specifies the motor's horsepower, they are specifying it at rated current, which you won't reach unless you can control the current. You will not get the rated horsepower if you only apply the rated voltage to a DC motor, .
– Mark
Jul 22, 2016 at 19:37
• @mactro - Sorry, but I forgot to cite you in my comment above, so you probably didn't see my response (until now).
– Mark
Jul 24, 2016 at 5:08
• ok, but keeping constant torque will limit speed range greately, as it would require overvoltage to speed grawer than rated. Jul 24, 2016 at 6:50
• @mactro - Yes, it requires higher voltage to get maximum speed, but that is not a problem. I typically run 24 volt motors from a 120vdc to 180vdc bus. You are fine as long as you run a closed current-loop, don't exceed the peak and continuous current limits, and don't exceed the insulation breakdown voltage (which is typically hundreds of volts). My servo controllers also monitor motor temperature, just to be safe.
– Mark
Jul 24, 2016 at 6:57