# Calculating torque without power

1. Dec 17, 2015

### eng_hussain

is there a way to calculate torque without knowing the power? consider this:

P = T * rpm

I can calculate rpm easily as I have a tachometer but without power, I can never find the torque.

In case of translation, you can find the force propelling an object without knowing the power. For example, if you wanna find the force propelling a car at a constant speed, you find it by calculating drag, which is exactly the force the car is experiencing the opposite way

Force propelling the car = drag = 0.5 * rho * V2 * A * CD

All quantities in the equation are readily available (or almost)
- rho is tabulated
- v is easily calculated through speedometer or speed gun
- A can be provided
- CD can be provided

As seen from the equation, no need to know the power. So no need for the equation P = F*V to calculate the force.

Now, is there such a way to calculate torque by only knowing rpm and some other variables other than power?

I'm asking this because I'm working on a small gas turbine (single shaft - single centrifugal compressor - single turbine) project and I want to calculate the torque acting on the shaft at a constant rpm. I can obtain the rpm through my cheap tachometer but I'm having troubles with calculating the power.

Last edited: Dec 17, 2015
2. Dec 17, 2015

### billy_joule

What load is your turbine driving? Generator? Prony brake? Disc brake? The shaft power is going somewhere, if you don't want to measure the torque directly (those meters are expensive iirc) you could use a multimeter on the generator output or a pressure gauge on the brake line etc to get a ball park figure for power out.

3. Dec 17, 2015

### eng_hussain

My turbine is extremely simple and light and it does not drive anything except it assembly (i'm planning to make this turbine a stand-alone thrust engine). The shaft is carrying a centrifugal compressor, two ball bearings, and a turbine wheel. Although I haven't weighted these objects, but the assembly is (approx) as heavy as mini water bottle (filled)

These are the overall approximate dimensions

Shaft length: 200 mm
Shaft dia: 7 mm
Compressor outer dia : 68 mm
Turbine outer dia : 68 mm
Ball bearing inner dia: 7 mm

I hope you get the idea of how small the thing is

4. Dec 17, 2015

### billy_joule

If there's no load there's no shaft power out so no torque out. That is, all your input power is lost as friction.

You could spin it up to speed, turn it off and measure the rate of deacceleration. This, along with the moment of inertia, can be used to find an estimate of the frictional torque acting via T=Iα

5. Dec 17, 2015

### Staff: Mentor

That sounds like a jet engine, in which case the turbine is powering the compressor. Do you have the power requirement of the compressor?

6. Dec 17, 2015

### eng_hussain

I was thinking prony brake. But assuming my project works, it's very dangerous to use since the shaft will spin at a very high rpm plus the heat that is given off from burning fuel.

As for T = I * alpha. I have to calculate I which I think I can manage. Btw, do I have to take the ball bearings into account when calculating I?

7. Dec 17, 2015

### eng_hussain

No. I have no solid math behind my project because I'm doing just for the fun of it.