# How to determine the torque and rpm of a Stirling engine?

I am actually working on making of a Stirling engine. I did some research work but most of the content on the internet is qualitative. So I am trying to build a small scale Stirling engine and trying to gather knowledge through trial and error way.

But since this is not my field of expertise so I thought to raise the question to the community first.

Suppose there is a Stirling engine whose Tcold is 0-degree Celsius and Thot is 200-degree Celsius. The piston is 35mm in diameter and the stroke is 24mm. The engine is made to run using air at a pressure of 2 bar.

Can anyone help me to determine the torque and rpm of this engine?

• Perhaps because other tags are more than relevant. – Solar Mike Dec 20 '20 at 15:03

It will be determined by the system load and internal friction factors.

Here's some initial thoughts on how to determien this:

Your power, $$P$$, is equal to the product of the torque, $$\tau$$ and your angular velocity, $$\omega$$,

$$P = \tau \omega.$$

Assuming a completely adiabatic system, $$\dot Q = P,$$ where $$\dot Q$$ is your heat in.

Therefore, you'd be able to write,

$$\tau = \frac{\dot Q}{\omega}.$$

Now, what you need to know from your system is, $$\omega = f(\tau)$$. how much torque is required to produce a certain angular velocity. Once you know this, the intersection of the two curves give you your operating point.

• one of the curve is w=f(torque) but what is the other curve? – Tank Dec 22 '20 at 6:12
• It's the curve of the system. How much torque is required to produce a certain rotational velocity. This can be measured or derived through system modeling. It should be noted, this would only be for steady state analysis. Transient analysis is another matter. – Terry Price Dec 22 '20 at 20:22