# Find optimal configuration for Stirling Engine

I'm trying to figure out the theoretical calculations for a Stirling Engine system so I can determine optimal piston size, optimal piston displacement and number of pistons. I want to calculate which configuration has the most amount to torque to turn something else, and the highest amount of RPM's.

What I have managed to achieve:

(1) Internal energy = Thermal difference + Work

$$ΔU = Q + W$$

(2) Work = Rotational Kinetic Energy

$$W = \dfrac{1}{2}Iw^2$$ (3) Assuming that Inertia is standard wheel

$$I = \dfrac{1}{2}Mr^2$$

(4) Equation I have so far

$$\dfrac{1}{4}Mr^2w^2 = ΔU - Q$$

I am unsure on how I can relate the equation to the pistons. According to HyperPhysics

Internal energy is defined as the energy associated with the random, disordered motion of molecules.

That sounds like pressure to me, and I know that:

Pressure = Force / Area

But I think I need a better way to express the physics of pistons.

The Q component of internal energy is also difficult for me to find, because a heat source (like a candle flame), will be creating a heat differential on the piston. This heat differential in Joules, will be a little difficult to find as well.

• You should probably start by analyzing an idealized Otto or Diesel cycle; these are textbook cases for which most thermodynamics books will go into great detail. This will teach you how to set up the governing equations for any thermodynamic cycle, including the Stirling engine. The whole process is quite in-depth and might be beyond the scope of a StackExchange answer. Oct 9, 2015 at 18:42
• @Carlton you wouldn't happen to know any good online resources on engine physics would you? Oct 9, 2015 at 19:17
• Wikipedia is pretty good, I think. Look at the page for the Otto cycle to get yourself started. Oct 11, 2015 at 23:24

To "optimize" requires a desired outcome. Sterling engines, like most mechanical/thermodynamic systems are highly complex. You could optimize for efficiency, cost, power-to-weight, and many others. For learning the theory before you get to that stage I would recommend the wiki article, then do web searches based on your new vocabulary after that.

https://en.wikipedia.org/wiki/Stirling_engine#Theory