A Stirling engine is a heat engine that is operated by the cyclic compression and expansion of air or other gas (the working fluid) between different temperatures, resulting in a net conversion of heat energy to mechanical work. In this example, that mechanical work is converted to electricity.
Let's calculate the torque of a Stirling engine - a homemade model kit with a flywheel
We need the flywheel mass (kg), the radius (m), and the angular acceleration (rad/s^2)
\(T_{fw} = \frac{1}{2} * m * r^{2} * \alpha} [Nm]\)
\(T_{fw}\) = \frac{1}{2} 0.02 kg 0.00075625 m2 * 125.663706144 rad / sec) = 0.000015125 / 2 / 125.663706144 rad / sec2 = 0.000950395 [Nm]
Or dissecting the formula.
The moment of inertia of the disc is:
\(I = \frac{1}{2} * m * r^{2}\) \(I =\)0.5 0.02 kg 0.00075625 m2 = 0.000007563 kg m2
\(T_{fw} = I * \alpha [Nm]\) \(T_{fw} = 0.000007563 kg m2 * 125.663706144 rad / sec2 = 0.000950395 [Nm]\)
\(\alpha = \frac{\Delta \omega }{\Delta t}\) \(\alpha\) = 125.663706144 [rad] \ 1 sec = 125.663706144 rad / sec2
\(\Delta \omega = \omega_{1} - \omega_{0}\) \(\Delta \omega\) = 125.663706144 [rad] - 0 [rad] = 125.663706144 [rad/s]
\(\omega_{0}\) = 0 [rad]
\(\omega_{1} = 1200 RPM = 1200 RPM * 2\pi * \frac{1}{60} sec\) \(\omega_{1}\) = 125.663706144 [rad]
Usually you can convert that torque and RPM to watts, which could give you a rough estimate power output of your engine. You can multiply the amount of torque in Newton-meters (Nm) by the rotational speed (rad/sec) in order to find the power (watts). Although it does not account for losses and the such.
A basic formula would be:
\(\P_{W} = \(T_{fw} * speed [rad/s] = 0.000950395 [Nm] * 125.663706144 [rad/s] = 0.1194301580007269 [W]\)
Now, if we want to generate electricity using a brushed motor for electric generator (dynamo), our engine outputs 0.119 W and we can choose a motor of 0.119 W or a bit less and start from there.