Open letter to the ebay seller of the improved fan engine

[onecycleDan1990]

According to your ebay posts your small unpressurized engine is able to produce 750 watts at 800 rpm
I have reason to believe this claim is inaccurate.

It all boils down to basic thermodynamics and gas laws.

lets start with the facts: PV=NkT, and as such PV is directly proportional to T, one litre of displacement against one atmosphere equals 101.3 newton meters (joules) of energy, assume a upper temperature of the working fluid of 700^o Kelvin, and a lower working fluid temperature of 350 kelvin
assume Isothermal behavior of the working fluid, sinusoidal crank movements and pressure time graph, and no friction or thermal shorts.
Lacking better data assume P_min= 1 atm, V_max / V_min = 1.5, and assume V^max-V_min=180 millilitres, or .18 litre, and running speed of 850 rpm

Compress a finite volume of gas isothermally to 1/1.5 times its original volume then heat it from 350 kelvin to 700 kelvin. According to P being proportional to T/V the new pressure will be (700/350)*1.5= 3 times original. Assuming the initial pressure is one atmosphere then: pressure difference=P_new-P_Initial=3-1=2 atmospheres.

now the above are peak values on a sinusoidal curve. The average difference in pressure is equal to the area under that curve.
the area of a rectangle 1 x pi is pi square units. The area under a sin curve of peak y value of 1 and from o to pi is 2 square units.

therefore the average pressure difference is the peak difference divided by pi/2
taking the aforementioned peak pressure difference of 2 then: average pressure difference= 2/(pi/2)=1.273

The pressure volume work per cycle is then average pressure difference*displacement=1.273atmospheres*.18litres=.229AtmL
this is equivalent to .229*101.3=23.2 newton meters of work

power=work/time
assuming your advertised speed under load of 850 rpm is true then Joules per cycle*frequency=.229*(850/30)=657 watts

This value is the absolute maximum that could be produced by your engine in an absolutely perfect and therefore nonexistent world.
In real life Air is not a perfect ideal gas, Stirling engines always show large deviations from perfect isothermal behaviour therefore the pressure difference is substantially lower than predicted by the above rosy, primitive, oversimplified, and unreasonably optimistic model. Then there are thermal shorts, friction, and pumping losses, all of which are inevitable in reality. On top of this the massive temperature differences assumed above reflect a powerful ring or cyclonic burner bringing the hot cap to red heat, and an effective forced water cooling system, as well as a well designed heat exchange system. If you are using said burner and cooler in your tests, the hot cap is made of thin 18-10 stainless or other high temperature alloy, and your annular gap is well optimized (Dr Allan Organ estimates a displacer length to displacer-cylinder gap ratio of 400 to 800 is best iirc) then I might believe a temperature difference of that level. The small open flame and the small cooling fins an ambient air shown being used in your videos could never get the needed temperatures.

Even the best engines in the world produce less than half of the ideal value.

As such I refuse to believe any claim over 250 watts for your engine with an improved burner and water cooling, and any claim over 50 watts for the engine as sold.

In short the claimed output is physically impossible to achieve with your engine.

In informal terms: I call BS