## Open letter to the ebay seller of the improved fan engine

Discussion on Stirling or "hot air" engines (all types)
onecycleDan1990
Posts: 22
Joined: Tue Jan 18, 2011 1:43 pm
Location: Massachusetts, United States

### Open letter to the ebay seller of the improved fan engine

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 700o 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 Pmin= 1 atm, Vmax / Vmin = 1.5, and assume Vmax-Vmin=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=Pnew-PInitial=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