the volume ratio between displacer cylinder and power cylinder

[OscarMike]

Hello,

I'm doing a research on the gamma type Stirling and i found that the volume ratio between the displacer cylinder and the power cylinder should be in the range from 1.5 to 2. may i ask why is this the optimum ratio? and what will happen if the displacer cylinder volume became smaller than the power cylinder volume?

thanks in advance. :)

[Ian S C]

You won't get enough hot air to the power cylinder. I don't do complex maths for my motors, but 1.5 : 1 is the ratio that Robert Stirling used, and it worked OK for him, and it works for me. The formula is probably quite simple, and probably in the info from NASA that is available on the net.
Ian S C

[OscarMike]

Thanks Ian for your reply,

i understand that there will not be enough hot air to the power cylinder if it has a bigger volume and it is logical btw, but do you have a mathematical proof or a heat transfer derivation for example you can send me to prove it?

[Trevor]

Hello OscarmikeIan
Ian is correct with the ratios 1.5:1 for Stirling Engines. It is the optimal ratio that has been tested for a very long time.
When using LTD Engines then this will be different.
You cannot have a larger piston capacity that the displacer as the engine will not work at all
Trev

[Bumpkin]

Hi Oscarmike. Here's a link to something about the math stuff. The relevant stuff is towards the top.

http://www.spragueriver.com/index.php/bumpkin-tech

Bumpkin