calculating relative dimensions

[Bill-W]

Hello,

Could somebody please look over this calculation and tell me where I have gone wrong ? The answer doesnt look right and am sure I've made a mistake somewhere.

See attached jpeg.

Sketch is from book by Roy Darlington and Kieth Strong "Stirling and Hot AIr Engines" 2005

Seems like a good book

Bill

[PlaniTechic]

Hi Bill

I agree with you, that the cooling volume is pi x R x R x h which again is pi x R x R x r. But this does not equal pi x R x R X 2R!
If I take pi x R x R x r = 1.5 x (pi x r^3)
then I get

R = SQRT(1.5 x r^2)

what I think makes sense


Best Regards
Plani

[Bumpkin]

For relative displacement, pi doesn't matter. You could have square pistons and the answer would still be the same. So all you need to do is compare bore x bore x stroke. And if there's just one crank pin as is likely in the example picture, you don't even need to know the stroke - just bore x bore of one cylinder compared to bore times bore of the other cylinder. Obviously, for actual displacement you need a more complete equation.

Bumpkin

[Bill-W]

Hey Planitech,

Have another look at the diagram.

Cylinder length = 3x cylinder diameter and the cooling end is 1/3 of the overall length

Therefore the length of the cooling end is D and this is the same as 2R

So the volume is pi x R x R x 2R

Bill

[Bill-W]

Bumpkin,

Yep agreed - the pis cancelled out and dont really matter - square pistons ? I could understand a square displacer but somehow I just intuitively don't like a square power piston. However am happy to be wrong about that. Do many people use them ?

What do you mean by relative displacement ?

Bill

[Ian S C]

Probably best to not go there(sq piston), nothing is impossible---but.
with the piston and displacer with the same stroke, the diameter of the displacer is increased until its displacement is about 1.5 that of the power piston.
Ian S C

[PlaniTechic]

Sorry for the confusion.

Your formula is correct, if you want to have it in a way that R and r correspond together like in the diagram. (although imho this does not really make sense)
My formula was under the assumption, that both pistons have the same stroke. Therefore to obtain a displacer volume of 1.5 times the working piston volume you get a Radius of SQRT(1.5) of the working piston.

PlaniTech

[Aviator168]

I will go with an alpha configuration. Just build two of the same cylinder.

[Bumpkin]

Wow. Sorry for the confusion. But honestly, if you were really going to go that way, triangles might be more fun.

Bill, "relative" was meant to reference the equation where it looked like you wanted to work out the displacment to match the famous, or infamous, 1.5/1 ratio. Comparing squares to circles was obviously only meant to point out that pi was irrelevent to the equation, but in looking at it again I see you already made that comment in the diagram, so again, sorry. Try this one - to get 1.5 times displacement from the same stroke, multiply bore by 1.224745. I don't think it'd work for triangles though.

Bumpkin

[Bill-W]

Thanks for all the help and comments.

It seemed to me that if I believed that diagram, then as soon as one parameter is defined ie diameter of power piston, then the rest must follow from the volume calculations and relationships in the above equations.

I see from the various comments above that the same stroke length is often assumed for both displacer and power piston, that doesnt gel with what I have been reading.

Have I misunderstood something important ?

Bill

[Bumpkin]

In numerous prior posts Ian has explained traditional ratios far better than the illustration above. For modeling, history, and art, staying reasonably close to those recommendations should serve well for high-temperature engines. Other goals might need other ratios, derived from understanding a bit about absolute zero and ideal gas, and a bit about good and bad heat transfer, materials, aerodynamics, kinematics, etc... The traditional ratios should produce an engine that runs in traditional practice, but to be honest, I'm more interested in theory than practice until I can see the way to an engine that could serve different goals.
Either way it's addictive though.
Bumpkin
P.S. Sorry for the long-winded posts, I've been a few weeks with a sore back, and it's an outlet.

[Ian S C]

Bumpkin, don't worry about long posts, or anything like that, as long as it takes your mind off your back, even for a few minutes, go for it.
Researching for Stirling Engines, or any engine involves many branches of science and engineering. Don't think it involves astronomy, but then again it might with Stirling Engines in space.
Ian S C