Shop math - scaling down engines. Specifically, cylinder volume.

[David Morrow]

I'm just finishing a Moriya Stirling and, before moving on to an IC engine, I wanted to try another Stirling. I found a site where a 50% scale Moriya was built by Orrin B. Iseminger.

http://users.moscow.com/oiseming/lc_ant_p/pic_Prj8.htm

He gave a few dimensions on his web site for his scaled down bore and stroke. ( I use his piston size as the bore dimension although that is not strictly correct for the displacer as there is supposed to be a small air space around the outside. But that's close enough for this discussion ).

While out for a walk tonight, I realized that following a strict 50% scaling of the original bore & stroke would end up with a displacement figure well under 50% of the original. I think that you really need to determine the desired scaled down displacement and work backwards to arrive at the correctly scaled bore and stroke.

The original plan dimensions for the power cylinder are as follows :
Bore : 0.750"
Stoke : 1.000"

I used a formula for displacement of Pi x Radius squared x stroke =

In Excel I used a formula of 3.14159265 x ((.750 *.500)^2) x 1.000 = .4418 cubic inch.

Mr. Iseminger uses the following dimensions for his 50% scale engine :
Bore : .375" ( which is 50% x the original bore )
Stroke : .600" ( which is 60% x the original stroke )
That results in a displacement, using my formula, of 0.0663 cubic inches which is only 15% of the original displacement.

My question is, why would Mr Iseminger's engine run so well; he was most pleased with the result. Or, is my math way out of whack ?

If I start with a scaled down displacement of 0.2209" and keeping the same ratio of bore to stroke, I calculate that I will need the following :
Bore : 0.5950"
Stroke : 0.7933"

 

[Kermit]

The cubic portion of this engine/math. will not behave the same way as other numbers to scaling.

But you are correct in your result. A scaling of displacement will give you numbers for stroke and bore that are not a proper scaled ratio to the original stroke and bore.

Scaling the displacement is the Proper way to scale down an engines power cylinder.

i.e. making a cyl of .5 cu in. scaled down from an original 1.0 cu in. will not give a stroke or displacement that are 1/2 of the original. This would give you an engine with approx 50% of the capacity of the original but not necessarily 50% the size of the original.

I think I'm more confused now...

 

[kvom]

Remember that scaling all parts by 1/2 will reduce their mass to 1/8 of the original, or 12.5%. If the displacement is 15%, then the power to weight ratio is pretty close.

 

[mklotz]

Scaling Stirling engines is an iffy process at best. I've scaled at least two designs and neither worked well until I redesigned the displacer chambers.

James Rizzo's book, "The Stirling Engine Manual" offers some rules of thumb for Stirling design...


1. The length of the displacer chamber = 3 times is diameter.

2. The length of the heated chamber = 2/3 of the length of the displacer chamber (cylinder).

3. The length of the cooling chamber = 1/3 of the length of the displacer cylinder.

4. Swept volume of the displacer = 1 1/2 times the swept volume of the power piston.

5. Length of the displacer = 2/3 of the length of the displacer cylinder.

6. Stroke of the displacer = 1/3 of the length of the displacer cylinder.

Once you've done your geometric scaling, check your new engine design against these rules. If you don't depart too much from them, you should have a runner.