Stirlingengineforum.com

Hi all,
I'm new to the Stirling Engine and am fasinated by it so would like to build one.

Firstly, I am no math expert. In fact, I don't understand all the fancy equations and all the goesinta's related to same. But, I can understand a well written sentence so if you're willing to spend a little time answering some questions for me, and can keep the answers without too much fancy terminolgy, well, I could probably understand what you mean.

The machine I wish to build is a single cylinder design with both the displacer and the piston in that cylinder. That is a Beta correct?

So, I've done much research on the machine and I think I have the therory of operation down but I don't understand the math involved. That is, there is a displacer and a piston but I don't know what the relationship should be between them for it's most efficient operation.

And now the math. For simplicity, let's say the cylinder is 1 foot long and 2 inches in diameter. How long then should the displacer and the piston be? What is the relationship between the two for opimal performance? I mean, if I have "x" amount of air volume within the cylinder, how much of that air needs to be compressed, and by how much? I would think that if the pistons' stroke is too long the pressure created by the piston would be too great for the system to overcome it and it wouldn't run. On the contrary, if the pistons' stroke is too short, there wouldn't be any real power created. There must be an easily understandable formula (for a non math expert) to understand.

I know there is much more to understand about this engine but before I select the cylinder size, I need to know how big to make the Piston and the Displacer and their relationship to each other. Thanks in advance for any insight into my query.
Bill

Bill, start with the displacer dimensions, for a 2" cylinder the displace could be about 1 7/8" diameter, it should be about three times the diameter long, 5 1/2" to 6" will do.
The power piston should just slide down the bore under its own weight, and if you block the end of the cylinder it should almost stop, and with the cylinder blocked, if you push it in it should bounce out a bit. A skirt on the piston about 1 1/2" long is a good average, can be a little shorter if the motor is vertical.
On my motor of similar size (2 1/4" bore) the power stroke is 1 1/4", and the displacer stroke is 1 3/4" and the over all length of the cylinder is about 1ft. You can see the motor in my gallery, it's the one with 4 cast iron legs, with a 12" rule leaning on it.
The ratio that you need to know is the one between the displacer volume and the power piston volume, this is 1.5 : 1, on a GAMMA motor the ratio can be adjusted by using a smaller diameter for the power cylinder, that way both parts can have the same stroke, this can be an advantage if you make a V type motor as you only need one crank. Ian S C

Let me take one thing at a time here so as to better understand things. I was wondering about resistance that the moving displacer would have upon the system. I used an online calculator to figure what the volume of air is around a 1.9375 (1 7/8") displacer in a 2" cylinder at any given time. I came up with an answer of 2.28 cu. in. With the displacer and piston (2") inside the cylinder the volume of air is 13.84 cu. in. that the displacer has to move. That would tell me that it can't move that amount of air with it creating some resistance upon the displacer.

What I mean is, how can 13.84" of air move through a channel that can only hold 2.28" at one time? It can but not without creating a pressure buildup on the side it's moving toward. Now, this pressure and resistance might be negligable in the grand scheme of things but it's a resistance nonetheless, no? I ran the numbers for a slightly bigger gap (1.75" displacer) and got twice the area around the displacer; 4.42 cu. in.

What the numbers tell me is that the smaller the displacer, the easier it will move through the air but there would be a point where not enough hot and cold air will be displaced efficiently enough to allow the engine to run. So there has to be that "sweet spot" in the dimensioning of the displacer inside the cylinder.

In all the reading and research I've done no one has really said what that sweet spot is. It's all just "kind of sort of around here" sort of information. So I guess what I'm asking is have you done any experimenting with different sizes of displacers and gotten better results with one than the other from those experiments? I'm trying to learn from others' mistakes before I attempt to build one for myself and forgo all the mistakes that I know I'm going to make. I'm going to make enough of them as it is so I'm just trying to minimize them. :)