Alpha stirling engine working principle

[jpigg55]

Forgive me if this is a repeat. I used the "Search" function, but always got the same "too common term" results.
I worked for 36 years in the nuclear energy field with 6 years in the US Navy and 30 years in commercial nuclear power plants as a mechanic and operator, thus I have a very good understanding of thermodynamics and mechanical operating principles.
This made it fairly easy to understand how Beta, & Gamma Stirling engines work, but struggled somewhat on the Alpha engine.
While the Alpha is a differential heat engine working, at least partly, on the expansion and contraction of the working gas, I had trouble getting past the concept that the force acting on the pistons was equal due to the equivalent surface area.
After much thought, the conclusion I came to was there was something else at play. I concluded the was (what I term as) a "differential leverage" working principle derived from the 90 degree offset of the connecting rods wherein the force acting on the crank from the pistons differed during rotation.
Can anyone point me to threads here or links elsewhere that can put new light to my understanding ?

[Bumpkin]

I've never seen it explained well, and this probably won't help; but I'll take a stab at it:
Visualize a single-crank-pin 90 degree V twin Alpha. Minimum volume is the crank centered at 45 degrees between the cylinders and maximum is 180 degrees further along, similar to tdc to bdc of a Gamma power piston. Then consider the placement of the air between the hot and cold ends of an Alpha as similar to the air in a Gamma displacer chamber. At first glance, it looks like the Alpha placement change is only leading the volume change by 45 degrees, but I think you can add to that the 45 degree average of the two pistons working for and against each other; as you said, differential leverage (and differential volumes.) Clear as mud, right?

Bumpkin

[matt brown]

While the Alpha is a differential heat engine working, at least partly, on the expansion and contraction of the working gas, I had trouble getting past the concept that the force acting on the pistons was equal due to the equivalent surface area.

Xlnt observation which many miss or discount due to other issues. Even with the common assumption (Schmidt analysis) that the pressure is equal thruout engine at any given time, the force on identical alpha pistons is not due to crankpin location (bellcrank effect).

After much thought, the conclusion I came to was there was something else at play. I concluded that was (what I term as) a "differential leverage" working principle derived from the 90 degree offset of the connecting rods wherein the force acting on the crank from the pistons differed during rotation.

Most SE guys are in the gamma/beta camp, but I'm an alpha fanboy for various reasons. SE mindset is loaded with various falsehoods that allow guys to carry the torch, but get nowhere. Your 'differential leverage' is a perfect example where the common assumption is that Wpos vs Wneg per piston can be simply summed per cycle (rpm) whereby these force issues cross-cancel during rotation. This isn't true with ICE, so why would anyone assume this is true for SE ?

One reason I favor the alpha is simply for your callout where an ideal alpha with pistons/slider-crank/90deg phasing has expansion start at 90 deg near torque max vs similar ideal gamma where expansion starts with PP at TDC. If new to SE, these mechanical issues are dwarfed by numerous thermo issues. Another reason I favor alpha is that each cycle (rpm) ideally uses entire gas mass for output vs gamma/beta rarely exceed 2/3 before regen and commonly around 1/2. So, gamma/beta require far more regen per gas mass than alpha which is no problem when regen=1.0 except for relatively larger regen. However, as regen efficiency declines from 1.0 this thermo "differential" will dwarf most mechanical issues due to regen "load"...the ratio of ideal heat of regen divided by ideal heat source input (where regen>source).

Can anyone point me to threads here or links elsewhere that can put new light to my understanding ?

I've seen studies in past, but can't recall any, offhand.

[Tom Booth]

Can anyone tell me where or when Alpha type "Stirling" engines originated?

They don't appear, afaik, to have originated with the Stirling brothers.

Also, I don't think I've ever seen an actual "pure" V type Alpha that actually works, without modifying the original(?) concept and making one of the pistons basically function as a displacer.

[matt brown]

AFAIK the first alpha is credited to Alexander Rider in 1875, but often referred to now as the original Rider to distinguish it from a later Rider engine. The original version had two distinct cylinders vs later version had a single cylinder and effectively a beta. Adding to confusion is Rider-Ericsson company name which is a small history in itself. Here's the original Rider which forum member "spinnmagnets" posted recently

Rider.png (277.83 KiB) Viewed 568 times

The is my favorite hot air engine of past.

[matt brown]

Here's a screenshot of some alpha links, note one on right and bottom where heater and cooler are between regen and cylinders...

alpha links.png (267.07 KiB) Viewed 565 times

[matt brown]

While the Alpha is a differential heat engine working, at least partly, on the expansion and contraction of the working gas, I had trouble getting past the concept that the force acting on the pistons was equal due to the equivalent surface area.

Xlnt observation which many miss or discount due to other issues. Even with the common assumption (Schmidt analysis) that the pressure is equal thruout engine at any given time, the force on identical alpha pistons is not due to crankpin location (bellcrank effect).

edit: my last sentence should end...the force on identical alpha pistons is not [equal] due to crankpin location...

[jpigg55]

edit: my last sentence should end...the force on identical alpha pistons is not [equal] due to crankpin location...

The combination of factors, to me, is where it gets tough to wrap ones head around. Each component is fairly easy, but the combination starts to muddy things up.
From just the piston perspective, both pistons are of equal diameter, and thus surface area, in an Alpha SE. The "Ideal Gas Law" tells us that pressure=force/area or, put another way, force=pressure x area. Since the pressure acting on the pistons is equal, the downward force on each piston is equal.
From the perspective of the crank, this is where "Torque" comes into play. The effective "lever" length gets longer as rotation moves from 0 (TDC) to 90 degrees with max torque at 90 degrees rotation.
Now we get to the "Work" & "Acceleration" parts of the equation. Work=Force over some distance and Acceleration being the rate of change of the change in distance. This depends on the type of connection between the piston and crank that also doubles as the means of conversion between linear motion and rotational motion. The 2 types I'm aware of are the Connecting Rod and the Scotch Yoke.
Here again, we run into a perspective issue. Like an ICE, the piston moves a greater distance in the first 90 degrees of rotation than in the second with a crank pin connection for a given crank shaft RPM. This is what defines the acceleration of the piston in that the piston spends more time/travel distance in acceleration than it does in deceleration. Conversely, the acceleration/deceleration travel distances of the piston are equal with a Scotch Yoke connection configuration.
Now we add in the second piston with the 90 degree connection offset. This is where things get muddy for me. Trying to envision where in the rotation angle that equates to max and min volume, torque, and work of the system exists.

[Fool]

The way I think of the Alpha engine is that the two pistons work in concert to increase volume and decrease volume.

If most of the heat is applied during most of the expansion, it will speed up the engine.

As the opening post said, "lever action", from the difference in crank positions makes a preferred direction. Yes. The pressure in both cylinders is approximately the same for the same force on both pistons.

If most of the cooling happens during the compression stroke, less energy is wasted during the return compression stroke.

[spinningmagnets]

Part of the 90-degree separation between the pistons is the lag-time for the gasses to absorb and shed heat. You "could" separate the pistons by 180-degrees, so all of the gasses are in the hot side or cold side, but then you'd need a third piston to use the gas temp change to spin the thing.

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I've come to appreciate recently that the Rider derived significant benefit from orienting the engine to have two parallel vertical cylinders, and it uses heavy pistons "on purpose". I don't recall the reference, but after manufacture, the engine could be fired up by the customer and they could slowly add weight to the inside of the pistons (molten lead?), until a they find a point where the engine runs more smoothly.

As we have seen on the internet, Alpha-Stirlings can be built with horizontal cylinders, and they can also have the cylinders in a 90-degree V-configuration. However, the vertical cylinders with the crank located on the top mean that the heated internal gas lifts both the pistons (again, 90-degrees apart) but them they are falling when the gas is cooled. This means that the design uses the weight of the pistons falling to apply two power pulses.

If this is correct, then the Rider applies four evenly-spaced power pulses to the crank per rotation, rather than the obvious two that come from heat expansion.