Ted Warbrooke's Stirling 1: Question

[Alphax]

The more the merrier!

[Tom Booth]

BTW, at the start of the thread, the main interest seemed to be the simplicity of the Stirling 1, due to having a minimum of moving parts.

Are you familiar with "Mower of Doom" ?

https://youtu.be/GJh_fYwFnIg

His YouTube has some videos of his work putting together a progressive series of similar Stirling 1 type engines.

Unfortunately, from comments left on his channel by a family member, he passed away, I think about ten years ago.

Anyway, he discovered, by accident, that his Lamina flow / thermo-acoustic / thermal Lag, or whatever engine could operate without a flywheel. Essentially just one moving part - the piston. So, from there he worked at a series of similar engines, adding magnets and linear alternator. Still just one moving part, as the generator was just an extension of the piston similar to, but even simpler than a NASA type "free piston" engine (which uses a displacer)

[Alphax]

Tom

This thread is about TWO things:-

1. The simplicity of Stirling-1 and related engines (lots of these); and

2. Scaling up (to larger versions).



I wasn't aware of "Mower of Doom", but thanks for pointing me to his video channel. He has some really nice examples of engines that I would say are closely related to Ted Warbrooke's Stirling 1.

There is nothing magical in Ted's design (now over 20 years old and therefor pre-dating Youtube), it just happens to be the first one of its type that captured wide public interest (because he wrote a book that sold well and lots of people built them).

As for not needing flywheel, that has been known about for approximately 60 years and goes back to at least William Beale and his free piston Stirling engine (FPSE) work. Read https://www.ohio.edu/mechanical/stirlin ... Beale.html


Here is a nice visual example of someone actually taking the crank off the flywheel of a Stirling-1 type of engine and the engine runs better for it (less friction without the flywheel and crank link):-

https://www.youtube.com/watch?v=HUWt3YrxoB4

[Alphax]

Just for the record, it is actually quite difficult to keep track of different ideas and progress on developing small simple Stirling engines.

I think that is because individuals building or using them (and showing them on Youtube, for example) often have their own ideas about what is going on and assume they know how they work. This is understandable. After all, if you've built it, you know how it works, right? But it is easy to show that statement can't be correct because the different ideas that builders and tinkerers have frequently conflict with each other and arguments often ensue (sometimes quite heated which may be appropriate for hot air engines!).

In a simple (hypothetical) example where two people are arguing about one technical point with two contradictory interpretations, ONE of them might be right or BOTH of them might be wrong, but BOTH of them can't be right at the same time. Sadly, an all too common outcome is that the interpretation of that technical point doesn't get resolved (often because someone feels they have to "back down" or "lose face" if they concede the point).

Consequently individual developers often wander off and waste time "reinventing the wheel" - (or deinventing the flywheel when it has been done already). Debate would have been a more productive use of time.

A good example is this very forum on the question of flywheels on Stirling engines. Does a Stirling engine need a flywheel? - the real answer seems to be that it depends quite a lot on which type and design (of Stirling engine) you are considering. Obviously - as you know - SOME Stirling engines do NOT need flywheels, but take a look at this discussion where someone asks the question but is promptly shut down by others who say (in essence) that ALL Stirling engines need flywheels:-

https://www.stirlingengine.com/forums/v ... ?f=2&t=250


So the poor guy got the wrong answer!


MY POINT HERE (in case anyone might be wondering) is that it is genuinely difficult to know what is important and what isn't when trying to develop what looks like the simplest of engines with the fewest of moving parts!

[Tom Booth]

Hey Alphax and Tom, this looks like fun so I’ll jump in and disagree with both of you. Firstly take a cube one unit high — six sides = six square units. Three dimensions is 1X1X1 units =1 cubic unit. Ratio of six to one area to volume.
Now compare to a cube two units high — each side is four square units X six sides = 24 square units. Three dimensions is 2X2X2 units = 8 cubic units. Ratio of three to one area to volume. And on and on.
But I disagree that for a given shape a greater surface to volume ratio is a disadvantage. As much thermal transfer area as possible (in the right places) is just what we want. That “in the right places” is where I reckon we could all agree, though I’m sure there could be many different “right’ approaches. I like pancakes myself.
Bumpkin

To be perfectly honest, this is the first I've ever heard about, or gave any consideration to "surface area to volume ratio" but as a carpenter/draftsman, (my father was a carpenter/cabinet maker) artist, machinist, having taken courses in mechanical drawing, I'm familiar with scaling things up and down, reading blueprints etc.

I don't claim to be an expert on the subject, but the idea that a scaled up "bigger" but otherwise identical engine has a different surface area to volume ratio struck me immediately as somehow false. Obviously untrue.

BTW I also graduated at the top of my class in mathematics and am very familiar with weird mathematical puzzles and apparent anomalies, brain teasers etc. I do these things as a diversion. For fun.

Could I be wrong?

Well,, I don't think so. It's just common sense. But in reading the Wiki articles, web pages, various tutorials etc etc.there is very broad consensus that I am in fact wrong and that SA to V ratio changes between large and small is a REAL thing. Not just a mathematical illusion.

So apparently, it is me against the world. (once again).

So, as a lone voice in the wilderness, I will make one last appeal to reason, in the form of a sketch.

Resize_20220208_081520_0070.jpg (324.21 KiB) Viewed 3097 times

Imagine yourself as the "Giant", then as the tiny person. Then imagine as the "Giant" you are really a normal size person. Then as the tiny person, imagine you are a normal human and the engine is giant size.

The drawing has not changed through all this, the engine is the same identical engine.

The only thing changing is perspective. Point of view.

So, given that the "Giant engine" and the "tiny model" are both the same engine, only seen from a different perspective, how could ANYTHING, actually be different?

ALL the ratios between all parts of the engine are identical. That is the very definition of a scale model.

So is it even possible the surface area to volume ratio is different? No! It's just a mathematical trick that the entire world has fallen for, or failed to notice or unravel.

As I demonstrated previously, it IS possible mathematically, for the same engine to have many different SA:V ratios by just changing unit of measure.

Volume and Surface Area are really not comparable on the same scale mathematically, they in effect use two different units of measure, or two different systems of measure entirely.

It is the same sort of error as confusing fahrenheit and Celsius, or inches and centimeters

Volume and Surface area are geometrically entirely different and attempting to compare them as if they could be measured by the same ruler on the same scale leads to hogwash

That the SA:V ratio changes just by scaling things up or down is just that:. Hogwash, and I don't. really care if I'm the only one in the world who can see that. It doesn't make it any less a fact.

[Alphax]

Tom

I get that you don't understand. That is OK.


Have a quick look at this - it might help.....

https://onscale.com/blog/the-importance ... ling-laws/

[Tom Booth]

Tom

I get that you don't understand. That is OK.


Have a quick look at this - it might help.....

https://onscale.com/blog/the-importance ... ling-laws/

I understand very well.

Nothing on that page changes anything.

If a model engine cannot be scaled up, it is not because of this mythical ratio morphing. Scaling is maintaining the same ratios.

Obviously a finite heat source like a candle will not operate a scaled up engine, etc. etc. But the ratio between the length of a side of a scale model, it's surface area and it's volume are all identical to the ratios of a scaled up version.

Resize_20220208_102415_5313.jpg (42.85 KiB) Viewed 3086 times

If the length of a side of a "cube" is *a* then the surface area is always

6a²

the volume is always

a ³

[Alphax]

Tom,

An example often used to illustrate the scaling problem is that of the water strider (we call them water boatmen in the UK) and a human. The water strider can stand on water because it doesn't break the water surface tension. A larger version (human size) of the water strider would instantly sink because its weight is too large for the surface tension to support it.

Notice the issue is the same...... a small water strider shape "works" but a much larger one "sinks" on water, even though the shape is the same - size not only matters, but matters totally if you want to live life as a water strider.

The point is that some forces scale with area, others with volume and because the ratio of surface area to volume depends on size then the forces within a Stirling engine are unavoidably different at different size. The real question (which so far we haven't been able to get to) is to what extent that matters.


If your intuition and belief were correct, you would be able to make a six foot long water strider that would be able to happily skim along the surface of the water without breaking the surface tension and then sinking. But that is a physical impossibility for all the reasons already explained to you.

So I guess I have to ask...... do you actually believe that a six foot water skimmer could support its body weight on water surface tension alone?

[Alphax]

Tom, yes I agree with this:-

If the length of a side of a "cube" is *a* then the surface area is always

6a2

the volume is always

a 3

That is always true as I've said all along, and we both agree it (as we have all along). Now pick two values for 'a' - say a=5 inches and then a=10 inches. Look at the ratio 6a2:a3 when you use firstly a=5 and then subsequently when you use a=10. They are different (they are 1.2 when a=5 and 0.6 when a=10) at different lengths.

That is - as I say - completely and perfectly true and correct!! You cannot rationally argue otherwise (at least if you think you can I would like to see the arithmetic calculations you carry out step by step).

But what matters is to what extent internal forces that affect heat transfer between working fluid and engine surfaces in any Stirling engine are affected by scaling (by size, in other words). That is a discussion I'd very much like to have - which is why I started this thread!

[Tom Booth]

...

That is - as I say - completely and perfectly true and correct!! You cannot rationally argue otherwise (at least if you think you can I would like to see the arithmetic calculations you carry out step by step).

I can do that.

Briefly though, imagining that surface area and volume somehow scale differently is the same sort of thing as thinking that zero Celsius is somehow physically and/or qualitatively different than 32° F. Or that 212°F is ACTUALLY hotter than 100°C

The algebraic formulas are conversion formulas that bring things back from a mathematical Alice in Wonderland where enlarging something seems to somehow bloat or shrink the internal volume.

Right now I'm between runs fueling up tanks at different locations, so when I have a moment I'll get back to you with that step by step analysis.

[Alphax]

Tom, you started saying:-

Briefly though, imagining that surface area and volume somehow scale differently is the same sort of thing..........

It is the RATIO of surface area to volume that scales differently (gives different answers) as you change the length. I think you know that, really, and are just having a bit of fun pretending otherwise!


Have a look at the wikipedia page for 'surface-area-to-volume ratio' on Wikipedia:-

https://en.wikipedia.org/wiki/Surface-a ... lume_ratio

Looking forward to seeing your arithmetic..........

[Alphax]

Tom,

when you do your calculations you will get the same answers as shown in the table at the bottom of that Wikipedia page (assuming you do them correctly!)


https://en.wikipedia.org/wiki/Surface-a ... lume_ratio

The table uses the following sizes of cubes (called "side of cube"): 2, 4, 6, 8, 12, 20, 50 and 1000. The units (feet, inches, cubits) are irrelevant and not given as they apply to any unit of length (provided you don't change units when calculating your ratios).


In other words..... you should get the same answers as Wikipedia for the ratios of surface areas to volumes (3:1, 3:2, 3:3, 3:4, 3:6, 3:10, 3:25 and 3:500 (or, if you prefer to see the ratios expressed as numbers, then 3, 1.5, 1.0, 0.75, 0.5, 0.3, 0.12 and 0.006) if you use those cube sizes.


If you don't get the same answers for the surface area to volume ratios for those cube sizes then you have made a mistake somewhere.

So.... you aren't really arguing with me as a person, but with mathematical reason itself. I'll be interested in seeing your arithmetic steps.

Good luck!

[ccspring3021]

Hi,

Maybe the "surface to volume ratio" is a factor which will impact the efficiency of the machine, but I think it is not the important one.
Since the machine is not working like the sun or coal. It absorb heat and transfer to force, then it release the heat. So volume determine how much the heat it can absorb in a circle, the surface determine the speed it absorb or release heat, which will impact the period length.
Power = F * V, or "Energy in a circle" * Frequency. So the power sometimes relates to volume * suface.

For efficiency, it relates to T1(High temperature) & T2(Low temperature), and the mechanism or structure of the machine. But I think it less possible relative to "surface to volume ratio".
So pay more attention to the structure of stirling.

[Alphax]

So pay more attention to the structure of stirling.

OK.... can you be more specific? Which aspect of the structure would you like to see discussed?


One thing to think about when we begin to discuss the structure is that we are considering an engine that has only one essential moving part (the piston).

Whilst it is true that engines of this type usually have more than one moving part, it seems they can generally be reduced to just the one (the piston) and still be made to work.



Here is the really curious thing when we consider the structure of this general form of single piston single cylinder Stirling engine - they have more names than moving parts.


So, here are some of the names, which may be applied to single piston, single cylinder small Stirling engines similar in proportions, size and general arrangement to the Warbrooke Stirling 1 engine :-

Laminar Flow Engines

Thermal Lag Engines

Thermoacoustic Engines

Thermopulse Engine


Just to be absolutely clear, I'm NOT saying that these are all identically equivalent to each other (even though they all appear to exploit essentially the same basic thermodynamic cycle).

However, I am saying that they might be closely related in view of the fact that when any one of those engines has been scientifically investigated (as some of them have because they have potential use in helping to combat global warming), even the inventors themselves cannot agree how they actually work!

I think it is very interesting that such different interpretations of the detailed underlying physics exist for engines with just one fixed part (cylinder), one moving part (piston) and a constant mass of working fluid. Engines cannot be simpler to conceive or make than that, but apparently cannot be harder to understand!

A good example (you'll need to do a bit of reading) is the invention, development and subsequent university research on the Thermal Lag Stirling Engine invented and patented by Tailer (in 1995 - almost 30 years ago!) and worked on subsequently by several people including Allen Organ.


Now..... who has some thoughts on Structure?

For my part, I started this thread to explore Size (i.e. would a big one work better than a small one?). But I'm very happy to hear contributions from anyone regarding structure.

Any thoughts?

[Alphax]

Small clarification, strictly speaking, the term "Thermoacoustic" really can be considered as separate type of Stirling engine when it is applied to commercially available units (and which physically look not much like Stirling-1).

However, when it comes to "home brewed" single piston Stirling engines and to the mass produced little Chinese desktop engines you will find that the term "Thermoacoustic" is freely applied to little single cylinder engines where perhaps it isn't really that appropriate to do so. This does add a little to the confused or blurred terminology currently in use and reinforces the fact that there are more different names and more different interpretations for what amounts to the same sort of engine than there are moving parts in the engine itself!

Thats why I included the term "Thermoacoustic" in the list above (my previous post).

Any comments on Structure (as requested by ccspring3021) are caudially invited.......