# How to calculate rpm of an aeolipile

• B
Hi!
I am making an aeolipile as a school project, and I was wondering if you could calculate the rpm.

This is the basic principle of an aeolipile.

You should be able to calculate the rotating velocity right? Knowing the mass and ignoring any resistance.
But then you'll need the rotating force. I looked at the rocket equation, but you need to know the exiting gas velocity for that. The diameter of the nozzle is 3mm, would it be possible to calculate the velocity steam could move out of such a nozzle after calculating the pressure inside the hollow ball?

Tino

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## Answers and Replies

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sophiecentaur
Gold Member
In the absence of friction and turbulence, the tangential velocity of the wheel would increase without limit - which is what would happen in a space rocket with an engine that can run for ever. I think the limiting rotational speed will be governed entirely by the losses and the exit velocity of the steam jets.

CWatters and anorlunda
In the absence of friction and turbulence, the tangential velocity of the wheel would increase without limit - which is what would happen in a space rocket with an engine that can run for ever. I think the limiting rotational speed will be governed entirely by the losses and the exit velocity of the steam jets.
Ah yes of course, but what formulas would you use to calculate that rotational force? Or are there just too many variables to get a reasonable answer?

You would need something like this I assume?

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Nidum
Gold Member
It is not that complicated for your turbine . You only have subsonic flow through parallel nozzles . That is not too difficult to deal with .

To answer your original question though the top speed running free is hard to estimate .

A more useful and interesting thing to do would be to put some controllable load on the turbine and measure the turbines load/speed characteristics . You could also experiment then with different arm/nozzle configurations to get best results .

Tinokoloski
sophiecentaur
Gold Member
Something like that probably . Then you would need to estimate the drag. I bet there's a formula somewhere for a rotating sphere and you could approximate the jets to cylinders and assume they are travelling in a straight line normal to the axis. Drag formula for a short cylinder must also be available.

Tinokoloski
Interesting school project. What are you using for seals where the steam tubes enter the rotating drum?

sophiecentaur
RonL
Gold Member
Hi!
I am making an aeolipile as a school project, and I was wondering if you could calculate the rpm.

View attachment 215250
This is the basic principle of an aeolipile.

You should be able to calculate the rotating velocity right? Knowing the mass and ignoring any resistance.
But then you'll need the rotating force. I looked at the rocket equation, but you need to know the exiting gas velocity for that. The diameter of the nozzle is 3mm, would it be possible to calculate the velocity steam could move out of such a nozzle after calculating the pressure inside the hollow ball?

Tino
I would like to encourage you to consider adding this compressor design to the inside of the sphere and see if there is any usable thermal energy value between intake air and discharge through the tip jets.
The design should be changed to draw air in through the center of the rotor and then discharged into the sphere.

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Interesting school project. What are you using for seals where the steam tubes enter the rotating drum?
That's the tricky part, we have to use the materials that were available during that period of time (the roman ages). So we are going to solder the tubes to the drum and then have a sleeve bearing on one of the connecting tubes. So the only way to prevent too much steam to leak out is to use some kind of viscous lubrication right? Then of course you don't want to have too much resistance as it does not generate a lot of force.

I would like to encourage you to consider adding this compressor design to the inside of the sphere and see if there is any usable thermal energy value between intake air and discharge through the tip jets.
The design should be changed to draw air in through the center of the rotor and then discharged into the sphere.

View attachment 215329
That's an interesting idea!
However, as stated we are trying to build it with the techniques that were available in the roman ages! I don't believe this was invented back then...

Thanks for your help!

RonL
Gold Member
That's an interesting idea!
However, as stated we are trying to build it with the techniques that were available in the roman ages! I don't believe this was invented back then...

Thanks for your help!
Sorry, I didn't think about the fact that you were trying to replicate the original thinking part of the process. Best wishes for your project

Tinokoloski
That's the tricky part, we have to use the materials that were available during that period of time (the roman ages). So we are going to solder the tubes to the drum and then have a sleeve bearing on one of the connecting tubes. So the only way to prevent too much steam to leak out is to use some kind of viscous lubrication right?
Well, that is kind of tricky. Perhaps you could make some kind of stuffing box? I guess they wouldn't let you use teflon-coated packing, but you could probably come up with something that would work, even just hemp rope.

Well, that is kind of tricky. Perhaps you could make some kind of stuffing box? I guess they wouldn't let you use teflon-coated packing, but you could probably come up with something that would work, even just hemp rope.
Ah yes of course! That is a good idea, we could indeed use some kind of simple fabric to make it a bit more air tight.

Thanks!

The original did not rely on gas-tight seals, as far as I'm aware.
The bracket just "pinched" the sphere, much like they picked-up big stone blocks in those days - a couple of indents and some pincers.
The sphere had pipes that went roughly to the middle - to get steam without water, and the whole thing was heated - in an open flame.
So, don't fill more than half full to start with, the centrifugal action will throw the water to the edges in full operation.
This is a lot easier to build than anything with bearings or pressure seals.

nice thing about the simple approach is that if it's a bit off-centre, wobbly, then you can change the axis points with a hammer - just deepen the indent a little as you move it a few mm in the desired direction.

Indeed. Simple is always better.

this sort of thing - the bearings do not puncture the sphere.
as you can see, if the pipes don't extend into the centre of the sphere then water will come out, and the duration will be short.

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The original did not rely on gas-tight seals, as far as I'm aware.
The bracket just "pinched" the sphere, much like they picked-up big stone blocks in those days - a couple of indents and some pincers.
The sphere had pipes that went roughly to the middle - to get steam without water, and the whole thing was heated - in an open flame.
So, don't fill more than half full to start with, the centrifugal action will throw the water to the edges in full operation.
This is a lot easier to build than anything with bearings or pressure seals.
We looked into something like this, but heron specifies the bowl in the bottom containing the water and the steam traveling through the pipes to the ball on top! Of course there is no evidence that he really managed to make it, but that’s what we’re trying to find out by building it ourselves!

It has been built this way a few times, the bearing does not have to be completely air tight, as long as some pressure can build up in the ball.

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