If this was ever invented, how effective would it be? And how can it be improved upon to perhaps be the first steam train?
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You could effectively use it to make a cup of tea. You should have enough water on the boil after all.
As a vehicle? It would struggle to move down a hill with the wind behind it.
Aeolipile's have minimal torque and struggle to spin themselves up if they contain a significant amount of water. Remember that, with the best will in the world, it generates about as much motive force as a modern electric kettle. Even with modern gearing and clutch systems such an engine wouldn't be able to move any significant mass.
The main problem with this is not the amount of power it would produce but the amount of torque it would need to overcome everything between "engine" and the road.
And with Aeolipile there is no way to get more revs. Or to build up power required to get that thing moving.
Also the biggest force it produce is just at the end of "steam spout". Which we know was just enough to turn it. I assume the transmission belt would be enough to stop it from rotating.
SZCZERZO KŁY is right about that thing. I agree with him, and this is my explanation: The "Ball" is powered by the jet of steam, much like a jet engine. If the jet is strong enough to make the ball turn and eventually turning the wheel, then a jet that pushes the vehicle directly is more efficient.
Exception: For heavy vehicles, a reduction gear ratio between the spout and the wheels is possible. Still, too inefficient. A reciprocating engine is much better.