Is there any particular reason for some wheels having 7 floats or maybe 9? Medway Queen has 7, John H Amos looks the same as does Eppleton Hall but not quite sure about that. Most model ones I have seen have 8 or some other number that divides easily into 360 degrees. The Westbury paddles have 8 floats while K N Harris for his inverted twin cylinder oscillating engines calls for 9. I am not thinking of the large wheels fitted in US or Great Eastern nor stern wheelers so maybe someone can come up with a reason. the best I can think of is 7 do not interfere with each other when entering or leaving the water so result in a more efficient wheel but that may just be wishful thinking.
John.

Welcome John......paddlewheels!...that's a rather large subject on design  ... however we must have some consideration for the 200 years these have edvolved from

1. installed power and output shaft speed?
2. size & type of vessel?
3. number/size & depth of blade immersion
4. feathering or fixed?
5. available width...etc, etc?

Our forefather Engineers had some excellent skills in geomerty, so I discount any issue with any number being divisable into the 360 degrees

You would need if possible to read & understand the engineering calculations for each of the wheel sets associated for the Proprietry manufacturer/designers you mention, many of which are not available

Derek   

Radial aero engines always have an odd number of cylinders. I think it is for the same reason. Unfortunately I have forgotten the reason since I read up on it some years ago.

The odd cylinder number of radial engines doesn't, of course, have anything to do with paddle wheels.
There's only one common crank pin for all cylinders. In a 4-stroke-engine, cylinders ignite every two revolutions. So as the crank passes all cylinders in a row, one cylinder ignites, one doesn't, one ignites, one doesn't and so on. After two revolutions, everything repeats. This would not be possible for an even number.

Moritz

Thanks Moritz for the correct explanation which makes complete sense.

Perhaps this alternating cycle gets replicated in a steam paddler?