HydroKart, eh?

http://www.hydrokart.com.au/Just kidding - you probably mean the HydroKart plans available right here on the Muskoka Sea Flea site:

http://www.muskokaseaflea.ca/staticweb/index.php?option=com_content&view=article&id=61&Itemid=50Well, I hesitate to make any recommendations because, truth be known, I don't know squat about boat propeller design. I am, however, curious that they were supposedly getting 50 mph out of the Michigan Wheel Co. 7" diameter, 10" pitch propellers mentioned in the Materials List on page 7 of the plans.

Think about it. To convert the 50 mph to feet per minute, multiply by the conversion factor 88 to get 4400 ft/min. Converting to inches per minute, 12*4400 = 52800 in/min. Now, if the propeller is nominally advancing 10" with each revolution, how many revolutions are required to go 52800"? That would be 52800/10 = 5280 rpm. Since the engines were turning faster than the propellers at the ratio 2.5:1, the engines were supposedly running at 13200 rpm, and this is for an ideal propeller without "slippage".

I suppose that's in the realm of possibility for small 2-cycle racing engines. If that sounds reasonable to you, we can take a look at a related process to arrive at an approximate pitch for your propeller.

The approach starts out simple enough. The article claims the HydroKart will go 50 mph on two 6.5 hp Power-Products kart engines from a bygone era. Since you've got 10 hp instead of a total of 13 hp, your boat will be a bit slower, say 45 mph. To convert that to inches per minute,

12 x 88 x 45 = 47520 in/min

It would probably be wise to start your experimentation with the middle gear of your transmission so you will have some leeway to go either up or down on the propeller speed. Whatever gear you pick, figure out what rpm the propeller will be turning when the engine is at full speed. Let's say for the sake of an example calculation that it's 3600 rpm. Then the pitch would be

47520/3600 = 13.2"

Now here is where the cheese gets a little binding. A propeller with 13.2" geometric pitch will NOT advance the boat 13.2" in one revolution because of losses that necessarily occur due to generating the thrust. (For this reason, our beleaguered little Power-Product engines would have had to be turning even faster than 13,200 rpm.) The experts will have to chime in here, but I would guess the "slippage" is on the order of 15 to 20 percent. Probably better to err toward the lower efficiency side, so 120% of 13.2" is roughly 16".

For your propeller speed, call it N, your approximate pitch would be 1.2 x 47520/N

If you like cheese that binds, you can indulge in some more of it by considering the propeller diameter. The Power-Products engines were turning 7" diameter propellers. The approximate pitch you would start from is pretty much independent of the engine power, but your extra 3.5 hp will probably need to be absorbed by a larger diameter or a larger total blade area or a combination of the two. Lacking detailed information about the Michigan Wheel Co. 7" x 10" vis a vis the proposed modern propellers, we might speculate that the blade areas would be generally similar for same size diameters, so the extra power should be absorbed by increasing the diameter. At least for airplane propellers, the torque and thrust coefficients go up by the cube and the square of the diameter, respectively. I suspect something similar applies to boat propellers, so the diameter shouldn't be increased by too much - go up to maybe 8", certainly no more than 9".

This line of reasoning is probably all full of holes, so I've got a request for all the true experts out there:

Don't hold back on the brickbats.