Not sure you're asking the right question here.
From 1/2 a century ago, schoolboy physics. horse power is rate of doing work.
So the horsepower a sail develops depends on weight of rider and rig, friction overcome and speed of board.

The force in a windsurfing sail is limited by the ability of the rider to counterbalance the sideways force.
Heavier the rider, more force is available and more work is done, so more horsepower generated.
So you have to specify riders weight as well.

Hmm, very interesting.
Horsepower is the rate of doing work. It was determined a long time ago that a "husky horse" could lift 550 pounds weight, one foot in one second so this was called 1 horsepower. (don't laugh. It was all very logical back then. )
Thus a horsepower is 550 foot pounds per second.

Sooooooo,.. for a windsurfer, you need to guess how many pounds force is required to pull the windsurfer over the water at so many feet per second.

Sooooo,. first the easy bit,. how many feet per second?
Typically this would be around 20 to 30 knots, lets say 25 knots.
25 knots is about 29 miles per hour and,.. there are 5280 feet in a mile.
Thus, 29 mph = 29 X 5280 / 3600 = about 42.5 feet per second.

The tricky bit is guessing how many pounds force it takes to pull you along at that speed.
This would be a combination of the forward component of your foot pressure, the forward component of the force on your arms and harness lines, and the forward component of the mast foot force.
The forward component of all these forces would vary considerably with how the whole rig was trimmed, but I would guess that trimmed properly, it would be around 50% of the force on each.
My guess on the total on all of these would be around 40 pounds. (just my guess thinking about the forces on my arms and legs.
Someone might have a better guess on this one, but let's go with this for the moment.)

Sooooo,.. (wait for it, nearly there,..) horsepower is
42.5 ft per sec X 40 pounds / 550 ft lbs per sec = 3.1 horsepower.
and if you're interested, wattage = 3.1 X 746 = 2312 watts. i.e 2.3 KW.

This would probably vary in an almost linear manner with speed.
i.e. twice as fast is about twice the horsepower, because I think the forward force does not increase greatly with speed. In fact, if the board gets up and skates then the forward force could even be less.
Half as fast is about half the horsepower.

Power : weight ratio depends on how fat you are.
Lets say 150 pounds total weight. gives 150 / 3.1 = 50 pounds per horsepower, which is pretty pathetic really.
It will never get off the ground!

decrepit said...

Not sure you're asking the right question here.
From 1/2 a century ago, schoolboy physics. horse power is rate of doing work.
So the horsepower a sail develops depends on weight of rider and rig, friction overcome and speed of board.

The force in a windsurfing sail is limited by the ability of the rider to counterbalance the sideways force.
Heavier the rider, more force is available and more work is done, so more horsepower generated.
So you have to specify riders weight as well.

Is that why Im not as fast as the heavier guys..? Great at least now I have an excuse!

whats that in "dogpower"..??

Someone needs to waterski a windsurfer hull behind a motor boat with a spring balance in the tow rope.

Or you could estimate it by comparing regular windsurfers to hydrofoiling windsurfers. The hydrofoilers seem to be go with about half the horsepower of a planing windsurfer, judging by the way they use smaller sails and the riders don't hike out as hard.

A human can develop 1 hp for a period of 1 minute. ref. Bicycling Science Whitt and Wilson 1974.

1 person can only just get hydrofoilers up and going.

lancet.mit.edu/decavitator/

If you allow for a bit of inefficiency in the propellor - That's ~ 3 hp to keep a windsurfer hull going.