Originally Posted by TrueBlue
In all due respect to your presumed intelligence, apparent wind and fan-generated wind are two completely different forces. My wife and I just returned from three days of both "pure" sailing and motorsailing - since we own a motorsailer, and that is what they're designed for.
Winds were variable in speed and direction. So, during those 5 knot lulls, I kicked on the 90 hp iron genny . . . at a low rpm - and put up full sail, 150 Genoa, main & mizzen. Where the other sailboats on the Bay were barely motorsailing at 4 knots, we kicked butt at 9 knots & 1,700 rpm.
Show me a powered fan which can get a 9 ton, 33 ft boat moving at 9 knots with that meager energy usage. Admit that this notion of yours is simply ridiculous.
It is probably
correct that you can't do better than using a propeller in the water.
However, that's not the only scenario I'm considering. Fan boats of course have to use fans. It is conceivable placing a sail behind the fan on those boats could improve efficiency and speed.
It's still not certain to me that you could get better speed by using a fan in front of a sail than one after the sail, but here's a start at something:
A motorsailer, with a water propeller, creates its own apparent wind. Then an obvious guess to make is that the increase in speed for the motorsailer is just like there was a true wind operating. So to find the increase in speed, calculate the total velocity as the vector sum of the velocity due the motor alone plus the velocity given to the sailboat alone tacking into a true wind of the same speed as that due to the motor alone.
IF that is true, then the obvious guess to make is that the speed of the fan in front of sail case, would be given by calculating the vector sum of the velocity due to the momentum thrust of the fan alone plus the velocity of the sailboat alone tacking into a true wind that is the same as the apparent wind due to the fan plus the speed of air flow through the fan.
That is, imagine the speed of the boat produced by the fan with no sail. Then the magnitude of the effective "true" wind you would calculate with would be this speed plus the air speed from the fan.
Under this hypothesis
then, you see an increase in the fan air speed could result in a marked improvement in the boat speed. It would be just like an increase in the true wind speed.
Here's a start at understanding how much horsepower could improve the boat speed IF this hypothesis is correct:
This page gives a formula for calculating how much power a wind turbine or windmill can put out for a given wind speed and rotor size:
Practical Wind Generated Electricity.
Then we may suppose an engine of that horspower could turn rotors of the equivalent size and generate an equivalent wind speed.
Here's the formula for calculating the horsepower of the wind turbine:
Practical Wind Generated Electricity.
"Any moving material carries kinetic energy and momentum. The basic laws of kinematics allow an easy analysis of a first approximation of performance. Essentially, any wind-power mechanism captures energy by slowing down the speed of the wind involved.
Undisturbed wind contains power from kinetic energy (energy flux) equal to:
E = 0.5 * (rho) * V^3 * (pi) * R^2.
Note that this is a simple application of the kinetic energy definition. Also note that the power is dependent on the THIRD power of V, the wind speed. A 20-mph wind has about 8 times as much power as a 10-mph wind, and a 40-mph wind has about 64 times as much power. (rho) is the density of air.)
In case you're curious, a 60-mph wind (88 feet/second) has:
E = 0.5 * (0.00237) * (883) * 12
E = 810 ft-lb/sec, about 1.5 horsepower per square foot of wind area!
You can probably see why strong winds can knock buildings down!
A 10-mph wind has far less power in it, around 4 ft-lb/sec, or about 1/150 horsepower per square foot. A ten-foot diameter farm windmill intercepts about 78 square feet of wind area, so that (10 mph) wind initially contained about 0.5 horsepower in it. At its maximum efficiency of 30%, the farm windmill could capture around 0.15 horsepower, a sufficient amount for pumping water."
So a .15 horsepower engine turning a 10 ft rotor could produce a 10 mph wind. A 10 foot rotor would be small for sails though. But by the formula a 3*10 = 30 ft rotor for the same wind could be driven by a engine with 3^2 = 9 times more power or 1.35 horsepower.
Now again by the formula, this 30 ft rotor could produce a 4*10 = 40 mph wind by using a 4^3 times more powerful engine: 1.35*4^3 = 1.35*64 = 86.4 horsepower, within the range of your engine for your motorsailer
A 40 mph wind would be quite a significant wind for a sailboat and could give it significant speed.
This is assuming the hypothesis for how the fan air speed would contribute to the boat speed is the correct one.