Is there a way to find out the horse power of a sail?

Question

I'm trying to determine what horse power motor would be roughly equivalent to a sail of certain a certain size? Does anyone know a formula to do this? Are there any other variables need besides wind speed and sail area?

Answer 1

This is going to be monumentally complicated because sails can be rectangular square rigged or triangular sloop rigged and the force created by the sail will vary with the angle and curvature of the sail.

  Horse power would require knowing the average force applied over a distance in a period of time, which depends on the drag of the boat, the velocity of the boat and the boat's design (for example, some sailboats will plane, like some motor boats do, sharply reducing the drag and increasing the velocity.)

  The only way I can think of getting a rough comparison would be doing velocity measurements on a boat that can take a motor (like a Snipe or Cub with a transom or motor mount) then take down the sails and lower the motor and see what it takes to get to the same velocity.

Answer 2

Hydrodynamics is often studied using similarity studies and dimensionless numbers. One of these is the Admiralty Coefficient, typically 400 to 450.

D^2/3 * S^3 / 400 = P

D = displacement in US short tons

S = speed in knots (1.15 * mph)

P = horsepower

So, for a 2 ton boat at 5 kt, power is 2^2/3 * 5^3 / 400 = 0.5 HP

Converting the speed,

5kt * 1.15 * 5280 / 3600 = 8.4 ft/sec

Since power = force * velocity,

0.5HP * 550 / (8.4 ft/sec) = 32 lb

I have used this on a number of larger vessels, accurate to about ±10%, possibly need to determine number for your vessel. Could use small high thrust motor, say trolling motor, to propel boat on windless day, measure current * voltage * 70% to get power using estimated 70% motor/propeller efficiency, put back into formula to get AC. Motor should be 80% or so, prop about 85%.

For more accuracy, tow boat with another using a long rope with a heavy duty fish scale in the rope. Measure 2 or 3 points in the area of interest, and get your AC.