# Thread: Formula for "Sail area/ Horsepower"?

1. Senior Member
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## Formula for "Sail area/ Horsepower"?

I keep looking through my small collection of boaty-type reference books, and I KNOW I once read it, but I can't find it anywhere. Frustrating! Do any of you remember the formula? Mr. Long? Mr. Conlin? Thanks!

2. ## Re: Formula for "Sail area/ Horsepower"?

Very basic rule of thumb.....with an efficient sail rig on a clean boat hull, 100 sq. feet of sail in a 15 mph breeze will generate 1 hp or the basic equivalent......

3. ## Re: Formula for "Sail area/ Horsepower"?

Based solely on personal experience, I've settled on something closer 50 sq. ft/hp. But clearly wind speed is a huge variable, not to mention how much the hull under the sail can stand up to. My 25' tri could easily go faster on 300 sq. foot or so of sail than the 6 hp. motor could push it --even in 15 knots of wind. And my 16' Whisp on 75 sq. foot of sail can easily go much faster than it ever did on an approx. 1/2 hp. electric motor --the sail feels somewhere between 1 and 2 horses at work to me. But my 35-foot catamaran can do about 6.5 knots with 36 diesel horses (2x18 hp.), but pushed by 700 sq. feet of sail, she will do about 8 knots in 15 knots of wind. So that would suggest scale is a big factor, too. Even at 50 sq. feet per horse, those 700 square feet would be producing just 14 horses, like running one engine throttled back a bit, 5 knots at the most.

Of course, the other question is is the comparison with the actual thrust derived from a motor and prop, or the theoretical force created? That itself would be something like the difference between a factor of 50 and 100 square feet per horse. I'm basing my ratio on observed thrust from the engines' rated output. Whatever values you use, most days the engine will still get you there quicker.

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## Re: Formula for "Sail area/ Horsepower"?

We do roughly seven knots in calm water with a 30 hp. engine. We do the same in 15 knots under sail, with 1000 sq. ft. of working rig. That would mean about one hp. for 30 sq. ft of sail. I doubt this is a universal formula, however. The issue isn't sail area, but area X wind velocity, as the wind energy increases as the square of velocity.

5. ## Re: Formula for "Sail area/ Horsepower"?

I should have also said/inserted displacement monohull....but the figures also relate to the rig.

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## Re: Formula for "Sail area/ Horsepower"?

There can't be a relationship between sail area and horsepower, since sail area alone doesn't do any work without wind. The calculation becomes interesting when calculating the power produced by a windmill at a given wind speed, which is a function of the sail area of the blades. The power produced still ends up as a function of the sail area times wind speed, just as horsepower is a function of torque times rpm.

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## Re: Formula for "Sail area/ Horsepower"?

remember that the energy in the wind varies as to the square of the wind velocity. Hp equals 550 foot pounds per second. Also remember that the drag on the hull also increases as to the square of the speed. so that at low speeds the sailis are more efficient.

8. ## Re: Formula for "Sail area/ Horsepower"?

In The Nature of Boats, David Gerr states that it is roughly 50 sqft/hp in a force four breeze. He has a chapter on it.

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## Re: Formula for "Sail area/ Horsepower"?

Remember, as a boat reaches its 'waterline speed' the power needed for the slightest speed increase of speed gets vastly greater. (a rough top speed approx. is speed in kts =1.25x sq. root LWL in feet) Put another way, you can increase the power input by a factor of 4 and see just a tiny increase as the waterline speed is reached. So, discussions about sail area v. horsepower based on empirical observation are bound to be unreliable.

I once established a true power-needed curve by towing the test hull on a long, light, dyneema cord with a spring balance, recording the GPS speed and line tension in the same video screen, then plotting the two numbers on a frame by frame basis. The test hull had its prop removed. The method took out the unknown factor, drive train efficiency. The result was amazing (and disproved the performance claims of an electric powered GRP boat supplier). Towing Between 4 and 5 kts the drag increased from 28 to 84lbs.... and then went off the scale at 5.25kts!

Originally Posted by LongIslandBoy
I keep looking through my small collection of boaty-type reference books, and I KNOW I once read it, but I can't find it anywhere. Frustrating! Do any of you remember the formula? Mr. Long? Mr. Conlin? Thanks!

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