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I am new to sailing- can a sailboat travel faster than the wind? Hypothetically, if the hull speed is 7kn and the winds are only 4kn can the boat go 5 or 6 kn?
 

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On a broad reach, a sail powered vehicle can exceed wind speed. It's been done on ice and salt flats or paved surfaces, but to my knowledge not on water. Or maybe only on land. I remember reading about a windmill sort of contraption that used wind power to drive the wheels mechanically. I don't recall the details, but think this moment that its claim to fame was its ability to exceed windspeed directly upwind. (In all cases, the apparent wind is the issue. Dead downwind, you can never exceed windspeed. Upwind, though, the v-squared relationship is beneficial, although aero drag also increases at that same rate.)
 

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It is absolutely possible to out sail the wind. I can think of any number of boats that can do so regularly at all points of sail. While I don't think it is possible to sail directly downwind at faster than the wind speed, it is possible to make it to a leeward mark faster than the wind, by jibeing downwind.

Take a look at
Extreme 40
AC 45
VX One
Pretty much any off shore record breaker in the last 15 years
Almost anything with a canting keel
 

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The 72ft cats in the Americas Cup are advertised to be able to make speeds up to twice that of the wind.
 

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Almost any performance cat and many performance monos can do this.

BUT you posted this in a cruising and liveaboard forum. Only a miniscule % of boats that are truly cruised as liveaboards can do this.

My fast old lady propably could do it on a beam reach but only AFTER I unloaded the lockers of 400 FEET OF CHAIN AND TWO OF THE THREE ANCHORS all the spares, the 300 books, the 150 galls of water the 70 galls of diesel the Tohatsu 18 the AB dink the dodger etc etc. It is a cruiser, paint the water line higher!
 

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I remember reading about a windmill sort of contraption that used wind power to drive the wheels mechanically. I don't recall the details, but think this moment that its claim to fame was its ability to exceed windspeed directly upwind.
I guess you mean the Blackbird:
http://en.wikipedia.org/wiki/Blackbird_(land_yacht)

It went directly downwind at 2.8 x windspeed, and direclty upwind at 2.1 x windspeed:
DownindRecord


(In all cases, the apparent wind is the issue. Dead downwind, you can never exceed windspeed. Upwind, though, the v-squared relationship is beneficial, although aero drag also increases at that same rate.)
A conventional sail craft can neither go directly upwind (at any speed), nor directly downwind faster than wind. Using rotors, like the Blackbird, you can do both.
 

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The other part of this discussion is what you mean by wind, true or apparent.

In winds under about 7 knots, upwind and close reaching, my boat routinely goes faster than the true wind. Of course, the apparent wind is closer to 11-12 knots at the time so that is why it is happens. Its is much harder to exceed tru wind speed when the wind is beyond a beam reach.

Jeff
 

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See
for a simple video demonstration. Be sure to check the links since he has done other videos with more detailed explanations.

edit: actually the links weren't readily available, so here's the other one:

 

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I think more relevant to conventional sailboats are those two animations, showing a downwind velocity made good greater than true wind speeed on broad reach:


 

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The first two are specifically DDWFTTW, which is impossible for conventional sailboats.
 
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