Maximum Velocity of a Sailboat

I just watched a program on TV on racing sailboats where the voiceover said that the maximum speed of a sailboat was = 2.79 x windspeed without any qualifiers. This sounded suspiciously too exact to be an actual measured top speed. Is this a theoretical top speed? How is it arrived at? Looks like maybe the inverse cosecant (or some such) of the angle between direction of travel and wind direction.

Do ice boats get counted?
Hydra foils?
Catamarans?
Sail boards?
Only displacement boats?

Or can we say, “So far?”

Looks like overall, the determining factor is actually hull length, as in, the longer the hull, the faster the boat can sail. Boats in a race are probably limited in how long the hull can be, so then the determining factor would be wind speed.

As I said, the figure of 2.79 seemed too precise to be based on anything but a theoretical construct and so would apply to anything that moved by wind power on a level surface.

It is true that the maximum speed of a heavy displacement boat (one that rides in the water by buoyancy) is limited by the wetted length of the hull; this is because the physics of waves in water limits the speed at which the wave can move to 1.34 times the square root of the length of the wave, and a displacement boat will create a wave that is at minimum the length of the hull. The lower the displacement to length ratio (DLR) the closer a boat can achieve this theoretical maximum. However, very lightweight boats that are designed to hydroplane on top of the surface of the water (creating a lift effect in the water similar to ground effect in air) can move considerably faster on a beam or broad reach under high wind loading. For the most part, these boats are multihull boats, where one hull may come completely out of the water and the other rides a fine balance, creating a high pressure zone just below the wetted surface that pushes the hull out of the water, minimizing contact area; however, small daggerboard dinghies like the Sunfish and Laser can also plane under light-to-moderate winds on flat water.

I don’t know of a theoretical maximum for sailboat speed using a planing hull; in theory, if you could develop sufficient lift on an absolutely flat surface (and enough power to drive the boat at an arbitrary speed) you could ride on top of the water at any speed up to the acoustic speed in the water with minimal drag, and if you created a non-viscous high pressure boundary so the water never actually touches the hull, there would be essentially no drag; this is basically how a hovercraft works, though there is obviously drag on the skirt that retains the pressurized air. In reality, water with any wind significant always has a bit of chop, so there are practical limits to how fast a sailboat could possibly go, and sustained winds will create large swell moving normal to the wind, which limits the speed of the boat by forcing it to periodically go upward onto the oncoming swell, limiting how much momentum it can retain between waves. The boat is obviously limited, too, by the amount of lift the sails can create; making a mast higher makes more surface area, and making the genoa larger gives a higher jet speed between the sails, but there are practical limits of stability, rig loading, and the feasibility of sail handling that limit just how big of a mainsail and genoa you can put on a boat of a given hull length.

I believe the 2.79 factor cited by the o.p. is an empirical measurement on the fastest planing multihulls on a shallow broad reach (across the wind). While not a theoretical calculated maximum, I’d be surprised if it weren’t within five percent of the maximum that anyone will ever get out of a sailboat without resorting to auxiliary propulsion. Just about the only thing left to optimize on a modern racing sailboat is the shape of the sails, which is limited by control of the textile surface, and even that is pretty refined. A self-tensioning sail that can maximize wind speed across the sail without separating at the top of the leech could possibly eke out a little more power than can be done with any practical rigging arrangement but the amount of sail area that could be optimized to generate more lift is just too limited to get more than a small amount of additional lift.

Stranger

Stranger – Well I certainly learned more about sailboats than I ever thought I would know - thanks. Are you saying nobody has ever tried to develop a theoretical idealized model of the relation between windspeed and max. velocity? No friction with the water, no chop, no interaction between sails, no effect from hull shape, etc. There has got to be a relationship between the 3 relevant angles. Heading and the angle this makes with wind direction and the angle the plane of the sail makes with both for maximum theoretical speed. Then by a simple force vector diagram one could calculate the ratio between windspeed and max theoretical speed.

From what you say it seems as if (assuming the 2.79is correct) that designers have approached this theoretical speed.

They can get up to some impressive speeds though:

ERROR: Inconsistent units.

Absolutely – as already said, everything else being equal (which of course it never is) the waterline length (wetted hull length) is the determining speed factor of a displacement hull sailboat. Which is why some boats have aft hull designs like this to extend the waterline length. It’s also why small-ish planing motorboats are very inefficient as they exceed their natural hull speeds until they start to plane.

It smells like a derived figure that pitches the lift/drag ratio of a sail against the problem of apparent shift wind for a sail. You would guess that there could be an absolute limit. But 2.79 probably isn’t it. Greenbird set a land sailing record of 126mph in about 30mph of wind. Paul Larsen has hinted that he is working on an offshore boat that takes some of the design idea from Sailrocket - but despite some prodding he hasn’t said much for some months. 65knots is seriously fast. (Language warning, nobody swears like us Aussies.)

Could be.

And you need something else thrown in there. The physics of the keel, which also acts like a lift/drag device. And the keel serves another purpose. It “turns” the sideways force of wind on the boat into a forward force.

I think the 2.79 is probably based on a basic fundamental series of physics equations and how they interact. But, to actually use those equations, you have to use some actual real world numbers.

Well, probably may be a bit strong. Could well be might be a better word choice.

Hey, and misleading precision for that matter :slight_smile:

“Hull speed” for a boat with length to width ratio of 3 is different than one with length to width ratio of 7.

And "hull speed for a given boat with a bigger motor is different than for one with a smaller motor.

And for that matter, put enough power in a boat and hull speed could possible turn into planing speed. Though I would not want to be in a displacement designed hull that was powered by something like rocket engines to make it plane.

It’s a nice guideline. And unless your design is pretty far outside the norm in some way, 1.4 plus I dunno, plus or minus 15 percent, is close enough for back of the envelope calculations.

And the 1.4 is an engineering equation. Max hull speed in knots (or is it mph?) is 1.4 times the square root of the boat length in feet.

Agree. You need lateral force from the foil, and this is a key difference between a water craft and a land craft (or ice). At speed foil design is black magic - and super cavitating designs are needed. Sailrocket probably managed a bit over twice the wind speed. It may be that the sweet spot for multiple of wind speed is in lower wind than absolute speed record setting conditions. A C-class cat is probably one of the more efficient beasts around, they can get to remarkable speeds in low wind, even if their fragility means they get trounced as the wind gets up.

Good point.

Also consider this. Sailboats (well at least decent ones) can sail upwind. But IIRC as the wind gets stronger, at some point they no longer can. So, it is obvious that its not just a more power from the wind, the more power we have to fight it. Which is why sailboat captians get a bit nervous when they are upwind of a rocky coast and the wind starts picking up.

Though all this may have more to do with real world realities than actual basic fundamental sailboat physics.

From the OP, it sounds to me like the voiceover was trying to point out that a sailboat can attain a speed that is faster than the wind speed (which is something that some people may not know) and the limit is 2.79 times the wind speed. The lack of qualifiers seems to indicate that the limit comes from the aerodynamics of optimum sail designs and not hull performance. The way it is phrased in the OP, this limit may not have ever been achieved by an actual boat.

Yes, but with no hull/keel physics you don’t have a sailboat, you have something more like a vertical wing trying to go upwind. Which might be like a glider or a soaring bird going upwind I suppose.

Though if you are right that would be hard limit, as once you throw in the hull and keel I’m not seeing how that is going to do anything but bring the speed down.

Maximum hull speed (of any deep displacement vessel) is 1.34 kt/ftSUP[/SUP] * L[SUB]wl[/SUB][SUP]1/2[/SUP], where L[SUB]wl[/SUB] is the length of the hull at the waterline in feet. (Since all marine engineering is done in traditional nautical units, the speed in knots/hr and length in feet is assumed.) I’m pulling this from Leonard’s The Voyager’s Handbook because it is the closest reference I can reach, but it is a common relationship in naval engineering.

Okay, let’s stop guessing and just use the magic of this new-fangled device called a “search engine” to see if it is explained somewhere. Hey, look here: *This year, two new classes of boat were announced in the America’s Cup – the AC72 and a scaled-down version, the AC45, which was used for the preliminary training and racing.

These catamarans use innovative wing sail designs and hydrofoils that were initially expected to achieve speeds of up to 1.6 times the speed of the wind when sailing downwind.

However, the yachts have achieved almost 2.79 times the wind speed and reached speeds of up to 47 knots, or 55 miles per hour.*

The maximum speed that could be achieved by the sails in theory (negating viscosity effects and all of the hull drag and stability parameters) can in theory be calculated from the application of Bernoulli’s principle to the jetted two airfoil configuration of a genoa-rigged sailboat. When the speed of the wind exiting between the mainsail and genoa drops below the speed of the wind coming around the backside of the mainsail at leech there will be more drag than lift and the wing will slow down. The larger (taller, and to some extent, wider at the foot) the sails are, the more force they can develop and thus, a higher speed can be attained. However, where this point occurs depends very much on the parameters of the sail, and for practical purposes, sails can only be flown to a certain size for a given wind condition before rigging starts breaking or the boat becomes unstable. Racing boats will typically carry three or more sizes of foresail (a #1 genoa for light winds (usually up to 12-15 its), a #2 genoa for medium winds (usually up to 25-30 kts its or thereabouts) and a storm jib for heavy wind or gale conditions. Assuming no mass and no drag on the sails, I don’t believe there is a theoretical maximum speed for an arbitrarily optimized airfoil up to the transonic region, where thermodynamic and turbulence effects will dominate. In reality, form drag of the sails and rigging will limit practical speeds to some small fraction of that.

Stranger

For theory see:


http://www.onemetre.net/Design/CourseTheorem/CourseTheorem.htm

I happened to be visiting Aukland in 2003 when the Louis Vuitton races were occurring. The big story there was the “HULA”.

NZL 82

Not that it helped:

More info here.

It should be noted that performance taken from races does not necessarily represent the maximal speed as a multiple of true wind speed, because in races the boats don’t try to maximize that parameter. Instead they try to maximize the velocity made good (VMG) towards some given mark. For example downwind VMG and upwind VMG. If you really wanted to maximize the true wind multiple, you would choose the course optimal for that (see course theorem), but also optimal wind conditions. The true wind cannot be too strong, because the requires higher absolute speed, which creates its own problems.

I suspect that the optimal boat to maximize true windspeed multiple, without perscribed course, would the ones with the biggest airfoil sail, like this one:


From the actual performance of the boat during the 2010 America’s Cup races, it can be seen that she could achieve a velocity made good upwind of over twice the wind speed and downwind of over 2.5 times the wind speed; this means that downwind she was sailing at nearly four times the speed of the true wind.

The more recent boats of type are smaller than the huge USA-17, but they can lift the hulls completely out of the water, leaving just the hydrofoil and keel submerged.