# Approximate sailboat speed prediction

Discussion in 'Sailboats' started by laukejas, Apr 16, 2015.

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### laukejasSenior Member

Hello,

I'm designing a boat right now, and though this isn't very important, I've been wondering what speeds it will achieve in different kinds of wind conditions.

Since I've been modeling the hull shape with Delftship, it produces a very handy graph of water resistance in Nm (wave resistance + viscous resistance, I believe) in the speed range from 0 kt to hull speed.

I also know the formula to link wind speed with sail area to roughly determine the force which sail will produce (1/2 * air density * wind velocity ^2 * sail area), which is often used in heeling force calculations.

However, I'm not sure how to link that resistance information with sail force, because the vector of the force is dependent on sheeting angle, the boat speed changes apparent wind speed and direction, which in turn influences sheeting angle...

In practice, there is a certain true wind angle and speed at which boat finds equilibrium, meaning it cannot go any faster or closer to the wind. But I don't know how to calculate that with the information I have.

I know that there are dozens of factors, like sail type, hull and rigging windage, boat oscillation due to waves, leeway, underwater appendages efficiency, and so on. Some of these might be more important, some less.

Now, I know that the true answer can be found only by practical sailing or by simulations with advanced and expensive software, but I'm not looking for that kind of accuracy. Velocity Prediction Programs (VPP's) also do this stuff, but they are also meant to give very precise answer.

What I'm looking for is some simplified, approximate calculation, taking in account only the most influencing factors. For example, I just want to roughly know what kind of wind speed I'll need to hit hull speed. Or what the speed will be at 8 kt wind at 140° true wind angle.

Again, I emphasize on simplified Accuracy within 10% of reality would be perfectly adequate.

Could anybody help a little?

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Too many variables Laukejas. Displacement is a major one. It is pretty certain that the boat will move faster at 100kg displacement than it will at 160 given the same wind strength. Your boat, as designed, is a decent little dinghy. It is too short to make any impressive speed. It will almost surely go as well as can be expected in light airs.

So what does "expected" mean? I would make a wild guess that it will top out at somewhere around 6 km/hr more or less. It might do that in an 8 knot breeze. The operative words are; wild guess. That guess is based on the observed performance of a zillion other small dinghies of similar size.

With a complete re-design with emphasis placed on speed it could even be made to plane. A design of that sort would likely be less efficient in very light airs. Go with what you have drawn and do your best to put a slick finish on the wetted parts. Since you anticipate predominantly light airs, skin friction and wetted surface area will be a major determinate. The size and quality of the sail will be the other major factor.

There are too many variables to get within the ten percent prediction that you wish for. None of this is to suggest that you abandon your speed prediction efforts. It is a good mental exercise if nothing else. Sure enough a ten percent plus or minus difference in VMG could matter if you were in a hurry or had a long distance to go and you could keep the boat in the groove for the full distance traveled. ( maintaining the groove is another variable )

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### laukejasSenior Member

I was hoping you'd join the fun

I gave example with my boat just as a conversation starter. Sure, I pretty much know what can be expected from it and what not, so this topic isn't meant for this specific boat. I'm just wondering how this can be done in general. As you say, a good mental exercise.

Variables are many, but surely they don't have the same weight in the equation. If we rule out the most unpredictable ones, we can have a crude formula. Then, step by step, we can add more variables to make the final result more accurate.

What I want to do here is to form the basic equation, the skeleton of this calculation, to which other variables can be added later, depending on how accurate you want to go.

Problem is that I'm bad at maths. I imagine how this should be done, but I can't put it into numbers.

Thinking of it, as speed increases, so does the hull resistance. Apparent wind speed also increases, giving sail more power, but the angle closes, reducing forward force vector. Sheeting angle is a function of apparent wind speed (the higher the windspeed, the lesser angle between wind direction and sail chord), and it can be approximated for simplicity.
Sail force can be calculated with the formula I cited earlier.
Hull resistance can be drawn by variables such as prismatic coefficient, displacement, waterline length, or by using data from DelftShip, which should be simpler.

All in all, it seems like a simple vector problem - find equilibrium speed at which boat can accelerate no further, because sheeting angle becomes too tight and driving vector becomes too small to overcome hull resistance.

Maybe this would give a basic ballpark figure with 30% accuracy, I don't know. But if we could write that down, it would be a good start.

Messabout, you're smarter in this than me. I believe that taking only these variables I mentioned into account, you would know how to put them in the same equation, solved for speed. Are you brewing some idea as you're reading this?

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### PetrosSenior Member

there was a paper on performance that Eric Sponberg posted that gives a listing of factors or ratios that affect performance, and a formula that gives a performance rating. You can run your boats ratios though the formula and get a rating. I think he also has a fairly large list of common or popular boats with their ratings, so you can compare those with the rating on yours.

The output is just a rating or parameter to compare with other boats. But it should give you an idea of the relative performance of your boat with others.

I saved a copy, he made it available for free so I do not think he will mind me posting it here (so you do not have to look for it in the archives):

#### Attached Files:

• ###### THE DESIGN RATIOS.pdf
File size:
865.6 KB
Views:
743
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Laukejas try to reserve some time to read and study the link that Petros provided. The link is the result of the outstanding generosity of Eric Sponberg. After you work your way through all the information that Eric has furnished, we'll pretty much be back to the same generalities.

You are constrained by several requirements unique to your circumstances. Your boat is a short one. Your displacement length ratio is going to be in the ballpark of 100 when sailing single handed and 150 when with a crew. Those numbers imply that the boat is not going to go very fast. Your sail area displacement ratio is not favorable for speed either. I do not mean to be a doomsayer here, you are operating within the constraints that you are saddled with so you have to take what you can get.

......................................................................................

If I was doing the boat, I'd make it longer, a lot narrower, and flat bottomed, all the while fighting weight. A longer boat is much more comfortable and it has the potential for additional speed. A 4.3 Meter LOA, for example, would change the DLR favorably. You could still stay close to the 30kg limit you have placed on the design.

I'm thinking of a delightful little ultra light skiff called Whisp. By Thomas J. Hill. It is a performance rowing/ sailing boat that is also very nice to look at. It can do a mile in 12 minutes using ordinary oars and not much sweat. It will also plane in a breeze.

I wish that we could get his book for you. Hill is a real craftsman who builds elegant light weight boats. His book is titled; Ultralight Boat Building. He shows all sorts of details and instructions for building light and strong little boats.

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### laukejasSenior Member

Thank you, Petros, I had this paper in my PC for a while, red through it several times. I am pretty familiar with most of these rations. Indeed, they allow you to compare the performance of your boat to that of other known boats.

But it is implied that you must have an idea about how these other boats perform.

What I'm trying to work out is a way to estimate boat performance without comparison to other boats, but by using various parameters of the boat to link them to the wind speed and angle.

Thanks, I'll look up that book, maybe it can be found somewhere on the net.

Again, thank you for these comments, but as I've said, let's not dwell on my design choice for this specific boat. It is beside the point. I'm not trying to make a racer boat in this topic, I am trying to work out a way to calculate boat speed in various wind conditions.

For example, David Gerr gives a formula to calculate how much engine horsepower is required to accelerate a boat to a specific speed. Sure, it relies on the same famous design ratios, but that is at least something - it says "if you want to hit X knots, you have to have an engine with Y horsepower".

I'm trying to do the same with sailing vessel scenario. Hull resistance is pretty well documented, and it can be calculated by those design ratios or by taking data from easily obtainable software like Delftship.

Sail power is also pretty easy to calculate.

What's missing is the link between the two.

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### PARYacht Designer/Builder

50 sq. ft of area is equal to 1 HP in force 3 winds. Getting a precise polar plot isn't especially practical with formulas and a rudimentary VPP packages. There are so many variables, some of which simply are too random to calculate, that getting more then pretty close, is the best you can expect. Unlike a number of other engineering disciplines, yacht design has some black magic involved, mostly based in experience and familiarity with the particular "problem(s)" you're attempting to work through.

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### laukejasSenior Member

Is that driving force, or a total force? Because I have formulas to determine total force dependent on sail area and wind speed - the problem is to transfer it into driving force.

You mean to say that the most speed-influencing variables are also too random to get a result of any reasonable accuracy?

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### gggGuest...

I'm not sure how much you will achieve with a calculation. Pragmatically speaking a boat that isn't a high performance racing type will not greatly exceed the Froude number speed in any conditions, so you can regard that as a practical top end, no matter what wind conditions. On a run the faster conventional types, like a Laser, seem to go downwind at roughly gust speed, which is about 2/3 windspeed, slower boats probably around half windspeed, so if you reckon 50% of wind speed up to the point at which wavemaking severely limits increased speed then you'll be in the right sort of area. Crosswind a bit faster, maybe 60% to put a finger in the air. Upwind speed is the most difficult to predict because far more than the others its about efficiency.

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### StripOC1Junior Member

Practical Experience and Feel

I'm by no means an engineer. I can build a small boat and I have years of practical experience and believe I am a good judge of hull/sail shape from just experience of a variety of designs.

Without a spinnaker, Hull shape/type is the most important factor in speed or performance! Broad reach is the angle to the wind that you can achieve the fastest speed and pointing into the wind short of luffing the slowest. I've done cartwheels at incredible speed in a Hobie cat when the bow submerged tripping us up! Usually the best design upwind is a bit slower downwind when comparing similar weight/length/girth. Wider hull shapes go downwind faster, narrow go upwind faster; longer has more ability to plane, shorter more responsive to wind change and pointing into the wind; weight is a more complicated feature and really depends on where the critical points are located and the sailing conditions you are expecting. A hulls keel/centerboard and its placement fore/aft its shape hydrodynamics, but also the additional subtle to strong effects to pointing/running. In smaller craft it just where you place your own weight, but also the rocker for/aft in the hull shape.
Next would be Sail shape/size. Sails that point well into the wind are not usually the best design for flying downwind. Stiffer sails with plenty of capabilities to read the wind (Cassette tape strategically through the sail at key positions was my fathers secret weapon, followed closely by the boom-vang "for tightening the luff") these two items were the factors that put my family at the top of competition in the 8' el toro for many many years. Sailing downwind the spinnaker and skills of the crew/person can propel a craft above its designed planing speed, because it creates lift and reduces the amount of hull in the water/resistance, but also increases instability and relies so much on the pilots weather senses/reaction-time/skills/experience.

Bill

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### SkyakSenior Member

VPP are common and reasonably accurate for keel boats where the variation from one design to the next is very small (lots of empirical support) and the value of the boat is relatively large. Dingy designs vary wildly and if you don't include crew variation you are missing half the terms. I have been thinking about dingy VPP for some time and the factors I can't estimate are
-crew windage (varies with position)
-hull windage
-drag on the hull due to leeway (your software prediction is for zero leeway)
-drag due to waves
-loss of sail lift due to waves (hobbyhorse motion)
-sail drag due to trim error and deflection

So with this stack of significant unknowns I gave up hope of a good general purpose dingy VPP.

I am a nerd and a sailor so I am always looking to characterize performance with equations so I can do the optimization. I can't stand just saying "not worth it" so I will make the most constructive suggestion I can. Simplify the equation to three terms

Drag=Thrust-unknowns

and only do a few true wind angles 45, 90, and 180 (filling in the curve is pretty easy). There is no such thing as good drag. There is no such thing as bad thrust. The unknowns can be bounded enough that the calculation will produce reasonable cost/performance guidance. The only problem is if the unknown is sensitive to a parameter you are tweeking in your drag or thrust optimization but as you see in my list above the big unknowns are orthogonal.

Relating geometry to performance is the only benefit of calculation, and when the boat is done you can fill in the unknown factor for each point of sail and have a model for similar boats in the future.

Messabout, I have been barking up that tree for years! He is always looking for speed but it is always subordinate to having a wide stable hull. Memories of capsizing canoes in Siberia when he was young put a block in his thinking. If the exercise I suggest above has any value it will be to show him that speed is proportional to the square root of length and sail area just lowers the wind speed you need to get there.

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### StripOC1Junior Member

Oh fastest/most unstable sailing

Oh Almost forgot, the fastest I've been was in an 18' Hobie catamaran going downwind with a spinnaker where a large gust came for a short period and caused us to literally skip across the tops of the waves going faster than the waves is already a rare occurrence, but skipping over them was freakish! When I was younger I was always excited by the roughest strongest weather! I guess you could call me a sailing speed freak, I've always wanted to try the hydrofoil sailboats and see how much they can take! Years later and several sinking vessels I have a bit more respect for the weather and probably wouldn't take the risks I did when I was younger!

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### laukejasSenior Member

Now you're talking! Indeed, these variables you mentioned seem to be of utmost importance, and truly hard to predict. But I think it can be approximated somewhat.
Crew windage varies with crew position in relation to the wind. In most dinghies crew sits sideways. So, knowing the apparent wind angle it should be pretty much clear. The amount of drag - that's a tough one. It depends on clothing mostly, I believe. I'm not sure about this one. But it could be approximated.
Hull windage - well, isn't it calculated pretty much the same as with larger yachts? What's the difference?
Drag due to waves... That's beyond my understanding. Do dinghies behave that much different than yachts in regard to waves?
Hobbyhorse - same as with yachts, but probably with shorter period? I don't know if that is included in commercial yacht VPP's.
Trim error may be discounted, maybe... It depends on sailor ability anyway. We can assume perfect scenario here. What did you mean by deflection, though? Sail twist?

You make it sound like I had some kind of childhood trauma Well, people said that since my boat is that light, it might be less stable because of less inertia. So I tried to compensate for that by increasing the beam.
Anyway, what would you say is an appropriate length/beam ratio for a dinghy of such size? Mine is 3m long and 1.3m wide, so that's 0.43 (2.3)

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Skyak, I had my head messed up a long time ago when I was sailing International 10 meter canoes. Long, skinny, and very quick. The length to beam ratio of those boats is more than 5.

I never quite got over the long skinny notion. I am the oldest guy on the whole forum and I still sail happily and confidently in my 15.5 foot flattie skiff with a L/B of 4.6. Planes like crazy, and I have never dumped it even in a 25 knot, gusty, breeze. It goes pretty well in light air too. I confess that I usually know when to reef or to hit the beach.

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### tdemSenior Member

An interesting paper on the topic is "Predicting the speed of sailing yachts" by Van Oossaanen (available online). But not exactly simple. Dinghies are in some ways easier than keelboats because you can assume sailing upright.

You need lift-drag curves of the sail and foils, and a drag curve for the hull. Then it's "just" a balancing act. The simpler you make it the more assumptions you need. For example, it's pretty safe to assume a leeway angle similar to a similar boat.

Like you say you need to solve iteratively, there is no way to avoid this. If you really want to be within 10% just pick a similar boat and say it's within 10% of its performance, if you can find the figures.

The next step up would be to work out the actual lift and drag and resistance of your boat at that speed based on you formulas. Compare the drive produced by the rig to the resistance. Do they match? Does the sideforce of the sail match that of the foils? If not guess the speed to be slightly higher or lower, and re-calculate. Again and again and again. There are a lot of vector diagrams involved!

Think about what will limit the speed. Upwind it will likely be the righting moment available. Downwind it might be hull drag.

A VPP does this blindly and should find an equilibrium eventually. If you do it manually, you might get pretty close within a few iterations, because you can make smarter guesses.

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