Why exactly are small yachts slower than large ones?

[jakeroyd]

I'm talking about displacement hulls here , not planing designs.
I am totally familiar with the formulae here (mainly the empirical ones) and it is a given that boats with longer lwl's are faster than those with shorter lwl's.

I am also familiar with the scaling factor , ie. to a certain extent why model boats heel in the slightest winds compared with their up scaled cousins. To a degree this is to do with both form stability and where their ballast is located.
What I may fail to comprehend is the basic that is operative as any design is scaled , ie what happens to beam , displacement and wave theory etc.
A small boat can have the same sail area to displacement ratio as a large one.

So I hope I understand the principles as in real life and in boat design.

What i would like to understand is how does this work at the basic hydrodynamic level?
Would somebody please explain with formulae if necessary but in a way i can understand the basics.

It seems something like a Volvo boat (mono's anyway) can play be different rules, even when not planing.

TIA

 

[lpdsn]

Depending upon how seriously you are interested, there are a number of authors who have written books for the popular market. CA Marchaj for one. As well as a couple by him, I have one by Fabio Fosatti translated from Italian.

It is quite complex with many factors coming into play but at a basic level the predominant resistance above slow speeds is the wave making resistance which is a factor of (approximately - i.e other hull & foil design factor can't be ignored) the waterline length. Basically the hull generates waves (the energy to do this comes from the boat) and those waves have a certain speed which is dependent upon their wavelength. It takes an awful lot more energy to drive a boat at a faster speed than the waves it generates. This is known as hull speed. A simplistic way to think about it is that once you're at that speed you are climbing a wave that you've created. Planning hulls break out of this by rising above that wave.

Very simplistic, but I hope it gives you a general idea.

 

[jakeroyd]

Depending upon how seriously you are interested, there are a number of authors who have written books for the popular market. CA Marchaj for one. As well as a couple by him, I have one by Fabio Fosatti translated from Italian.

It is quite complex with many factors coming into play but at a basic level the predominant resistance above slow speeds is the wave making resistance which is a factor of (approximately - i.e other hull & foil design factor can't be ignored) the waterline length. Basically the hull generates waves (the energy to do this comes from the boat) and those waves have a certain speed which is dependent upon their wavelength. It takes an awful lot more energy to drive a boat at a faster speed than the waves it generates. This is known as hull speed. A simplistic way to think about it is that once you're at that speed you are climbing a wave that you've created. Planning hulls break out of this by rising above that wave.

Very simplistic, but I hope it gives you a general idea.

Yes. I understand to some extent the fact that a boat has to displace the mass of water equal to the boats mass as it moves.
Obviously a larger boat must displace a greater mass but also has more power available from a greater sail area so I assume the lwl is effectively correlated to weight.
Again a cat uses a different set of physics.

However it can't be a linear relationship.
(Stops rambling)

 

[lpdsn]

I think you've misunderstood what I'm trying to say. It is not the weight of water displaced, it is the wavelength of the waves generated by that displacement of water that is the main factor.

LWL is waterline length. At hull speed it determines the wave length of the waves generated by the hull. The longer the wavelength the faster the waves travel so in the same way the higher the hull speed is. It's certainly not linear but I can't remember the exact forumla of wavelength to wave speed off the top of my head. Generally hull speed has a relationship based on 1/SQRT(LWL) but it is only the main factor and not the only factor.

There's not a fixed relationship between weight of a boat and length. I remember a pontoon neighbour a few years ago had a boat only 1' longer than mine but with a design displacement about 190% of mine. Different boats different design approaches.

Cats don't use a different set of physics (in fact they illustrate that lwl is not the only factor). Planning boats do.

 

[NormanB]

Its all about friction.

 

[alant]

I think you've misunderstood what I'm trying to say. It is not the weight of water displaced, it is the wavelength of the waves generated by that displacement of water that is the main factor.

LWL is waterline length. At hull speed it determines the wave length of the waves generated by the hull. The longer the wavelength the faster the waves travel so in the same way the higher the hull speed is. It's certainly not linear but I can't remember the exact forumla of wavelength to wave speed off the top of my head. Generally hull speed has a relationship based on 1/SQRT(LWL) but it is only the main factor and not the only factor.

There's not a fixed relationship between weight of a boat and length. I remember a pontoon neighbour a few years ago had a boat only 1' longer than mine but with a design displacement about 190% of mine. Different boats different design approaches.

Cats don't use a different set of physics (in fact they illustrate that lwl is not the only factor). Planning boats do.

Just a diversion, a submariner once told me that they arrived at the speed of a target, by measuring the bow wave seen through the periscope. This was before bulbous noses were being used (not sure how this affects hull speed).

 

[Sticky Fingers]

...I am totally familiar with the formulae here (mainly the empirical ones)

Or not, obviously. Or you wouldn't be asking the question, or for that matter making sweepingly general remarks that bear no relationship to the hydrodynamics that underlie this issue.

Start here (one example, but it is a good summary of some of the key principles). You'll find some of the content you're interested in, starting at Acrobat page 157, or document page number 143, onwards.
http://www.homepages.ed.ac.uk/shs/C...to Naval Architecture 4th Ed. by E Tupper.pdf

 

[lpdsn]

Just a diversion, a submariner once told me that they arrived at the speed of a target, by measuring the bow wave seen through the periscope. This was before bulbous noses were being used (not sure how this affects hull speed).

Sounds plausible, although they had bulbous bows before they had submarines even though they didn't understand exactly how they worked. The idea of bulbous bows is that the trough of the first wave (from the bulb) partially cancels the peak of the second wave (from the bow) so overall less energy goes into the generated bow wave.

 

[solent clown]

large boats are faster because of the S/V - G tto LWLratio, although this may seem awfully technical, it is very easy to understand in an empirical manner with simple observation.
This is best done from a small sailing dinghy moving as fast as you can make it go. Look behind and you will see a yacht with a superior S/V-G to LWL ratio bearing down on you with the crew waving glinting hands in the sunshine, seemingly holding a magical talisman of speed.
The hand glints as a direct result of the superior ratio and directly affects the performance of the boat.
Expressed in it's simplest terms it is as follows
Space/volume of gin to the size of the boat. It is a simple fact larger boats carry more gin, this enables the crew to perform feats of seamanship such as would put Odysseus himself to shame. Fine tuning can be achieved by varying the tonic/ice ratio.

 

[lpdsn]

Space/volume of gin to the size of the boat. It is a simple fact larger boats carry more gin, this enables the crew to perform feats of seamanship such as would put Odysseus himself to shame. Fine tuning can be achieved by varying the tonic/ice ratio.

It's the same effect that causes the wind speed to increase retrospectively once safely ensconced in the club bar. Towards the end of the evening it is possible for a Westerly Centaur to be sailed faster than a Volvo 70.

 

[Triassic]

.
Space/volume of gin to the size of the boat. It is a simple fact larger boats carry more gin, this enables the crew to perform feats of seamanship such as would put Odysseus himself to shame. Fine tuning can be achieved by varying the tonic/ice ratio.

Adrenalin however trumps Gin every time, no matter the length of the boat. This is why you will see multihulls half the size of said Gin palace sail past as if they are standing still......

 

[jakeroyd]

large boats are faster because of the S/V - G tto LWLratio, although this may seem awfully technical, it is very easy to understand in an empirical manner with simple observation.
This is best done from a small sailing dinghy moving as fast as you can make it go. Look behind and you will see a yacht with a superior S/V-G to LWL ratio bearing down on you with the crew waving glinting hands in the sunshine, seemingly holding a magical talisman of speed.
The hand glints as a direct result of the superior ratio and directly affects the performance of the boat.
Expressed in it's simplest terms it is as follows
Space/volume of gin to the size of the boat. It is a simple fact larger boats carry more gin, this enables the crew to perform feats of seamanship such as would put Odysseus himself to shame. Fine tuning can be achieved by varying the tonic/ice ratio.

Yes, of course, now I get it ?

 

[solent clown]

excellent, sometimes it just takes a simple explanation to cut through all the nonsense and tell it like it is. ;-)

 

[nimbusgb]

The water has the same physical characteristics for any size boat.

Scale wise for a tiny boat the only way to go fast is to skim over the stuff ...... bigger boats the limits are further out.

 

[oldmanofthehills]

A crude approximation is that max speed = square route of (2 times water line length in feet). Thus my old cruiser at 25ft lwl can do 7kt absolute max and a Volvo 70 can do 11kt. Its just like the speed of sound being a limit. Essentially when the wave generated by the bows reaches the stern it slows the boat down, and wavelength depends on speed. Of course if a boat is slippery enough that effect is reduced so Volvos a bit faster than 11kt. Planning boats get their sterns out of the water so go faster

 

[RupertW]

A crude approximation is that max speed = square route of (2 times water line length in feet). Thus my old cruiser at 25ft lwl can do 7kt absolute max and a Volvo 70 can do 11kt. Its just like the speed of sound being a limit. Essentially when the wave generated by the bows reaches the stern it slows the boat down, and wavelength depends on speed. Of course if a boat is slippery enough that effect is reduced so Volvos a bit faster than 11kt. Planning boats get their sterns out of the water so go faster

I thought it was 1.4 x sqrt of LWL in feet?

 

[jakeroyd]

I thought it was 1.4 x sqrt of LWL in feet?

I'm familiar with this empirical formula and wonder about how it affects scale.
What i'm trying to get at is something that explains why this is.

I can see that any displacement hull moving through the water creates a wave at the bow where the boat is moving the water out of the way.
At hull speed there then tends to be a trough maybe halfway down the hull length and another wave somewhere near the stern.

The bigger the boat the greater the distance between these waves and perhaps the slower the period between crests ? Is this because the waves have a natural frequency related to water ?
This might explain why then bigger boats straddle these waves differently to small ones and hence experience less resistance to motion.

However this does not explain why a larger boat with very similar ratios is stiffer (heelwise) and faster than it's smaller stablemate when sailarea/dispacement etc. is similar.

I guess what i am wondering about is how is this explained in laymans terms.

With thanks to all posters but I have not understood this yet.

Maybe i'm a bit thick but in that simple relationship it's the fact that you take the root of the lwl that gives the formula it's basis for longer lwl's being faster. But why is this ?
What hydrodynamic law or water property is it hinting at?

TIA.

 

[Hydrozoan]

... I can see that any displacement hull moving through the water creates a wave at the bow where the boat is moving the water out of the way.

At hull speed there then tends to be a trough maybe halfway down the hull length and another wave somewhere near the stern.

The bigger the boat the greater the distance between these waves and perhaps the slower the period between crests ? Is this because the waves have a natural frequency related to water ? ...

Both the bow and stern wave travel at the phase velocity c = Square Root (gL/2Pi) where g is the gravitational constant, Pi is 3.14 and L is the wavelength of the waves. So the velocity is proportional to the square root of L (which equals LWL at hull speed), and longer waves – and longer boats, other things being equal – travel faster. The wave frequency is 1/T where T is the wave period, and the phase velocity c = L/T.

If you then go on to ask why the formula c = Square Root of (gL/2Pi) is as it is, you need some hydrodynamics and mathematics – take a look here https://en.wikipedia.org/wiki/Dispersion_(water_waves) (or for a full derivation see http://web.mit.edu/1.138j/www/material/chap-4.pdf).

 

[weustace]

I'm familiar with this empirical formula and wonder about how it affects scale.
What i'm trying to get at is something that explains why this is.
[...]
Maybe i'm a bit thick but in that simple relationship it's the fact that you take the root of the lwl that gives the formula it's basis for longer lwl's being faster. But why is this ?
What hydrodynamic law or water property is it hinting at?

This answer comes from somebody with only a basic undergrad-level knowledge of fluid mechanics... you have been warned.
One must bear in mind that water waves consist of water particles going round and round in a circle, rather than merely oscillating up and down or forward and back; this is the point I think which permits the understanding of Hydrozoan's more thorough answer below. I have yet to study the derivation provided there; it looks entertaining, if rather heavy on the vector calculus (at least for the first bit I've glanced at).

I suggest you consider instead an alternative viewpoint: there is such a thing as a "dimensionless group", which is effectively a series of properties of a situation or object that have been arranged such that they have no units; it's a plain ratio. This is rather useful in scaling laws, since it doesn't matter which part of the equation you scale. This is a very common approach in fluids, especially because of the difficulty in solving the involved equations often generated. The Froude number (https://en.wikipedia.org/wiki/Froude_number ) is effectively an indication of how much wake a particular hull shape generates—whether it is a full sized aircraft carrier or a model at risk of being capsized by a duck on the local pond, if a hull shape has the same Froude number, it generates a similar wake. The formula (1.34 * sqrt(LWL [ft])) [kn] represents an assumption that all sailing yachts operate at the same Froude number, after inserting some horrendous unit fudge factors—in other words, that all yachts are the same shape... (to a first order approximation).

How well does this work? Let us do some sums for two very different boats I sail on frequently: V [knots] = k [knots/sqrt(ft)] * sqrt(LWL [ft]) (with units in square brackets)

Achilles 24 triple keel: V = 6kn, LWL = 20ft. k = 1.342 knots/sqrt(ft)
First 40.7 'shallow' (1.8m?) bulb: V = 8kn, LWL = 35ft. k = 1.352 knots/sqrt(ft)
Well, this is looking promising, isn't it? The latter is a less traditional hull shape but still represented quite well. Both are rounded and broad figures, and k is given to a misleading resolution given this, but it comes out satisfyingly close to the oft-stated figure.

Class 40: ARC 24h run = 333nm or so, from a YBW article; V = 14kn, LWL = 40ft. k = 2.21 knots/sqrt(ft)
Volvo Open 70: V = 24kn, LWL: assuming 65ft. k = 3 knots/sqrt(ft)
International Moth: V = 28kn, LWL = ~3ft (on foils? Just a guess). k = 16 knots/sqrt(ft)

Oh dear. What happened? Well, all of these are hard-core racers: they are designed for lower wave-making resistance than a cruiser-racer like those above, and may in some cases (likely the Class 40 and the Moth, and maybe the Volvo 70) be operating towards the 'planing' domain; at this point, the skin drag comes into play in a big way, which would explain why one can wander round Cowes Yacht Haven in the lead up to races and see yachts being polished to a high gloss. In the case of the Moth, the foils are displacing very little water indeed, so almost all lift is hydrodynamic and a lot of the drag is due to the friction of the water against the foil.

For this reason it really annoys me when I am told authoritatively that boats go at 1.34 * sqrt(LWL); this is true of moderately traditional sailing yachts operating in a displacement mode, but once you start to push the envelope a bit (I would expect even less extreme dinghies, an RS Feva for example, significantly to exceed this prediction—movable ballast and a planing hull) it rapidly fails. Bear in mind then that this is an approximation, and don't bandy it about as the undisputed scientific truth!

 

[oldmanofthehills]

I thought it was 1.4 x sqrt of LWL in feet?

the square route of 2 is 1.414 so your formula also works. Its just easier to multiply by 2 and take square route of the lot. My boat is 25 foot LWl so sqrt of (25 x 2) = sqrt of 50 which is 7.1 kts and I can do in my head, whereas to multiply by 1.4 I would need a calculator ;=)