Why exactly are small yachts slower than large ones?

[jakeroyd]

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.




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

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.

Thank you both Hydrozoan and Weustace.
I'm getting closer now to an understanding.

The two exerts from the posts above are describing in my mind the same fluid dynamics or at least similar practical effects.

I understand the Froude number describes scaleable hull shapes making the same wake.
I undestand , I hope that Hydrozoans explanation concerns itself with the fact that waves made by a hull shape passing through the water want to flatten out or accelerate downwards due to gravity once the hull has created them and this also is a function of the wave period.
These wave forms are all created by the hull which therefore are related to the power (and i'm talking here about power in it's correct sense 'the rate of doing work' ) required to make them.

For the same Froude numbered hull shape there will be on a shorter lwl a shorter crest to crest pitch, maybe a higher crest height and perhaps a faster wave period than a longer lwl.
Hence more energy will be required for the shorter lwl to get up to hull speed.

If I then (thread drift here maybe) think about power and forget energy from sails for a moment and consider a displacement hull under power. For a hull at various sizes to reach hull speed a certain amount of power will be required.
If you plot lwl vs engine size I wonder what relationship you get?
Intuitively it must take less power per unit of lwl to reach hull speed as you consider longer hulls?

having written this I think I have just realised in the intuition above I am am only really looking at the same relationship from a different direction.

So I still haven't quite got this at the basic level but hopefully i'm getting there.

 

[Hydrozoan]

... 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 was trying to offer jake some explanation only of the part of his post which I quoted, and at least give him an inkling of whence the oft-quoted hull speed formula (and especially the dependence on the square root of L) arises – which was one (but only one) of the things he was after. I suggest that he accept the equation c = Square Root (gL/2Pi), and the first (Wiki) link I provided gives some more background and detail.

(It is half a lifetime since I was ‘entertained’ by the hydrodynamics of sea surface waves, and approached – I never was much of a mathematician! – something like the level of my second link. I didn’t think that is what jake wants but if his – or somebody else’s – maths is up to it, it provides the material upon which to apply it.)

 

[jakeroyd]

You are about right.
My maths , though not too bad, is not up to the stuff given here.

My train of thought was triggered by a youtube video posted on YBW which showed exciting footage of the Volvo , from a helicopter.
The first bit showed Mapfre charging along with 3 headsails and i thought "how does it stand up to that much canvas"
Of course the main reason is the canted keel moved to windward.

This then started me thinking of my boat, which of course is much smaller and tender. which is not only a function of lwl but also of the beam stiffness or righting couple the hull sections provide.

Sort of if the beam on my boat was increased to give sufficient stiffness to carry that area , it's Froud number would be something terrible and it still could not approach anywhere near that speed.

 

[weustace]

I suspect it is ultimately an issue related to hull design and mass. The heavier you make it, the more difficult it is to drive. If you look at all the above 'racing boats', they are pretty Spartan--the Moth exceptionally so . No doors, no woodwork, no unnecessary weight. They usually use carbon rigs. They get away with a smaller ballast ratio by having lots of form stability (which I suspect plays quite well with a planing hull anyway) and a very, very deep keel—e.g. the Pogo 40S3 (Class 40) draws 3m and has a 4.5m beam. It displaces 4.5 tonnes!! Compare this to the rather comfortable First 40.7, which displaces 7 tonnes despite being somewhat smaller, and you start to see why the Pogo goes faster. Add in the upwind sail areas—115m^2 for the 40S3 vs 75m^2 for the First 40.7, and you can really see where this comes from. It has 50% more power, almost 40% less mass, and is almost certainly a more aggressive design of hull. As you see, it is by no means a question of power and beam alone: the mass is critical. As somebody told me once, "gentlemen win on corrected time"... as one very new to the art of non-dinghy racing myself, I couldn't possibly comment.

 

[Seajet]

Simple Answer - ' Wetted Area Drag '

this applies to aeroplanes as well as boats ( 'wetted ' means subject to water or air mass volume friction ) - the reason my fabled Anderson 22 managed to average 7 knots across the Channel, well above the ' 1.4 x square root ' of her 19'3" waterline length - but low wetted area keel - and the boat doesn't even have a big rig to push it.

 

[lpdsn]

Now I understand. The Anderson 22 drags the wetted area with her rather like the warp drive on the Starship Enterprise drags the space time continuum with her to allow her to go so fast without exceeding c.

Which brand of di-Lithium crystals do you use?

 

[weustace]

It should be noted that, although as Seajet remarks the wetted area is a key component, this is to some extent independent of the hull geometry; it is important to distinguish the two key kinds of drag at play here, wave-making drag and viscous drag—the latter being the most strongly related to wetted area by my understanding. With the following answer, bear in mind that this is not very well researched, being based largely on my existing and tenuous understanding of fluid mechanics, and I will happily take corrections...

As the water moves past the surface, there is a 'boundary layer' at the surface which is stationary due to friction with the hull. The velocity of the flow increases as you move away from the surface, and after a certain distance you are substantially out of the disturbed region. This is important: if you can manage to persuade the flow around your object to be laminar, the disturbed region is smaller—this means the viscous drag tends to be less. If on the other hand the flow ends up turbulent, you get more 'viscous drag'.

Then there is the matter of wave-making drag: you drag a wake behind the boat. You can get an idea of this by looking at a sphere/cylinder: https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html
In the second figure, "Flow past a cylinder", you can see the difference between the two regimes available to a fast boat: 4 and 5. In case 5, where the flow is turbulent (so there is more viscous drag), the area behind the sphere (the 'wake') is much cleaner than in case 4, where the laminar flow separates quite messily from the surface. Why is this relevant? Well, if you ever wonder why traditional yachts tend to have gentle, curving transoms and high-speed boats (whether it's the Class 40 discussed earlier or a RIB) have plumb sterns, I believe this offers a glimpse at the answer: it's better at high speed to have neater flow separation than to have laminar flow all the way round. You can then aim to have laminar flow as far as the stern, then a nice sharp transition at the back. I believe this is also why powerboats tend to show more drag at the transition between displacement speed and planing speed than a good way into either region: they drag a bigger wake behind them, because they have not yet got to a high enough speed for the boundary layer to separate cleanly at the stern. Slow down, and the boat is below hull speed, so wave-making drag decreases nicely, and the viscous drag also falls; speed up, and, if nothing else changed, the viscous drag would increase and the wave-making drag fall as the flow separates (or at least not increase—see the graph at the top of the NASA page for the sudden drop in drag around Re = 10^5). In practice, the boat lifts itself hydrodynamically further out of the water, decreasing the wetted surface area and limiting the viscous drag increase to push the top speed higher.

 

[lpdsn]

It should be noted that, although as Seajet remarks the wetted area is a key component, this is to some extent independent of the hull geometry; it is important to distinguish the two key kinds of drag at play here, wave-making drag and viscous drag—the latter being the most strongly related to wetted area by my understanding. With the following answer, bear in mind that this is not very well researched, being based largely on my existing and tenuous understanding of fluid mechanics, and I will happily take corrections...

What is normally known as frictional resistance is significant at low speeds (low being well below hull speed) and makes a big difference in light airs racing (hence the effort racers put into fairing the hull and foils, the trim of the boat, and the very gentle movements about the boat that are de-riguer on a competitive boat). However frictional resistance becomes a pretty insignificant component of total resistance as a boat approaches hull speed (or in the case of an Anderson 22 whizzes straight past hull speed without noticing what all the fuss is about).

 

[weustace]

What is normally known as frictional resistance is significant at low speeds (low being well below hull speed) and makes a big difference in light airs racing (hence the effort racers put into fairing the hull and foils, the trim of the boat, and the very gentle movements about the boat that are de-riguer on a competitive boat). However frictional resistance becomes a pretty insignificant component of total resistance as a boat approaches hull speed (or in the case of an Anderson 22 whizzes straight past hull speed without noticing what all the fuss is about).

It does make one wonder whether, for typical wind strength racing at least, whether in fact it is those in the classic design categories who should be polishing their hulls to a micron-level finish while those in high speed racing yachts sit about varnishing their interiors...but of course these don't have any woodwork inside anyway so they have to fill in the time somehow!

 

[jakeroyd]

Now I understand. The Anderson 22 drags the wetted area with her rather like the warp drive on the Starship Enterprise drags the space time continuum with her to allow her to go so fast without exceeding c.

Which brand of di-Lithium crystals do you use?

Yes, I do realise that Anderson 22's operate in a different way to other small boats

 

[jakeroyd]

It should be noted that, although as Seajet remarks the wetted area is a key component, this is to some extent independent of the hull geometry; it is important to distinguish the two key kinds of drag at play here, wave-making drag and viscous drag—the latter being the most strongly related to wetted area by my understanding. With the following answer, bear in mind that this is not very well researched, being based largely on my existing and tenuous understanding of fluid mechanics, and I will happily take corrections...

As the water moves past the surface, there is a 'boundary layer' at the surface which is stationary due to friction with the hull. The velocity of the flow increases as you move away from the surface, and after a certain distance you are substantially out of the disturbed region. This is important: if you can manage to persuade the flow around your object to be laminar, the disturbed region is smaller—this means the viscous drag tends to be less. If on the other hand the flow ends up turbulent, you get more 'viscous drag'.

Then there is the matter of wave-making drag: you drag a wake behind the boat. You can get an idea of this by looking at a sphere/cylinder: https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html
In the second figure, "Flow past a cylinder", you can see the difference between the two regimes available to a fast boat: 4 and 5. In case 5, where the flow is turbulent (so there is more viscous drag), the area behind the sphere (the 'wake') is much cleaner than in case 4, where the laminar flow separates quite messily from the surface. Why is this relevant? Well, if you ever wonder why traditional yachts tend to have gentle, curving transoms and high-speed boats (whether it's the Class 40 discussed earlier or a RIB) have plumb sterns, I believe this offers a glimpse at the answer: it's better at high speed to have neater flow separation than to have laminar flow all the way round. You can then aim to have laminar flow as far as the stern, then a nice sharp transition at the back. I believe this is also why powerboats tend to show more drag at the transition between displacement speed and planing speed than a good way into either region: they drag a bigger wake behind them, because they have not yet got to a high enough speed for the boundary layer to separate cleanly at the stern. Slow down, and the boat is below hull speed, so wave-making drag decreases nicely, and the viscous drag also falls; speed up, and, if nothing else changed, the viscous drag would increase and the wave-making drag fall as the flow separates (or at least not increase—see the graph at the top of the NASA page for the sudden drop in drag around Re = 10^5). In practice, the boat lifts itself hydrodynamically further out of the water, decreasing the wetted surface area and limiting the viscous drag increase to push the top speed higher.

Thank you for this comment which I understand the gist of.

However, If I have understood correctly this does explain quite succinctly the differences between a traditional hull and a modern hull it may only hint at why two modern hulls of similar shape , or in other words scaled (I know this is not really correct because as size increases with yacht design all of the other major parameters , beam , ballast , sail area , draft etc. do not scale proportionally) create a situation where the larger boat is always faster with a higher hull speed.

This is really what facinates me.

 

[lpdsn]

Thank you for this comment which I understand the gist of.

Seriously, get one of the books on popular naval architecture rather than reading posts by someone trying to work it out as they go along. The prices on Amazon are ridiculous at the moment but you should be able to get one of them from your local library.

https://www.amazon.co.uk/Sail-Perfo...TF8&qid=1511959672&sr=8-3&keywords=CA+Marchaj

https://www.amazon.co.uk/Aerohydrod...TF8&qid=1511959672&sr=8-4&keywords=CA+Marchaj

https://www.amazon.co.uk/Aero-hydro...1511959796&sr=1-1&keywords=aero+hydrodynamics

 

[wotayottie]

Thank you for this comment which I understand the gist of.

However, If I have understood correctly this does explain quite succinctly the differences between a traditional hull and a modern hull it may only hint at why two modern hulls of similar shape , or in other words scaled (I know this is not really correct because as size increases with yacht design all of the other major parameters , beam , ballast , sail area , draft etc. do not scale proportionally) create a situation where the larger boat is always faster with a higher hull speed.

This is really what facinates me.

The fascinating link provided by Scala provides the answer. There are several resistances to a sailboat going through the water but the big two are wave making which is proportional to sqrt of LWL and frictional which is proportional to wetted area and mass. But there is the other side of the equation - the power developed by the rig and for similar hull shapes, the power capability goes up with size. Note the word capability - being able to put 65sqm of sail on a 35 footer doesnt mean the designer will always do so.

So the larger boat isnt always faster. At one time I used to race a Moody 336 bilge and I always lost out to a First 31.7. The First had 10% less sail area but an almost identical LWL - the key factor was that it weighed 35% less. Thanks to my two big bilge keels and 30% more weight , the first had far less wetted area and frictional drag. . If you like, and yes this is a big generalisation, it had 10% less power but 35% less frictional resistance to overcome. It didnt help that we pointed in a different direction. So bigger boats arent always faster.

However if you bring a J109 into the equation, chosen because there were a couple in the same fleet, its bigger sizeallows 50% more sail area for just 31.7% more weight, and it has a 6% longer LWL. So it has maybe 50% more power, maybe 30% more frictional drag but a bit less wave making drag. Its faster by some margin than the First. And unlike the Moody which was all cruiser, both the 31.7 and J109 are cruiser racers of a similar generation and approach and in that sense scaled.

So to sumarise ( until a naval architect comes along and says I'm writing spheroids :nonchalance: ) bigger boats arent always faster. It all depends on the balance or power which can go up with size, frictional drag which also increases with size / weight and wave making which decreases with LWL

 

[Tranona]

So to sumarise ( until a naval architect comes along and says I'm writing spheroids :nonchalance: ) bigger boats arent always faster. It all depends on the balance or power which can go up with size, frictional drag which also increases with size / weight and wave making which decreases with LWL

You could also add wind resistance into the mix so bulk above the waterline is another variable that affects speed potential.

You have started to mix speed potential with the ability to actual achieve that speed. as you identified the First and the Moody have the same theoretical "maximum" speed based on their LWL, but the First will have less resistance at lower speed because of the lower wetted area. Being able to achieve the speed is a function of the amount of power and the key ratio there is SA/Disp. Your examples clearly illustrate that light boats with low wetted surface area that can carry large sail areas are likely to be faster throughout the speed range even if still constrained to the same maximum. Of course there are other variables, particularly prevailing wind and sea conditions that can limit the ability to use this additional potential, but that is part of the skill of designing boats for a specific purpose.

 

[Lucky Duck]

Simple Answer - ' Wetted Area Drag '

this applies to aeroplanes as well as boats ( 'wetted ' means subject to water or air mass volume friction ) - the reason my fabled Anderson 22 managed to average 7 knots across the Channel, well above the ' 1.4 x square root ' of her 19'3" waterline length - but low wetted area keel - and the boat doesn't even have a big rig to push it.

Now I understand. The Anderson 22 drags the wetted area with her rather like the warp drive on the Starship Enterprise drags the space time continuum with her to allow her to go so fast without exceeding c.

Which brand of di-Lithium crystals do you use?

With each channel crossing I do I find that claim less and less credible

 

[Tranona]

With each channel crossing I do I find that claim less and less credible

You have to understand he inhabits a completely different world from the rest of us who can only dream of a 9 hour crossing Poole to Cherbourg when 11 hours is a cause for celebration.

 

[oldmanofthehills]

Thank you for this comment which I understand the gist of.

However, If I have understood correctly this does explain quite succinctly the differences between a traditional hull and a modern hull it may only hint at why two modern hulls of similar shape , or in other words scaled (I know this is not really correct because as size increases with yacht design all of the other major parameters , beam , ballast , sail area , draft etc. do not scale proportionally) create a situation where the larger boat is always faster with a higher hull speed.

This is really what facinates me.

What we may have failed to make clear is that the worst wave drag occurs when the wavelength from the wake is the same as the hull length. As the wavelength increases with boat speed a longer boat can go a bit faster before the wave reaches the stern and critical speed for worst drag is reached. Doesn't depend on hull shape, and a square root function not linear. Cats minimise the problem by having less hull in the water to be affected by drag though there should still be an effect at the exactly critical speed, and hydrofoils rise above it, and obviously with enough power you can break through the speed barrier in a similar way to planes breaking the sound barrier

 

[Lucky Duck]

You have to understand he inhabits a completely different world from the rest of us who can only dream of a 9 hour crossing Poole to Cherbourg when 11 hours is a cause for celebration.

I've sailed from Needles Fairway to Cherbourg in a little bit less than nine hours just once and that required an almost brand new boat and a force 4 just forward of the beam for the entire trip

 

[Tranona]

I've sailed from Needles Fairway to Cherbourg in a little bit less than nine hours just once and that required an almost brand new boat and a force 4 just forward of the beam for the entire trip

Those are the days to cherish. Mine was 11 hours from Cherbourg to Poole singlehanded in my old Eventide with a 5/6 from SE on a late August Bank Holiday Monday. Hung on to the tiller the whole way!