1.34 times square root LWL and model yachts?

[grumpy_o_g]

The 1.34 rule is a bit of a misnomer as there's actually no such rule really. The "1.34" is only true for a very specific hull shape and size. It gets further confused by the fact that a given vessels hull shape changes dependent on the boat speed, the angle heel, the sea state, etc. Even leeway can throw things out as you're now trying to drive the hull sideways. The 'k' factor ghostlymoron refers to is actually a result of at least two dimensionless numbers (Reynolds and Froude as mentioned) though I have been assured by people more knowledgeable, cleverer and, at the time, drunker than me that there's other factors too.

 

[Amulet]

There is a huge amount of confusion flying about here. Firstly, the waves are governed by laws of physics which state that the speed of a series of waves in knots equals 1.34 times the square root of their wavelength. This is not a rule of thumb. It is not based on sampling observations - it is based on science. It does not just apply to one shape of boat. This means that to exceed a speed of 1.34 times its waterline length a boat has to leave its stern wave behind and sail up its own bow wave. This causes an inflection in the energy to speed function. All of this is solid physics. For conventional displacement style sailing yachts this inflection is severe enough that you are pretty damned unlikely to carry enough sail to break the rule. (There are all sorts of other complicated things affecting velocity, but cause of the inflection is to do with wave generation.)

It is possible to apply enough energy to push through the inflection, and you may have seen displacement yachts towed so fast that their front end sticks up in the air. Hull shape can seriously change the severity of the inflection, and very narrow hulls can make it pretty much disappear I believe. I have read a "rule of thumb" that says that a beam to lwl ratio of 1:11 or 1:12 is the turning point.

This all started when I asked whether there was something special about model yachts, because to me they look as if they are going too fast for their size.

I realised from the responses that it had been a mistake to ask the question based on my vague impression and not many of the responses seemed connected to the physics of the issue. For interest I had an email exchange with Graham Bantock (referred to as "your model yacht designer" in some of the above). Graham is arguably the most successful model yacht designer to have existed, a naval architecture graduate and a consultant to America Cup Yacht designers, so I thought he might know something useful. I was flattered that he took the time to answer. His basic answer was that the same rules apply to model yachts, and that they are mostly sailing within the limits of predicted hull speed. They just look as if they are going faster to my untutored eyes. So my question was answered to my satisfaction.

Various factors enable boats to break through (or appear to break though) the inflection in the function. Long overhangs can be supported by the stern wave, effectively increasing the waterline length. Narrow pointy bows can diminish the severity of the inflection and flat bottomed boats can plane.
Destroyers have enough power and a shape to surge right on through it. Tugs have so much power that nothing so trivial as an uphill bow wave is going to stop them. And of course most of us have surfed down a wave at way over hull speed.

I had read all this in the past, and really was just asking if there was something special about teenie weenie models. The answer is "NO".

 

[lw395]

One thing that is special about model boats is that they often sail in shallow water.
When the water is shallower than a wavelength, the wave equation is different.
The speed of the wave is constant and the whole wave system can be different.

 

[lw395]

Have a look at these:
https://www.youtube.com/watch?v=UIBMw4oL73I
There basically is not anywhere near the amount of wave generation as you'd get in a full sized boat traveling at a similar speed in terms of lengths per second.
They are very narrow with the ballast low down.

 

[johnalison]

Amulet is right, in they certainly look as if they are sailing faster than their scale size. I had always assumed that this was due to their very light weight, since this varies with the cube of the length, and the sail area with the square.

 

[Amulet]

Have a look at these:
https://www.youtube.com/watch?v=UIBMw4oL73I
There basically is not anywhere near the amount of wave generation as you'd get in a full sized boat traveling at a similar speed in terms of lengths per second.
They are very narrow with the ballast low down.

I made the mistake of reacting to a mere impression and was wrong. I was reasonably happy with Graham Bantock's assessment actually. All I was asking was if the 1.34 rule was subverted for wee boats. It's not.

I've built one of Graham's designs and am building another. It could be that they can generate enough energy to power through the inflection. They aren't really utra thin. They can put their ballast 0.5 LWL below the water on a very thin fin. Which could create a very powerful rig.

 

[Lon nan Gruagach]

One thing that is special about model boats is that they often sail in shallow water.
When the water is shallower than a wavelength, the wave equation is different.
The speed of the wave is constant and the whole wave system can be different.

That had just started niggling away in my mind too.

I also am still seeing a bucket load of 1.34 on this thread but precious little square root of LWL.
If I remember right, there was mention of a 1m boat doing 2.5 Kts... if that were a 1/10th model then it would look like the full sized one doing 25Kts. Now, 'scuse me here if I'm being a bit pessimistic, but I really dont think 25Kts is a sensible "hull speed" for a 30 foot tub.

edit: changed no mention to precious little mention...

 

[grumpy_o_g]

There is a huge amount of confusion flying about here. Firstly, the waves are governed by laws of physics which state that the speed of a series of waves in knots equals 1.34 times the square root of their wavelength. This is not a rule of thumb. It is not based on sampling observations - it is based on science. It does not just apply to one shape of boat. This means that to exceed a speed of 1.34 times its waterline length a boat has to leave its stern wave behind and sail up its own bow wave. This causes an inflection in the energy to speed function. All of this is solid physics. For conventional displacement style sailing yachts this inflection is severe enough that you are pretty damned unlikely to carry enough sail to break the rule. (There are all sorts of other complicated things affecting velocity, but cause of the inflection is to do with wave generation.)

It is possible to apply enough energy to push through the inflection, and you may have seen displacement yachts towed so fast that their front end sticks up in the air. Hull shape can seriously change the severity of the inflection, and very narrow hulls can make it pretty much disappear I believe. I have read a "rule of thumb" that says that a beam to lwl ratio of 1:11 or 1:12 is the turning point.

This all started when I asked whether there was something special about model yachts, because to me they look as if they are going too fast for their size.

I realised from the responses that it had been a mistake to ask the question based on my vague impression and not many of the responses seemed connected to the physics of the issue. For interest I had an email exchange with Graham Bantock (referred to as "your model yacht designer" in some of the above). Graham is arguably the most successful model yacht designer to have existed, a naval architecture graduate and a consultant to America Cup Yacht designers, so I thought he might know something useful. I was flattered that he took the time to answer. His basic answer was that the same rules apply to model yachts, and that they are mostly sailing within the limits of predicted hull speed. They just look as if they are going faster to my untutored eyes. So my question was answered to my satisfaction.

Various factors enable boats to break through (or appear to break though) the inflection in the function. Long overhangs can be supported by the stern wave, effectively increasing the waterline length. Narrow pointy bows can diminish the severity of the inflection and flat bottomed boats can plane.
Destroyers have enough power and a shape to surge right on through it. Tugs have so much power that nothing so trivial as an uphill bow wave is going to stop them. And of course most of us have surfed down a wave at way over hull speed.

I had read all this in the past, and really was just asking if there was something special about teenie weenie models. The answer is "NO".

There's no confusion at this end. I think you are confusing hull speed with the speed at which a boat can travel through water for a given amount of thrust. The two are very different.

 

[lukedh]

That had just started niggling away in my mind too.

I also am still seeing a bucket load of 1.34 on this thread but precious little square root of LWL.
If I remember right, there was mention of a 1m boat doing 2.5 Kts... if that were a 1/10th model then it would look like the full sized one doing 25Kts. Now, 'scuse me here if I'm being a bit pessimistic, but I really dont think 25Kts is a sensible "hull speed" for a 30 foot tub.

edit: changed no mention to precious little mention...

Seems about right to me.

1.34 x Sq Root of waterline length in feet.

! Meter boat approximately 3.28 ft, Sq Root is about 1.81 times 1.34 gives 2.43 knots.

10 Metre boat say 30 ft 25ft on the waterline Sq Root 5 times 1.34 gives 6.7 knots.

30 ft on the waterline would be a little quicker.

100ft on the waterline Root equals 10, times 1.34 gives 13.4 knots !!! Seems to be diminishing returns.

 

[Amulet]

There's no confusion at this end. I think you are confusing hull speed with the speed at which a boat can travel through water for a given amount of thrust. The two are very different.

No I'm not. I'm simply saying that there is an inflection in the energy speed function at the point at which the stern wave is left behind. That inflection is entirely due to wave making effects. I am not saying that this an explanation of the entirety of the energy speed function, but it is the entire cause of that inflection and it affects all vessels travelling in displacement mode. I am also making no comment on the scale of the inflection. I do understand the physics and have read the maths that makes this so. It is very simple.

 

[Amulet]

That had just started niggling away in my mind too.

I also am still seeing a bucket load of 1.34 on this thread but precious little square root of LWL.
If I remember right, there was mention of a 1m boat doing 2.5 Kts... if that were a 1/10th model then it would look like the full sized one doing 25Kts. Now, 'scuse me here if I'm being a bit pessimistic, but I really dont think 25Kts is a sensible "hull speed" for a 30 foot tub.

edit: changed no mention to precious little mention...

Sorry, I was using 1.34 rule to mean 1.34 times square root. I assumed no-one would think the relationship linear. You are correct of course.

 

[Amulet]

Seems about right to me.

1.34 x Sq Root of waterline length in feet.

! Meter boat approximately 3.28 ft, Sq Root is about 1.81 times 1.34 gives 2.43 knots.

10 Metre boat say 30 ft 25ft on the waterline Sq Root 5 times 1.34 gives 6.7 knots.

30 ft on the waterline would be a little quicker.

100ft on the waterline Root equals 10, times 1.34 gives 13.4 knots !!! Seems to be diminishing returns.

That's exactly right, and diminishing returns are what the square root gives you. Those of us with fairly conventional displacement boats are stuck with this maximum speed. Any boat can go faster if you input enough energy, and some do, but it is unlikely that you can put enough sail on a conventional yacht to break through this barrier.

 

[Flica]

That's exactly right, and diminishing returns are what the square root gives you. Those of us with fairly conventional displacement boats are stuck with this maximum speed. Any boat can go faster if you input enough energy, and some do, but it is unlikely that you can put enough sail on a conventional yacht to break through this barrier.

Unless you can surf!!!
But then you're using wave momentum as the additional force input.
You can, however keep it up for a very long time - once for 16 hours.

 

[lw395]

That's exactly right, and diminishing returns are what the square root gives you. Those of us with fairly conventional displacement boats are stuck with this maximum speed. Any boat can go faster if you input enough energy, and some do, but it is unlikely that you can put enough sail on a conventional yacht to break through this barrier.

Depends on what you call a 'conventional yacht'.
It seems to me that the factor of 1.34 is pretentiously precise, depending on hull shape and displacement, values of anywhere from 1.3 to over 1.4 are fair for post-war yachts. 1.3 might be a bit optimistic for a heavy canoe stern design, but at least they tend to get a reasonable lwl for their loa.

 

[Amulet]

Depends on what you call a 'conventional yacht'.
It seems to me that the factor of 1.34 is pretentiously precise, depending on hull shape and displacement, values of anywhere from 1.3 to over 1.4 are fair for post-war yachts. 1.3 might be a bit optimistic for a heavy canoe stern design, but at least they tend to get a reasonable lwl for their loa.

The 1.34 figure is to do with the speed of waves in seawater. It is correct. The speed at which waves travel in knots is 1.34 times the square root of their length. This has nothing to do with boats. When the wave length equals your length you hit the barrier. All of the theory relates to lwl (not loa) of course, or square root lwl to be precise. Overhangs do matter. A long overhang can be supported by the stern wave, effectively increasing the waterline length. Of course it is the actual waterline length not the design waterline length that matters. There are various things like this which cause minor tweaks to when a boat hits the limit and how hard it is to break through it, but none of them change the fundamental relationship between wavelength and speed.

Conventionally shaped yachts will find it very hard indeed to break this limit and almost never do. Surfing is indeed an exception but is relatively unusual and rarely sustained (unless you're flica above). When you surf you are going downhill on the wave not climbing your bow wave - which is fun.

This matter is discussed in all the naval architecture books I have read, as indeed are the exceptions, of which there are many. Displacement sailing yachts are very unlikely exceptions.

 

[lw395]

The 1.34 figure is to do with the speed of waves in seawater. It is correct. The speed at which waves travel in knots is 1.34 times the square root of their length. This has nothing to do with boats. When the wave length equals your length you hit the barrier. All of the theory relates to lwl (not loa) of course, or square root lwl to be precise........

Sorry, that's basically a case of the 1.34 being far more precise than the assumptions.
The shape of the stern has a big influence on the factor, how the stern interacts with the wave matters.
Also the measured drag/speed curve for many hulls does not have a hugely steep slope around the 1.3 to 1.4 region, so where you draw a line and declare 'hull speed' moves around that area depending on what drag, i.e. power you care to assume. For a given hull form, the drag will increase with displacement.
I suggest referring to some good books on the matter, I can recommend Larrson and Elliason, also Bethwaite.
That is engineering based on measurement and observation.
To look at the mathematics/physics, there are several flaws with your assertion. It is a first order linear approximation, reasonably valid within limits.
Firstly, the bow and the stern of the yacht don't interact with the waves as simple points exactly at the ends of the lwl.
Secondly the simply liner equation for a gravity wave is only valid within limits, too steep a wave and you need to add in more factors. Waves of bigger amplitude travel faster, so push harder and you find the brick wall is somewhat elastic.

Thirdly, Out There in the real wet world, lots of us have had 'more than hull speed' out of non planing boats, not surfing, just pushing hard. But it's diminishing returns, in a non-planing boat, you have to add increasing amounts of power for every 0.1 knot as push the hull speed area. That is obvious in everything from rowing boats to pre-war keelboats when you try it.

It's far more reasonable to say hull speed is an imprecise figure in the 1.3 to 1.4 region generally.
On a boat like yours, the waterline length is going to hard to define to 1% accuracy when it's sailing anyway. The length that matters is not lwl is it?

 

[Tranona]

It's far more reasonable to say hull speed is an imprecise figure in the 1.3 to 1.4 region generally.
On a boat like yours, the waterline length is going to hard to define to 1% accuracy when it's sailing anyway. The length that matters is not lwl is it?

Agree with this. While the 1.34 is the theoretical point as Amulet says, the additional factors some related to the hull shape and others to the wave shape mean the speed at which the boat meets the resistance is not fixed, but approximately at the theoretical point. Your suggestion that it is in the range of 1.3-1.4 would give a margin of +/- approx 0.3 knots on a 32' LWL which is roughly what we see in practice (at least what I see on my boat of that size).

How much you can exceed that upper limit depends entirely on the power you can apply. I can just exceed the 1.34 speed under motor. Under sail however it is not difficult to generate enough power, particularly on sporty boats with SA/Disp ratios of well over 20 and possible even on more staid boats like mine, particularly with large off wind sails. It can get quite exciting bordering on brown trousers time running at those limits, but I understand it gets calmer if you can break through and plane - at least it was in my Osprey all those year ago.

 

[grumpy_o_g]

No I'm not. I'm simply saying that there is an inflection in the energy speed function at the point at which the stern wave is left behind. That inflection is entirely due to wave making effects. I am not saying that this an explanation of the entirety of the energy speed function, but it is the entire cause of that inflection and it affects all vessels travelling in displacement mode. I am also making no comment on the scale of the inflection. I do understand the physics and have read the maths that makes this so. It is very simple.

OK, my apologies then - I'll rephrase that to say that maybe some people are confused about how specific hull speed and equating it to me mean that their boat will go x knots max regardless of power applied.

 

[Amulet]

Sorry, that's basically a case of the 1.34 being far more precise than the assumptions.
The shape of the stern has a big influence on the factor, how the stern interacts with the wave matters.
Also the measured drag/speed curve for many hulls does not have a hugely steep slope around the 1.3 to 1.4 region, so where you draw a line and declare 'hull speed' moves around that area depending on what drag, i.e. power you care to assume. For a given hull form, the drag will increase with displacement.
I suggest referring to some good books on the matter, I can recommend Larrson and Elliason, also Bethwaite.
That is engineering based on measurement and observation.
To look at the mathematics/physics, there are several flaws with your assertion. It is a first order linear approximation, reasonably valid within limits.
Firstly, the bow and the stern of the yacht don't interact with the waves as simple points exactly at the ends of the lwl.
Secondly the simply liner equation for a gravity wave is only valid within limits, too steep a wave and you need to add in more factors. Waves of bigger amplitude travel faster, so push harder and you find the brick wall is somewhat elastic.

Thirdly, Out There in the real wet world, lots of us have had 'more than hull speed' out of non planing boats, not surfing, just pushing hard. But it's diminishing returns, in a non-planing boat, you have to add increasing amounts of power for every 0.1 knot as push the hull speed area. That is obvious in everything from rowing boats to pre-war keelboats when you try it.

It's far more reasonable to say hull speed is an imprecise figure in the 1.3 to 1.4 region generally.
On a boat like yours, the waterline length is going to hard to define to 1% accuracy when it's sailing anyway. The length that matters is not lwl is it?

OK, Peace... there is a theoretical limit and the 1.34 number is a figure which is correct for idealised conditions. We all know that conditions are not idealised. All I was saying is that for traditional shaped boats you hit a fairly hard limit at this point. The naval architects I know tell me this. There are all sorts of ways of making boats break this limit, but in a conventional displacement boat you will not routinely deviate far from it.

My original question was as to whether models can break it. Although they don't experience any special rules, I actually still think that they might be able to. With impressive ballast ratios and deep, high aspect ratio foils, and a draught of sometimes more than half LWL they may be able to carry proportionately more powerful rigs. They often sail under when overpowered.

I agree with your choice of reading.

 

[lw395]

....
My original question was as to whether models can break it. Although they don't experience any special rules, I actually still think that they might be able to. With impressive ballast ratios and deep, high aspect ratio foils, and a draught of sometimes more than half LWL they may be able to carry proportionately more powerful rigs. They often sail under when overpowered.

I agree with your choice of reading.

Looking at videos of models, I'm wondering if they really are sailing where the simple analysis does not apply.
But it is hard to tell.
For a start many of them are very slender so work like half a catamaran, not making big enough waves to care.
A bit like a single scull that will do 10knots with 1 man-power, its length would say 7 knots.

It's deceptive, I think we tend to look at them and judge their speed as fast in proportion to their size, not the sqrt of it.
Then there's the telephoto lens effect.
But even so they still look quick to me.
They race on a pond near me, but it's at a time when I'm normally racing my boat.