1.34 times square root LWL and model yachts?

Amulet

Amulet

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We are all versed in the notion that conventional displacement hulls are limited to 1.34*root(LWL) knots because of the massive cost of climbing your bow wave. Plane and you can overcome it, or if you are really skinny like a catamaran hull, there is some escape route I don't completely understand.

I'm building a one metre model yacht just now (it's fun being retired). Looking at such models sailing they seem to go much faster than the displacement rule, which would put them at about 2.5 knots max. Am I just misjudging their speed because they are so small? The beam is about beam lwl ratio is about 5, so they are not thin enough to be like cats.
 
I was watching a swan swimming past today - not in any great hurry - and it occurred to me he was well past the speed the usual calc gives for hull speed, also it was making very little wash....
 
Scala said:
Reynolds number & Froude number are the two factors here. One scales as a factor of length; the other as the reciprocal of length. So no model can behave as its full scale counterpart, or vice versa.
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Mmm. I was certainly not implying that a model was a replica of a full scale yacht. These are just small yachts designed for their size. I haven't quite grasped the Reynolds and Froude calculations. All I was really asking was whether the 1.34 rule of thumb, which seems to work over a large size range, breaks down when boats get really small. They are, after all, just normal displacement hulls. (If a draft of 0.5 LWL is normal!)
 
Scala said:
Reynolds number & Froude number are the two factors here. One scales as a factor of length; the other as the reciprocal of length. So no model can behave as its full scale counterpart, or vice versa.
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towtank_03.jpg
 
The water density and hydrodynamics, water/hull interfaces, and water/air boundary are constants but the model hull is tiny in comparison with the full size. the bits of the model in the water (Froude), and the waterline of the model at the boundary (Reynolds) cannot behave linearly. The rule of thumb is just that, it breaks down as the sizes change (up or down).

Don't think LWL/D ratio is relevant.
 
Amulet said:
Mmm. I was certainly not implying that a model was a replica of a full scale yacht. These are just small yachts designed for their size. I haven't quite grasped the Reynolds and Froude calculations. All I was really asking was whether the 1.34 rule of thumb, which seems to work over a large size range, breaks down when boats get really small.
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Yes. Basically, the water is relatively more viscous for small craft (think how unrealistic models always look in films) so the waves created are not, relatively, as big and so do not cause the same drag.
 
As JD's photo (or any movie using model ships) tells you. Looks like a scale model. Is a scale model. But great value nonetheless.

"...Basically, the water is relatively more viscous for small craft (think how unrealistic models always look in films) so the waves created are not, relatively, as big and so do not cause the same drag."

EDIT crossed in the posts. Yes.
 
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Scala said:
The water density and hydrodynamics, water/hull interfaces, and water/air boundary are constants but the model hull is tiny in comparison with the full size. the bits of the model in the water (Froude), and the waterline of the model at the boundary (Reynolds) cannot behave linearly. The rule of thumb is just that, it breaks down as the sizes change (up or down).

Don't think LWL/D ratio is relevant.
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Not convinced. The physics of the relationship between bow and stern wave is pretty robust, and of course the rule of thumb is not linear - it doesn't pretend to be. I didn't mean to imply that LWL/D was relevant, but rather that the extreme small size means that the ratios of some parameters that vary non-linearly with size get pretty damned strange in models. Given the vast range over which the rule of thumb is reasonable, I was wondering how far it holds. Actually it'd be best to get real data. I just think they look like they're going too fast.
 
Amulet said:
We are all versed in the notion that conventional displacement hulls are limited to 1.34*root(LWL) knots because of the massive cost of climbing your bow wave. Plane and you can overcome it, or if you are really skinny like a catamaran hull, there is some escape route I don't completely understand.

I'm building a one metre model yacht just now (it's fun being retired). Looking at such models sailing they seem to go much faster than the displacement rule, which would put them at about 2.5 knots max. Am I just misjudging their speed because they are so small? The beam is about beam lwl ratio is about 5, so they are not thin enough to be like cats.
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Mostly what you are seeing is the effect of square root vs linear relationship.
Consider "hull speed" if the relationship was linear: something like speed = some factor * LWL. if your 1m model does 2.5 knots then a 10 m boat would do 25!
So, given that the relationship is proportional to the square root, small boats seem to go faster, very small boats (sorry) seem to go much faster.

And thats all before Mr Reynolds and co.
 
Dougal Tolan said:
Mostly what you are seeing is the effect of square root vs linear relationship.
Consider "hull speed" if the relationship was linear: something like speed = some factor * LWL. if your 1m model does 2.5 knots then a 10 m boat would do 25!
So, given that the relationship is proportional to the square root, small boats seem to go faster, very small boats (sorry) seem to go much faster.

And thats all before Mr Reynolds and co.
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Yes, I can work that out easily enough. If the max speed of a 1 metre is about 2.5 knots then the relationship is preserved. They look like they are going faster, but I made the mistake of asking the question on the basis of impression rather than data.

I've emailed the great Graham Bantock. If he is kind enough to answer we'll have expert input.
 
Graham Bantock assures me that the 1.34 sqrt LWL rule is every bit as valid for model yachts as big boats. They must just look as if they are quicker than that.
 
JumbleDuck said:
I hear a sarcastic tone of voice there.
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No sarcasm intended. It's a very good approximation for displacement hulls, and the physics behind it is completely robust. All it appeals to is the relationship between wave length and wave speed in water. Some minor tweaks can cause a bit of deviation from the rule, but if a hull is not planing and not exceedingly long and thin it holds pretty well.
 
Amulet said:
No sarcasm intended. It's a very good approximation for displacement hulls, and the physics behind it is completely robust. All it appeals to is the relationship between wave length and wave speed in water. Some minor tweaks can cause a bit of deviation from the rule, but if a hull is not planing and not exceedingly long and thin it holds pretty well.
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I don't think I'd be quite as optimistic. It's a pretty good rule of thumb for most traditional hull shapes, but that's about all. Like much of fluid dynamics, it's based as much on empirical observation as on any robust theory. Which is what I suspect your model yacht designer was saying ...
 
Model boats often have a lot of power:weight.
Hull speed is not a brick wall, it is a guide to where disproportionate increases in power are needed for small increases in speed.
It also doesn't really apply to some hull shapes, e.g. canoes and catamarans.

Also the 1.34 factor has changed over the years, ISTR 'Mary Rose' era warships used close to 1:1, wide stern dinghies will do 1.4:1, yachts are somewhere between.
 
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