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Comment by lutusp | Hacker News Reader

Scale models of nautical craft have always been limited by some unrealistic assumptions -- assumptions that are recognized but not well-adjusted for.

One important aspect of a scale-model ship/boat is that as you change the size of a model but keep the relative dimensions constant, its surface area changes as the square of its length, but its mass and volume change as the cube. If you halve the size of a model, its surface area is 1/4 the original, but its volume and mass will be 1/8 the original. Simply put, this means a scale model won't behave very much like the full-size craft.

As models become more sophisticated, these unavoidable limitations of scale modeling begin to argue for computer modeling, where you can model the full-size vessel using a carefully designed numerical simulation, including many factors that can't be realistically modeled in a laboratory tank experiment.

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Does the volume matter? Can the weight be offset?

You can scale the geometry and accommodate dynamic and kinematic similarity by matching Froude, Reynolds, Drag and Pressure coefficients - or what non-dimensional parameters you have based on the identified variables (http://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem)

I would expect that the surface tension would have negligible impact on the physics of the boat in open ocean, maybe unless you are interested on the behaviour of the spray across the decks.

> Does the volume matter? Can the weight be offset?

There are remedies for some of these scaling issues, but they're accommodations, not cures. It's not at all uncommon for a craft based on a scale model to behave substantially differently when it's finally built.

> Simply put, this means a scale model won't behave very much like the full-size craft.

This is a basic fact that is known for decades in the field of science and engineering. This isn't pose any problem in modelling.

Sometimes, it's far better to study scale models instead of CFD models because in spite of the scale differences, it's possible to reproduce fluid dynamics results in reducd models while computational models fail to even account for them.

See: http://en.wikipedia.org/wiki/Dimensional_analysis

And for some cases you actually model at over scale >1:1 as this give better results its screamingly expensive so only tends to get done for flows inside nuclear rectors and so on.

This explains a lot.

I've always wondered about how insects can survive large falls (e.g. from desks or ceilings) mostly unharmed, yet for humans a fall from a similar height, relatively to the body size, would be certain death.

Yes -- there's a folk tale about how a bumblebee is an aerodynamic impossibility. What that actually means is if a bumblebee is scaled up to the size of a bird, say, it can't stay aloft because its wing area is only increasing as the square, but its volume and mass as the cube, of the size change.

The same applies to scaling up helicopters. It is much easier to scale up a plane than to scale up a chopper. A nice example of this is the little 3/4/6/hex copters that you see RC models of.

Scaling those up is very hard if not impossible.

https://en.wikipedia.org/wiki/Bumblebee#Misconceptions

couldn't you build a heavier model to compensate? I mean most boats are hollow right?

I guess that changes some of the internal distribution of weight but if its done in a uniform fashion things should work out ok right?

> but if its done in a uniform fashion things should work out ok right?

I wouldn't be so certain of this. If the "uniform distribution" of the added weight results in the walls being (proportionately) thicker or denser than in the original, the model may be an invalid one.

I don't think buoyancy would be much of an issue with scaling, because that's just related to density and shape, neither of which change when scaling the model (at least until you get small enough that surface tension becomes noticeable, which I presume doesn't happen for ship modeling). I suspect the bigger issue would be the structural integrity of the boat. A 10 foot steel ship is going to be a heck of a lot stronger than the same ship scaled up to 100 feet.

> I don't think buoyancy would be much of an issue with scaling, because that's just related to density and shape, neither of which change when scaling the model ...

But that's false. The hull wetted area of the model changes as the square, while the volume and mass change as the cube, of the size change. If corrective measures aren't taken, the model will displace more water proportional to its wetted area as it becomes larger, as a result of which it will gradually sit lower in the water as its size increases.

There are a number of ways to deal with these issues, but it's not true that one can scale a model without considering them in detail, and carefully ballasting the model to force it into an approximation of full-size reality.

Interesting. That doesn't match my initial intuition, but it sounds like you're right. Can you point to a source, or perhaps explain this a little more? I'm trying to imagine a pathological shape that would obviously float at one size but not when scaled up.

> I'm trying to imagine a pathological shape that would obviously float at one size but not when scaled up.

I wouldn't go that far. I know models sit at different heights for different scales, all else being equal, but I don't think you will ever see a non-pathological object sink at one scale but remain afloat at another. The reason I think this is true is that, if I take two objects having the same overall density and connect them together, this cannot change their position in the water, their buoyancy. If I think of the two objects as a single model, the same should be true.

But the difference between connecting two models, and a proportional scaled-up model, is that the ratio of surface area to volume is different for the scaled-up model compared to the two independent models. So the comparison isn't perfect.

(pause for thought ...)

For a solid object sitting on a table, making the object larger and noting the previously described square-versus-cube rule, the table loading should increase for each square unit of table area as the model's size increases, by a unit rule, meaning if you double one of the three dimensions, the table loading (per unit of area) doubles also. But because a boat model sinks into the water as its mass increases, and because that sinking is across curved surfaces, it's more like a three-dimensional area increase than a two-dimensional one, so it can't be compared to an object with a flat bottom sitting on a table.

The tl;dr: the more I think about this, the more I think I was wrong to say it the way I did -- and I say this because the shape of the boat hull means the wetted area can increase as fast as the boat's mass, i.e. as the cube of a dimensional change.

Expressed another way, even though a larger boat model sits lower in the water, with some care the waterline position on the hull can be made to stay the same.

My mistake -- sorry.

If the water line can be made to change when scaling the boat up, it should be trivial to make a pathological object that will sink when scaled. Just make the shape of a box without a lid, weighted so that the water line is just at the top of the walls. If scaling the shape raises the waterline, then water will flow into the box and it will sink. I still can't intuitively convince myself that the waterline would shift when the model scales.

I should have made clear what I meant by "sits lower in the water", and I'm responsible for the confusion.

Because the boat is a three-dimensional object, and because the subsurface part contacts the water in three dimensions, if it is scaled up with all else the same, it should still have the same waterline, but (obviously) its keel is deeper in the water.

> I still can't intuitively convince myself that the waterline would shift when the model scales.

Your instincts are serving you well, and the answer is simple -- I wasn't sufficiently careful in how I described it, and I let an error creep into yesterday's conversation. In fact, a model whose dimensions are held constant but is scaled up, should show the same waterline at all scales.

Again, I apologize for sounding so sure of myself when I wasn't.

Okay, so you were talking about the keel of the larger model being deeper underwater in absolute terms. I suppose that would effect buoyancy, because pressure increases as depth increases. This might be significant enough to warrant adjustments, at least when scaling very large ships down to very small models.

You're discussing surface area and surface tension so fair to bring up that a water strider bug walks on water much better than I do.

I already mentioned that obviously surface tension becomes noticeable at very small scales, but that model boats are presumably nowhere near that small.

> couldn't you build a heavier model to compensate? I mean most boats are hollow right?

Yes, it's possible. In fact, dimensional adjustments and compensations are standard practice in scale modeling.

So are you saying everyone doing these tests is knowingly wasting their time?

Not at all. Scale modeling is better than nothing, but its limitations must be kept in mind.

But you said tests with scale models give wrong results: “a scale model won't behave very much like the full-size craft”.

That's true, but it doesn't contradict what I said above. And I wouldn't call them "wrong" results. Obviously all modeling efforts are approximations, efforts to produce an estimate of the final craft's behavior. No one expects perfect modeling, except of course by the finished craft.

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