Eli5: How do they effectively test scale models of giant ships in water? Doesn’t the water behave differently in the small vs large scale?
In: Physics
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They see how it holds up to a toddler in a bath tub. If the toddler can’t sink it or break it, then they scale up.
Yes, there are limits, you can’t test many features in a one-foot model, because the viscosity of water has a length dimension.
The solution is to test in very large tanks, like the [Carderock Test Tank](https://en.wikipedia.org/wiki/David_Taylor_Model_Basin ). The closer your scale is to reality, the smaller these side effects.
There’s something called the Froude number, which is a number that represents the relationship between how heavy a bit of water is, its weight, and how that same bit of water will resist any sort of movement, its inertia. The Froude number needs to remain the same for any scale, and that number helps people find the right scaling factors for different components of the model, such as how fast the model should go, how big the waves should be, how large the scale should be, etc. Time would also need to be slowed down by the same factor, and that would be done by slowing down video recordings of the test. Check out the Veritasium video that talks about your exact question.
If you want to know more I suggest the book Scale by Geoffrey West.
In the old days, they just had to test it in real size. There was no other way.
There is alot of calculations that go into it. Unfortunately I forgot alot from my Naval Architecture class but you use the Reynolds number and Froudes number.
Using Froudes number you can build a relationship between the scale models speed and the designed speed of the vessel. This often means that the scale speed is not a linear relationship because the goal of the model is to have turbulent flow to have measurable effects from the wake.
This is the equation used with V equal to velocity and g equal to force of gravity (9.81m/s) and L is length. Froudes number should be constant for a vessels hull shape so you just need to make them equal to each other.
Fn = (V/g√L)
This is the best of my memory but if i remembered properly you can use froudes when you have a higher reynolds number for the model meaning you have turbulent flow on the model because that helps simulate the waves for a full scale vessel
A supplementary question would be if using a liquid with a lower viscosity than water assist in adjusting for the issues of scaling?
Acetone for instance has a viscosity of .36 that of water. Leaving aside the practical limitations, would this be a more suitable liquid for modelling at a smaller scale?
Certain behaviors of the water can be scaled, others not. As has already been pointed out, the Froude and Reynolds numbers are crucial. These numbers describe the similarity laws for different types of forces.
By adjusting the speed accordingly, a model ship can run at the same Froude number as the full scale ship, resulting in wave generation to scale and hence, the wavemaking resistance of the ship can be determined in the experiment. The same Reynolds number, however, cannot realistically be attained, which means that viscosity of the water, and therefore the viscous resistance, is not to scale. The viscous resistance, however, which is mostly dependent of the wetted surface area of the ship and the viscosity, can be calculated for the model ship, subtracted from the measured total resistance, and replaced by the viscous resistance calculated for the full scale ship.
So there is this concept called ‘dimensionless numbers’, and they’re really effective tools to tackle the problem you’re asking about. Essentially, a dimensionless number has no physical dimension like time, distance, temperature, mass, etc. because they denote ratios of certain things. Let’s consider probably the most famous dimensionless number: the Reynolds number.
If you have a fluid flow it can be ordered, what we call laminar flow, or very chaotic, what we call turbulent flow. The Reynolds number tells us something about whether or not a flow will be laminar, turbulent or maybe somewhere inbetween. It can be calculated using a very simple formula:
Re = ρ • U • L / μ
In this equation ρ is the density of the fluid, U is the velocity of the fluid, μ is the viscosity of the fluid (how ‘thick’ the fluid is, syrup for instance has a high viscosity). L is more special, and is called the ‘characteristic length’. If you hold a sphere in a fluid flow L could for instance be the diameter of the sphere.
Say you have two spheres, a big sphere and a small sphere, but you want to have the same flow over the spheres. In that case what you can do is try to match the Reynold numbers of the two cases:
Re_big = Re_small
Because then the flows should be both laminar or turbulent. Say we have control over how fast the fluid flows, in that case we can work out a relation to make sure the Reynold numbers match:
ρ•U_big•L_big / μ = ρ•U_small•L_small / μ
U_small•L_small = U_big•L_big
U_small = U_big•L_big / L_small
So in order for the flow to also have e.g. a turbulent profile with the tiny sphere, the velocity of the flow in the tiny sphere case needs to be L_big/L_small as fast. Because the big sphere has a larger diameter than the small sphere, U_small will be higher than U_big.
There are other dimensionless numbers engineers can match to achieve different similarities between scale and full-sized models in the same way.
Dynamical similarity.
Essentially you have to scale other factors as well as the ship (e.g. the surface of the model needs to be smoother, speed changes between model and real life etc.).
There’s a method in fluid dynamics called dimensional analysis – which is the method of finding “non-dimensional” parameters (variables which have no units of mass, length, time etc.) which must be constant between the model and the real ship, and you can use this to find out numerically exactly how much you need to scale everything else by in order to get an accurate test.
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