You've answered your own question really. The scale is actually a linear measurement, i.e. a model of 1 foot long represents a real life vessel of 72 feet for a scale of 1/72nd. As the speed is also a linear measurement, i.e. a certain distance traveled in a certain time, then that behaves in the same ratio. Consequently whatever distance a real vessel would cover in a minute would be divided by 72 for a 1/72nd scale model. So if the real vessel traveled 720 feet in a minute then the model should travel 10 feet in the same time. This would give you the correct scale speed.

Taking your narrow boat in say 1/12th scale travelling at 4 knots. In a minute the real boat would travel 405 feet so your model should travel:

405/12 = 33 feet. So to operate your model at scale speed it should travel 33 feet in a minute or 16.5 feet in 30 seconds or just over six inches in ten seconds. Yes, it seems slow, but so is 4 knots!

Also considering your 1/72nd scale warship with a real life speed of 36 knots, in one minute it would have travelled 3645 feet.  Your model should therefore travel:

3645/72 = 50 feet in a minute or 25 feet in 30 seconds.

Many modellers do not really grasp the concept of scale speed and all too frequently go for what they 'think' looks right. If they actually did some measurements and a quick calculation they would find their tug boat in real life would be doing 45 knots. It is always worth having a little bit of extra speed in reserve for emergencies but the trick is to only use it in emergencies.

You'll find this handy for playing with the numbers:

Knots to feet/minute converter

Edited By Richard Simpson on 15/07/2022 22:56:14

That's just the explanation Ashley, I don't expect many to pay much attention to it.

A couple of other factors for you to consider.

1. Wind doesn't scale. That 10mph breeze that caused the 1in ripples is much more to a small scale model.

2. Colour changes with distance & atmospheric effects. If you colours are "right" when on you building board they will be wrong when the model is on the water and your 1/144 model is 36ft away which is a scale mile out to sea.

3. The way a full size ship moves cannot be modelled. Models often appear "bobbly" in the water but a full size ships moves with a much lower frequency.

This subject has frequently cropped up over the decades! In the February 1983 issue, Ron Warring wrote a two page general article on scaling which I republished in the 60th Anniversary Special Issue. I have managed to extract and reformat the section on scale speed from the pdf file and it is reproduced below.

Colin

Scale Speed

Ron Warring Model Boats February 1983

Scale speed is another interesting subject, but most boat modellers probably know this one. True scale speed equals the square root of S x full size speed, where S is the scale. In other words, for a 1 ⁄12th scale model scale speed is the square root of 1⁄12 = 0.2886 x full size speed. (This is where a pocket calculator with a square root function comes in handy). Let's apply this first to our original powerboat example and take a full size speed of 90mph. Scale speed for a 1⁄12th scale model would be 0.2886 x90 = 26mph. Back to our 1⁄100th scale model frigate, full size speed 30 knots. Scale speed in this case = 1⁄10 x 30 = 3 knots, or around walking pace.
Of course, this calculation can be worked the other way round. Speeds of 80mph are claimed for model hydros say, nominally, 1⁄8th the size of a full size hydro. The square root of the scale is 1⁄8 = 0.3535. To scale up we divide scale speed by this figure. So equivalent full size speed = 80⁄0.3535 = 226mph.

Naval architects use a slightly different formula – Froude’s law for dynamic similarity. This states that the speed ratio between model and full size is equal to the ratio of the square roots of the respective waterline lengths. This gives exactly the same results as above. It is no accident that all these ‘equivalent’ speed figures are realistic – unlike the strength comparison calculators that were not. At equivalent speeds – i.e. scale speed on a scale model and full size speed on the full size craft – both the wave patterns and spray patterns generated are the same, with one slight difference. Because of the relatively greater effect on surface tension on the smaller size hull, spray droplets will be relatively larger but the general nature and direction of the spray is not materially affected. If you are puzzled by the greater effect of surface tension, think of this. You can float a steel needle on water because of surface tension. But the same surface tension would not support a ‘scaled-up’ needle in the form of an iron bar.

Edited By Colin Bishop on 16/07/2022 10:18:20

Strictly speaking, we should be using "waterline length" in the maths (ask a naval architect), but, for a barge /narrow boat this closely equates to length overall I should think.

The answer, I feel, lies in the throttle stick (not the soil !) – waggle it about a bit and see what happens…

At the end of the day, it's your model and so it's whatever pleases you.

Happy modelling,

Dave

Applying maths is fine but after calculating the scale speed most folks aren't going to measure what their model is actually achieving. I'm firmly in the camp of if it looks right it is right.

It's usually fairly obvious when a model is going well over its scale speed. As has been said though, it's good to have a bit in hand to take evasive action but only use it when needed.

Chris

Hi Richard,

The square root explanation goes back yonks and has been mentioned in the magazines since the Sixties to my knowledge and is in turn based on Froude's much earlier work. I recall visiting the Nartional Physical Laboratory Test Tank Facility in Teddington back in the 70s which was used to evaluate models of full size designs, many of them made in wax. The larger the model, the easier it was to assess the likely performance of the full size vessel as you would expect.

There was an interesting artticle on the test facility in Shipping Wonders of the World back in the 1930s. I have the original article but it is now also online here:

**LINK**

Ron Warring's article encapsulates much of this and , as you will have gathered, the 'official' view of scale speed is that it is not simply a matter of linear measurement but needs to take into account other factors such as spray and wake characteristics and to allow for the viscosity of water, all of which impact on the 'seakeeping' appearance of the model. In our case it is essentially about the appearance of the model on the pond but the NPL test tank was all about assessing the characteristics of the full size hull design in varying sea conditions. As I'm sure you are aware, similar test tank facilities still exist but I imagine much of the evaluation work is now computer based.

The site you refer to is for land based models where the additional factors referred to above don't apply.

Colin

Edited By Colin Bishop on 17/07/2022 20:29:54

I did a little reading reading on the subject last night and boy does it get complicated. It would even seem that different hull forms scale differently etc.. etc.

Interesting that another seemingly simple question from Stephen can unearth such a huge can of worms. We can obviously all choose for ourselves how to determine the scale speed of our models, whether taking the simply "It looks right" approach right through to unbelievably complex naval architecture approaches. I don't think I will change my own method and accept that while it may not be the most accurate, it is still a reasonable approximation that puts you in the right ball park.

I wait with trepidation to see what Stephen comes up with for his next question.

Moving from Test Tank to computers is an interesting one. I believe most of the measuring kit at Teddington used to be analogue (reading from the tests performed by Barnes Wallis in the '40's). They've probably gone "digital" now like most other things.

For computer software, there is Computational Fluid Dynamics (CFD). The models (mathematical) can be set up for both air (wind) and water (liquids /fluids). However, if you can understand partial differential equations (PDE's) you need no further help from me ! You'll need a very powerful machine though and be prepared for the 'solvers' to run for days…it seems to be able to cope with laminar (smooth) flow quite well, but, if there's any turbulence or vortex involved then results can be not very reliable.

Let's keep it simple folks and just try moving the throttle stick and see what happens – that's the one that matters surely.

Regards to all,

Dave

Right!

I do think the formula has value in suggesting a model speed that will look 'right' in tems of how the boat handles and the wave patterns it generates. After all it has a pretty solid scientific provenance and is a readily understandable way of distilling all those calculations and experiments by naval architects.

Of course, no one is compelled to follow it. If you are familiar with how full size vessels look when underway then it's not too difficult to make a MK1 eyeball judgement as to what is right. But a lot of modellers don't actually have that experience and it is all too common to see scale models ramapaging around a pond at distinctly unscale speeds. I think there is a You Tube video of a Flower class corvette virtually planing somewhere. Presumably its owner thought it looked just fine.

Colin