What Makes A Bow Wave? – by Mike Creasy

Good question…. maybe when the Queen drives past? Seriously, a bow wave is created by the hull forcing water out of the way, creating a dolphin’s playground at the pointy end, and a stern wave farther back. The sound and look of these waves, which form the ship’s wake, is strangely fascinating and always calming. Who hasn’t stood at the rail and contemplated the price of gasoline while gazing at the white foam sliding by?

The puzzling part for many scale modellers is the relationship between scale speed and a realistic looking bow wave. The answer is sort of simple.

A model’s bow wave will never look completely realistic because our models don’t go fast enough to generate the aeration needed to create the white foam that makes a bow wave “real”. The actual speed of most models is less than 5 knots, and most are displacing only 10 to 20 pounds of water. There’s just not enough water being pushed out of the way fast enough to cause air bubbles to form.

That being said, why do marine designers use scale models to test hull designs?

There’s much in common between a good model and a real ship or boat. Ignore for the moment the foamy white of a real bow wave and look instead at its shape. Much of the real (full-size) boat’s wave is solid, un-foamy water, just like we see on the yacht pond.

Now, if your model is a true representation of the real thing – in terms of underwater shape, length/width ratio and all that stuff, it will produce a wave that is very similar to the real thing. Not identical, and not foamy white, but similar in shape and location relative to stem and stern. The stern wave and the combined wake behind the boat will also be very similar to the real thing. Of course, this also assumes that your model is running at the correct scale speed, and for that we have to thank a fellow named William Froude, an English physicist who developed something called Froude’s Law of Comparison.

Froude’s Law gives us an easy way to compare the speed of a model with the speed of a full-size boat, using the square root of whichever scale you use. Details are available online at many sites including Wikipedia, and I’ve posted a spreadsheet file on the VIRCB group website. If you time your boat over a 100 foot straight line (such as we now have at Harrison Model Yacht Pond), you can read the scale speed of your model from this spreadsheet.

Alright, so now we have a well-built model running at the appropriate scale speed. The next question is, why do some models go so much faster than the real thing? Certain battleships come to mind. After all, if the laws of physics and hydrodynamics are transferable from ship to model, and real ships have a maximum hull speed, then why can models smash this speed in scale?

Most of us have heard that a boat’s speed is limited by the bow wave, and that as a boat goes faster, it will try to rise up over the bow wave. It turns out this isn’t really true.

A displacement hull’s speed is not limited at all – if you have the power, you can push it as fast as you want. You might run out of fuel very soon, or even start making your displacement hull get up and plane, but it’ll go if you push hard enough.

There is instead a practical speed for displacement hulls, and it all has to do with the rise in drag created by speed, and the power needed to overcome this drag. What many of us might not know is that most of this drag is created by the interaction of the bow and stern waves, and not by the boat trying to climb over the bow wave created.

Wave making resistance is the term used by naval architects and designers (and no, I’m not) to calculate the speed at which the wave created by the hull’s forward motion is equal to the waterline length. Once this wave begins to interfere with the stern wave, drag rises sharply.

For displacement hulls, the calculation of wave making resistance is the same – regardless of whether they are in a model yacht pond or out on the deep blue. This speed, essentially, is the speed at which thrust and drag are in reasonable balance. Often called the “hull speed”, it can be roughly calculated as a ratio of speed and length, using the formula:

speed in knots = 1.34 × square root of length in feet.

The fascinating part of all this for scale model builders is that “hull speed” or wave making resistance calculations are the same for our boats too. If you try this calculation for a 60 foot boat, the

result is 10.4 knots. If you have a 30” model of that 60 foot boat, its “hull speed” is 2.12 knots. Applying Froude’s Law of Comparison for a 1:24 scale model, we find that 2.12 knots actual speed is the correct scale equivalent of 10.4 knots in the full size boat!

This relationship between speed and drag also explains why the most economical cruising speed is usually somewhere closer to a 1.00 value, where speed-related drag is much lower (see chart).

One thing to keep in mind when considering hull speed is that the values were developed at a time when steam was king, and powerplants were heavy. Speed for many displacement hulls of First and Second World War vintage are much higher the “hull speed”. For example, the British 1943 Manxman class minelayers had a waterline length of 410 feet, giving a theoretical hull speed of 27.2 knots. In reality, they could do more than 40 knots! Mind you, it took 72,000 shp to do it!

With power from a modern, lightweight powerplant, you can see that an awful lot of drag can be overcome. For modellers, the power available from a small electric motor is, in scale, immense.

What’s it all mean? Three things: 1) there is no absolute limit on how fast a displacement hull will go, 2) if you want a realistic looking bow wave, you’ll have to fake it (white paint & airbrush), and 3) we have a scientific basis for calculating the scale speed of our models.

I’ll take that as proof that my 60 knot scale model battleships aren’t overpowered!

Bibliography:

Jane’s Fighting Ships of World War II, 1946/47

Wikipedia