Naval Engineering - Bow Waves, Speed & Turns
While I’m still working out how to demonstrate the choices between face hardened and homogenous armour plate for turret roofs with the resources available in the UK, I thought we’d continue our occasional looks into naval engineering by a review of some other essentially features of ships to help people understand how they behave a bit better, reveal a small but interesting detail about how a ship turns and also give you a neat little trick for working out how fast a ship is moving based purely on a photo.
Before we continue, I should mention that the formulas and diagrams you’ll see that underpin this video are taken from two publications, one is Knight’s Modern Seamanship, a tried and tested publication that’s about as close to a Bible for sailors as its possible to get in the realms of ship handling. First published in 1901, it’s still available in its 18th edition, although the one I’m using is an 11th edition from 1945, as that sits nicely in the channels time period. The other is Fundamentals of Construction and Stability of Naval Ships, which is/was an essential textbook at the USN Academy.
Firstly we’re going to discuss bow waves and speed. It goes without saying that a ship in water is displacing a certain amount of water from where it would otherwise be, this is why a ships mass is registered as displacement. However, when a ship is moving through the water it is obviously displacing previously undisturbed water ahead of it whilst other water moves in behind it to fill the void left by its passing. This requires energy as the ship has to push the water aside to pass through, and the more water that has to be moved aside in a given amount of time, the more energy you need. Hence why you need more power in your boilers to go faster and why a slim bow is better than a blunt one.
One of the features this is cause is a bow wave, which at any appreciable speed will be quite visible and indeed methods of faking or disguising a bow wave to give a false impression of what a ship was doing was one of the key concepts of warship camouflage in WW1 and WW2. The more energy that is put into displacing water the higher this wave will go, so as a general rule the faster the ship moves the larger the bow wave, although you can get some pretty impressive bow waves at lower speeds with ships that have bluffer bows, simply because the greater immediate frontage of the ship means more water has to be moved immediately, which of course also needs more energy.
But the energy that creates the bow wave doesn’t just vanish when the white spray falls back into the ocean, that is really only a small part of the total water displacement that’s going on. The wave created is a wave in the true sense of physics as well as the colloquial, and will continue to oscillate in the matter of a sin wave for some time until the energy in it is dissipated. This energy will spread from the ship in the form of the ships wash, but also run along a ship in a series of waves and troughs of gradually decreasing magnitude, each cycle of which sends out its own peak and trough in the ships wash. Hence why if you are moored on a river and a ship passes by a little fast or close, you ship or boat will rock back and forth multiple times as each successive peak and trough hits you, whereas if the bow wave energy just magically vanished after the initial bow wave itself you’d just feel the one hit.
As a ships speed increases, not only does the starting amplitude of the wave increase due to the aforementioned greater energy, but the length of the wave also increases as perceived by the peaks and troughs down a ships side. These two functions of wavelength and amplitude are independent of each other, as mentioned previously you could be towing a barge at 4 knots and thus have a short wavelength but with high amplitude, or you could be moving a battlecruiser through the water at 18 knots with a longer wavelength but a similar or even smaller amplitude depending on how sleek the bow is.
Now there are some things that can affect this bow wave’s features, a bulbous bow, intentional or not in the cases of some ram bows, can decrease the amplitude of wave as a whole, and the waves of the sea can also amplify or reduce the amplitude in certain circumstances. This is because of what is known as constructive and destructive interference, essentially if two waves in any sort of medium, water, light, radio etc, overlap then if the peaks and troughs align, they are said to be in phase and the magnitude of the resulting waveform is increased, conversely if they are out of phase and the peak of one overlaps the trough of the other and vice versa then the resultant waveform is reduced or even cancelled out if the two waves are of similar power. Of course this relies on the wavelength being similar in both waves, so a given sea state may mitigate or enhance a ships bow waveform at one speed but have less effect at another speed. This is the principle on which bulbous bows work, by generating a wave ahead of the ship that’s 180 degree out of phase with the actual bow wave at a given speed, it means the ship can cruise more efficiently at or around that speed by minimizing the wave profile down the side of the ship, which otherwise causes drag.
When the wavelengths are very out of step with each other this can result in slightly irregular behaviour of the stronger wave, but the effect depends on the amplitude and energy of two waves in question, a series of short wavelength sea waves with peaks a foot high will have little visible effect on a bow wave that’s cresting at 10ft, but a ship moving slower might find its 2ft bow wave form completely obliterated if it’s moving through 20ft seas, but the former situation is far more common than the latter.
Incidentally, this entire principle of the bow wave and its form is the main thing behind the idea of hull speed, which is a matter we’ll talk about in detail another time but very briefly speaking, if a ship approaches a certain speed, which is proportional to hull length, then the wavelength of the bow wave becomes so long that it’s one long slope from crest to trough that matches the waterline length of the ship. At that point the ship is essentially constantly trying to move not just forward but uphill and the energy required to do this becomes insane. But as said, more on that in another video.
Now, why, apart from establishing and bow waves and their crests and troughs down the side of a ship are in fact a thing, which a few people over the years have denied in various comments here, why is this useful to you?
Well, the wavelength of these waves, that is the distance between two crests or two troughs, has a mathematical formula related to the speed of the ship. L = 0.557V^2 where L is the wavelength measured in feet and V is the ships absolute velocity measured in knots. For those of you who use metric you’ll have to then divide the result by approximately 3.3 to get the wavelength in metres.
Using basic mathematics we can derive that the square root of wavelength divided by 0.557 is equal to V, the speed in knots.
This in turn means that if you have a picture of a ship where you can see the peaks and troughs of the bow wave and you know the length of the ship in question, you can then work out the wavelength and thus calculate the approximate speed of the ship. This is much better than looking for the amount of smoke from a ships funnels or the rate at which that is being swept back, because a stiff headwind can blow funnel smoke back sharply even if the ship is standing still, and lots of smoke just means inefficient combustion, which more often means the ship is powering up to move at speed, but most of the time hasn’t actually reached top speed yet, since photos of ships moving at their top speed, especially when oil fired, tend to show remarkably little smoke since at that point the boiler temperature and pressure has stabilised and most of the fuel is actually being burnt.
So lets take a few examples, there is photo of Hood on her way to the Battle of Denmark Strait which some of you may recognise, now apart from the rather large trough right where I suspect she was hit, we can also derive her speed in this photo. We know Hood was about 860ft long, and we can see the three crests and two troughs just about fitting along her length, the bow crest itself and the second crest peaking roughly abreast the second funnel. This is about 420ft along the ship, exact figures depend on to which part of the funnel you are measuring to. This tells us that at this point Hood was moving at about 27.5knots.
The only problem with this method is that ‘sea level’ shots taken from other ships or even boats at any kind of distance can slightly obscure the waveform along the hull, either from intervening sea waves getting in the wave of even the rolling crest of the bow wave, the ships wash, which at a low enough angle might obscure things, so shots from ahead are less useful than shots from alongside or from the air. You can also measure from a crest to a trough and just double it to get wavelength if you only have a partial picture. But for example if we look at this picture of USS Illinois the peak of the first crest after the bow is about level with the funnel. She’s about 375ft long, with scaling suggesting the gap between troughs is about 160-170ft, suggesting she’s doing just about 17 knots. Now, if you look at the Illinois classes rated speed of 16 knots you might think we have a problem, but look closer and you’ll see Illinois actually managed almost 17.5knots on trials, which means this shot represents her absolutely booking it but is entirely plausible.
One last example, here’s USS New Jersey in the late 1960’s, you can see a beautiful wave profile down her hull, with a crest right underneath turret one and another just under the fourth of the port 5” gun mounts. The Iowa’s are about 887ft at the waterline, so scaling from this suggests the ship is moving at a comfortable 22-23 knots in this photo.
So there you go, as long as you can get a good view of the side of the ship and you’re scaling is ok, you can now tell roughly how fast a ship in a photo is moving.
The other principle is a fine detail of large ships turning that I was not aware of until in discussion with a serving naval officer who is a navigation specialist a few years ago, but which is also right there in Knight’s Seamanship. That is, when a ship that works with a stern mounted rudder is put into a turn, it does not actually go in that direction at first. This may seem counter-intuitive but is such a fundamental part of shiphandling it has it’s own specific designation, it’s known as kick. I’ll read the relevant part from Knight’s Seamanship:
SEE VIDEO
This means that, as seem in these diagrams, when a ship first puts the rudder over, you’ll initially just keep going and the ship will actually turn slightly away from where you want to go, so in a starboard turn the bow goes slightly to port and vice versa, then as the full effects of the rudder takeover the ship will start to turn in the direction you wanted her to go in the first place. This is very important in navigation for all sorts of reasons. For example if you are in a narrow shipping channel you can ride too close to the edge otherwise when you try and turn back towards the centre of the channel or make a turn towards the opposite side, if the channel itself changes course, you run the risk of running aground as the ship will kick slightly, taking you out of the channel. Likewise if you find yourself in a near-head-on, it will actually be safer to pass down the side of the other ship and turn later, as turning just before will cause you to kick towards the other ship and collide. It’s one of the reasons by side-by-side resupply has to be done with a degree of space between the two ships, and of course can affect the exact nature of what a ship is doing if you are trying to work out its precise behaviour at the very start of an ordered turn.
So, I hope this short introduction to some fundamentals of ship engineering was useful, as I mentioned I’ll be progressing this mini-series generally on Friday’s as and when possible, sometimes covering things from this kind of academic perspective with worked examples, and other times such as when we look at armour, I’ll do my best to rig up some kind of practical demonstration.
