- #1
Jezza
- 37
- 0
There is a well known rule of thumb amongst sailors that a boat has a theoretical maximum speed called the hull speed, given by [itex]v_h \approx 1.34 \sqrt{L_{wl}}[/itex], where LWL is the waterline length of the hull. This so-called rule is pretty much complete rubbish; a boat can overcome this speed with enough power, and modern hull designs basically subvert the problem. In any case, it's not a hard speed limit. Having said that, it's a useful indication of how fast a boat can be expected to go, because increasing amounts of power are required to increase one's speed beyond hull speed.
The online literature surrounding the matter is largely qualitative, and where numerical, any constants are empirically obtained numbers. Today I discovered why upon consulting a fluid dynamics textbook (T. E. Faber, Fluid Dynamics for Physicists); the analytical treatment is beyond my understanding just yet, and is at any rate beyond the scope of a 15 minute talk I have to give about boats in a few weeks.
Having said this, I did pick up a useful way of looking at the topic of hull speed from the book. The issue is that this seems to be completely at odds with any information I can find online.
Everywhere online says the hull speed is reached when the second crest of the bow wave coincides with the stern. Beyond this speed, the stern begins to dip down as it falls down the 'other side' of the crest, and the boat is left trying to climb up its own bow wave. It follows that hull speed is reached when the length of the boat reaches the wavelength of the waves. I have a few issues with this explanation. The main one is this notion of the boat trying to 'climb up its bow wave.' The boat is still moving horizontally; the only thing happening to the boat is that it's rotating; and it will never succeed in climbing its own bow wave because the boat is creating it!
The textbook, on the other hand, offers an explanation which seems more concrete but, as I say, is at odds with everything I've read online. It begins by explaining that the bow must coincide with the crest of its wave, and that there is also a separate stern wave. It explains that the stern always coincides with the trough of its wave. This seems familiar from experience, but also seems to make qualitative sense by analogy with the bow; the bow pushes the water in front of it, whereas the stern pulls water along with it. The book then asserts, reasonably enough, that these waves carry energy away from the boat. The two waves inevitably interfere with each other. The energy transported away, and hence the drag, is therefore maximised when the bow and stern waves interfere constructively. By this argument, hull speed is reached when the wavelength of the waves is twice the length of the boat, so that the trough can line up with the stern. The book never explicitly refers to this speed as the 'hull speed' however.
My question really amounts to who's right? The talk I'm giving is part of my degree and the audience includes professors, so I'd really rather not have to turn up with the first explanation, and so if the internet is right (and I think it frankly must be), can anyone provide a more concrete explanation?
Many thanks for any help :)
The online literature surrounding the matter is largely qualitative, and where numerical, any constants are empirically obtained numbers. Today I discovered why upon consulting a fluid dynamics textbook (T. E. Faber, Fluid Dynamics for Physicists); the analytical treatment is beyond my understanding just yet, and is at any rate beyond the scope of a 15 minute talk I have to give about boats in a few weeks.
Having said this, I did pick up a useful way of looking at the topic of hull speed from the book. The issue is that this seems to be completely at odds with any information I can find online.
Everywhere online says the hull speed is reached when the second crest of the bow wave coincides with the stern. Beyond this speed, the stern begins to dip down as it falls down the 'other side' of the crest, and the boat is left trying to climb up its own bow wave. It follows that hull speed is reached when the length of the boat reaches the wavelength of the waves. I have a few issues with this explanation. The main one is this notion of the boat trying to 'climb up its bow wave.' The boat is still moving horizontally; the only thing happening to the boat is that it's rotating; and it will never succeed in climbing its own bow wave because the boat is creating it!
The textbook, on the other hand, offers an explanation which seems more concrete but, as I say, is at odds with everything I've read online. It begins by explaining that the bow must coincide with the crest of its wave, and that there is also a separate stern wave. It explains that the stern always coincides with the trough of its wave. This seems familiar from experience, but also seems to make qualitative sense by analogy with the bow; the bow pushes the water in front of it, whereas the stern pulls water along with it. The book then asserts, reasonably enough, that these waves carry energy away from the boat. The two waves inevitably interfere with each other. The energy transported away, and hence the drag, is therefore maximised when the bow and stern waves interfere constructively. By this argument, hull speed is reached when the wavelength of the waves is twice the length of the boat, so that the trough can line up with the stern. The book never explicitly refers to this speed as the 'hull speed' however.
My question really amounts to who's right? The talk I'm giving is part of my degree and the audience includes professors, so I'd really rather not have to turn up with the first explanation, and so if the internet is right (and I think it frankly must be), can anyone provide a more concrete explanation?
Many thanks for any help :)