Length matters

Longer boats are faster. We tend to take that for granted, because it tends to be true. Put two boats of similar type in a race, and the longer one is almost certain to beat the shorter one to the finish line. The difference that length makes is quite remarkable, but we rarely get to look at it on its own- and that is the subject of today's post.

There are very good reasons why length is such a critical factor in determining speed. A boat never operates in flat water; if it's moving, it'll be affected by its own wake. Waves are rather stubborn- it's hard to force them to do things they don't want to do. And left to their own devices, they'll travel at a speed proportional to the square root of their length.

Consider a boat with a displacement hull- one that relies purely on good ol' Archimedes, with none of that new-fangled dynamic lift. The waves it produces are forced to travel at a certain speed (the speed of the boat) and, therefore, they naturally adopt a length appropriate for that speed. As the boat speeds up, the waves get longer. Eventually, we reach a speed range where the waves created near the bow have their second crest a bit ahead of the stern. The boat likes this- around this speed, the various wave systems often partly cancel each other out, reducing the resistance and allowing for efficient running. The longer the boat, the higher the speed at which this occurs.

If we go just a little bit faster, so that the waves are about the same length as the boat, things look much less rosy. The stern sinks into a trough as the bow is lifted, and the boat is literally trying to climb a hill of water. This is where the simplistic concept of "hull speed" comes from: in a displacement hull, throwing more power at the problem will only make the crest higher, the trough deeper, and the hill steeper. In many displacement-hulled boats, once you hit this point, you can multiply the engine power by five and gain only a fraction of a knot. (I will leave planing and semi-displacement hulls out of today's discussion.)

Generally speaking, we don't scale boats by length alone. A longer boat will usually also be wider, deeper, and much heavier than its short sister. The benefits of added length are therefore not as obvious as they should be: of course the longer boat is faster, it has much more sail and a bigger engine. So let's try to look at the effect of length on its own, without changing too much else at the same time.

I'm working on three concept powerboats right now that provide us with an interesting look at the effect of length alone. These boats have to fit in standard ISO shipping containers, so they all must have the same beam and total height- and they may as well have the same draught, too. They share essentially the same statement of requirements, with the exception of range and cabin volume. They're pure displacement hulls, with upswept aft buttocks and soft chines. The parent hulls are all of the same family, and their key parameters- block coefficient, prismatic coefficients, sectional area curves- are within a few rounding errors of each other. From a hydrodynamics standpoint, the only appreciable differences between these three are their length and their displacement.

Here are some approximate resistance curves for these concept hulls. First, the shorty, 5.7 m long and weighing 2620 kg in "standard" condition.

A mid-size 7.9 m version, 3660 kg at its design waterline.

And the stretch limo of the fleet, 11.8 m long and tipping the scales at 5480 kg on the green curve.

The long one is a bit over twice the length of the short one and weighs a hair over twice as much. Its efficient cruise speed is faster by 1.0 m/s (about 2 knots). The resistance at cruise speed is almost exactly the same.

Think about that. Our 11.8 m boat is 40% faster and twice the size, yet it is no harder to push through the water than its little sister. Its engine will be bigger, but its fuel consumption per mile will be nearly the same. That's the beauty of a long, slender hull.

Eagle-eyed readers might note a few other features in these curves. Look back at the one for our short boat. The blue line- for "empty" resistance- is above the purple "heavy" line in most of the operating range. How does adding more than a tonne- half again the boat's empty weight- make the boat faster and more efficient?

The answer lies in the hull shape. Designers try to optimize a boat for a particular range of speeds, carrying a particular range of loads. These boats are pretty close to ideal for their intended speeds and weights. If you run them a bit heavier, it doesn't change much- the shape of the immersed hull body stays more or less the same. Running them light, though, puts the chines on the verge of coming out of the water- and the shape the water sees is therefore quite different, and quite far from optimal.

The slope of the resistance curves past "hull speed", or "on the hump", is also noticeably different. There is no way you're going to get the 5.7 m boat to climb that hump. The stretch model, though, stands a chance. (Indeed, if I were to flatten out her aft buttock lines and give her a hundred horsepower or so, she might be able to climb halfway to plane- but with some loss of low-speed efficiency and seaworthiness.)

Key points:

  • Among displacement hulls, a longer vessel will be faster and more efficient than a short one.
  • If you have a choice, making a new design longer is usually a better way to get the space you need than adding more beam or bulk.
  • Displacement hulls can sometimes burn more fuel when empty than when loaded down, if the hull shape was optimized for carrying a load.




Dip in resistance

Very cool read. Thanks!

Can you enlighten me about those dips in resistance? Especially on the short boat you notice dips at around 1.7m/s and 2.2 m/s. I was guessing it had something to do with having close to two and three wavelengths along the hull. And also, is this effect exploited to save fuel? I guess you could imagine cases where increasing power will increase fuel efficiency then.



Dip in resistance

Matthew's picture

Hi Andreas,

You got it right- the small peaks and dips in the resistance curve are due to the wake, or more precisely, the wavelength of the transverse wake relative to the length of the hull.

The dip at ~2.3 m/s corresponds to a wavelength of ~3.4 m, and the boat's waterline length is 5.2 m. In this condition, the bow and stern are both well supported on crests of the transverse wake, so she's trimmed pretty close to level.

If we slow her down a bit, to 2.0 m/s, the wavelength is 2.6 m and the second crest of the wake is just a hair aft of the stern- while the most buoyant parts of the stern are in a trough. So the stern will drop, and she'll feel like she's climbing a hill. Speed up a bit, and the wake gets a bit longer, the first crest moves aft to lift the stern, and she'll level out and run more efficiently.

You can exploit this effect on any boat whose trim changes noticeably with speed. If the stern is settling into a trough in the wake, she'll trim up by the bow and her fuel burn (per mile) will increase. Speed up or slow down until she's trimmed level, and you will probably have a more fuel efficient trip.

Long, slender displacement hulls (like the third example) produce much smaller transverse wakes and are more resistant to changes in trim, so you won't see this effect to any great degree on them.

Dip in resistance

Thanks Matthew! It's good to have ones intuitions checked once in a while. I have noticed this effect on boats, but I never made the link with hull speed.

This should settle a discussion I had with my father, who insists that less throttle means less fuel spent;)


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