Hull speed is bogus, but not because the math is wrong.  This formula supposedly predicts the maximum speed of a yacht based solely on length.  It gets discussed frequently in sailing yacht communities.  Surprisingly, hull speed is partially correct, with a very simple and strong theoretical basis.  But don’t sell yourself short; there are ways around hull speed limits.  Today we discuss the basis for hull speed and fill in the rest of the story.

1.0 Theory Behind Hull Speed

The hull speed theory predicts a maximum speed for sailing yachts from a simple formula.

Table 1:  Hull Speed Formula [1]

Imperial UnitsMetric Units
Boat length in feet = LftBoat length in meters = Lm
Speed limit in knots = VSpeed limit in knots = V
Hull Speed:

Hull Speed:

 

Ever wonder where those coefficients came from?  They result from two interesting quirks of physics.  First, any waves generated by the hull have to move at the same speed as the hull.  Our boat generates two major sets of waves:  one at the bow, and one at the stern.  Once they spread away from the hull, they get to slow down.  Until then, they must do whatever is necessary to keep up with the boat.

And just how do they manage to keep up with the boat?  By changing their wavelength.  This isn’t the wave height.  It’s the distance from one wave crest to the next.  Our second quirk of physics:  that wavelength gets tied to the speed limit for the wave.  If the wave wants to go faster, it must stretch out longer, following this simple formula:

Equation 1

Where g is the acceleration due to gravity.  Plug in the constants, work out the unit conversions, and you get the formulas in Table 1.

But that formula only describes the speed limit for a wave, not a boat.  This is where we get to put the two ideas together.  As the boat goes faster, the waves at the bow and stern get longer.  When you reach hull speed, the bow wave lines up with the stern wave.  The two waves double up on you.  Your boat appears to sink down into one big wave trough. (Figure 1‑1)  The hull speed theory states your sailboat will not go any faster once this happens.

Sailboat at Hull Speed

Figure 1-1: Boat At Hull Speed
Notice the Bow and Stern Waves

 

2.0 The Rest of the Story

If you leave hull speed at this simple theory, you miss all the good parts of the story.  So far, hull speed is this impenetrable limit, like the speed of light.  But physicists already imagined theoretical ways to get around lightspeed.  And this story has a few good parts that let us get around the hull speed limit.

It doesn’t break any rules to go faster than hull speed.  If you push beyond the speed limit, the wavelength gets longer than your boat length.  No law against that.  At this point, most boats start to surf on their own bow wave; nothing wrong with that. (Figure 2‑1)  No limiting formulas here.  Sure, hull speed is a difficult hump to get over, but the shape of your hull determines the resistance from those waves.  Not some magical formula.

Example of Sailboat Surfing

Figure 2-1: Example of Sailboat Surfing [2]

Hull speed is bogus.  It predicts when you face a big hump, true enough.  But we reach too far when we assume this creates an impenetrable speed limit.  It only tells you a speed when the bow and stern waves get bigger.  So what?  Your boat sees big waves on a stormy day, and you go through those just fine.  The ultimate speed of your boat depends on only two things:  resistance and power.

 

3.0 What Really Makes Resistance

Resistance depends completely on the shape of your hull.  The best hulls are long and skinny; they minimize the size of your bow wave and stern wave.  To minimize wave resistance, we want a hull that cuts straight through the wave instead of bouncing over it.

With an efficient hull, hull speed becomes just another hump in the resistance graph.  A typical resistance graph for a ship looks like Figure 3‑1.  The humps happen when waves line up and add to increase your resistance.  You get multiple humps, and hull speed is just one of those humps.  The ship powers over the hump and continues to go faster, if you have the right hull shape.  Of course, getting the best hull shape becomes tricky due to the other major component:  viscous resistance.

Typical Resistance Graph

Figure 3 1: Typical Resistance Graph [3]

Viscous resistance is basically surface friction, plus some extra pieces.  When the water runs along your hull, it generates friction, which slows you down.  Especially when you travel in the range of 0 – 3 knots, almost all your resistance comes from friction.  This is why many sailing hulls are shaped to reduce their underwater surface area as they heel over in light winds.  All part of the strategy to minimize surface friction.  Even at higher speeds, friction can form 20-40% of your total resistance.  The catch is that not all hull surfaces are equal.

Appendages are the worst source of viscous resistance, in my opinion.  Your bow thruster, rudder, propeller, and keel all form the extra pieces of viscous resistance, and they concentrate a lot of penalty into a small area.  Consider a bow thruster.  As the water runs over that, it ducks into the thruster tunnel, swirls around, and pops out all confused and turbulent. (Figure 3‑2)  All that motion takes energy.  Energy that slows down your ship.  Similar stories for the other appendages.  Sometimes, these little bits and pieces add up to more than the skin friction of your entire hull.  And don’t forget about wave resistance.  Put all the resistance sources together, and you see that going faster becomes increasingly difficult.

Bow Thruster Tunnels

Figure 3-2: Bow Thruster Tunnels [4]

4.0 Limits on Power

To go faster, we need more power.  But as a sailing ship, all the power comes from those sails.  You might think to add larger sails.  Unfortunately, sails do not limit your maximum power.  The sail plan gets limited by the righting moment of your hull. [5] [6]  As the wind heels the boat over, the hull pushes back with a righting moment.  Try to push more power into the sails, and the boat just heels farther, dumping that power. (Figure 4‑1)  In extreme cases, this is how the wind capsizes a boat.  If you want more power in your sail plan, the first step is not larger sails.  The trick is more righting moment in the hull.

 

 

Figure 4 1: Comparison of Sail Areas with Heeling Figure 4 1: Comparison of Sail Areas with Heeling [7]

Figure 4‑1:  Comparison of Sail Areas with Heeling [7]

 

But how to get more righting moment from the hull?  Unfortunately, you need to increase the beam of your hull.  Except that increasing the beam also increases your wave resistance.  This is one of the many conflicts that yacht designs have to compromise on.    That is also why catamarans have a reputation for speed.  They get to combine long and skinny hulls (low resistance) with a huge righting moment (high power).  Though even they run into other limits.  The maximum speed of your hull is an integrated part of the vessel design.  It becomes a performance target, strategically decided by the naval architect.  Far more complicated than a simple formula.

 

5.0 Conclusion

With all the added evidence, why does the myth of hull speed persist.  Simply put, designers are not stupid.  We designers all recognize that any given boat has a point of diminishing return, where extra power barely adds any more speed.  That point of diminishing return often happens near hull speed.  This coincidence reinforces the belief that hull speed predicts a reliable limit.  Boats often top out near hull speed, but not exactly at hull speed.  Ship design has many tricks available to push faster than hull speed.  Don’t limit your expectations to a simple formula.

 

6.0 References

[1]A. Lloyd, Seakeeping: Ship Behaviour in Rough Weather, Gosport, Hampshire, UK: ARJM Lloyd, 1998.
[2]G. Day, “Choosing a Safe Sailboat,” Boats.com, 4 February 2002. [Online]. Available: http://www.boats.com/how-to/choosing-a-safe-boat-5934/#.WtgAoC4bNpg. [Accessed 18 April 2018].
[3]R. C. Brancho, “Basics of Ship Resistance,” LinkedIn Learning, 23 June 2011. [Online]. Available: https://www.slideshare.net/adsokant/basics-ofshipresistance. [Accessed 20 Apr 2018].
[4]Wikipedia Authors, “File: Pourquoi_pas_bow_thrusters.jpg,” Wikimedia Commons, 24 Oct 2006. [Online]. Available: https://commons.wikimedia.org/wiki/File:Pourquoi_pas_bow_thrusters.jpg. [Accessed 20 Apr 2018].
[5]N. L. Skene, Elements of Yacht Design, Dobbs Ferry, NY: Sheridan House, 2001.
[6]Claughton, Wellicome and Shenoi, Sailing Yacht Design: Theory, Southampton, Hampshire, U.K.: University of Southampton, 2006.
[7]Don Adzigian, “501 Heeling Dynamics,” Anything and Everything Catalina 22, [Online]. Available: http://www.catalina22experiment.com/home/basics-for-advanced-sailors-501. [Accessed 20 Apr 2018].
[8]C. Doane, “Crunching Numbers: Hull Speed & Boat Length,” Boats.com, 26 March 2010. [Online]. Available: http://www.boats.com/reviews/crunching-numbers-hull-speed-boat-length/#.WtfzIC4bNph. [Accessed 18 April 2018].
[9]Cloughton, Wellicome and Shenoi, Sail Yacht Design: Practice, Southampton, Hampshire, U.K.: University of Southampton, 2006.