CRUNCHING NUMBERS: A Better Way to Estimate Hull Speed

Spirit of Adventure under sail

It’s been a while since we discussed all those mysterious numbers that both boat designers and journalists are always throwing around to confuse us when they talk about boats. You’ll recall last time I bloviated about displacement/length ratios. One big reason it’s a good idea to go to the trouble to calculate a boat’s D/L ratio is that you can use this number to refine your estimate of the boat’s maximum speed potential beyond the relatively rough estimate afforded by the classic hull-speed formula we discussed earlier.

This more accurate method of finding a boat’s potential top speed, devised by designer Dave Gerr and published in his tome, The Propeller Handbook, can also be used to estimate the hull speeds of multihulls (both catamarans and trimarans). Dave warns, however, that catamarans with very narrow hulls (for mysterious reasons that no one really understands) will often exceed the speeds predicted by his method.

To comprehend Dave’s formula, we first need to comprehend that the famous multiplier we used in the classic hull-speed formula (1.34) is in fact what is known as a speed/length ratio (S/L ratio). This ratio quantifies the relationship between a boat’s speed (BS), whatever it happens to be at any given point in time, and its waterline length, according to a formula that holds that S/L ratio equals a boat’s speed in knots divided by the square root of the boat’s load waterline length (S/L ratio = BS ÷ √LWL).

The brightest kids in class will instantly note that this is simply the classic hull-speed formula (HS = 1.34 x √LWL) run backwards to solve for the speed/length ratio instead of speed. What the classic hull-speed formula assumes is that 1.34 is the maximum S/L ratio that can ever be achieved (due to the characteristics of waves we discussed before) and thus always serves to limit a boat’s top speed potential.

What Dave’s formula does is estimate a boat’s maximum S/L ratio based on its D/L ratio so as to more accurately reflect the fact that lightweight boats are more capable of exceeding their nominal hull speed. Once we’ve arrived at a new and more accurate S/L ratio for a given boat, we can then plug it into the classic hull-speed formula to derive a new, more accurate estimate of that boat’s nominal hull speed.

Dave’s formula holds that a boat’s maximum S/L ratio equals 8.26 divided by its D/L ratio to the .311 power (Max S/L ratio = 8.26 ÷ D/L ratio↑.311). For a 12,000-pound boat with a 28-foot waterline and a D/L ratio of 244, we thus get the following results:  244 to the .311 power equals 5.53 (you’ll obviously need a scientific calculator to figure that out!), therefore 8.26 ÷ 5.53 equals a maximum S/L ratio of 1.49.  Plug 1.49 into the hull-speed formula (1.49 x √LWL) and you get a new nominal hull speed of 7.9 knots (1.49 x 5.29 = 7.88), as compared to the boat’s old nominal hull speed of 7 knots (1.34 x 5.29 = 7.08).

This in itself is an appreciable difference, but it grows even larger as the boat grows lighter. Assume, for example, that our 12,000-pound boat has shed 3,000 pounds to become a 9,000-pound boat with the same load waterline length, and its D/L ratio drops to 183. Its old nominal hull speed, based solely on its LWL, remains exactly the same at 7 knots, but its new nominal hull speed, figured according to Dave’s method, now becomes 8.6 knots!

Things get even more exciting if you bear in mind that this revised hull-speed estimate still does not account for a boat’s potential to plane. That is, we’re still only talking about the top potential speed that may be achieved by a hull in displacement mode. Dave further warns that getting the extra hull speed his method predicts will require a lot of extra power, but he does maintain that his method is ultimately more accurate than the old one.

I, for one, happen to believe him. Running Dave’s formula on your own boat and finding out that its top speed is higher than you thought is an easy way to put a smile on your face. Unless you own a classic CCA-style cruiser with long overhangs. These boats have exaggerated D/L ratios, due to their short static waterlines (which get longer when the boat starts sailing and heels over) and when you run Dave’s formula on them you usually get a lower top speed. In cases like this, I always assume the classic hull-speed formula is more accurate.

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13 Responses
  1. dwight looi

    This may be a reasonable estimate for BOATS, but it is not scalable to larger SHIPS. Let me give you an examples.

    The Iowa Class Battleship has a displacement of 50,000 long tons and a length of 860 ft. This gives a D/L ratio of 78.6 and a S/L ratio of 2.12. This then indicates that Hull Speed = 2.12 x Sqrt (860) = 62.17 knots. We know that is bullshit because the Iowa has 212,000 shp for it’s 50,000 tons or greater than 4 shp per ton. We also know that it is a 33~35 knots ship depending on load (and hence draft). There is no way her hull speed is 62 knots.

    The Queen Mary 2 cruise ship is about 87,000 tons and 1132 ft long. This gives a D/L ratio of 136.8 and a S/L ratio of 1.79. THis then indicates that the Hull Speed = 1.78 x Sqrt (1132) = 59.9 knots. The QM2 has 115,300 shp delivered via her four mermaid pods or about 1.33 shp per ton. In service she is a 28 knots vessel which reached 30 knots during her trials. Again, there is no way her Hull Speed is 60 knots.

  2. Javier Rosado

    Great article but I have a question.
    How can this be applied to displacement hulls? Specifically to kayaks or surfskis.
    Does the constants and formulas hold true for this kind of vessels?

  3. Javier Rosado

    I have an Epic v7 surfski which measures 17′ long and weighs 53 lbs.
    According to the standard hull speed calculations, it has a theoretical hull speed of 5.52 knots. However, if I try to use these formulas, the Boat Speed comes to 20.89 knots. Its creator, an olympic medallist, is able to push it to 7.18 Knots for long distances which could very probably translate to a slightly higher speed for shorter distances; but no one on muscle power alone could drive it to 20 knots or even close to that.

    Something clearly needs to be adjusted for it to apply to small displacement hulls.

  4. Tony H

    Interesting. I am currently boatless and looking at purchasing something in the 30′ range (sail) and comparing potential hull speeds. One boat has a 24 ft waterline and the other 25. I assumed the longer wl would give me a bit more speed as the old formula shows. However the longer WL boat also displaces 1,400 lbs more so by this new formula the shorter boat has the same theoretical hull speed. Good to know. Thanks!

  5. Mark Barendt

    The math shown in the example doesn’t work. 12000/28=428.57 not 244. Raise that to the power of .311 and you get 6.585. 8.26/6.585=1.254

  6. Terry eh

    Mark: you need to scroll up and click on the previous article on D/L ratios; (in red)
    The exact number works out to 243.6, rounded to 244.

  7. Michael Ossipoff

    Did I miss something, or does David’s sailboat speed-prediction formula ignore sail-area. ,,,& is based only on D/L & boat-length?

    So then, is Dave saying that sail-area is irrelevant to a sailboat’s speed?

    1. Charles Doane

      Hi Michael! Thanks for the comment. The answer is yes, Dave’s formula ignores sail area and treats only the maximum speed potential of any given hull. But no, sail area is obviously not irrelevant. Dave’s formula, like the traditional speed-prediction formula it replaces, merely assumes a sailplan powerful enough to drive the boat at its maximum speed.

  8. I ran into this formula in your book The Modern Cruising Sailboat. Running the numbers for our 31ft double ender gave pretty interesting results:

    Traditional hull speed: 6.8kt
    Gerr’s hull speed (light ship): 7.1kt
    Gerr’s hull speed (2t load): 6.4kt

    Now, there are no polars (or much other performance material) available on our boat, so I’ve constructed polars based on the actual recorded wind speeds and angles vs. actual sailing speeds during last two summers of cruising. And you know what is the top speeds I get there? 6.4kt! Coincidence? Probably not.

  9. Carl Damm

    I always find these exercises interesting. And probably very worth while to designers, as an end user the only thing that matters is real world sailing characteristics. To reflect on theoretical speed potential of my boat, which has over 700 sisters and an established racing record would just be frustrating. When shopping for a new boat I would look at established history and PERF ratings. They are a long term average of a particular hull form and should predict what the sailor can expect. Theory is would only come into my calculations if I were comissioning a new design, but once she is built the proof is in the boat.

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