Hullspeed and the
Speed/Length Ratio

So what gives one boat better hullspeed than another? This question was pondered long and hard by William Froude (1810 to 1869), a British engineer who had a special fascination with the sea and ships.

Funded by the Admiralty, who were clearly very keen to get some answers to this question, he built a tank testing facility at Torquay, where he experimented with various model hull forms.

As an early expert in model analysis he was well acquainted with the 'law of mechanical similitude', which demonstrates among other things that there are few linear relationships in hull design.

So just what is the answer?

Let's take a look...

Hullspeed and the Matchbox Analogy

Hullspeed and the Matchbox AnalogyThe Matchbox Analogy

Consider your hull as a matchbox - not wonderfully efficient hydrodynamically, but stick with it for a moment.

Dissatisfied with the constraints of matchbox living, you decide to double its size. You add another matchbox ahead to double its length, two alongside to double its beam and four on top to double its draft.

Now wetted area has increased by four, volume and displacement by eight and stability - as the product of its mass and acceleration - has increased sixteenfold.

So by doubling a hull's dimensions, wetted area is squared, displacement is cubed and stability increases by the power of four.

With this knowledge and that gained by carefully measuring applied force and resultant movement, Froude was able to both calculate and demonstrate that a relationship existed between hull speed and waterline length - that relationship being known and described in the metric world as 'Froude Numbers'.

The Speed/Length Ratio

However, most of us more accustomed to units of feet and knots are probably more familiar with the Froude Number's close relation - the Speed/Length Ratio.

The Speed/Length Ratio

S/L Ratio = hullspeed (in knots) divided by the square root of the waterline length (in feet)

This discovery enabled Froude to compare the performance of boats of different length. For example a 25ft sailboat moving at 5 knots would have the same S/L Ratio at a 100ft patrol boat steaming along at 10knots, and consequently both would develop the same resistance per ton of displacement at those speeds.

For Froude's models, having no rig above the waterline to create windage, this resistance was caused by two principal factors; hull drag and wave making resistance.

Maximum Hull Speed

Maximum hull speed (in knots) = 1.34 x the square root of the waterline length (in feet)

Waterline Length

20 feet

25 feet

30 feet

35 feet

40 feet

45 feet

50 feet

Max Hull Speed

6.0 knots

6.7 knots

7.3 knots

7.9 knots

8.5 knots

9.0 knots

9.5 knots

These figures relate to a boat in displacement mode. If sufficient power can be applied to overcome hull drag and enable the boat to plane, then other criteria will affect ultimate hullspeed.

Any Questions?

What is the theoretical hull speed of a non-planing boat?

The theoretical hull speed is the maximum speed that a non-planing boat can achieve in displacement mode, when the wavelength of its bow wave is equal to its waterline length. Beyond this speed, the boat will encounter increasing wave resistance and will need more power to overcome it.

What factors affect the theoretical hull speed of a boat?

The main factor that affects the theoretical hull speed of a boat is its waterline length, which determines the wavelength of its bow wave. The longer the waterline length, the higher the theoretical hull speed. Other factors that may influence the actual speed of a boat include its hull shape, displacement, draft, trim, sail area, wind and sea conditions, and propeller efficiency.

What is the difference between planing and non-planing boats?

Planing boats are boats that can lift themselves partially or fully out of the water and ride on top of their own bow wave, reducing their wetted surface area and drag. Planing boats can exceed their theoretical hull speed and reach higher speeds with less power. Non-planing boats are boats that remain fully submerged in the water and cannot climb over their own bow wave. Non-planing boats are limited by their theoretical hull speed and require more power to increase their speed.

What is the 'half angle of entrance' and how does it affect wave resistance?

The half angle of entrance is the angle between the waterline and the centerline of a boat at its bow. The smaller the half angle of entrance, the finer the bow shape and the lower the wave resistance. A fine bow can slice through water with minimal disturbance, while a blunt bow can generate large waves and drag. The half angle of entrance is one of the key factors that determines the wave-making resistance of a boat.

How can I increase the speed of my non-planing boat?

There are several ways to increase the speed of your non-planing boat, such as:

  • Increasing your sail area or using more efficient sails;
  • Reducing your displacement or weight;
  • Optimizing your trim or balance;
  • Improving your propeller efficiency or reducing your propeller drag;
  • Choosing a finer or longer hull shape;
  • Sailing in favorable wind and sea conditions.

What are some common misconceptions about hull speed?

Some common misconceptions about hull speed are: - Hull speed is a fixed limit that cannot be exceeded by non-planing boats. In reality, hull speed is a theoretical estimate that can be surpassed by some boats with sufficient power or sail area, but at the cost of increased wave resistance and drag.

  • Hull speed is the same for all boats with the same waterline length. In reality, hull speed can vary depending on the hull shape, displacement, draft, and trim of the boat, as well as the wind and sea conditions;
  • Hull speed is the optimal speed for non-planing boats. In reality, hull speed is often too high for non-planing boats to maintain efficiently or comfortably, especially in adverse conditions. A lower speed that minimizes wave-making resistance and maximizes fuel or power efficiency may be more desirable.

The above answers were drafted by using GPT-4 (OpenAI’s large-scale language-generation model) as a research assistant to develop source material; to the best of our knowledge, we believe them to be accurate.

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