So you are in the market for a boat. Hundreds of boats are sold every year and every salesman has his or her own sales pitch trying to persuade you of the brand they are selling. If you have the time on your hand to compare shops, I have a few useful computational tools to help make a comparison between boats…

These numbers are nondimensional and can be applied to any size of boat. If using these tools, don’t let the spread between boat sizes get too large otherwise the comparison will be distorted. Try to keep a maximum range of about 2.4 – 3m between the smallest and largest boat you compare.

**SPEED–LENGTH** RATIO

The speed-length (S/L) ratio is derived from the Froude number.

Froude Number? William Froude did a number of tests on thin planks in the 1890s. Froude discovered that a boat’s speed tops out when the wave it is creating has the same length as the boat’s waterline in a displacement mode. I have touched on this a bit in my previous article on Leisure boating explaining the different modes of planning.

The equation for S/L is:

An S/L of less than 1.5 shows that the boat is in displacement mode.

Between 1.5 and 2.5, the boat is operating in a semi-displacement mode.

Above 2.5 and sometimes even higher, the boat is in planning mode.

**DISPLACEMENT–LENGTH RATIO**

Calculate the boat’s displacement-length ratio by dividing the boat’s displacement in pounds by 2240 to get long tons. Divide this figure by one-hundredth of the waterline length (ft) cubed. In other words, the ratio is:

If the weight of the boat is 8500 pounds(3856 kg) and the waterline is 31ft (9.5m), the displacement length ratio equals:

In general, the higher the number, the heavier the boat for its length and the slower it is. At sea, the heavier the boat, the more likely to handle waves better than a similar lighter boat. Planing hulls are in the 130 to 220 range whereas trawler hulls are above 300. Semiplaning boats are typically between 225 and 300.

Don’t fall into the trap of lightweight numbers. Many buyers fall for the trap that “heavy” boats are a drawback and so many salespeople use the comparison to sell their product using the words “our boat is so much lighter than our opposition. You as a buyer need to ask yourself the question –

How many boats do I need in terms of displacement?

Simply take the total weight of the crew and stores you’ll carry and multiply it by 7.5. This is the reciprocal of 8 percent times 60 percent loading – [ (1/0.08) x 0.6] = 7.5. The answer is displacement you’ll need plus or minus 10 percent.

Let’s calculate the displacement required for a Cruiser, Crew of 4 on an ordinary 10-day vacation:

4 x 72kg = 228 Crew

4 crew x 10 days x 6.6kg/day x 1.5 reserve = 396kg food and water

4 crew x 10 days x 2.3kg/day = 92kg personal gear

TOTAL: crew, food, water, personal gear = 776kg

776kg x 7.5 = 5820 kg displacement

Plus or minus 10% = 5240kg – 6040kg displacement boat required.

**LENGTH-TO-BEAM RATIO**

The length-to-beam ratio gives an indication of how long the boat is relative to its beam and allows you to compare two boats of different sizes.

For example, comparing a 50ft (15.3m) cruiser with a 12ft (3.7m) Beam to a 40ft (12.21m) cruiser with a 10ft (3m) beam.

We find that the larger boat has a length-to-beam ratio of 4.167 whilst the smaller boat has a ratio of 4.

This just shows that for its length, the smaller boat has more beam. A smaller ratio indicates a boat with greater transverse stability, making it better for trolling or drifting in beam seas.

POWER-TO-WEIGHT RATIO

When I design a boat, I use the power-to-weight ratio to indicate whether the boat has sufficient horsepower for its weight. The ratio is:

This is merely an indicator of the amount of horsepower a boat needs to push its own weight through the water. When comparing boats, make sure that you use the same horsepower number whether it is brake horsepower (bhp) or shaft horsepower (shp).

CUBIC NUMBER

This is a good way to compare two boats of different sizes.

Multiply the waterline length by the boat’s beam and depth (from the bottom of the hull to the deck edge), you get a cubic number (CN).

For example:

Boat 1 is 30ft (9.14m) on the waterline and has a maximum beam of 10 ft (3.04m) and a depth of 6 ft (1.83m) and therefore a CN of 1800 ft³ (50.9 m³)

Boat 2 is 34ft (10.36m) Lwl, has a beam of 11ft (3.35m) and a depth of 7ft (2.13m), and therefore has a CN of 2618 ft³ (73.9m³).

By dividing the CN of the first boat into the CN of the second boat, you can see that the second boat is 2618 / 1800 = 1.45 (73.9 / 50.9 = 1.45) as large as the first boat. In other words, it is 45 percent larger and all other things being equal should cost more to buy and maintain.

COMFORT RATIO

This is a measure of motion comfort between boats of a similar size and type. It is based on the fact that the quickness of motion or corkiness of a hull in a choppy sea is what causes discomfort and seasickness. The corkiness is determined by two factors:

(1) The beam of the hull and (2) the area of the waterline. The formula is as follows:

Displacement is measured in pounds and the Lwl and Loa in ft.

Lightweight boats and smaller yachts that have a higher Beam/length ratio will rate poorly on the comfort scale while as we would expect, heavy oceangoing cruisers rate more favorably. The ratio ranges from 10 or less for lightweight day cruisers to the higher 50-60 such as an old sailing pilot boat. Average ocean cruisers come up somewhere in the mid-’30s.

PRISMATIC COEFFICIENT (Cp)

The prismatic coefficient is the ratio of the largest underwater section of the hull

multiplied by the hull’s waterline length, to the volume of the displacement of the boat.

To simplify, if you took a block of wood, the length of the waterline, and shaped it to the underwater portion of the midships section, then carved it away to model the ends of the boat, the Cp is the remaining percentage of the original midships-shaped block. See fig.1

The optimum Cp ratio varies in direct proportion to the hull resistance and the boat speed. Designers use their experience and knowledge of other designs to select the best Cp for the style and speed of the boat they design.

The Cp of a powerboat hull should become higher as boat speed increases. Obviously, the fastest boat is not a barge which has a Cp of 1.

A typical displacement boat has a Cp of around 0.55 – 0.65.

A high-speed deep V hull can have a Cp as high as 0.75, Put in another way, the planing hull needs to be fuller at the ends – especially aft – to develop dynamic lift.

Now you have some tools to evaluate boats of more or less the same lengths. Hope this makes your decision easier.