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Understanding the math

Posted on 26 May 2010
Written by Ted Hood

**Let's take a 45-foot DWL yacht. **

The speed would be equal to the square root of the waterline length multiplied by 1.34. This is the maximum hull speed.

For example, the square root of 45 is 6.7 and multiplied by 1.34 equals 8.9 knots maximum speed, with a very efficient cruising speed of 7.5 to 8 knots. This measurement would be based on approximately 450 hp running at an efficient rpm, resulting in very fuel-efficient cruising at 7.5 knots.

A lighter-weight, higher-speed yacht could be calculated with the square route of the waterline length multiplied by 3 or 4, which would be much faster but would need more horsepower. The speed of a heavy displacement boat is related to the distance between the crest of the bow wave and the crest of the stern wave. The greater the distance between them, the faster a heavy displacement hull will go.

Our 52 Long Range Fast Explorer (above) is like a trawler, but it can get up on plane because of bigger engines, whereas a real ocean trawler is very efficient at 2 knots under maximum speed. For example, a 60-foot boat weighing 200,000 pounds is very efficient at 8 to 9 knots with twin 260-hp engines, and the maximum speed would be about 10 knots (square root of DWL times 1.34). However, we have found that by using a special bulbous bow shape, having different lines aft to the transom, and twin screws with skegs spaced far apart increases speed up to 18 percent, or 11.8 knots.

Heavy displacement ships are very efficient at speeds approximately 20 percent less than their estimated maximum speed.

**See related stories:**

- Cracking the trawler code

- Stabilized or not?

This article originally appeared in the June 2010 issue.