In a message dated 10/26/06 12:01:10 AM, trawlers-and-trawlering-request@lists.samurai.com writes: > > > > I have applied Keith's Formula to an excell SS. Any thoughts on the > > validity of Keith's to a powercat? Coefficients? > > I am unfamiliar with this formula, and I generally suspect that catamaran > hulls are different enough from monohulls that great modifications would > need to be made to it to get realistic predictions. > > Keith's formula for relating speed, power, length, and displacement is described on p. 105 of "Skene's Elements of Yacht Design, 8th ed." revised by Francis S. Kinney. It is published by Dodd, Mead & Co., New York, ISBN: 0-396-06582-1. The book also has a number of other techniques for calculating the power requirements of boats and is a compendium of material useful to yacht designers. I use the following formula: KTS = (LWL)^.5 x C x ((HP x 1000)/D)^.333 This is essentially Keith's formula restated for easy computer calculation. LWL is measured in feet. D is measured in lbs. C is a scaling constant which varies between 1.1 and 1.5 and must be determined by observation or experimentation with a specific type of boat. I use a constant of 1.18 for a typical displacement trawler hull. This is based on experience, not on theory. Lower values of the constant imply a more pessimistic outlook and prescribe more power for a given speed. Values above 1.2 tend to be too optimistic. The presence of arbitrary constants in an equation are a serious fudge factor. I was once told by a professor of mathematics that if you have two arbitrary constants in an equation, you can make the resulting curve look like a puppy dog, and if you throw in a third arbitrary constant, you can make it wag its tail. What the scaling constant in Keith's formula does is correct for difference in hull shape (prismatic coefficient, etc), hull condition (squeaky clean or barnacle covered), sea state (mill pond or "real world"), measurement units (statute miles, knots, kilometers, lbs., kilograms, tons, etc.), and propeller efficiency (usually assumed to be about 50%). All the basic formula does is provide the shape of the curve of increasing power requirement with speed for a hull of given length and displacement. The scaling constant changes the axes of the graph to meaningful units. The best way to use Keith's formula, or any similar formula, is to make exact measurements of a boat's power requirements at a specific speed and displacement. Then calculate the proper constant. Using this constant, power requirements (and fuel consumption) can then be estimated for that same hull for a range of speeds and displacements. You can generalize to other boats of the same general type with less accurate results. It would not do, however, to use Keith's formula to compare displacement, semi-displacement, and planing boats. Keith's formula makes no provision for the beam or shape of a hull. That is all handled by appropriate changes to the scaling constant. I assume that the formula would be applicable for catamarans or trimarans at displacement speeds with the right scaling constant but that would have to be determined by experiment. You can't accept any of the maritime formulas on blind faith but Keith's formula seems to be one of the more reliable ones for approximating power required to move a displacement hull. It considers LWL, displacement, speed, and power. Inherent in the calculations are assumptions made about propeller efficiency, specific hull configuration, units of measurement, and sea conditions. These are included in the scaling constant. Generally the mathematical formulas give results which are in error by no more than 10% when compared with actual in-water trials. Nothing beats actual tank tests or full scale prototypes, but using a computer is a lot cheaper. Larry Z