Irving Dunn writes: I have been fooling around with calculations to get the shaft power required for a particular boat. Most methods use the inputs of water-line length and weight. In the book, Propeller Handbook, by Dave Gerr, Ch 2 outlines a method involving displacement ratio to get the speed-length ratio and then using this to get the lb per hp required. What makes me wonder about the method is that the results show weight to have hardly any influence on the resulting required hp. I have programed the few equations using a simple software available on the web, so that I can get curves of hp versus length for various values of weight. I wonder if any of you have experience with such calculations, in other words what method would you use to get the power needed to reach hull speed? REPLY At a first approximation, the power required to move a normally shaped hull through the water is a function of three variables, skin friction, displacement, and length. Skin friction is the major component of drag at low speeds below a S/L ratio of .8 or .9. It rises as the square of the speed. Above a S/L ratio of .9 form resistance or wave making resistance is the greatest component of drag. It increases at nearly the cube of the speed. Both of these components swamp the drag caused by displacement which increases directly proportionate to the weight of the hull. The standard boat designer's rule of thumb is that a displacement hull requires 1 horsepower per 500 pounds of displacement to achieve hull speed. Actually the boat can achieve hull speed with less horsepower but the recommendation is slightly inflated to take care of moderate fouling and other contingencies. If you want to be more mathematical, Keith's formula is the most reliable simple equation for relating speed, power, length, and displacement. It 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. The following is a computer friendly restatement of Keith's formula: KTS = (LWL)^.5 x C x ((HP x 1000)/D)^.333 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. What the scaling constant in Keith's formula does is correct for difference in hull shape (prismatic coefficient, etc), hull condition (squeeky 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. Generally, when used with displacement boats, the formula gives results which are in error by no more than 10% when compared with actual in-water trials. The conclusion that displacement is one of the lesser components of drag for displacement boats is correct. Not so for planing or semi-displacement boats, however, where the weight has to be lifted out of the water by engine power. Here are some actual figures based on my Willard trawler. The boat has a LWL of 27.5' and a lightly loaded displacement of 15,000 lbs. It takes 13.7 horsepower to reach a cruising speed of 6 knots (S/L ratio of 1.15). This figure is quite accurate based on fuel consumption figures for long cruises. Adding another 2000 pounds of load to the displacement, i.e. tanks full and loaded for a long trip, increases the required power to 15.5 horsepower for the same cruising speed. This is a 13% increase in power for a 13% increase in displacement. Increasing the cruising speed to the boat's hull speed of 7 knots (S/L ratio of 1.35) at a 15,000 lb. displacement requires 21.7 hp. With a 17,000 lb. displacement, the power required is 24.6 hp. Simply increasing the cruising speed by one knot (17%) requires a 58% increase in engine power. Should I attempt to reach 8 knots with a 15,000 lb. displacement, the required power would be 32.5 hp., a 132% power increase for a 33% speed increase. Larry Z ************************************** See what's new at http://www.aol.com