In "Voyaging Under Power", Beebe presents a method of estimating the range of a displacement boat. The book includes tables that can be used to look up two "factors" related to the boat's displacement (F1) and speed (F2). These values, when multiplied, give an estimate of the horsepower required to move a boat of normal proportions (presumably a monohull with "typical" prismatic and other ratios) in calm conditions. Once the horsepower is known, the specific fuel consumption of the engine can be used to get fuel consumption in gal/hr, which in turn can be used to compute the number of hours the boat can run until it's tanks are dry. Multiplying these hours by the boat's speed gives the desired range estimate. The first factor, F1, can be computed directly from the boat's displacement. Find the displacement in long tons (displacement in pounds divided by 2240) and raise this to the 7/6 power. (D^1.16667) For example, if displacement is 32,670 lbs or 14.6 long tons, F1 would be 22.80. The second factor, F2, can be approximated by raising the S/L to the power 47.67 and dividing the result by 77.28 (SL^47.67/77.28). For example, if the boat has waterline length of 36.5 feet, then 6.5 kts would be S/L of 1.08, and F2 would be 0.83. This formula is a bit more conservative than Beebe's tables for S/L values below 1.0, and bit more optimistic for S/Ls above 1.2. The product of F1 and F2 is the horsepower required. In this case, the 32,670 lb boat with a 36.5 foot waterline moving at 6.5 kts requires 22.80*0.83 = 18.9 hp. Specific fuel consumption numbers vary from engine to engine, but are usually in the range 15 to 20 hp per gal/hr. Choosing a typical figure of 18 gives our boat a fuel burn rate of 18.9/18 = 1.05 gal/hr. If the boat carries 600 gallons of fuel, this will run the engine for 600/1.05 = 573 hrs. Maintaining a speed of 6.5 kts for 573 hrs will take you 6.5*573 = 3,724 nm. For real voyage planning, several factors need to be kept in mind. First, the actual weight of the vessel changes, rising as she is loaded up with fuel, water, food, spares, people, etc., and falling as fuel is burned off and food and water are consumed (hopefully not by losing people overboard during the voyage, however!) The hp required to push the boat when she departs fully loaded will be more than that required when she arrives almost empty after a long passage. For range estimating, an average value should be used. This figure may be much larger than that given by the manufacturer as the "design displacement". For example, the Nordhavn 46 has a design displacement of around 48,000 lbs, but Jim Sink has indicated that Salvation II was probably over 60,000 lbs when loaded for a long passage. As fuel weighs about 7.35 lbs/gal, and the Nordhavn carries 1,100 gal (or 8,085 lbs) a reasonable displacement for range calculation might be 56,000 lbs in the case of Salvation II. As a side note, waterline length also varies with loading, generally lengthening as the overhangs are pushed down into the water. In general, this causes only a slight offset effect when compared to the effect of the change in displacement. Second, a fuel reserve should be planned. Many use a figure of 10 to 15%, "just in case." In the example above, you might use 600*0.85 = 510 gals to allow a 15% reserve. This would give a running time of 485.7 hrs at 6.5 kts = 3,157 nm. Third, weather, currents and other factors may cause these "calm water" estimates to be overly optimistic for real ocean crossings. In the case of Salvation II's circumnavigation, actual observed range was between 1.3 and 4.0 times LESS than the Beebe predictions for the speed used. In fact, the range based on observed data was about the same for all ocean passages (2,500 to 3,000 nm) but where heavy weather was a factor, speed was reduced even though engine hp remained about the same. For example: Salvation II Actual Beebe Passage nm hrs gal kts gph nm/g S/L hp range hp range ratio -------------------------------------------------------------------------------- ------------- Majuro to Johnston 1,280 264 577 4.8 2.19 2.22 0.78 37.7 2,440 10.6 8,660 3.5 Johnston to HNL 720 137 333 5.3 2.43 2.16 0.85 41.9 2,378 15.3 6,533 2.7 HNL to Dana Point 2,272 354 805 6.4 2.27 2.82 1.03 39.2 3,105 30.8 3,958 1.3 All 23 ocean legs 16,997 2,996 7,153 6.0 2.39 2.38 0.97 41.2 2,614 24.0 4,748 1.7 The nm, hrs and gal data came from a Lugger promo piece. The gph, nm/g, S/L, actual hp and actual range numbers were calculated from them assuming a displacement of 60,000 lbs, LWL of 38.5 feet, specific fuel consumption of 17.3 hp/gal/hr and 1,100 gallon fuel capacity. The Beebe hp and Beebe range numbers were computed from the same data for comparison. The "ratio" given is the ratio between the range Beebe's method predicts and the actual range for the given speed. In talking with Jim Sink, it seems that the smallest ratios correspond to fine weather passages, and the larger ratios correspond to heavy weather passages. It should also be noted that factors such as propeller choice (which are not included in Beebe's analysis) can make a big difference in the real world. Salvation II showed a 28% improvement in milage when their prop was changed from a 4 blade 30x18 to a 3 blade 30x24. Of course bottom fouling, paravane deployment, use of auxiliary sails and other factors also can make a big difference. This highlights the importance of keeping a "how goes it" graph when making passages that will push your boat's range to anywhere near it's limits. I am very interested in collecting more real world data about trawler voyages to get a better handle on this "reality factor". Michael Kasten mailto:redpath@olympus.net has suggested an excellent format for such data in his 11 May post "Re: Defining Trawler Range". I plan to contribute some real world data once I get Boojum into the water, and I hope that some of the voyagers on the list will pass along data from their adventures, too. Michael and I will be happy to post anything we learn from this analysis. Charles ps -- There are many other ways of predicting power and range besides Beebe. Gerr, Holtrop, Van Ortmeerson, Skene, Kinney, Phillips-Birt and the Delft Series (I, II, and III) all offer sightly different perspectives, and take into account different aspects of hull design. Beebe seems to be a relatively conservative (and very easy to calculate) method, which makes it particularly attractive. I have comparative data on many of these methods computed for the Boojum design, and would be happy to make it available to any who are interested, perhaps through adding it to the Boojum web pages. I also have a more detailed spreadsheet on Salvation II's voyages (from which the table above was excerpted) that I could make available. __________________________ Charles Vollum 2373 NW 185th #505 Hillsboro, OR 97124 USA mailto:moana@xsw.com http://xsw.com/Boojum - a 25' trailerable all ocean trawler! (503) 827-4930 work (503) 227-7873 fax