D = 0.00339 * Cd * V^2 * S

There seems to be continued interest in defining Trawler range. As I have said before, this is a very complicated issue and some of the most important issues have not been even touched upon. What follows might get a little rambling, but I'll try to cover a few of the issues. 1. Beebe Speed/Range Table Michael Kasten has provided information for equations for Beebe's F1 and F2 factors. He got the F2 information from Charles Vollum. With those factors in hand, it was possible to write a Windows-95(98) program which will compute the results with greater accuracy than can be obtained trying to read those factors from grafts in the texts. It has been pointed out that the results of this procedure are more conservative that would be obtained from the grafts themselves. The program allows the user to select the percentage of reserve capacity as well the gallons-per-hour-per-horse-power of the main engine. In addition, the user can specify an amount of auxiliary fuel burned (generator for example). Along with the basic data, the user may compute the table using either S/L or Knots as input. Printing capability is provided. The computer computes the results to about 16 digits, which is much greater accuracy than can be expected in practice. If you would like a copy of the program, send me a private E- Mail. Be sure the message has your E-Mail address and not the List's E-Mail address. I'll send it to you in zip format. 1.1 Computing the Beebe formula with the improved accuracy gives some very interesting comparisons to the actual sea-trial run on my KK-42. They are as follows: Long Tons 17.16 LWL 39.16 Fuel capacity 700 gals. Reserve Fuel 10% F1 28.44 ---Range--- S/L Knots F2 Beebe Test Diff Test/Beebe 1.12 7.0 0.98 2649 3250 601 1.23 1.28 8.0 1.82 1623 2150 527 1.42 1.34 8.34 2.29 1349 1800 451 1.33 1.44 9.0 3.38 991 1450 459 1.46 1.49 9.3 4.10 851 1300 449 1.53 These are truly significant differences and display a great difference in the actual results from the calculated ones. There is no data about the sea state or wind when the sea trial was done, but knowing what I do about Jim Krogen, I feel sure it was done in, or corrected for, flat water. 2. Engine Performance All of the planning formulas use some fixed specific fuel consumption for the engine at all speeds and assumed propeller efficiency. Beebe uses 0.06 gal/hp/hr. He does not speak about propeller efficiency. In actual practice the specific fuel consumption not only changes with RPM, but also changes with load at any RPM. 2.1 All diesel engines do not respond alike to load changes and, contrary to common belief, the load on a boat engine changes constantly. Those load changes are caused by wave, wind, and current and can be considerable as well as sudden. on the vessel can be calculated by the equation D = 0.00339 * Cd * V^2 * S where: D : Drag on the boat in pounds Cd : Coefficient of drag (usually 1.0 for Trawlers) V : Velocity of wind in knots S : Sq. Ft. facing the wind A 30-knot wind on the nose of a vessel with 200 sq. ft. exposed to the wind would produce a drag of 610 pounds, and a 50-knot wind would produce a drag of 1695 pounds. The 1695 pounds is more than half the force my boat can produce. When making way against a 2-knot current, a vessel making 7-knots SOG would burn at least as much fuel as it would making 9-knots in still water. In the Krogen test that is a difference in range from 3250 kn to 1450 kn. THAT'S LESS THAN HALF! When the vessel encounters waves, the load changes materially and quickly. When the vessel must go up a swell, it's just like a truck going up a hill. The minimum increase in load is the weight of the boat times the percentage of slope. On AfterSail, a swell with a 6-percent slope would add at least 39,000 * 0.06 = 2340 lbs. of load to the prop and engine suddenly. When it comes off the other side, the load is suddenly removed. When the vessel encounters chop spaced close together, it receives sudden loads as the hull feels the chop. I have no way to estimate this force, but it makes the load on the engine vary rapidly. With DGPS, you can actually see this SOG change in this condition, even as the knot-meter stays the same. Engine curves not only show the engine power and specific fuel consumption at different RPM, but how the engine responds to load changes. The curve that gives this information is called the torque curve. When the engine comes under additional load, the RPM will be inclined to fall. The shape of the torque curve at the RPM when the additional load is applied will tell how the engine responds to the increased load. 2.1 Non Turbo-Charged Engines In non turbo-charged engines, this curve is generally a very gentle curve with its high point somewhere near the middle of the RPM range. When the extra load is applied, the RPM begins to fall and the torque does not increase. Because the torque didn't rise, the performance of the engine will suffer. This is often referred to as lugging. It is mitigated to some extent if the engine is not operating at full power -- as is the case much of the time in our Trawlers. 2.2 Turbo-Charged Engines By use of a turbo-charger, the manufacturer can design what is called a "High-Torque-Rise" engine. In this engine, the torque curve rises to some high point, generally just below best specific fuel consumption, then drops sharply to maximum RPM. If such an engine is operating in the proper RPM range, when the sudden load occurs, the RPM begins to be reduced, but the torque rises sharply. This allows the engine to keep the RPM up and not lug the engine while absorbing the sudden load. It also provides for better fuel economy in this situation than a non-high-torque- rise engine. This benefit of a turbo-charger will not be obtained if the engine does not operate at the optimum RPM. Something to think about when operating at less than designed cruising RPM. 2.3 Effect of Engine Selection All of this section is intended to show that not only the type of engine selected, but how it is matched to the vessel will have a profound effect on the fuel performance of the engine. I don't know of any method to evaluate engine performance on the range of a Trawler except that generally, a more efficient engine will provide greater range than a less efficient engine. 3. Propeller Not only does the selection of the engine and its operating range affect fuel range, but how it and the propeller relate to the boat has a marked effect on range. Those interested in this subject should read, "Propeller Handbook" by Dave Gerr. None of the general range formula take differences in propeller efficiency into account. 4. Set and Drift Set and Drift is used to describe the net external forces which cause the vessel to deviate from its intended track. Until the availability of DGPS, it was almost impossible to steer a straight course along the intended track. Straying from the intended track constantly by even a small amount, materially increases the distance traveled along the track. The effect is to reduce effective range by the error. Computation of set by a current is simple in theory, but almost never achieved in practice because the velocity of the current is almost constantly changing and the speed of the boat is constantly changing, and because of steering errors. Computation of drift caused by wind is almost impossible to even estimate. It causes the course to be run in a series of long arcs as the error is discovered and corrected. 4.1 Steering Errors Even in still water, small steering errors in long tracks give rise to what amounts to large steering errors. In rough waters, the errors are almost always large. 4.2 Help With Set and Drift and Steering Errors Perhaps one of the best benefits of DGPS is its ability to automatically correct not only for set and drift, but for steering errors as well. Adding electronic charting to DGPS makes it possible to steer an almost perfect track and to see any errors on a real chart. On my month long cruise, I kept a careful eye on this, and I never observed the track with more than a 0.02 nm cross-track error. 5. Summing It Up Taking just the things listed above into account, it is obvious to me why estimating the range of Trawlers is such a difficult task. It is obvious that no single formula can do more than get you into the ball park at best, and that actual results may be greatly different. Those differences will certainly show up as a result of the architect's skill in designing the hull, and the suitability and efficiency of the machinery. Beyond that, great differences will show up as a result of the natural forces present at the time. After thinking about all of these matters, it seems to me that a very conservative method is necessary for range calculations because it is almost impossible to define all that will reduce the actual range. After that, individual tests should be conducted to get some handle on how the particular boat performs. Manufacturers who provide actual sea-trial results provide a very valuable service, and results of such tests should always be requested by the owner. The Krogen test results show that a KK-42 is much more efficient than the Beebe formula indicates, but putting absolute faith in the ranges indicated by the tests would not be prudent. It is most likely that the Beebe formula has been so well received because it is conservative, and mariners were able to rejoice that they got to the end of the voyage with more fuel left than the Beebe formula indicated instead of lamenting the fact that they were out of fuel 500 miles away from safe harbor. 6. Beebe Curve on Hand-Held Calculator The difficult things about the Beebe curve is calculating F1 and F2. The following are from Michael Kasten and Charles Vollum. F1 = Long Tons ^(7/6) F2 = 47.67^S/L / 77.28 Where S/L = Knots / LWL^0.5 If there is interest by those who are not friendly with exponents on hand-held calculators but who wish to compute the Beebe curve by calculator, I'll post detailed instructions in a later post. CaptnWil 40 Pier Pointe New Bern NC 28562 (252) 636-3601 captnwil@coastalnet.com