The Comfortable Pocket Yacht 
|
|
|
Flicka Sailing
|
The calculations below come mostly from Douglas Little's book - Electric Boats - The Handbook of Clean, Quiet Boating. They are duplicated here to show how I convinced myself that an electric motor was worth a try for a small sailboat. The major factor not taken into consideration with these formulas is wind resistance and unusual hull shape issues. These factors would have to be determined on each boat. My determination to try electric propulsion was an experiment. After all, I had no time tables to meet and could afford to take it slow and easy. In addition, I felt that it would really force me to learn to make maximum use of sail power and thus be a better sailor. I must emphasize that this approach is not for everyone and under many conditions would be totally impractical. This is especially true where the boat must travel several miles of narrow channel or river every time out in order to arrive at open water suitable for sailing. For my purposes, I would also consider the option of a small gasoline powered generator for those few times that I would be traveling to an area that required motor power for a significant period. Assumptions and Examples For all of these calculations I will use a Com-Pac 19 as the vessel. The gasoline outboard motor examples will use a Honda 5 HP motor and the electric motor examples will use the data for a Motorguide T47. The Com-Pac 19 has an empty displacement of 2,000 pounds and I will assume an additional displacement of 500 pounds for crew, supplies and equipment. The beam for this vessel is 7 feet and the length at the water line (LWL) is 16.5 feet. A 5 Horsepower Honda Outboard Motor develops it's rated output at 5,000 rpm and uses a 2.1:1 gear reduction drive system. The standard propeller for this motor is 7 7/8 X 7 1/2. A Motorguide T47 motor draws 50 amps at 12.8 volts and produces 47 pounds of static thrust at 1,100 rpm. One Horsepower is equal to 750 watts An electric motor is 95% efficient One Nautical Mile = 6,076.1 feet = 72,913.2 inches Hull Speed Formula Determines the theoretical boat speed for a displacement hull shape. This formula assumes that there is no current or wind resistance and the hull is clean and free of objects that could cause excess drag. Hull Speed = (1.34) * (LWL)0.5 = (1.34) * (4.062) = 5.4 knots = (1.34) * (4.062) = 5.4 knots Please note that the above calculation uses a notation of LWL to the POWER of 0.5. This is the same as the square root of the quantity. Horsepower Required for Hull Speed Determines the theoretical horsepower required for a displacement hull shape to reach hull speed. This formula assumes that there is no current or wind resistance and the hull is clean and free of objects that could cause excess drag. Horsepower = Displacement / ((150)2 / (Hull Speed)2) = 2500 / (22500 / 29.16) = 3.24 As can be seen from this equation doubling the speed requires 4 times the horsepower so, if you set the speed down one half of hull speed (2.7 knots), the energy required will be reduced to just a little more than 3/4 horsepower. For my purposes, this tradeoff in speed would be well worth the experiment with an electric motor. Maximum Boat Speed for a Propeller As a propeller turns, it's pitch determines how far it travels through the water. No propeller is 100% efficient so that in reality it "slips" by moving water aside rather than straight backward. For a planing hull shape, this propeller slip can be as low as 10%. For a displacement hull shape with a high speed propeller, this slip is usually around 45%. This means that the maximum vessel speed is a function of the shaft speed in revolutions per minute, the pitch of the propeller, and the amount of propeller slip. The Honda outboard motor described above will generate 5 HP at the engine shaft at 5,000 rpm which results in 2381 rpm at the propeller. Assuming no propeller slip, the maximum boat speed will be: Boat Speed = (RPM * 60 * Pitch) / 72913.2 = (2381* 60 * 7.5) / 72913.2 = 14.7 Knots If the propeller slip is 45% then the propeller's forward motion is 55% utilized so the maximum speed for this combination would be: 14.7 * 0.55 = 8.1 knots However, since the maximum boat speed is 5.4 knots, the propeller will function with an inefficient 63% slip. As this shows, the pitch of the propeller must be decreased to between 5 and 5.5 inches to achieve a more normal propeller slip of 45%. In this case, the propeller diameter must also be increased in order to prevent the motor from speeding up beyond 5,000 rpm. As a general rule, if you purchase a typical outboard motor for use on a sailboat, you should instruct the dealer to provide the lowest pitch and largest diameter propeller possible consistent with the motor's designed operating speed and horsepower. The "standard" propellers provided with these motors will just not be efficient with a small sailboat. Either you will be running at 1/2 throttle and therefore never use all the available horsepower, or you will be running at full throttle and wasting the energy in propeller slip. Boat Speed with an Electric Trolling Motor Most modern 12 volt trolling motors draw one amp of current for every pound of thrust. At an assumed electrical efficiency of 95%, the Motorguide T47 motor (rated at 47 pounds of thrust) will consume (47 * 12.8) = 601.6 watts and deliver 601.6 * .95 = 571.5 watts of useful work. Since one horsepower is equivalent to 750 watts, this amounts to approximately 3/4 horsepower at the propeller shaft. The "Weed Free" propeller designs may sacrifice some of this efficiency. I did contact the manufacturer for additional specifications on this design. They confirmed that the T47 motor is designed to operate at a maximum of 1,400 rpm and produce the rated thrust with the two bladed propeller. They did caution me that the motor was not designed to function as the primary propulsion for a vessel. The motor was designed to operate at it's top speed for only a few minutes. The intent was to operate this motor for longer time periods only at one of it's lower speed settings. We must first calculate the Speed to Length ratio for the vessel: S/L = 10.655 / (Displacement/Shaft Horsepower)0.33 Please note that the above calculation uses a notation of (Displacement/Shaft Horsepower) to the POWER of 0.33. This is the same as the cube root of the quantity. For the Com-Pac 19 with it's 2,500 pounds of displacement (boat, crew, and equipment), this means an S/L of 0.73. Knowing the S/L ratio, we can calculate the projected speed: Boat Speed = (S/L) * (LWL)0.5 = 0.73 * 4.06 = 2.96 knots Please note that the above calculation uses a notation of LWL to the POWER of 0.5. This is the same as the square root of the quantity. Of course, this assumes a clean hull without wind or current resistance. As can be seen, this different method of calculation results in almost the same answer as the 1/2 hull speed requirement calculated above. Sail Area To Displacement Ratio - SA/D Used for boat comparisons. High numbers are associated with racing boats. The calculation is Sail Area in square feet divided by displacement in cubic feet to the 2/3 power. The cubic feet of displacement is calculated as the equivalent of sea water. Therefore there is one cubic foot of displacement for every 64 pounds of cruising weight. SA/D = Sail Area / (Displacement)2/3
Displacement to Length Ratio - D/L Used for boat comparisons. Low numbers are associated with racing boats. The calculation is Displacement in long tons (2240 pounds) divided by the quantity 0.01 times the length of the waterline cubed. D/L = (Displacement) / (0.01 * LWL)3
Capsize Screening Formula Used for screen a boat design for offshore use. Please note that this formula is very controversial and should be used as a screening test only. Boats with capsize ratios below two are said to be more suitable for offshore use. The calculation is Beam dimension in feet divided by the cube root of Displacement expressed in cubic feet of sea water (64 pounds per cubic foot). Capsize Ratio = Beam / (Displacement / 64)0.333
This page was last updated: 03/20/01 07:59:27 AM |
|
Copyright © 1999-2002 Jobst Vandrey |