HANDS-ON APPROACH TO PREDICTING THE PRELIMINARY POWER REQUIREMENT OF SMALL BOATS

Abstract

A method of quickly predicting the power requirement in the preliminary design stage of hard-chine deep-V (inboard, outboard) boats and round-bilge boats is presented here together with worked out examples.

Introduction

Small-boat designers are often faced with the problem of deciding the power required to produce a given speed in the preliminary stage of design. The answer to estimating with a fair degree of accuracy the horsepower required in the very preliminary stages of design when nothing but length, speed and displacement of a specific type of boat are known, lies in making use of your own database of boats for which speed trials are available and working out the power requirement for the new boat.

Method

Two formulae that express the relationships between, speed, power and displacement come to mind - Crouch's formula and Keith's formula, mentioned in Skene's Elements of Yacht Design. Both methods make use of a constant C, where C is derived from the trials of existing boats of the same type.

Crouch's Formula:

In the formula above, HP is the brake horsepower, taken as 85% of the full-rated HP, speed is in statute miles per hour, while D is the displacement or weight of the boat in pounds, and C is a constant which varies for size and type of boat, with the suggested value lying between 180 and 200, according to the type of boat.

Keith's Formula:

Note that Keith’s Formula includes the length parameter L, where L is the designed waterline length of the boat at rest, in feet. The constant C suggested for Keith's formula is a value between 1.3 to 1.5 according to the type of boat. The other parameters are similar to those in Crouch's formula.

With a view to making use of data more readily available, while at the same time preserving the nature of the well-tried and used formulae, the terms in Keith’s formula were modified as below:


where,

Vk : Speed in knots

K: Kundu constant (so named in fond remembrance of Prof. Kundu)

L: Length overall in feet

HP: Installed brake horsepower

D: Displacement in pounds

From the above formula, K can be found from trial data knowing the speed, installed horsepower and length overall.

By redefining the parameters this way, data that can be more easily collected can be made use of, although a slight degree of error may be expected in using length overall rather than length of the waterline at rest or chine length in case of hard-chine boats. However, the increase in the number of data for determining the constant K is expected to offset the small error that may arise from assuming L as the overall length.

By plotting the parameters above in various ways, it was found that a plot of the speed length ratio (V/sq. root L) vs the Kundu constant (K) (see Fig. 1) mapped into a straight line for a set of trial data of round-bilge hulls. The same exercise was repeated for a different set of hard-chine deep-V boats, which again gave similar results. The line for each data set was defined by a linear equation.

Round-bilge boats

The figures in the following pages were plotted using trial data of 120 round-bilge boats built in Japan in the eighties. The ranges of parameters are given in Fig. 2, 3, and 4, and a summary of the range of parameters at the end of the figures.
 

Fig. 1 Preliminary power prediction chart for round-bilge boats

　

Fig. 2 Speed-length ratio versus length overall in feet

　

　

　

Fig. 3 Displacement in thousands of pounds versus speed-length ratio

Fig. 4 BHP versus speed in knots

　

Summary of range of parameters for round-bilge boats

19 > LOA (feet) > 123

0.8 > V/sq.root LOA> 7.8

2090 > Displacement (lbs) > 574800

10 > BHP > 3000

Estimation of Power - Calculation Example

Flying Fish, a round-bilge boat with a length overall of 39 feet fitted with an engine of 140 HP develops a trial speed of 23.2 knots at a displacement of 6116 lbs

The steps of the calculation are as follows:

Check that the parameters fall within the ranges defined. In this case, they do.

    a. Speed-length ratio = V/( L)^(1/2)
                                   = 3.715
    b. Kundu coefficient K = 0.1854 * 3.71 + 0.6573
                                 = 1.345
    c. Estimated HP = [(Vk/sq,root L)/K]3 * D/1000
                        = [3.715/1.345]3 * 6116/1000
                        = 129 (actually installed HP = 140)
          e. Error in prediction = (140 - 129)*100/140
                                        = 7.85%
 

Hard-chine planing boats with inboard engines

Trial data of 35 boats with inboard engines were used to plot figures 5 to 8 in the following pages, similar to the figures for round-bilge boats.
 

Fig. 5 Power prediction chart for hard-chine planing boats with inboard engines
 

　

Fig. 6 Speed coefficient versus length overall in feet
 

 

Fig. 7 Speed-length ratio versus displacement in pounds

Fig. 8 Length overall versus displacement

Summary of range of parameters for hard-chine planing boats with inboard engines

16 > LOA (feet) > 37

5.1 > V/sq. root LOA > 9.5

1330 > Displacement (lbs) > 7000

45 > BHP > 650
 
 

Estimation of Power - Calculation example

A hard-chine boat with an overall length of 25.5 feet, fitted with an inboard engine of 325 HP develops a trial speed of 41.9 knots at a displacement of 4884 pounds.

  1. The particulars given above lie within the range of parameters.
  2. V/sq.root LOA = 41.9/sq.root 25.5

    3. = 8.3
  3. Kundu constant = 0.1069x + 1.1862

    4. = 0.0169 * 8.3 + 1.1862
    = 2.073
  4. HP = [(Vk/sq. root LOA)/K]3 x D/1000

    5. = [8.3/2.073]3 x 4884/1000
    = 313 HP
  5. Error in prediction = (325-313)*100/325

    6. = 3.7%
　

Hard-chine planing boats with outboard motors

Trial data of 15 boats with outboard motors were used to plot figures 9 to 12 in the following pages, similar to the figures above. An example of power prediction in the preliminary design stage is also illustrated

Fig. 9 Preliminary power prediction chart for hard-chine planing boats with OB motors
 

Fig. 10 Speed-length ratio versus length overall in feet

　

Fig. 11 Speed-length ratio versus displacement in pounds

　

　

Fig. 12 BHP versus speed in knots

　

Summary of range of parameters for hard-chine planing boats with outboard motors

　

6.8 > V/sq.root LOA > 13

9.8 > LOA (feet) > 18

310 > Displacement (lbs) > 1750

14 > BHP > 100

　

Estimation of Power - Calculation example

1. A hard-chine planing boat with an overall length of 14.33 feet, fitted with an outboard motor of 50 HP (Mercury 50 EL) develops a speed of 28.25 knots at a displacement of 1075 pounds (the above trial data taken from Boat House Bulletin, Mercury Outboards).

　

  1. The first step in the power estimation is to check whether the particulars (L, V, displacement) of the boat fall within the range of parameters (Fig. 10 to Fig. 12) or the summary of range of parameters for hard-chine boats with outboard motors. For this boat, the particulars do fall within the ranges.
  2. Next, we find the speed-length ratio.

    3. Speed-length ratio = V/sq. root LOA = 28.25/sq. root 14.33
    = 7.46
  3. Next, we find the Kundu coefficient K, at a speed-length ratio of 7.46 from Fig. 9, or alternately from the equation to the straight line y=0.1069x + 1.1862, where x is the speed-length ratio
y = 0.2036*7.46 + 0.4598

= 1.978 (which is the Kundu constant K)

d. Transposing the modified Keith's formula,

we get: HP = [(Vk/sq. root LOA)/K]3 x D/1000

= [7.46/1.978]3 x 1075/1000

= 57.6

The estimation agrees well with the installed 50 HP.

Diagnosing the performance of an existing boat

The preliminary power prediction charts (Fig. 1, Fig. 5 and Fig. 9) may also be used to roughly assess the performance of existing round-bilge boats and hard-chine planing boats (inboard engines, outboard motors).

First confirm that the particulars of the boat (L, V, displacement, BHP) fall within the range of parameters given in the figures or in the summary of parameters. Next, calculate the trial speed attained, and find the speed-length ratio V/sq. root L. Depending on type of boat, calculate the Kundu constant K, given by the equation y=ax + b, where x is the speed-length ratio and y is the Kundu constant.

Plot the point on the power prediction chart. If the point lies well below the straight line, you have a performance problem. It would be advisable to check for problems such as whether the propeller has been properly selected, or whether the LCG position is appropriate.
　

Constraints

  1. The above charts may work for you only if the particulars of the boat for which you are performing the estimation lie within the ranges of parameters given above.
  2. The method should be used only for a preliminary estimation of power for conventional types of boats. Detailed power estimates should be carried out after the lines plan of the boat is finalized.
  3. In case of planing boats, particular care needs to be exercised because the method above assumes that the LCG of the boat is located at approximately the optimum position (around 35% of the length from the aft of the boat).

Conclusion

The accuracy of preliminary power prediction can be significantly improved if the quantity of reliable trial data is increased. This essentially calls for boat designers in the industry getting together, putting together a voluminous database and sharing the fruits of the cooperative effort. For comments/suggestions/criticism, send e-mail to guru@msi.biglobe.ne.jp

Referrences

  1. Skene’s Elements of Yacht Design, Eighth Edition, Dodd, Mead and Co., New York, ISBN 0-396-07968-7
  2. High Speed Boats (in Japanese), Seiichi Niwa, 4th Edition, 1979 (ISBN not given)
  3. Boat House Bulletins, Mercury Outboards, Trial Data Sheets, No. 82-80, No. 82-79
  4. Wyman's Formula, Professional Boatbuilder, Number 54, Aug./September 1998
Updated: October 25, 1998