How much power? (displacement hull)

[Bruce46]

Is there a reasonably accurate formula for calculating the horsepower required to move a displacement hull at various speed / length ratios? I was running some numbers on a 60' displacement yacht and saw that according to a formula in Skene’s the resistance on my hull more then doubles when increasing the speed from s/l of 1.1 to 1.3 (532# vs 1330#)

[gonzo]

Skene's formula is quite accurate.

[Bruce46]

My hull has a displacement of 29.56 tons, a dwl of 56.6667', beam dwl 14.75'
Cp .62, Cb.407.
According to the chart for max hp @ dwl I need 200 hp, however, when I use the formula for efffective hp (resistance X speed X .003) 532 X 8.3 X .003=13.25 and input that into prop efficienencies (.55) I come up with 24.1 hp to move a 66000 pound boat at 8.3 kts. If this is correct the 250 hp Cummins in her belly has had a very easy life. (She tops out at just over 13 kts)

Thanks for your response
Bruce

[gonzo]

The hull speed should be about 11Kt. If you go over that, the power requirements increase enourmously.

[FAST FRED]

The first Passagemaker book has a very good table that will answer all the speed range questions.

Perhaps someone could post the pages?

FF

[Pierre R]

David Gerr's formula work pretty good for real world numbers.

Hp = Disp in lb/(10.665/S/L)^3

In the case of your boat at 8.3 knots that is around 73 hp. David's formula assumes a clean bottom and a prop efficiency of around 55%. You have to adjust if you are dirty or far off the 55% mark.

By his formula the max speed for a 250 hp Cummins is around 12.3 knots.

A quick check of another formula of his which is max theoretical hull speed puts you right at the top

Max S/L = 8.26/ D/L^.311 For your boat = 1.7 = 12.8 knots

D/L = Disp in long tones/ (LWL/100)^3 for your boat = 162

Your Cp would indicate that the designer expected you to cruise around 10 knots and burn about 7-7.5 gph depending on house load. A bit over 50% power.

My guess is the 250hp Cummins has plenty of reserve power for headseas and such at the 10 knot cruising speed. I would call it sized about right.

These formulas are also good for rough lie checkers. If the numbers are to good to be true you are probably dealing with a liar or a person who does not know the weight or design of his boat.

[terhohalme]

If the hull looks like a boat (yes Cp = 0.62 is fine) and not like a box, you need about 5 HP for each ton to reach hull speed. So if your fully loaded displacement is 30 tons, 150 HP is enough.

[FAST FRED]

"Skene’s the resistance on my hull more then doubles when increasing the speed from s/l of 1.1 to 1.3 (532# vs 1330#)"

These would be reasonable inshore cruise speeds but as slow as .9 might be even better offshore as far as MPG go.

IF willing to "go slow" the efficiency is incredible! "Hull Speed" is for sailors with free wind power, unless you love 15GPH.

FF