LB ratio & powercat fuel efficiency

Let's say a powercat has 12:1 L:B ratio, and with a certain weight and prismatic and design and engines...and... it makes for a certain fuel efficiency at 12-15knots (which is higher than "hull speed" (1.34x)).

Would a higher L:B improve the fuel efficiency (almost certainly yes?), and by how much (more pertinent question!).
I'll specify that the BOA doesn't change, which I understand would effect wave-making under the bridgedeck. I hope specifying higher speed (say 15kn) would negate this a little, as the wavemaking difference of 12:1 at 15kn at BOA=x and 15:1 at 15kn at BOA=x is probably not enormous(?).

So assuming weight, engines, and everything else including that the general hull shape could be kept the same, is it likely there's a linear relationship between L:B and fuel efficiency?
Something like: a 14:1 would be 15% more efficient at 10+knots compared to 12:1.

 

Well, that is a leading question.

A higher L/B ratio reduces residuary resistance.
But, if the same displacement, then the draft will be greater = greater WSA = more frictional drag.

However, if one assumes the displacement has not changed, then the L/D ratio remains unchanged.
Therefore the resistance, at the hump, will be pretty much the same...with only a slight difference owing to the L/B ratio difference.
The entire resistance will varying between the two variations of L/B, depending upon the speed range you're looking at, but, there will not be a significant difference that you appear to seek.

Thus, like most things in design... it depends!

 

What size of boat is involved here ?

 

Following on from Ad Hoc's excellent comments above.

Re your definition of 'hull speed', that figure of 1.34 (times the square root of the WL length) quoted is for a 'typical' monohull - which might have a 'typical' L/B ratio of approx 3.
If you have an L/B ratio of 12, then your 'hull speed' is going to increase dramatically compared to this tubby L/B = 3 vessel.

The hulls on the powercat (15 m. LOA) in my avatar have an L/B ratio of approx 15 at the waterline, and she is still comfortably in displacement mode (ie not planing) at 15 knots.
If your cat had two planks on edge for hulls (yes, this is a very extreme case - google Froude's plank experiments), with a VERY high L/B ratio, then she will mostly have frictional resistance (assuming that they are not very close to each other), and not much wave making (relatively) resistance.
This sounds ideal - but two planks on edge have virtually no buoyancy - they can hardly support their own weight.
So you need something a bit wider.
As Ad Hoc says 'it depends' - everything is a compromise in boat design.

 

You have too to consider the pitching behavior of the boat, and slimmer hulls tend to less resistance to pitching, and greater sensitivity to shifts in the longitudinal COG.

 

What definition of "hul speed" are you using?

 

I think that 'hull speed' for a displacement vessel is usually thought to be approx 1.34 times the square root of the waterline length?

But this will not apply to a hull that is much skinnier than the 'average' L/B ratio of approx 3?

 

1.34 times the square root of the waterline length in feet is the common definition of hull speed in knots. The 1.34 coefficient is based on the speed of a wave with wave length equal to one-half of the waterline length. It is independent of beam.

What do you mean by hull speed? Do you mean a speed where resistance is rapidly increasing?

 

1.34 is n/a here

 

Apologies David, but I do think that hull beam has an effect.

The powercat in my avatar has a waterline length of approx 49'.
So her hull speed should be 1.34 x 7 = 9.4 knots.
And yes, I think that hull speed for a displacement boat is where the resistance starts to rapidly increase?

My avatar cat (which definitely has displacement hulls, ie they are not planing) did 16 knots flat out with a pair of 70 hp O/B motors and 10 people on board - and this is almost twice her 'hull speed' if you use the 1.34 rule.
As Fallguy states above, 1.34 is not applicable surely when you have very skinny hulls?

 

Beam does not affect the speed of waves. Beam can have an effect on the magnitude and distribution of waves, and therefore on wavemaking resistance. Whether beam affects "hull speed" depends on what is mean by "hull speed".

Do you mean "hull speed" as the mythical speed which a displacement boat cannot exceed?

 

Yes.
I think a better definition might be the maximum practical / realistic speed for the boat in it's displacement mode.
Sure, you can apply lots more power, and the speed will increase a little bit, but the law of diminishing returns is kicking in very fast here.

 

there is no such thing as 1.34 rule for powercats, oops, cats

here is a good thread on the subject

Sponberg's pdf is pretty cool..

A useless formula (froude displacement formula) https://www.boatdesign.net/threads/a-useless-formula-froude-displacement-formula.45940/

 

Boats which are heavy for their length tend to have resistance rapidly increase as the speed in knots approaches 1.34 times the square root of waterline length in feet which is equivalent to the Froude number based on waterline lenght 0f 0.4. Boats which are light for their length tend not to have as rapid an increase in resistance as the speed approaches a certain speed. The displacement of the boat relative to the length has a stronger influence on how quickly resistance increases than hull L/B (though for multihulls the speed relative to the distance between the hulls can also be influential). One parameter to use to characterize displacement to length relationship is the waterline length divided by the cube root of the displacement, with the same unit of length being used for both (for example feet and cubic fee, or meters and cubic meters). Hull shape also affects the shape of the resistance curve. Two boats with the same L/B and L/D (actually L/cube root of D) with different hull shapes can have different shape reisistance curves. For example a V-bottom boat with a warped bottom and close to zero deadrise at the transom will typically have less of a hump than a boat with constant deadrise.

Ad Hoc has posted a plot of resistance vs speed for a family f similar shaped hulls with different L/D ratios.

 

Hmmm... i think the baby is being thrown out with the bath water here!!

Hull Speed....as DC rightly points out is a "mythical" term that most amateurs and none naval architects use. They use it to describe "what they think is happening" - hydrodynamically - and then incorrectly apply it to all boats.
It is based upon their perception of what they see....and understand... with their limited knowledge of hydrodynamics, especially high speed hydrodynamics, as well as "historical" observations thrown into the mix.

Before the days of light weight structures and high speed engines, going fast was not really possible. And I mean fast...i.e planning speeds.

Thus hulls of that "era" were predominately classical hull shape, that is to say, carrying large amount of weight for the length = displacement hulls, as it is carrying a lot of weight for its length!
These hulls all - in general - fall into the same type of shape - no surprises there. Since that is what the SOR seeks....
This shape being bluff or similar bows, and a stern with changing shape from the keel to the transom to facilitate a smooth flow of water - as much as possible - into the prop.
Something resembling a hull shape like this:



And endless variations of this.

The problem comes, as Bajansailir notes, the classical law of diminishing returns. So what does this mean?

The faster this type of hull form (displacement hull) goes the lower the pressure at the stern. The shape of the hull created for the water flow into the prop, accelerates the water = lower pressure.
Im over generalising here to get the basic message across.

Thus as the pressure gets lower, the water level, relative to the static waterline reduces, i.e gets lower. So the resulting wave profile, the increase in amplitude of said wave profile, "pulls down" the hull, or is what is termed squat.
A concomitant effect of less wave profile supporting the hull means the static equilibrium must move.

As the speed increases this effects becomes more and more pronounced. This is observed by extreme squatting or generally noted as a large trim.
The law of diminishing returns is that no matter how much additional power is provided for the hull to go faster, it can't. It is all about the flow of the water around and under the hull.
The curve of resistance climbs very steeply.

In tank testing of landing craft you see this effect very quickly and the resistance curve approximates the 7th power....ie near vertical above a certain/critical speed.

So this 'critical speed' is a cause and effect of the wave provide along the length of the hull.

The speed of a wave is simply = sqrt(g.L/2.Pi)

L = wave length = LWL.

Thus the wave speed = 1.25 sqrt(L)

In metric units, so this "hull speed" is really the "wave speed".

This has been incorrectly attributed with all hulls and thus their magic speed they cannot exceed, simply owing to ignorance of the hydrodynamics of what is occurring.

So..the question then becomes, well how does a hull go faster than this "wave speed" of 1.25xL, where L = LWL.

Simple... change the shape of the stern.
This encourages the flow of water aft and to separate from the hull at the transom, rather than "stick" to the hull.

We have designed many high speed catamarans (as have many others) which "technically" are displacement hulls.
However changing the shape of the stern allows the hull to go faster than this "mythical" notion of a brick wall of a speed limit.

It is a simple as that.... in a nut shell.

This has nothing to do with beam, which is a function of residuary resistance.

But as noted from the outset, if you reduce the beam, to increase the L/B ratio...and if the displacement remains the same, the draft must increase.
This equates to an increase in WSA (generally).

Thus what you have gained in reduction of residuary resistance (lower B) you loss in the roundabouts of additional frictional resistance (deeper T).
Ergo, not much overall effect - except as small speed range sweet spots - because the overall resistance is governed by the length-displacement ratio (L/D).