Mathematical definition of Boat planing

Now, Gonzo, that's just stirring the pot!

 

gonzo says: "Where do semi-displacement boats fit in?"

They're just a little bit slower than semi-planing boats ;-P

 

Now you people are just causing trouble

Hey I do recall some semi displacement craft doing much higher speeds than most planing hulls. And what about subs? For a displacement craft they can go pretty quick. Anybody like to try and summarise this in one sentence? It hurts my head...

 

Brett,
You say that subs are pretty quick for displacement boats, and could we sum it up in one sentence.
Well, I gits two words for ya :- "Nuclear Reactor" ;-))

Steve - anything can be fast with enough power.

 

Submarines & Entering wedges

No, deeply submerged objects do not have wave drag.

They do have more wetted surface, but at some speed this crosses and deeply submerged objects are more efficient.

Note that in nature we have submarines, (fish, etc.) fully immersed in a fluid, and birds, also fully immersed in a fluid, but no creatures that operate in the interface when they want to travel efficiently. Operating in the interface is costly in terms of energy given limited length and high speed.

Also, again, the easiest way to mathematically model planing is entering wedge approaches, and some of the most recent work is able to accurately derive both resistance and motions from basic physics. Journal of Ship Research had a very good paper a year or so ago, and Dick Akers has presented several papers and presentations through SNAME, MACC, HPYS, Workboat Show and IBEX.

The idea is to look at the hull from the point of view of a fixed particle of water. Then the hull looks like a series of wedges being driven downwards into the water, which we can solve from first principles.

 

The problem of wave resistance is because the boundary between air and water is not rigid. Eddies and waves create a huge resistance. In a completely submerged object eddies are much smaller and there are no waves.

 

Steve,
Picture Tim Allen fixing a nuclear reactor to his tinny in the garage and grunting "more power"... Perhaps a sold fuel rocket might work hmmmm...

Guest, I am guessing that the first princples approach to each element in the strip method you mention is almost similar to the simple flat panel?

Tom, many don't understand where the 1.34sqrt(L) eqn comes from. Hence I mentioned it. This forum is way too small to make a full discussion of it. Not to say I understand everything about it any way.

Brett

 

I originally posted this to rec.boats.building, but it serves well....

Here's a quote from a reputable source (which I won't name since they may not
like it) that explains it - sort of.

"THe energy associated with the transverse wave system travels at the "group
velocity" of the waves, which equals one-half of the phase velocity in deep
water. The propulsion system of the ship must therefore put additional energy
into the wave syste, to replace that which "falls behind". A nominal
relationship between ship speed and the length of the corresponding transverse
wave may be found by equating the ship velocity with the _celerity_ (phase
velocity) of a small-amplitude gravity wave in deep water,

Vship = Cwave = sqrt( g.Lw/(2.pi)) = 2.26 sqrt(Lw)

where Cwave = celerity or phase velocity of the wave in ft/sec
and Lw = length of the transverse wave in feet.

This can be converted into speeds in knots:

Vs = 1.34.sqrt(Lw) (sorry, no workings shown - trust me)

William Froude first pointed out the practical limiting speed for
surface-displacement ships whe he observed that "the speed with which wave
resistance is accumulating mosr rapidly, is the speed of an ocean wave the
length of which, from crest to crest, is about that of the ship from end to
end" (Froude 1955 p.280) This condition is found by substituting the length of
the ship for the length of the wave, giving a relationship commonly referred to
as the _hull speed_, or critical speed-length ratio:

Vs/sqrt(Ls) = 1.34

<end quote>

And there you have it.

Steve

 

I think my comment opened a can of worms I can go fishing with for a couple of years . Hull speed in knots defined as 1.25 to 1.3 times the square root of the waterline works for boats of moderate design. Barges have a much lower hull speed. Hulls with beam/length ratios of 10 or more can have hull speeds twice that.
And opening another can: how about bow bulbs. How do they affect hull speed?

 

Gonzo saith: "And opening another can: how about bow bulbs. How do they affect hull speed?"

ou're on your own, there, gonzo. I've done my bit, and my brain hurts.

Next!

 

Not as mathematically complex as much of the dicussion so far, but maybe relevant.
My Westlawn text describes planing as -

As far as we are concerned a high speed powerboat is one that is capable of exceeding a speed / length ratio of 3.5

where: speed / length = V (knots) / sqrt L (WL in feet)

As a boat gather speed, it commences to settle bodily in the water with the bow usually sinking a little more than the stern. As the 2nd wave crest passes the stern (S/L 1.34) the bow starts to lift and the stern to fall, until there is a pronounced bow-up trim. This state of affaris continues until a S/L of abit 2 is reached. Now the stern will start to rise, and with it the CG of the boat as a whole. At about S/L of 2.5, the CG will be back in its original (at rest) position. The CG continues to rise with further increments in speed. At a S/L of about 3.5 the boats trim will, or should, start to flatten out and it will loose some of its bow-up attitude. Water rushing along the bottom and meeting the wedge shape presented by the immersed hull will continue to lift the stern and the craft as a whole, until it is running flat and hight in the water. The boat is said to be planing when, with the boat in motion, the CG is back at the same height as it was when the boat was at rest. Physical evidence of the boat achieving the planing mode, ie exceeding speed hump, is water separating cleanly at the chine and transom.

 

Will says: "Physical evidence of the boat achieving the planing mode, ie exceeding speed hump, is water separating cleanly at the chine and transom."

But, but.... this can be achieved at anything more than 3 knots in some boats, with waterlines of 40 feet and up......

If you assume a deeply immersed transom, then "Yes", they are as correct as they need to be. ;-)

 

Entering wedge

No, entering wedge is based on an infinite Froude number added mass analysis. The most recent one uses something very like the kind of close fit theory used for ship motions in Hansel or SMP.

 

I've always been confused about the measurement of waterline length. It changes dynamically with speed. Many good designs use this change to their advantage. For example, overhangs on a hull. A fast boat may have 10% of the waterline at planing compared to displacement speed. Which waterline do you measure; the one at the particular speed or at rest?