astoffel0531
10-23-2003, 08:22 PM
I am a student doing some preliminary research about boats, with a special interest into planing. However, I have yet to come across a mathematical description of this behavior. Can anyone help me out?
View Full Version : Mathematical definition of Boat planing
cgorton
10-24-2003, 08:47 AM
I'm sure you'll get differing opinions on this, as I believe there are more than one definition out there.
For instance, a recent article in Professional Boatbuilder (No. 85 - pg. 78) states "in rough terms, a boat is planing when it's traveling faster than its transverse stern waves, which occurs roughly at a speed in knots of 3.4 times the square root of its transverse beam in feet. Full planing is about twice that speed..."
This seems like a rough estimate, but I can think of exceptions having to do with weight. A very light "skimming" hull with beam X could be on a full plane at the same speed that a heavier vessel, also with beam X, is not planing at all.
I don't think there's a clear definition, but I'd like to hear other ideas...
For instance, a recent article in Professional Boatbuilder (No. 85 - pg. 78) states "in rough terms, a boat is planing when it's traveling faster than its transverse stern waves, which occurs roughly at a speed in knots of 3.4 times the square root of its transverse beam in feet. Full planing is about twice that speed..."
This seems like a rough estimate, but I can think of exceptions having to do with weight. A very light "skimming" hull with beam X could be on a full plane at the same speed that a heavier vessel, also with beam X, is not planing at all.
I don't think there's a clear definition, but I'd like to hear other ideas...
Guest
10-24-2003, 09:22 AM
There is no mathmatical definition of planing. There are mathmatical formulae to calculate planiing AFTER you have decided on the definition of planing that you like. There is no clear consensus on exactly what constitutes planing except at higher speeds where everyone agrees that the boat is planing. The transition region from displacement to full planing is where the disagreements occour and this varies a lot with different hull types.
Guest
10-24-2003, 09:41 AM
Often the onset of planing is defined as when the boat's center of gravity moves up (presumably due to dynamic lift), but when "full planing" is acheived is another issue.
Guest
10-24-2003, 09:45 AM
The Journal of Ship Research (www.sname.org) has numerous papers on planing. Other papers are in Marine Technology (same source). SNAME is also publishing a CD of collected small craft papers, some of which will involve various aspects of planing.
Much current interest is focused on Zarnick entering wedge techniques for planing. One site for this is http://www.shipmotion.com (as well as the SNAME site).
Much current interest is focused on Zarnick entering wedge techniques for planing. One site for this is http://www.shipmotion.com (as well as the SNAME site).
gonzo
10-24-2003, 12:13 PM
There is no exact definition, particularly after you enter the semi-planing stage. There is general agreement that at planing speeds the hull is "over the bow wave". I usually assume it is about three times the hull speed.
SailDesign
10-24-2003, 01:42 PM
gonzo says: "I usually assume it is about three times the hull speed."
Which equates roughly to a Froude number of 1. Clever things, Froude numbers....
Which equates roughly to a Froude number of 1. Clever things, Froude numbers....
gonzo
10-25-2003, 02:33 AM
Saildesign: do you agree that the boundaries between displacement, semidisplacement and planing are arbitrary? I think that a twenty foot boat at fifty knots is planing without question. However, how about at ten knots?
SailDesign
10-25-2003, 06:53 PM
Gonzo - the boundaries are decidedly vague....
No-one has defined the limits of each mode to my entire satisfaction, and I think it is more a matter of observation of behaviour of the boat that makes the decision.
My 2-cents.
Steve
No-one has defined the limits of each mode to my entire satisfaction, and I think it is more a matter of observation of behaviour of the boat that makes the decision.
My 2-cents.
Steve
BrettM
10-26-2003, 05:23 PM
OK, we all know that in practice that the transition point is not clearly defined. However if you take the definition of going faster than the speed of a wave of the same length of the hull ie the point afterwhich the hull will climb over the bow wave (hull speed) it can be defined.
Based on the speed of a wave in deep water of c=sqrt(gL/(2 PI)) g=acceleration due to gravity, L = wavelength and substituting in L for LWL you get the hull speed definition. Watch your units here.
(Don't ask me to derive all the above as it has been several years since uni and I am working from memory of my ocean engineering/oceanography classes)- especiaaly the first eqn. (Note this is a deep water eqn)
As far as a mathematical planing theory, probably best to look at flat plate planing as a starting point for the forces/pressures involved. A number of sources should have something on this including most classical naval architecture texts and some others such as Peter Du Cane's "High speed light craft" or Principles of naval architecture.
Might get you pointed in the right direction anyway.
Brett
Based on the speed of a wave in deep water of c=sqrt(gL/(2 PI)) g=acceleration due to gravity, L = wavelength and substituting in L for LWL you get the hull speed definition. Watch your units here.
(Don't ask me to derive all the above as it has been several years since uni and I am working from memory of my ocean engineering/oceanography classes)- especiaaly the first eqn. (Note this is a deep water eqn)
As far as a mathematical planing theory, probably best to look at flat plate planing as a starting point for the forces/pressures involved. A number of sources should have something on this including most classical naval architecture texts and some others such as Peter Du Cane's "High speed light craft" or Principles of naval architecture.
Might get you pointed in the right direction anyway.
Brett
Guest
10-27-2003, 07:34 AM
Entering wedge theory is probbaly the most current technique. Ths is a stripwise approach to developing the forces based on the added mass of a wedge entering the free surface.
See papers by Martin, Payne, Zarnick, and recently by Troesch and his group at U. Mich.
Other researchers have used vortex lattice approaches.
See papers by Martin, Payne, Zarnick, and recently by Troesch and his group at U. Mich.
Other researchers have used vortex lattice approaches.
ErikG
10-27-2003, 07:54 AM
From someone that never went to University...
Where do I start searching for various intresting published papers about boat related research?
I guess SNAME and the Uni's themselves could be a startingpoint, but I don't have access to SNAME and dont know where to start looking/searching when it comes to published uni. papers...
--------------------------------------------------------------------------------
So much to learn, so much to know and so much I can't find
Where do I start searching for various intresting published papers about boat related research?
I guess SNAME and the Uni's themselves could be a startingpoint, but I don't have access to SNAME and dont know where to start looking/searching when it comes to published uni. papers...
--------------------------------------------------------------------------------
So much to learn, so much to know and so much I can't find
Guest
10-27-2003, 09:35 AM
Brett defines planing but needs to accept a definition before defining it. This is not wholly satisfactory.
There is a non-mathmetical explanation at:
http://www.woodenboatworld.com/boattalk.asp?contentid=135
If you can get access to the "Ideal Series" published by MotorBoating magazine years ago, there is a whole series of articles on the subject.
After reading all of the material available, there is still no universally agreed on definition. So what? No definition is needed to understand the phenomena or to design planing boats. In fact, if any one of the most popular definitions that I have seen is taken as the whole story, then the creative processes will be short-circuited.
Many will start with a definition of "hull speed" and go from there. That is the worst place to start since a full planing hull has little in common with a boat designed to increase hull speed and is usually absolutely awful in the lower transition speed range. That is why (along with heavy, low power engines) all early attempts at high speed resulted in long, narrow boats to raise the hull speed.
I quit worrying about just what defines planing and when it occurs and work on boats to run at whatever speed is desired. Being an amateur in this field, I don't pretend to follow all the papers published by Savitski and other researchers, but that does not keep me or many other amateurs from designing small boat hulls that work.
Tom Lathrop
There is a non-mathmetical explanation at:
http://www.woodenboatworld.com/boattalk.asp?contentid=135
If you can get access to the "Ideal Series" published by MotorBoating magazine years ago, there is a whole series of articles on the subject.
After reading all of the material available, there is still no universally agreed on definition. So what? No definition is needed to understand the phenomena or to design planing boats. In fact, if any one of the most popular definitions that I have seen is taken as the whole story, then the creative processes will be short-circuited.
Many will start with a definition of "hull speed" and go from there. That is the worst place to start since a full planing hull has little in common with a boat designed to increase hull speed and is usually absolutely awful in the lower transition speed range. That is why (along with heavy, low power engines) all early attempts at high speed resulted in long, narrow boats to raise the hull speed.
I quit worrying about just what defines planing and when it occurs and work on boats to run at whatever speed is desired. Being an amateur in this field, I don't pretend to follow all the papers published by Savitski and other researchers, but that does not keep me or many other amateurs from designing small boat hulls that work.
Tom Lathrop
BrettM
10-27-2003, 06:01 PM
Tom,
Most people can tell the difference between a displacement type hull and a planing type hull by simply looking at them. A planing hull reaches speeds where the weight of the vessel is supported by dynamic rather than static forces.
Hull speed is the generally accepted upper end limit of a displacment craft beyond which the power requirements become excessive. (Not to say it cannot be done without effort) Planing craft exceed this limit going over the hump and into pre planing regeime and then to full planing. Why not start here? Hence I defined this point.
As far as planing mathematics is concerned, a flat plate is the simplest and most basic concept available however far derived it might be from a real world boating application. Hence my suggestion as a starting point to the original poster who is looking for a mathematical description and not a design solution. There are plenty of ways to go from there.
Brett
Most people can tell the difference between a displacement type hull and a planing type hull by simply looking at them. A planing hull reaches speeds where the weight of the vessel is supported by dynamic rather than static forces.
Hull speed is the generally accepted upper end limit of a displacment craft beyond which the power requirements become excessive. (Not to say it cannot be done without effort) Planing craft exceed this limit going over the hump and into pre planing regeime and then to full planing. Why not start here? Hence I defined this point.
As far as planing mathematics is concerned, a flat plate is the simplest and most basic concept available however far derived it might be from a real world boating application. Hence my suggestion as a starting point to the original poster who is looking for a mathematical description and not a design solution. There are plenty of ways to go from there.
Brett
gonzo
10-27-2003, 07:14 PM
Where do semi-displacement boats fit in?
mmd
10-27-2003, 07:36 PM
Now, Gonzo, that's just stirring the pot! ;)
SailDesign
10-27-2003, 10:04 PM
gonzo says: "Where do semi-displacement boats fit in?"
They're just a little bit slower than semi-planing boats ;-P
They're just a little bit slower than semi-planing boats ;-P
BrettM
10-27-2003, 10:20 PM
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...
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...
Guest
10-28-2003, 12:37 AM
[QUOTE]Originally posted by BrettM
[B]Tom,
Hull speed is the generally accepted upper end limit of a displacment craft beyond which the power requirements become excessive. (Not to say it cannot be done without effort) Planing craft exceed this limit going over the hump and into pre planing regeime and then to full planing. Why not start here? Hence I defined this point.
>>>>Brett, you can certainly do that but it makes no difference how you define planing. Firstly, many will not agree and secondly, no such definition will make any difference to the boat. I can find boats that will not act like the "definition" says they should. Such definitions are only applicable when the discussion is limited to a narrow range of hulls. Hull speed works ok for slow, heavy boats of similar fat length/beam ratios but don't work well with very light boats or high length/beam ratios.<<<<
As far as planing mathematics is concerned, a flat plate is the simplest and most basic concept available however far derived it might be from a real world boating application. Hence my suggestion as a starting point to the original poster who is looking for a mathematical description and not a design solution. There are plenty of ways to go from there.
>>>>>I agree that a flat plate is both the most simple and the most appropriate place to start an explanation of planing. If you ignore the whole concept of hull speed, planing becomes much easier to understand. After that is clear, then a look at the problems of the transition speed range is much easier. One thing to keep in mind is that the sum of buoyancy and dynamic (planing) lift must always exactly equal the displacement of the boat. I did not say equal the weight of the boat since there is often some negative dynamic lift, especially in semi-displacement (semi-planing or whatever) hulls. In full displacement hulls, negative dynamic lift is greater than any positive dynamic lift, which is why they will sink if towed too fast.<<<<<
Tom Lathrop
[B]Tom,
Hull speed is the generally accepted upper end limit of a displacment craft beyond which the power requirements become excessive. (Not to say it cannot be done without effort) Planing craft exceed this limit going over the hump and into pre planing regeime and then to full planing. Why not start here? Hence I defined this point.
>>>>Brett, you can certainly do that but it makes no difference how you define planing. Firstly, many will not agree and secondly, no such definition will make any difference to the boat. I can find boats that will not act like the "definition" says they should. Such definitions are only applicable when the discussion is limited to a narrow range of hulls. Hull speed works ok for slow, heavy boats of similar fat length/beam ratios but don't work well with very light boats or high length/beam ratios.<<<<
As far as planing mathematics is concerned, a flat plate is the simplest and most basic concept available however far derived it might be from a real world boating application. Hence my suggestion as a starting point to the original poster who is looking for a mathematical description and not a design solution. There are plenty of ways to go from there.
>>>>>I agree that a flat plate is both the most simple and the most appropriate place to start an explanation of planing. If you ignore the whole concept of hull speed, planing becomes much easier to understand. After that is clear, then a look at the problems of the transition speed range is much easier. One thing to keep in mind is that the sum of buoyancy and dynamic (planing) lift must always exactly equal the displacement of the boat. I did not say equal the weight of the boat since there is often some negative dynamic lift, especially in semi-displacement (semi-planing or whatever) hulls. In full displacement hulls, negative dynamic lift is greater than any positive dynamic lift, which is why they will sink if towed too fast.<<<<<
Tom Lathrop
SailDesign
10-28-2003, 07:36 AM
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.
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.
Guest
10-28-2003, 08:06 AM
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.
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.
gonzo
10-28-2003, 03:10 PM
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.
BrettM
10-28-2003, 04:59 PM
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
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
SailDesign
10-28-2003, 05:51 PM
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
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
gonzo
10-28-2003, 06:31 PM
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?
And opening another can: how about bow bulbs. How do they affect hull speed?
SailDesign
10-28-2003, 09:25 PM
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!
ou're on your own, there, gonzo. I've done my bit, and my brain hurts.
Next!
Willallison
10-29-2003, 05:37 PM
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.
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.
SailDesign
10-29-2003, 06:11 PM
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. ;-)
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. ;-)
CDBarry
10-29-2003, 09:37 PM
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.
gonzo
10-30-2003, 04:08 PM
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?
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