Bottom Pressures - Newton vs Bernoulli

In the Box Keels thread ( http://www.boatdesign.net/forums/showthread.php?t=16066 ) Fast Fred (henceforth referred to as FF) made reference to statements made by Lindsay Lord in his book Naval Architecture of Planing Hulls, originally published in 1946, about suction present in the after sections of planing hulls...

Not wanting to hijack the (excellent) Box Keels thread, I thought this topic deserved more attention and it's own thread......

 

My Reply...

 

Then from Tom Lathrop -

 

Will (me) -

 

Tom -

 

I've done a little more research on the subject and it seems that Lord was not alone in his thinking. Indeed in his contribution to the original edition of Skene's Elements of Yacht Design and on the subject of hydroplanes (planing power boats) none other than George Crouch...

"The exact action of the water on the bottom of a stepless hydroplane has been the subject of much discussion. It is conceded today that, in addition to upward pressures on the bottom, a great part of the area in contact with the water is subjected to a downward suction. It is for this reason that the stepless type is less efficient than any of the other forms in which an attempt is made to avoid these suctions"

Then again, the idea has not been without its detractors either. Uffa Fox in Seamanlike Sense in Powercraft

"A great deal has been written to suggest that boats with flat sections aft have great suction. Waterski's are absolutely straight and flat throughought; thus according to this theory, they should suck the man on them under and not, as they in fact do, lift him out so that he plane's happily over the sea.

Once when running trial for a boat with a flat stern, we increased her length by continuing its bottom along a fair line with a planing board the full width of the vessel. This board had 5/8" holes either side.....
According to the theory that a flat bottom aft has great suction this 5/8" hole should have sucked water down, but the opposite was true; there was a steady jet of water....."

Bernoulli's Principle is definitely NOT simply a theory - indeed as Tom points out, it provides much of the reason why aeroplane wings give lift. But at the end of the day, it is Newton who comes up trumps - without his equal and opposite reaction we'd all be travelling a LOT slower!
I think in more detailed texts on planing theory, the negative pressures present as a result of Bernoulli's Principle should indeed be covered. For the sake of simplicity, it is only the resultant force - which is quite clearly upwards - that texts like Dave Gerr's Nature of Boats discuss.

Now, methods of minimising Bernoulli's "work"... that is something that is definitely worthy of further discussion

 

Just a side note: bernoulli does not make aicraft fly. The lift given by the pressure differential is around 25% of the whole lift. You should search on circulation theory.

 

A bit off topic but,
I remember when I studied, some students had t-shirts with the Navier-Stokes equations on the chest and "Bernoulli is for wimps/sissys!" on the back

 

I think Bernoulli can only be used when viscous effects and turbulence is neglible.

 

Willallison;

It is not the question of wether stagnation pressure (Newton) or energy methods (Bernoulli) dominate. Both are only case specific sub-sets of the total energy equation and, depending on your assumptions and boundary limitations, either can be used to determine an "answer". The question is what does that "answer" mean. Often a truely "incorrect" answer is all you need...like the speedometer in your automobile or the calculation of lead in a sailing rig. The speedometer tells you how fast it thinks you are going relative to the road based upon drive shaft RPM; it has very little to do with true velocity compared to some universally fixed reference point. The same with lead, it has nothing really to do with where the true CE and CLR are, but it is a calculatable value that can be used as a yardstick to measure an incalculatable couple.

The concept of "suction" (or pressure drag if you perfer) or "pressure" in the aft buttocks of a watercraft needs to be referenced to some other other energy state. The water spurting through a hole is a meaningless comparison as you cannot seperate the flow into pressure driven flow or residual kenetic velocity or even forced flow due to impact of the holes trailing edge on non-moving water. And are you comparing the "pressure" on the aft surface to the stagnation pressure, the viscious flow pressure, or the still waterline static pressure? And which should you compare it to? So long as the analysis in consistant within itself, the answer doesn't matter. The problem arises when one frames the analysis to measure and quantify a variable that is relatively independent of the true answer, such as trying to use density as the key variable to to determine stagnation pressure.

And, as fcfc and Raggi Thor mentioned, there are plenty of "physically incorrect" mathematical models out there that are accepted because they work, physics be damned. Circulation theory is just a mathematical contrivance of Lanchester and Prandtl, and Navier-Stokes hangs it hat on the Kutta-Joukowski condition. Both theories are patently incorrect if you look at the physics close enough.

 

Seems to me if the bow lifts an amount equivalent to (or greater than, for that matter) the rocker designed into the hull, then you have no negative pressure areas due to the hull's convexity because the aft portion of the hull would then be parallel to the water flow.

On the hole test, whether or not the water comes into the hull when you drill a hole is not the true test. It's the difference between what the water does when the boat's at rest vs in motion that will tell you wheter there's positive or negative pressure. If the water squirts up say, 6 inches when the boat is at rest, but only 4 inches when the boat is under way, then there is negative pressure being generated at that point on the hull.

Having said that, I vote for positive pressure while under way, since the whole point of a planing hull is to decrease wetted surface, and if the boat's weight is riding on a smaller surface area, then the net pressure per unit of surface area HAS to go up. If there are any negative pressure areas, then that would be due to either improper design (if unintentional) or to alter the hull's ride characteristics (if done intentionally).

 

(From Hydrodynamics of High-Speed Marine Vehicles. Odd M. Faltinsen. Cambridge University Press 2005)

The approximate equation giving the vertical force per unit length on a cross section , f3=U d(a33 U tau)/dx, predicts that negative hydrodynamic pressures on such a cross section occur when d(a33 tau)/dx is negative. For instance, if the cross sections are wedge-formed with constant deadrise angles, negative pressures relative to atmospheric pressure occur when b^2*tau decreases with increasing x, that is, towards the stern. If the keel line is convex, tau decreases with increasing x and thus negative pressures may appear.

U: boat speed
b: local beam
tau: trim angle
a33: two-dimensional infinite-frequency added mass in heave of the cross section.

The effects of propulsors are not considered here. A propeller may cause negative hydrodymnamic pressures on the hull.

 

I find this thread very helpful to my ego and am very glad that Will has extracted it from the other box keel thread. I have most often been beaten into silence by those that suscribe to the "suction is non-existent" group. The main problem has been the result of reading about the experiment that Gerr refers to.

Suction exists in the same way that cold exists. Both result from the absence of another element, either pressure or heat. It might be more correct to say that in winter we feel the lack of heat but it's much more understandable to say that it's just cold.

John and others make some very important points although pretty deep for an internet thread to handle. We have problems with a single variable.

There is often only a need to know the answer to this issue but that does not lead to any discovery of why that answer resulted and, most importantly, does not give any information on how the result might be improved. Only by recognizing the negative pressure elements can we hope to minimize them and their negative effects on boat performance.

This thread is unfortunately labeled "Bernoulli vs Newton". Sorry Will. Both theories are well proven and any attempt to slam either will further confuse the issue. Both are present under the hull of any boat moving in the water. The degree to which each affects the outcome is highly variable depending on the particular case.

I have an article on my website where I give my views on planing. It is neither complete nor does it contain a single equation. Hydrodynamicists need not bother, it's mainly for the interested layman, although it's clear that some who should know better might gain something of value.
http://www.bluejacketboats.com/planing_boat_theory1.htm

I hope that we can agree that no one will get violently upset (with their keyboard) because someone else disagrees with their theories.

 

Always difficult to choose the name for a thread - you want to catch everyone's attention, but at the same time give a good idea of what the discussion's about...
I wasn't suggesting that it's a case of Newton rather than Bernoulli applying here - rather trying to conjure the image of the two forces acting against one another...

 

My mistake Will, Now I understand what you intended. We get so many threads labeled this vs that and I interpreted it incorrectly. At least, we all know what was meant now.

One thing that often puzzles me is trying to determine the actual "flow" direction of water under a particular hull. In a V bottom there must be some transverse flow and this must have a bearing on the ideal shape of the bottom. That is, any transverse convexity or arc to the bottom would appear to invoke Bernoulli and be detrimental to lift. Likewise, any transverse concave surface, like a flat or strake that is at a negative angle to the local deadrise should increase lift. Some of this is obvious and substantiated by experience but how do we quantify it. The off axis flow deviation angle should be inversely proportional to the speed, yes?