Froude and planing

First, I am not very concerned what companies use although that would be interesting. I do not care about their costs either. I, as physicist, hydrodynamicist, former race driver, and race team owner am interested in understanding the planing and more. I think you are wrong: first, there is no length scale in planing that remains constant unless you have a flat bottom and use beam B as the length scale. But that makes no sense, physically: lifting requires doing work against gravity. The vertical displacement is the correct length scale in any case. For a boat with a firm, straight bottom the wet surface area, the lifting surface area, the planing area, will decrease as speed increases. That is exactly the point of drag reduction. Let us take the case of a boat with speed varying from 0 to 40 mph, 0 to 50 mph, or 0 to 100 mph or more, e.g. As the speed increases then the (wet) displacement V=bLd decreases, as do all three length scales in displacement V unless the bottom is flat, in which case only B can remain constant. The bottom is typically a V, a pad V, or a tunnel. The tunnel has sponsons with deadrise, like two Vs.

 

Just call me 'the dictionary'.

 

EDIT: ---Redacted Line---

Your understanding of the applied use of Froude numbers is wrong.

What is used is a length/dimension that remains constant. I'll say again, beam is often used for planing hulls.

The point of Froude numbers is comparison - if you aren't using the same definition, there can be no meaningful comparison.

A Froude number should vary linearly with speed. Your personal definition doesn't.

Vertical displacement is not the correct dimension to use in any case.
Length is preferred because it's most relevant (again, not suitable for planing hulls because it varies so much with speed).

 

I'm sorry but what you're writing is not very useful. I teach hydrodynamics. I know the difference between experiment and simulation. Simulations can be very misleading because of the input and numerical error that accumulates during a calculation. Now, as you claim to know so much then them please advise: what length scale do you think remains constant as a V bottom rises higher and higher onto the water as the speed increases? It can't be the beam.

 

For the planing boat it is just the bottom width, the deadrise at the stern and the total weight's center of gravity constant over the entire speed range. At least on my boats. The center of gravity distance from the stern should be an appropriate measurement of length to go out from.

JS

 

Lift sets in sharply when the flow separates from the bottom at the squared transom. Here, the boat is plowing bow-high. As the speed increases then the boat begins to lift at the transom while still plowing bow high. I take as 'planing' the point at which the transom lifts enough that the bow comes down and the boat's trim angle is, very roughly speaking, the same as the speed increases. With our 15' Glastron this trim angle is a few degrees. At that stage (about 18 mph) the boat is running flat and dragging a lot of water. Up to that point the motor is trimmed under. To gain speed the hydraulic trim is then used as the throttle is increased. The top speed is 46 mph GPS with 70 hp. The rig weighs 910 lb.

Now. If one demands a 'constant' length scale in F then it can only be a scale at top speed when the boat is running high and dry (again, I am only talking about firm, straight bottoms as with high performance hulls). You cannot avoid that the depth d of submerged hull comes into the equations. Specifically, the drag force is D=rcAU^2 where r=water density, c=drag
coeff., A=BL =wet area, which decreases with speed because both B and L decrease, and V=BLd=displacement, which decreases as speed increases. We then get D/Bu=cF^2 where buoyancy Bu=rAdg and F^2=U^2/gd. You cannot avoid a Froude nr. based on d if you want to compare drag and buoyancy, or drag and lift. This is good hydrodynamics, it prepares one for deriving the correct speed-power-weight scaling law that differs from Crouch and Wyman where lengths are involved so that their results do not scale.

Summary for our Glastron results (V with no pad, deadrise≈16 degrees):

-As the boat plows bow-high with the motor trimmed fully under, lift sets in at 8 mph. Transom is deep in the water, transom does not lift upward as lift begins at this speed. Trim angle does not change.

-boat continues to plow bow-high (trim angle of boat≈30 degrees) with transom deep as throttle is increased and boat begins to lift at the transom.

-At 18 mph the transom lifts enough that the bow comes down, the trim angle falls to a few degrees. I label this as the onset of planing (it's arbitrary but good-I take reduced trim angle as part of my definition of planing).

I have often watched a particular water-taxi in the Baltic (Schaprode-Vitte) run while never planing. It runs about 24 mph bow-high with the transom squatting in the water. Underpowered. A little more power and the transom would lift and the trim angle would fall.

The boat shown below is an 18' Laser with 235 hp at 85 mph. The point is that there is very little wet beam, wet length, or wet submerged depth. All of thoses lengths decrease as U increases for a properly-designed and properly-braced boat bottom.

 

Your reasoning might be formally correct but not practically useful, I am afraid.

In general, the main advantage of using non-dimensional coefficients (like Fn, Cl, Cd, Ct, Cp, Kt, Kp etc.) is the simplification of mathematical (engineering) analysis. They should allow the creation of test procedures and resulting graphs and tables which (at least in theory) are scale-independant and hence valid for a broad range of geometrically-and fluid-dynamically similar cases.

In order to make a calculation system which is reliable and reproducible, the reference length (or area, or volume) has to be chosen between quantities which can be measured with precision and confidence. If the reference is uncertain, the rest of math work may be theoretically valid but becomes practically useless.

Now, given a CoG setup (which can be measured), the static WL lenght, beam and wetted transom area are easily and reliably measurable - even at full-scale and on board. Same for the displacement, which depends on the boat's weight. Hence, when used as reference quantities for the analysis, they lead to repeatable (though often complex-shaped) graphs and coefficients' values, for the same hull geometry and flow conditions.

The depth of the submerged hull - how do you measure it? At what point along the hull, and against what reference plane? How do you do it on a full-scale moving boat?
Without the possibility to reliably measure this elementary value, the rest of the analysis turns into a formally nice academic exercise - but not much more than that.

Cheers

 

It becomes practically useful when you use my speed-power-weight formula, which I have compared with established APBA OPC kilo records.

Wetted transom area decreases with speed, it is very small at high speeds.

I have admittedly guestimated wet depth. To estimate it: take photos from another boat running along side.

 

That's the point of my comment.

 

Happy to oblige. In that case displacement^(1/3) would be a reasonable option.

Not a general truth. I don't claim it isn't the case for the hull(s) you have in mind, but it isn't the case for all squared transom hulls. Lift does not necessarily "set in sharply" when flow begins to separate cleanly from the transom (i.e. somewhere in the neighbourhood of Fr=0.4). Perhaps I shouldn't be so picky...it depends on what you mean by "sharply".

One does, if one wants the Froude number to be of any use.

You can, and naval architects all over the world do it every day.


If you want to dispute what Faltinsen has written then by all means do so, but you must bear two things in mind: the Froude number must scale proportionally with speed, and the Froude number you use must be the same definition as Faltinsen's to be able to compare with his.

Unfortunately, when you follow these essential guidelines, you'll find that he's correct: Fr=0.4 is approximately where full displacement ends (flow starts separating cleanly from squared transoms, for example) and Fr=1.0 is the region where lift starts becoming significant (to varying degrees, depending on the hull type).

 

Thanks. I use the depth Froude nr. with lift and drag coefficients. My main interests were/are in scaling laws for prop diameter, and speed-power-weight scaling.

 

The depth Froude number (Fn,T) is used for analysis of transom ventilation in 2D cases, and as such can be suitable for quasi-2D flows - which is a case of boats with large B/T (Beam/Draft) ratio at the transom.

In cases when Fn,T is used for the transom-drag analysis of 3-D boat hulls, the T value is usually the transom depth at zero speed (static value).

For as much as I know, the volumetric Froude number appears to be a much more appropriate and reliable parameter for general cases, and has been used in the majority of research papers on transom drag and planing-hulls resistance.

Again, the main problem associated to the speed-varying transom depth is that it is hard to measure with precision, both in towing tank and on board the full-scale boats. Quite frankly, taking photos of transoms while underway does not sound like a serious and viable option in most cases.

For that reason we are almost always obliged to use static lengths, beams, depths, areas and volumes as reference.

By the way, transom Fn,T is used in this well-known work by Doctors et al.:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.616.9183&rep=rep1&type=pdf
As well as in these two papers:
http://www.iwwwfb.org/Abstracts/iwwwfb19/iwwwfb19_32.pdf
http://www.marin.nl/upload_mm/9/9/d/1807556099_1999999096_StarkeAR_NSH_2007.pdf

(Reading spoiler - no universal value of Fn,T at which the ventilation starts has been determined)

 

I think that the fore-aft trim introduces a very important variable. It doesn't only affect the flow, but also the waterline length.

 

The common categorisation to displacement, semi-planing and planing speeds based on Fn is done using stationary LWL. If you change the definition of Fn, obviously the category values will be different.

At the limit of the planing (Fn~1) the planing LWL will be quite close to stationary LWL for vessels most interesting to the people making these categories, that is mainly heavy navy vessel etc.

Still the stationary LWL based catergories work quite well for most leisure and even racing boats, although they may have much shorter LWL at speed.

Chine beam is often used as the "lenght" for planing boats and can be considered the same as wetted beam for most planing boats. But light and fast boats will ride on the strikes with chines of the water.

You can calculte the riding depth with Savitsky method. It will depend very much on the trim as will the LWL at speed.

 

"Lift sets in sharply when the flow separates from the bottom at the squared transom".

As a practical matter, though, from a layman's perspective I see that there are craft that show a clean separated flow at displacement speeds. In addition, there are craft that produce several times there displacement in dynamic lift when the transom is fully submerged (and not just the lower tip of the transom, but the whole transom and indeed the whole craft. That seems to indicate that there is little correlation between lift and separate flow per se, doesn't it?