# Froude and planing

Discussion in 'Hydrodynamics and Aerodynamics' started by sandhammaren05, Feb 26, 2017.

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### sandhammaren05Senior Member

A 13' or 14' Allison pad-V with an Evinrude 75 runs on about one sq ft or less of wet surface area at 60 mph. I won 4 national championships with such rigs, and set the kilo record at 70.560 mph in 1981. Here's a photo of the boat trimmed under in rough water. The trim angle is less than 6 degrees, nearer to 2-3 degrees. At 6 degrees trim angle the rig in the photo breaks 67 mph. Pad width is 7".

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### sandhammaren05Senior Member

I'd like to see some correct hydrodynamics behind your claims above. A small component of lift contributes to drag, the rest supports the weight. Where's your calculation? Positive prop rake can't contribute to lift, it pulls the transom down. You can't run zero or negative rake on a V-bottom without killing the speed. The Allison rigs have a total weight of 840 lb with driver, fuel, battery. Here's a photo with about 6 degree trim angle running 66.5 mph gps speed. More than that and the boat would blow over backward running upwind.

In hydrodynamics the factor made of r (density), A (area), U^2, or rAU^2 has units of lb. This factor gives thrust and drag the correct dimension. The thrust and drag coefficients are dimensionless and depend on the dimensionless advance ratio J=U/nD where n is prop RPM and D is prop diameter. J is proportional to U. If you naively plot drag or thrust against speed U then the exponent will be less than 2 because the thrust and drag coefficients decrease with J. It is incorrect to assert that the form drag doesn't go like U^2. You should always plot dimensionless quantities in hydrodynamics. See, e.g., Du Cane 1951.

A boat like an Allison with a straight, firm bottom will never porpoise at top speed. If you trim it out crazy-far then it may blow over backward when encountering a wind puff or larger wave. Unlike the smaller lighter models, the 20' model could be trimmed out quite far, 85 mph with 235 hp Evinrude. The current Allison boats run well over 100 mph with 225 hp and only a small trim angle. The kilo record with one is nearly 130 mph with a modified Mercury V-6 2 stroke. A boat that porpoises at top speed has a flaw in the bottom design and/or construction.

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### RastapopNaval Architect

Circulation is required in a single, infinite fluid to create a pressure differential between the top surface and the bottom.
It isn't necessary in the case of a hull sitting in water, where a pressure differential can exist without circulation.

You persist in taking theorems and equations that are intended for use immersed in a single fluid, and using them elsewhere.

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### JoakimSenior Member

My calculations are based on Savitsky method. Read the papers by Savitsky. There are several of them from 60's to rather recent years. There used to be an online calculator, but I couldn't find it now. Mine is codec in C. Mine includes the models for aerodynamic drag and whisker spray drag Savitsky introduced much later than the original model. It also has a model for drive drag, and allows chines to get dry, which the original one do not include. I have also model for increased friction due to surface roughness.

Aerodynamic lift is not included, which can be very important for light and fast boats. The fact that you can drive at 6 degree trim is most likely due to aerodynamic lift of the hull keeping the boat from porpoising.

All the forces between the hull are pressure (perdendicular to hull) and friction (tangential to hull and paralle to flow). Since only bottom of the hull is touching water the pressure can act only at the bottom, which is at trim angle to water level and speed. The force supporting the boat must be equal to weight and the drag component of the pressure is TAN(trim) * weight. So in your case TAN(6)*840 lbs = 88 lbs. At 3 degrees trim it would only be 44 lbs. So much less than thrust.

Well for 99% of the world unit of force is Newton [N] and SI are used and now factor is needed to correct the units. Just the coefficient of drag or lift.

If the coefficient of drag or lift changes with speed, then lift or drag is not purely dependent on the square of speed. In the case of a planing boat there are so big changes that at some speed ranges the total drag is constant or even decreases with speed, at some it depends about linearly from speed and at some it is closer to square of speed. That is why you need a model like Savitsky to capture all the different phenomena.

Form drag is used for blunt bodies. A foil, a hydrodynamically well designed hull or a drive have very little form drag. They have mostly friction drag and pressure drag due to free surface. The latter doesn't work at all like form drag, nor does the pressure drag of a planing hull.

As I said earlier only aerodynamic drag and part of drive drag (or shaft etc) is form drag for planing boats. The rest is something else.

A boat that porpoises at full speed has too high trim angle, which is caused by having CG too far back. At the same time the trim angle just below porpoising is the fastest one, thus with lowest drag due to lowest wetted area.

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### sandhammaren05Senior Member

Show me how you would calculate a lift coefficient for a planing hull.

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### sandhammaren05Senior Member

I've had Savitsky's paper for a while but haven't found it informative. I would never run someone else's omcputer program, repeating their input assumptions and mistakes. We derive all results ourselves.

Sorry. In the U.S. we use lb, ft, hp, mph. I'm not a big fan of metric units although I regularly buy meat and cheese in kilos in Austria.

Form drag is used for all bodies, I refer you to the force integral in hydrodynamics. Form drag is used for wings, which are not blunt bodies. You calculated the drag wrong above. Better to use Power=force x speed, then you get the right result.

You haven't understood that lift and drag coefficients decrease with J. Again, see something easy to read like Du Cane 1951 or 1956, still available on amazon.com. Skin friction is negligible compared with form drag on a planing boat. Easy to calculate skin friction for a turbulent boundary layer. A few lb.

Your notion of porpoising doesn't apply to a well-designed boat bottom unless maybe the boat is underpowered. My 15' Allison bass boat with tiller handle and 35 hp may porpoise a little after planing, but as soon as I hit the throttle it levels out and runs.

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### JoakimSenior Member

No, no and no. Form drag is not used for wings. It's a similar looking formula, but it is not form drag. E.g. : https://www.grc.nasa.gov/www/k-12/airplane/drageq.html "The drag coefficient given above includes form drag, skin friction drag, wave drag, and induced drag components."

A wing has almost zero form drag. At low AoA it has basically only friction drag. With higher AoA it has also induced drag.

The area A in the formula is plan area for a wing, foil or keel, which makes much more sence than using frontal area. Frontal area would be good for bodies with mostly form drag and plan area is good for bodies with mostly friction.

If you integrate the forces over the parts of the planing prismatic hull touching water, you will find friction forces, which have direction backwards and slighty downwards along the keel and pressure forces, which have direction upwards and slightly backwards perpedicular to keel.

The pressure part is easy to calculate, since it must be very close to the weight of the boat and then you can calculte the drag due to pressure forces. This is what I have done. 88 lbs at 6 deg and 44 lbs at 3 deg trim.

Then you can compare that to thrust from your 75 HP at 67 mph, which is going to be about 250 lbs. So there is around 200 lbs missing depending on the trim. That is going to be something else than pressure drag caused by water. It will be friction drag from hul and drive and aerodynamic drag.

Skin friction is not at all neglible for a planing boat. The drive alone will have about square feet wetted area when installed high. The hull will have at least as much, even your light boat at 67 mph. Slower boats will have much more.

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### sandhammaren05Senior Member

A wing has a form drag where lift/drag is the inverse of the angle of attack. Skin friction should be much lower.

The area used for lift is the wet area reduced by trim angle. For boat form drag, the bottom accelerates a wedge of water, the wet area A again enters.
The drag you calculate is negligible. The main drag is form drag. Anything that creates a wake has form drag, wing and boat bottom included.

To get the form drag, take drag=power output/(speedxprop efficiency). A calculation that disagrees with that is based on a mistake.

Calculate the skin friction/area for a flat plate in a turbulent boundary layer and you'll agree that it's negligible. v Karman showed how to do that.

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Have a look at the attached file which was part of my thread few years ago

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### sandhammaren05Senior Member

Will do, thanks.

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### tom28571Senior Member

Barry,

I sent you a PM.

Tom

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### JoakimSenior Member

Calculate the skin friction with your formula for a foil and compare that to the measured drag coefficient. You will notice they are very much eaqual unless the foil is very fat and has some form drag. At higher AoA the drag starts to increase. Partly due to force creating lift and having a drag component as well and partly due to induced drag, if the span is not infinite.

The drag I calculated is all the drag caused by water pressure on the hull. There can't be anything else! It's just a simple geometric calculation.

Friction creates a wake as well and if you mean waves created by the hull that is not part of form drag in typical vessel hydrodynamics. Waves are caused by residual drag. Although for planing vessel residual drag is not considered separatly typically.

If you do the calculation for 67 mph, you will find out that skin friction even for the small area of 1 square feet hull + 1 square feet drive is quite a big portion of the total drag. 1 square feet will not be enough to support the 840 lbs weight at 67 mph and 6 degrees trim. Maybe with help from aerodynamic lift, but most planing boats are not that light, have less trim and neglible aerodynamic lift.

Also aerodynamic drag is very important at those speeds. A car which is not about the same size and most likely more aerodynamic will need about 20 HP at 67 mph. And that 20 HP is at very good efficiency, not with propeller having only 60% efficiency.

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### sandhammaren05Senior Member

You're making a mistake in calculating skin friction, it's low compared with form drag.

Form drag is one of the integrals of pressure over the shape of the body. The other integral is lift. You cannot get either the lift or drag right by trying to extrapolate using a body of infinite span/beam. You must use the empirically-found lift and drag coefficients for a boat bottom as 'wedge' of finite beam in three dimensions. Or, get the net drag from the power supplied by the prop (shaft hp divided by prop efficiency) divided by the speed.

The integrals of pressure over the body for lift and form drag can be transformed into integrals of velocity over a cross section of the flow (including wake) downstream of the body. Any body that creates a wake has form drag. See Landau-Lifshitz's 'Fluid Mechanics', e.g.

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### RastapopNaval Architect

EDIT: Post and image removed, see next page for corrected version. (or quotes below for the incorrect version)

Last edited: Mar 29, 2017

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### BarrySenior Member

Are these your cfd's or another's?