Froude and planing

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

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  1. sandhammaren05
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    sandhammaren05 Senior Member

    Yep. And if you take a gander at Faltinsen's derivation of lift in his book (ch. 8.9) you'll see that he starts with the approximation of the bottom as a cut on the horizontal axis (like the treatment of thin wing theory at small angles of attack) where the Kutta condition can be applied at the trailing edge in standard fashion to develop lift. The importance of the beam/span in his formula is that a pointed transom (one where beam=0) cannot develop lift.
     
  2. Rastapop
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    Rastapop Naval Architect

    Mine.

    I don't have time to search right this minute, but it doesn't look like this is in chapter 8.9 of my copy. Chapter 9 somewhere?
     
  3. Joakim
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    Joakim Senior Member

    Rastapop: How do you define hydrostatic and hydrodynamic lift from your CFD results? Transom is fully dry already at about 1/10 hull speed, thus about 0.5 knots for the 14' boat he is referring to.

    How relevant are your results regarding Sanhammarens claims?
     
  4. Rastapop
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    Rastapop Naval Architect

    Hydrostatic as you'd expect it to be defined, and dynamic for everything else.

    EDIT: Rest of post removed, see my post below with corrected image.
     
  5. Joakim
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    Joakim Senior Member

    How would you expect hydrostatic to be defined with free uneven surface?
     
  6. Rastapop
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    Rastapop Naval Architect

    Sounds like a question for the software developers, not me.
    Presumably the software is capable of generating iso-surfaces for a given pressure under an uneven free surface, and so is capable of generating the values you're referring to.
     
  7. Joakim
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    Joakim Senior Member

    You as a software user should definitely know how variables displayed are defined. The CFD softwares I have used (not specifically targeted to marine applications) define pressure as Ptot = Pstat + Pdyn, where Pdyn is 0.5*rho*V^2. Pstat is the one causing forces on surfaces. Usually hydrostatic pressure is taken away form Pstat (with e.g. Phstat = rho_ref * g * (h-h_ref)) in CFD in order to keep the numerical value of Pstat small, which helps reducing numerical errors.

    So, if that is the way it is done in the CFD you are using, then hydrostatic pressure and thus lift is most likely referenced to the static free surface level, not the real one. That is also how Savitsky has defined it.

    In the hydrostatic lift curve you showed the hydrodynamic lift is first negative and then becomes positive at a very low speed, but then is again negative for a long while. Also note that CG is higher than at still at all speed and clearly rises before transom is fully dry. Also stern gets higher during that negative dynamic lift (Fn < Transom fully dry). So what is actually happening there? The trim gets higher and the stern gets higher, which must mean the whole boat gets higher. At the same time both dynamic and static lift gets lower. What is lifting the boat higher? There can't be much thrust at such a low speed.
     
  8. Rastapop
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    Rastapop Naval Architect

    I read your post Joakim, and thought "obviously he's wrong, and if I examine the curves the reason why will become apparent".

    Except examining the curves reveals you are not wrong.

    There are two issues at play. The first, smaller one, is that the boat was meshed only in approximately the correct static position (height and trim), and so the curves jump around a bit as it settles early on in the equation. In the updated image below I've simply removed the most offensive bits - I have no wish to defend or explain them repeatedly.

    The second is far more critical and embarrassing.
    To find the point at which the transom became fully ventilated I visually examined each step save in a post processor, and marked the point at which it became fully ventilated by simply multiplying the time step length by the frame number I was examining.
    I had somehow forgotten that I had only saved the state of the computation every 4 time steps, instead of every time step...

    By unlucky coincidence the Froude number I marked ventilation on matched very well with dynamic lift becoming positive for the first time. So I assumed there was no coincidence, and didn't double check...
    Instead of occurring around 2.1 seconds, full ventilation actually occurred around 8.4 seconds, near Froude(L) 0.4 (which as I've posted earlier in this thread is around where you can typically expect it to happen).

    So I retract my retraction, correct my correction, withdraw my withdrawal, whatever it was!
    Full transom ventilation does not mark the point at which dynamic lift goes from zero to positive.

    As bruising as it is to (apparently) publicly admit being wrong for the second time in a very short period, it's also a relief: between posting the curves the first time and now I just could not fathom where my understanding had failed, and I couldn't justify the new position I was taking with any argument other than the curves themselves (which probably should have been a warning that I needed to check what I was looking at).
    And I also don't need to continue being surprised at transom ventilation happening at such a low Froude number.
    My ego needs some rest and recuperation...

    Thank you Joakim.

    [​IMG]
     
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  9. johnhazel
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    johnhazel Senior Member

    Guys, With flow only on the bottom surface, it seems that applying the concepts of circulation and the Kutta condition is ludicrous. To crate lift, the circulation has to be around the lifting surface. With no water going over the planing surface, there cannot be circulation. Simularly, you must have flow above and below for the "Kutta condition" to have any meaning.
    The flow coming off a dry transom is separation, not a manifestation of the Kutta condition.

    Edit: It looks like several guys already pointed this out in previous posts.
     
    Last edited: Aug 8, 2017
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  10. cmckesson
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    cmckesson Naval Architect

    It has been shown by various authors (Doctors, Taravella, etc.) that the transom Kutta condition can be nicely predicted as occurring when the transom Fn = ~2.5. Transom Fn is Fn based of the wetted draft of the transom. Below Fnt=2.5 the flow wraps around the edge, above 2.5 it separates cleanly. This is a very useful predictor of transom clearance.
     
  11. sandhammaren05
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    sandhammaren05 Senior Member

    It is not ludicrous, it is correct: there is no way mathematically to represent a lifting surface other than by integrating over a distribution of vortex lines. This represents the bottom of a planing hull as half of a vortex sheet. There is no other way to describe the lift. Just look over the back of a 'square' transom as the speed is increased and you'll see the backflow suddenly stop, that is exactly the shedding of the starting vortex. That vortex has circulation opposite those integrated over in the vortex sheet.
     
    Last edited: Aug 12, 2017
  12. DCockey
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    DCockey Senior Member

    Is this discussion about mathematical physics or physical physics? They overlap considerably but are not identical.

    Does "lifting surface" here mean a zero-thickness surface in potential flow? There are other ways than the explicit use of vortex lines to mathematically represent a zero-thickness surface in potential flows. However the various methods can be shown to be equivalent.

    That approximation for the bottom of a planning hull needs an assumption that the Froude number is sufficiently high that the effects of gravity on the water, i.e. free surface effects, can be neglected. This is not a valid assumption at the speeds at which boats start to plane.
     
  13. sandhammaren05
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    sandhammaren05 Senior Member

    The wet planing area of a v-bottom is roughly triangular. Exercise: calculate the lift on a triangular wing in 3D at angle of attack alpha, i.e., calculate the circulation density and integrate to get the lift. Take half of that for a v-bottom with deadrise angle beta and you'll get a lift coefficient of c=(pi/2)(alpha)cos (beta). For beta≈13 degrees this gives c≈1.5alpha. The correct empirical lift coefficient is c≈.96 alpha.
     
  14. patzefran
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    patzefran patzefran

    The wing lift is generated (roughly) 1/3 by the intrados and 2/3 by the extrados, if you use 1/3 instead of 1/2 you obtain c ~( pi/3)(alpha)cos(beta) and c~ 1. alpha for beta =13°!
     

  15. sandhammaren05
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    sandhammaren05 Senior Member

    Taking c=alpha(cos(beta)) is pretty close to Clement's data, also to my own experience with v-bottoms and tunnels. Thin wing theory fails us here because the lateral fluid velocity from a v-bottom or tunnel sponson is too large (waves and trough). A thin wing can't cause that effect.
     
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