Hull Asymmetry and Minimum Wave Drag

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, May 28, 2011.

  1. DCockey
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    DCockey Senior Member

    I understand Froude Number vs. speed and the significance of Froude number and waves. Have understood that for a very long time.

    I agree with your statements in the above example. But that doesn't have anything to do with the questions I raised in the first post of this thread.

    Why are you interjecting slenderness and L/D ratio in what was intended to be a discussion of the interaction of hull volume distribution as characterized by LCB and wave resistance?

    Did my use of the work "optimum" cause confusion?

    Did my comment in the first paragaph about Leo's statement about wave resistance based on "Mitchell's Thin Ship Theory" cause an assumption that this was about slenderness? If so it was that isn't what it's about.
     
    Last edited: May 29, 2011
  2. DCockey
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    DCockey Senior Member

    The image on the right is not intended to suggest equilibrium. Didn't say it did. Rather it illustrates one possibility of how the "moving" LCB could have been calculated using assumptions which may or may not be consistent with the other assumptions Leo made. Clearly the one on the left would be more "exact" and the one on the left would be an "approximation". Leo in his report says the hydrodynamic forces were calculated on the original hull surface, not on the more exact hull surface immersed while moving.

    The question I have about the results Leo reported is which way were the calculations made. I read the report Leo attached above and it does not say. Perhaps Leo will clarify.
     
  3. Ad Hoc
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    Ad Hoc Naval Architect

    Becasue of this:

    The same hull, same LCB just towed in different ways. Two when towed have the same L/D ratio, the 3rd method of towing (beam on) does not. The fact that the LCB has not changed in any of the 3 variations of towing …has this escaped you?

    Hence, the above highlights the flaw in your reasoning to understand the mechanisms.
     
  4. DCockey
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    DCockey Senior Member

    I also agree that a hull form which is "optimal" at one Froude Number will not be "optimal" at a different Froude Number. I don't think I ever implied it would be. In fact in the first post I talked about the "optimum" static LCB location varying with Froude number.
     
  5. DCockey
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    DCockey Senior Member

    No it didn't escape me. Different hull shapes with the same LCB can and will have different resistances. Never claimed they wouldn't.

    So what is the relevance to changes in LCB location leading to changes in resistance when other parameters stay the same?
     
  6. Ad Hoc
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    Ad Hoc Naval Architect

    Froude number.
     
  7. DCockey
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    DCockey Senior Member

    So we agree that changes in static LCB locations with other hull shape parameters staying the same will affect resistance differently at different Froude numbers?
     
  8. Ad Hoc
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    Ad Hoc Naval Architect

    Now you're getting it :)

    Now reread my posts in #3 and #7.
     
  9. DCockey
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    DCockey Senior Member

    Perhaps we were talking past each other. :)
     
  10. DCockey
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    DCockey Senior Member

    Leo, the graphs in your attachments in posts #17 and 18 show lower drag with a forward LCB at higher Froude numbers (approximately 0.26 or greater) based on the calculations which include sinkage. At first glance this seems to be opposite what is suggested in the sources I cited in post #1; that is drag going down with a aft LCB at higher Froude numbers.

    However, it looks like your variation in static LCB is about 9% forward of mid-ships for the Fish variant, and about 9% aft for the Swede variant. This is considerably more than shown in the the curves of "Optimum location of center of buoyancy versus Froude number" in Paulling, Figure 11-2 which has data from Holtrop, Delft, Jensen and Series 60. They show "optimum" LCB locations ranging from aft of 4% forward for Fn = 0.15 to forward of 3.5% aft for Fn of 0.4 and go to a maximum of about 6% aft at Fn = 1.0.

    So perhaps the apparent discrepancy isn't a discrepancy since the LCB locations are significantly different. It would be interesting to see what your analysis results in for LCB locations closer to mid-ships if someone has the time to make the runs. Any thoughts?
     
  11. DCockey
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    DCockey Senior Member

    The crossover is why I suspect it's more associated with sinakge and wave making (or wave making and sinkage, take you pick of the order) than with boundary layer and other viscous effects, at least for vessels without significant separation aft. Boundary layer and other viscous effects are not directly connected to Froude number, but sinkage is, and does cross-over, but not necessarially at the same Froude number as the "optimum" LCB does.

    Perhaps a study for a PhD student somewhere.
     
  12. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Sorry, but I am in the middle of other things so I haven't had time to go through all posts...

    1. In the report, a "one-shot" method is described, i.e. squat is calculated using the static LCB and LCF.

    2. A further refinement (not described in the report) is to iterate until equilibrium is reached, i.e. until the sinkage force and trimming moment become insignificant and there is no further sinkage or trim.

    Essentially, I use the one-shot method, and put the hull in the attitude predicted. The new LCB and LCF etc are calculated assuming a flat surface.
    Repeat until convergence.

    Doctors and Day in "Non-linear Free-Surface Effects on the Resistance and Squat of High-Speed Vessels with a Transom Stern" use the original static LCB, LCF etc throughout their iteration method. They call the LCF, LCB etc. the "hydrostatic stiffness coefficients". I use (what they say is the ideally consistent) "hydrodynamic stiffness coefficients" but that takes a bit more computing. Once equilibrium is reached there is no error introduced by using their simpler "hydrostatic stiffness" approach. (I need some intermediate calculations for some of my work, so I use the "hydrodynamic stiffness" approach).

    3. Of course, this means that my final LCB and LCF should be thought of as inconsistent or "nominal" values. They should not be used in isolation, i.e. without also referring to the sinkage, trim and sinkage force and trimming moment.

    I'll try to get back to this when I get time.
    Leo.
     
  13. daiquiri
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    daiquiri Engineering and Design

    This discussion is interesting. As I've understood it, DCockey is trying to comprehend the physical reasons behind the "travel" of the optimum (in terms of minimum drag or propulsive power) LCB location as the Fn changes, all the rest being equal.

    The fact that the optimum LCB changes with Fn is routinely mentioned in various textbooks and test reports, and is also reflected in the shape of some traditional boats and classic yachts (refined through first-hand on-board experience, rather than through controlled experiments), where slower sailboats have a fish-like (volume fwd) shape, whilst racers appear more volume-balanced towards aft.
    There are some nice illustrations of that concept in Carlo Sciarelli's book on traditional sailboats "Lo Yacht". I have at home, not in the office, so I can't post pictures right now.

    I can post this excerpt from Bertram's "Ship design for efficiency and economy":
    LCB.gif
    Please note the first formula (for cargo ships), which linearily decreases with Fn.

    A similar trend is visible in this (by now pretty famous on BD.net) paper by Blount about semi-displacement hull forms for megayachts (page n.8, figure n.5): http://www.boatdesign.net/forums/at...s-semi-displacement-mega-yacht-hull-forms.pdf
    You might also be interested to read this interesting paper by Volker: DTMB_1955_T257.pdf , which deals with the same issue.

    They all give the results of experiments and/or trials, but don't offer much when it comes to the physical reasons behind these values. Then again, there are so many variables involved in the fluid dynamics of a hull moving through a liquid-gas interface that the reasons for this LCB behaviour are probably more than just one, or more than just few.

    Cheers
     
  14. DCockey
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    DCockey Senior Member

    That's a good summary of what I'm interested in. Your comments about the "evolution" of boat design based on experience and how it corresponds to test results is good. I've been wondering about that.

    Your attachments are also appreciated. I've seen the first but the second one qualifies as obscure.
     

  15. daiquiri
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    daiquiri Engineering and Design

    Which one? And what do you mean by "obscure"? :confused:
     
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