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

    You may be using the term "source" in a somewhat different way than has developed in hydrodynamics over the last century.

    Reflection of waves by the hull does matter, and a proper analytical model will take it into account

    Perhaps you could provide some sketches of your ideas?
     
  2. Leo Lazauskas
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    Leo Lazauskas Senior Member

    I'm not sure if I have already mentioned Ward's Optimum Symmetric Ship.
    These are the result of analytic minimisations of wave resistance within the
    confines of thin-ship theory.

    See the post and attachments:
    http://www.boatdesign.net/forums/de...t-hull-shape-min-drag-27972-7.html#post283436

    The strange bumps and hollows are clearly not practical, but the measured
    wave resistance was very low at their design speeds, as predicted.

    Another "zero wave drag" assembly of theoretical interest is Krein's Caravans.
    These can be shown to have zero wave resistance, but they have an infinite
    number of hulls joined bow-to-stern. The individual hulls are not fore-aft
    symmetric, but the assembly as a whole is symmetric. The individual hulls
    have cusped waterplanes.

    Again, they are clearly impractical, but there are insights to be gleaned from
    their characteristics. For example, it is interesting to examine the free-wave
    spectrum of the caravan with different (finite) numbers of sub-hulls, and to
    see at which wave angles the most energy is being shed, and at which angles
    it is very low.
     
  3. Richard Pitblad
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    Richard Pitblad Richard Pitbladdo

    The Calypso II hull design happens to incorporate many of the elements I am pondering (see the video in http://www.cousteau.org/about-us/calypso2). It could be a practical ship in either direction, with appropriate fairings to address form drag. In deep, flat water I would put my money on less resistance in the original design direction at hull speed. A math or cfd analysis that models the various sides of the ship as reflecting barriers is beyond my own resources until I retire from my day job.
     
  4. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Those who are interested in theoretical zero wave-drag vessels can experiment with Krein's caravans in Michlet. See the manual.

    The first 4 vessels in the sequence are attached.
    The 1st has no "satellite" hulls. It is fore-aft symmetric with cusped waterplanes.
    The 2nd has one satellite hull at each end. The satellites have cusped waterplanes, but they are not fore-aft symmetric.
    The 3rd has two satellites at each end.
    Repeat unto infinity :)
     

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  5. Richard Pitblad
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    Richard Pitblad Richard Pitbladdo

    Another example: An arrow trimaran with laterally asymmetric amas can have very different wave resistance going forward and backward, when reflection and diffraction are accounted for.

    First a building block: Consider a single narrow hull with one flat side and one convex side. Say the curved side is to port. Then the bow wake will be larger on the port side due to reflection of the hull sides. Aft of the stern, any residual wake will cease to be reflected and will diffract to starboard.

    Moving on, now consider an arrow trimaran with half of its displacement in the center hull. Assume the thin center hull's length is one quarter of a wavelength at design speed and the amas are each the same length as the cetner hull. Assume each thin ama is flat side out, with a longitudinal distribution of volume proportional to the central hull.

    As far as positioning, assume the bows of the amas are one half wavelength behind the bow of the center hull (e.g. out of phase), and placed laterally so the bows form a Kelvin angle.

    Except to the extent that waves can transmit through the sides of the amas, the amas will absorb most of the energy of the wake created by the center hull. (Any "leakage" of wave energy under the amas can be countered by designing some curvature into the outsides of the amas.)

    If the trimaran were run backwards, the resistance would increase to the extent that diffraction at the sterns of the amas allow the wave energy to spread out, rather than propagating solely in the direction of the central hull for cancellation. (This would be exacerbated in the case that reflection is not 100% and the amas had some outward curvature.)
     
  6. Ad Hoc
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    Ad Hoc Naval Architect

    Richard

    You should read, if you haven't already,

    "Fundamental Study on Optimum Position of Outriggers of Trimaran from View Point of Wave Making Resistance" by Suzuki K., Ikehata M, Fast '93.

    They have performed experiments doing approximately half of what you are proposing above. It is an interesting read.
     
  7. DCockey
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    DCockey Senior Member

    Are you considering the waves generated by a hull as a single bow wave which is reflected as it travels along the hull and a single stern wave?

    Why wouldn't the amas reflect the wave energy rather than absorbing it?

    What is your intent? Describe a configuration which does not have the same wave resistance when direction of motion is reversed?
     
  8. Richard Pitblad
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    Richard Pitblad Richard Pitbladdo

    Thanks for the reference. I had some difficulty accessing the article you cited, but Iwas able to read some of the authors' follow-up work. It was nice to see that experimental results validate wave reflection off the outriggers.
     
  9. Richard Pitblad
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    Richard Pitblad Richard Pitbladdo

    Not really, I had in mind a more gradual distribution of sources and sinks.

    The reflection of the wave generated by the central hull and the wave generated by the sources and sinks of the amas are 180 degrees out of phase and cancel each other, resulting in the net effect of absorption. That's why I put half the displacement in the amas.

    Yes, this thread is about the optimality of longitudinal symmetry. A necessary (but not in my mind sufficient) part of the argument is that wave resistance is the same forward and backward. I hope I have established that reflection of waves between components of hulls invalidates the entire argument. Only in special circumstances will hull designs exhibit the same resistance going forwards and backwards, and longitudinally asymmetric hull forms and configurations can provide superior results in minimizing wave resistance.
     
  10. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Essentially, all you have done is to invalidate a 1st order theory by
    introducing 2nd order effects and using different boundary conditions. The
    1st order conclusions still hold. If you now introduce viscosity, you will find
    that reflection might not be all that important because short wavelength
    waves won't reach the other hulls, or they will be so small as to have an
    insignificant effect on the wave resistance after reflection.

    "All models are wrong. Some are useful." - George Box.
    To which I would add, simple models are much faster and often give
    the same results within experimental uncertainty as complicated models in
    appropriate circumstances. :)
     
  11. Richard Pitblad
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    Richard Pitblad Richard Pitbladdo

    In this case, Leo, I consider myself a student of your work, adding a few modifications that I do consider 1st order, not 2nd order. My thinking was particularly inspired by your diamond configuration tetrahull. The viscous effects you are referring to would apply equally to invalidating the wave cancellation for the tetrahull (such a beautiful animation at http://www.cyberiad.net/waketet.htm) . In the absence of viscous effects I have nothing to refute your results for a strutless SWATH or a pure pressure distribution. However, if we are talking about the surface penetrating hulls we are used to considering, the wake patterns would not match your model. There would be wakes generated on the outsides of the outside hulls (due to less than complete transmission of the out-of phase bow hull wavetrain through/under the outside hulls), and less net wake generated on the insides of the outside hulls (due to partial reflection of the bow hull wavetrain), and therefore less than complete cancellation at the sternmost hull.

    What I have done is transform these wrinkles into an advantage, that allows the same degree of cancellation by eliminating the sternmost hull and adding curvature to the outside hulls (the degree of inside or outside curvature would depend on the ratio of wave transmission under the outside hulls to wave reflection off the sides, which in turn depends on draft, keels, etc.). Cancellation can therefore occur with less hulls, less complexity, and within a total length less than one wavelength.

    I agree. For this reason, I would avoid complicating the analysis with interactions between viscous effects and wavemaking, unless data from experiments and sea trials clearly refute the simpler predictions in ways that such interactions help explain.
     
  12. Leo Lazauskas
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    Leo Lazauskas Senior Member

    That's probably a bad example, Richard :)
    The demihulls are unusual: SWATH-like in cross-section and trapezoidal in sideview.
    That means they individually shed little energy for large wave propagation
    angles (theta). The diamond arrangement cancels waves at lower theta
    leaving little at higher thetas (because there wasn't much there in the first
    place).

    I'd have to see experimental data to judge whether your configuration is
    better than a tri with symmetric demihulls, and if so, over what range of
    Froude numbers. Cambered hulls can create (wave-making) vortices, so
    the wave resistance might be similar to using uncambered hulls.
     
  13. philSweet
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    philSweet Senior Member

    I stumbled across this today looking for something else. It describes a minimum wake airframe shape developed using thin ship theory. At mach numbers > 1, the area is not based on the perpendicular plane, but is based on a cone, or an average of tilted planes in the case of complicated shapes. This creates and aft bias to the displacement of low wake drag bodies in high-speed airframes.

    http://en.wikipedia.org/wiki/Area_rule

    and here

    http://en.wikipedia.org/wiki/Sears–Haack_body

    It may be that a free surface begins to have, in effect, a mach speed that diminishes as you approach the surface. Thus, a hull's waterlines would look symmetrical until the draft was reduced to the point that the "mach 1" was exceeded, then the waterplanes should reflect a shape of the transonic form above this point. This would yield what we tend to see- a center of floatation moving aft as waterlines near the surface.
     
  14. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Tom Speer mentioned this body to me many years ago.
    I still think it doesn't have any role to play because of free-surface effects.
    It may, however, be of some use at very low Froude numbers and extremely
    high Fn, when the free-surface is very flat. I haven't worked out the high Fn
    benefits because the free-surface is a plane of anti-symmetry, as opposed
    to the low Fn case where it is a plane of symmetry.
    In any case, at high Fn the waterplane area is the main geometric parameter
    for wave resistance and the actual details of the shape are unimportant.
     

  15. DCockey
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    DCockey Senior Member

    The "area rule" for minimizing wave drag of aircraft does not apply to ships and boats moving on a free surface. Free surface waves such as generated by boats and ships are fundamentally different from pressure waves, including shock waves, generated by aircraft. Pressure waves are non-dispersive; the speed of propogation of the waves is independent of the wave length. Free surface waves are dispersive; the speed of propogation of the waves depends on the wave length. The dispersive characteristics of free-surface waves cause the characteristic Kelvin wave pattern of a ship or boat. The shapes and angles of the waves in the Kelvin wave pattern are independent of the vessel's speed. In contrast the shape and angles of the shock waves from an aircraft at supersonic or transonic speeds depend directly on the ratio of the speed of the aircraft to the speed of sound of the air, ie the Mach number of the aircraft.

    For free surface waves the depth to the bottom also affects the speed of wave propogation. As the depth to the bottom becomes small compared to the wave length free surface waves become less dispersive and their behaviour takes on some of the aspects of pressure waves. For vessels operating in water with depth much less than the length of the vessel than a variation of the Whitcomb et al "area rule" might apply.

    Can you elaborate? What do you mean by "a mach speed that diminishes as you approach the surface"?
     
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