Transom Stern Models: Hullspeed, Michlet, Hydros and Flotilla

Discussion in 'Hydrodynamics and Aerodynamics' started by Leo Lazauskas, Apr 24, 2011.

  1. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Several people have emailed me asking about the differences in the resistance predictions of several thin-ship computer codes and theories for hulls with transom sterns.

    The main differences, as noted by FormSys in their Hullspeed manual, are due to the transom stern models used in the computer programs. Another important issue (not noted) is the way in which the total drag is estimated.

    As an example, I will look at resistance predictions of a NPL 4a hull using the computer codes Hullspeed, Michlet, Hydros, and Flotilla, and the theory of Patrick Couser. (It should be emphasised that all of these models will yield almost identical results for hulls without transom sterns.)

    Couser, Hullspeed, and Hydros use the idea of a finite length, virtual appendage behind the transom as depicted in the plots at the top of Fig 1. In general, they assume a parabolic shape for the cavity. In the computer programs, the cavity is meshed and then used in thin-ship computations as if it was part of the main hull.

    Michlet and Flotilla make no assumptions about the length or shape of the hollow: they work directly with the Michell "P,Q" functions.

    Couser allows the hollow length to vary with Froude number and beam-to-draft ratio as shown in the plot at the bottom left of Fig. 1. Hullspeed (as does Couser for Fn > 0.7) assumes a constant length of 8 for all Fn.

    Hydros uses a variable hollow length model, however, in the most recent embodiments, a limit is placed on the minimum length. This length (based on the re-attachment length behind a backward-facing step) is about 6 times the draft of the transom. L.J. Doctors and Simon Robards have spent much time and effort trying to find how the hollow length varies with transom shape and the vessel's speed. Robards uses about 13 empirical parameters in Hydros to estimate the length.

    Hydros, Michlet and Flotilla attempt to estimate the extent of the dryness of the transom at low speeds. These three models also estimate the resistance due to the loss of hydrostatic pressure on the transom. Couser and Hullspeed do not account for transom dryness or loss of pressure.

    Michlet and Flotilla use a simple one-parameter equation based on a theoretical result to estimate the transom dryness; Robards uses about 10 empirical constants in Hydros.

    The plot at the top left of Figure 2 shows the total resistance coefficient C_T estimated by the five models. Here:

    C_T = C_W + C_F

    where C_F is the skin friction estimated using the ITTC line, and C_W is the predicted wave resistance. No form factors have been used, and the hulls are in their static, i.e. at rest, attitude.

    The resistances have been non-dimensionalised in the standard way, e.g.

    C_F = R_F/(0.5*rho*U^2 S),

    where R is the skin friction, rho is water density, U is ship speed, and S is the wetted surface area.

    The predictions tend to fall into two main groups: Couser and Hullspeed are, of course, similar to each other because they are based on the same theoretical work. Differences are due to the different assumed hollow lengths.

    Hydros, Michlet and Flotilla are all alike because they include a component of drag, C_HS, due to the loss of hydrostatic pressure on the transom.

    Couser, Hullspeed and Hydros use form factors applied to their computer predictions of wave resistance and/or skin-friction. Michlet and Flotilla do not use form factors, but attempt to estimate the additional effects on wave resistance, skin-friction and the hydrostatic drag more directly, by incorporating the effects of squat.

    To include form effects, Couser and Hullspeed proceed in the standard naval architectural way, by using a form factor based on experimental results. The viscous drag coefficient is

    C_V = (1 + k_F) C_F

    where k_F = 0.3 based on Couser's experiments.

    Robards uses a form factor applied to the wave resistance as well as the skin-friction. For the Uni of Southampton NPL series, he found

    C_V = (1 +k_W)C_W + (1+k_F) C_F

    with k_W = -0.2 and k_F = 0.347.
    The negative value of the "wave form factor" k_W reduces the wave resistance computed using Hydros by 20%.

    Michlet and Flotilla use the hull sinkage and trim from Couser's experiments.

    The results of including form drag or squat on the estimated total resistance are shown in the plot at the top left of Fig. 2.

    There are considerable differences between the predictions at lower Fn, but all models do a reasonable job for Fn > 0.8. Couser and Hullspeed yield identical results for Fn > 0.7 because the hollow length are the same for these Froude numbers. Results for Michlet and Flotilla are alike because they both use the hull attitude in their predictions. Hydros results tend to fall between the other two groups.

    Wave resistance coefficients are shown in the middle plot of Fig. 2. It can be seen that Couser and Flotilla do a great job for a wide range of Fn. Hydros results for wave resistance are not given explicitly in Robards' thesis.
    Michlet under-predicts for Fn > 0.45, but it should be remembered that its prediction method is bound up with the hydrostatic resistance which does enter into the "pure" wave pattern resistance shown here.

    Residuary resistance is here defined as

    C_R = C_T - C_F.

    For Couser and Hullspeed, this can be written as C_R = C_W + 0.3 C_F because they use a constant form factor.

    For Hydros, Michlet and Flotilla, C_R includes the transom hydrostatic resistance which is absent in Couser and Hullspeed.

    The plot at the bottom left of Fig. 2 shows that all models are reasonable for Fn > 0.8.

    Viscous resistance is here defined as

    C_V = C_T - C_W

    Couser and Hullspeed are identical with C_V = (1 + k_F) C_F, and k_F = 0.3. Flotilla does a very good job here for a wide range of Fn, but all models are reasonable for Fn > 0.8. Hydros results are not available because we do not have available an explicit estimate of C_W in Robards' thesis.

    The five models considered in this short note all require one or more empirical constants or factors in order to estimate the total resistance.

    Couser and Hullspeed need an estimate of the transom hollow length and a single form factor to be applied to the skin-friction.

    Hydros requires several factors to estimate the hollow length, several more for the extent of transom dryness, one form factor for the wave resistance, and another for the skin-friction.

    Michlet and Flotilla require a single constant to estimate transom dryness, and both require the attitude of the hull or, at least, the maximum trim and maximum sinkage. In addition, Flotilla requires another empirical constant to estimate the effects of wave resistance and hydrostatic pressure inside the hollow induced by the transom stern.

    It is impossible to recommend any one of the five models over the others: it all depends on what output is required, what Froude number range is of interest, and what "style" you prefer, i.e. "form factors" or some other method requiring as much faith and hope!

    Experimental results were supplied by Patrick Couser who performed the experiments. See:
    Molland, A.F., Wellicome, J.F. and Couser, P.R.,
    "Resistance experiments on a systematic series of high speed displacement
    catamaran forms: variation of length-displacement ratio and breadth-draught
    ratio", University of Southampton, Ship Science Report 71, 1994.

    Hullspeed estimates were provided in a previous thread. See:

    HYDROS results are from the thesis:
    Robards, Simon William,
    "The hydrodynamics of high-speed transom-stern vessels",
    M. Engineering thesis, The University of New South Wales, Nov. 2008.

    Michlet 8.07 results are from the free version version available at:

    Flotilla results were performed by me using version 3.01. Similar results can be obtained with version 2.07.

    Hope that helps!

    (Apologies in advance if I have inadvertently mis-represented anyone's work!)

    I've attached a pdf of the figures in case that is better for some readers.

    Attached Files:

    Last edited: Apr 25, 2011
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  2. Erwan
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    Erwan Senior Member

    Thank you very much for sharing your research.
    I am not able to make relevant comments regarding the validity of the different model. But I have an info related to that topic

    A long time ago an architect, working with VPLP had designed a F28 tri, and he told me that according to some water tank test at Delph university, they found the following empirical result:

    For hight speed and long hull like catamaran, the minimum drag is achieved when the "wetted"transom is around 25% of the main hull section.

    It is a 15+ years old research, so of course it can look a bit candid.

    Best regards

    1 person likes this.
  3. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Thanks, Erwan.

    If you haven't seen it, the video of the calculated flow past a transom stern is worth watching because it gives a hint of what a difficult flow problem we are dealing with.

    None of the empirical corrections to thin-ship theory (Hullspeed, Michlet, Hydros or Flotilla) can be expected to do really well on this problem. After all, we are trying to approximate a highly unsteady, turbulent flow with splashes and other non-linear effects with computer codes that are linear, steady, inviscid, and valid only for thin ships.

    It is remarkable that the codes get as close to the measured resistance as they do. At least they get a wrong answer in a reasonable amount of computer time: CFD can be even more wrong, and it will take days of processing on several workstations to get the results! :)

    All the best,
  4. idkfa
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    idkfa Senior Member

    Many, many thanks Leo, great stuff, yet to get my head around it.

  5. Erwan
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    Erwan Senior Member

    Same remark than idkfa, and I would add a semantic remarks, I am not sure that this is the code which is remarkable, I would guess that is the brains who achieved the code.:)

    Thank so much for sharing these great achievements


  6. patrik111
    Joined: Sep 2003
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    patrik111 Junior Member

    To transom or not to transom

    Hi Leo, all,

    I am trying to do an evaluation of an existing hull drawing, and possibly improve on it within a box rule (the NZ 8,5 rule for multihulls). I am using the 9 series as it allows for some speed, and my main limitations are for draft, GML (dont want pitchpoling), possible modifacation of forefoot to bring it up a bit. I am inputting existing offsets, and then try to create reasonable candidates with Godzilla using limitations reflecting original design.

    1) if I look at the graphs above, the squatted restistance graphs are (to my understanding) providing reasonable agreement to the test results, if I in reality would be able to control squat (large portion of movable ballast, forward push of mast), is a unsquatted prediction by michlet then as trustworthy as indicated in the squatted example shown? (in short, if I can force squat to be 0, is michlet a good indicator for resistance)

    2 If I am comparing (not in absolute numbers, but for concept choice) transom and no transom hulls, will I be able to draw any "reliable" conclusions for the lower froude numbers? (Fr<0,6). For above, there is a quite markedly advantage for the transom hull. (also below, but reading the above, I am not entirely sure if this region of the results is as reliable as the ones over Fr 0,8.

    3 Is there any good way to adress this lower speed region for transom hulls? Correct me kindly if I am wrong, but it seems litterature dwells more on the higher froude numbers for transom sterns, with less, at least layman readable, on the slower or transition regimes.

    4 If I compare existing offsets and godzilla generated hulls, would it be fair to say that a difference in the resistance numbers would be there in real life? (for the slower regime in particular)

    Thanks for providing us with these exiting programs, quite remarkable how addictive they are :)

    All input will be greatly appreciated


  7. Leo Lazauskas
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    Leo Lazauskas Senior Member

    Hi Patrick,
    I am unable to offer much advice on the low-speed regime where the
    transom is still partly wet. All I can do is to repeat my warning
    that we are expecting a lot of potential codes to handle an unsteady,
    non-linear, turbulent flow for hulls where the thin-ship assumption is
    violated. Have you had a look at how Robards addressed the issue in
    the thesis I cited in an earlier post in this thread?

    Michlet might give reasonable results for squatted hulls if you can
    estimate sinkage as well as trim. Trim is reasonably easy to simulate
    by your idea of moving ballast, or pushing the mast forward, but that
    won't increase the displacement weight.

    I can get very good agreement with other codes where squat and some
    other near-field effects can be calculated, but that is well beyond
    Michlet's capabilities.

    Good luck!
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