# Delft Series Resistance Equations - Variety

Discussion in 'Hydrodynamics and Aerodynamics' started by DCockey, Aug 4, 2011.

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### DCockeySenior Member

There are several, different equations available for bare/canoe hull residual resistance based on the Delft Systematic Yacht Hull Series data.

The derivation of one is discussed in The Bare Hull Resistance of the Delft Systematic Yacht Hull Series by Keuning, Onnink, Versluis and van Gulik, 1996 http://www.hiswasymposium.com/asset...ull resistance of the Delft Systematic Ya.pdf This is not the equation included in Principles of Yacht Design, Third Edition by Larsson and Eliasson, 2007. (Correction from original post.)

Fabio Fossati in Aero-Hydrodynamics and the Performance of Sailing Yachts, 2009, gives a different equation which he references as having been presented in 2008; A Bare Hull Resistance Prediction Method Derived from the Results of the Delft Systematic Yacht Hull Series Extend to Higher Speeds by Keuning and Katgert.

A third equation is given in OCR VPP Documentation 2011 http://www.orc.org/rules/ORC VPP Documentation 2011.pdf There's a statement that it's based on some of the DSYHS data but no specific references are provided for the origin of this equation.

There are fundamental differences between the three equations, not just variation in the coefficients. The first two equations have residual resistance proportional to the 4/3 power of the displacement divided by the length. The OCR VPP equation has it proportional to displacement. The parameters used to characterize the hull differ, and in some cases the same parameter is used in different ways.

Last edited: Aug 9, 2011
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### JRDSenior Member

I'm interested to know, have you made comparisons of the resulting drag using the 3 equations based on same base dimensions and displacement? are they comparable?

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### AlikSenior Member

The reason is probably that DSYS was ammended few times, and each time regression analysis was re-worked. As regression formulas are not physically based they might be different depending on significance of every regressor.

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### DCockeySenior Member

Alik is correct, the formulas are obtained by regression, not from physics. The first reference above discusses how several different formulas were obtained by regression before the particular one was selected. I haven't done any comparisons. The magnitude of the differences between results would depend in part on the hull shapes and corresponding parameters used. For a hull shape close to one used in the regression for each formula I would expect the differences to be small. For hull shapes not as close to one in the regression set but still within the bounds of claimed applicability the differences would likely be larger.

The parmeters used to characterize the hulls are not necessarially independent, so in general it's not possible to change only one parameter and keep the hull shape "similar". Trying to deduce the effect of varying only one parameter on a real world design directly from the equations may be misleading.

There are some fundamental differences in parameters used, and in the terms. Draft is used in the second and third but not the first. LCF is used in the first two and not in the third. Wetted are is used in the first only. Cm is used in the second only. And then there is the overall scaling by LWL/Vol^1/3 in the first and second.

Three different sets of parameters and three different formulas were selected to do the same thing, estimate residual resistance, based on variations of the the set of test results.

It's quite easy to read too much into these types of equations.

----------------

First equation for residual resistance divided by weight displacment uses:
Length waterline LWL, Beam waterline LWB, Displacement Vol, LCB, LCF, CP, Wetted surface area Sc, Area waterplane Awl
Terms multiplied by the Froude number dependent coefficeints are:
1 LCB/LWL CP Vol ^2/3/Awl Bwl/Lwl Vol^2/3/Sc LCB/LCF (LCB/LCF)^2 CP^2
The sum in turn is multiplied by the non-dimensional Vol^1/3/LWL
(LCB and LCF are dimensional lengths in this version).

Second equation for residual resistance divided by weight displacement uses:
Length waterline LWL, Beam waterline LWB , Displacement Vol, LCB, LCF, CP, Area waterplane Awl, Midships coefficient Cm, Draft Tc
Draft and Cm are introduced and Wetted surface area is not used.
Terms multiplied by Froude number dependent coefficients are:
LCB/LWL CP Vol^2/3/Awp Bwl/Awl LCB/LCF BWL/Tc Cm
(LCB and LCF are dimensional lengths in this version).

The third equation for residual resistance divided by weight displacment uses:
Length waterline LWL, Beam waterline LWB, Displacement Vol, LCB, CP, Area waterplane Awp
LCF and Midships coefficient are not used.
Terms multiplied by Froude number dependent coefficients are:
Cp BWL/Tc LWL/Vol^1/3 (LWL/Vol^1/3)^2 Awp/Vol^2/3 LCB*Vol^1/3/LWL^2 LCB^2*Vol^1/3/LWL^3
(Above uses dimensional length forms of LCB and LCF rather than the non-dimensional forms used in the OCR publication.)

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### Remmlingerengineer

Resistance equations

I have attached a comparison of the 3 different methods. The ORC-equation gives a meaningful curve only if LCB is taken as the percentage aft of midships.
The measured drag coefficients come from the towing tank and display some scatter. The friction line is the ITTC-line with 70% of waterline length (Delft definition) for comparison. Total drag below the friction line indicates a negative residual resistance. In other words the friction line is not correct and the assumed friction value is too large.
Hope this can give some direction
Uli

#### Attached Files:

• ###### DEHLER33.pdf
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### DCockeySenior Member

Thanks! Very interesting. It's not obvious which one is better.

Are the parameters for the Dehler 33 available or can they be published?

For Delft 2009 did you use the coefficients as published in Aero-Hydrodynamics or do you have another source?

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### AlikSenior Member

Interesting that for 2 methods (ORC and Delft1998) total drag coefficients are below friction line. Curves should not look like that.

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### DCockeySenior Member

Agree, they don't look right at the low Froude numbers, below 0.20, assuming the ITTC 1957 curve with Re based on 70% LWL properly estimates drag. The plots I've seen of the measured residual resistance for the DSYHS models at those Froude numbers show the deduced residual resistance to be very low. It would be interesting to know how the estimates of certainty of the base experimental data compares with the deduced residual drag after the viscous drag estimate from the ITTC 1957 70% LWL drag is subtracted from the measured drag. Likewise, a variation in the curve/methodolgy used to estimate viscous drag could have large impact on the relative magnitude of the residual drag.

Keep in mind that the Delft series based residudual drag methods all used coefficients which are dependent on Fn, and if the individual curves are plotted vs Fn there are bumps and hollow.

Perhaps the conclusion is none of these curves should be relied on below Fn below 0.20. On the other hand the residual drag at those slow speeds will be small relative to the total drag.

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### AlikSenior Member

I never had this problem with Delft series, namely I never got negative residual resistance in calculations. Could be some problems with using this particular method.

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### Leo LazauskasSenior Member

Subtracting the ITTC skin-friction from the total resistance of thin slender hulls often gives a negative value at low Fn. Maybe that inadequacy of the ITTC line has worked its way into the regression equations.
Do the negative values of Rr only occur for slender hulls at the limits of the allowable range?
Or do they also occur for stubbier Delft hulls too?

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### AlikSenior Member

I never got negative RR with Delft; but I used to work with older series and not with slender hulls.

Do they still include appendages in Delft the series?

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### Leo LazauskasSenior Member

My question was aimed at others, Alik. (I realise you never got negative values).

I agree with your suspicion. If a series includes appendages that could also cause negative values of Rr if you aren't careful.

Leo.

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### DCockeySenior Member

The Delft curves I discussed in the first post, and which Uli used for his calculations are for the "canoe" hull only without appendages.

The Dehler 33 which Uli used for his calculations has a Length Overall / Beam Overall ratio of around 3 so it's not slender. The negative values of residucal resistance on Uli's chart are at Fn from 0.10 to 0.175.

I used the YD-40 from Principles of Yacht Design in the ORC model and calculated a slightly negative residual resistance at Fn = 0.10.

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### AlikSenior Member

Do You have data for D32? I will check from my side.

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