# Calculating friction resistance, drag coefficient?

Discussion in 'Hydrodynamics and Aerodynamics' started by dustman, Jul 11, 2019.

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### dustmanJunior Member

Oh, yes, my mistake. You said his assumed drag coefficient was 0.00369? Did you mean 0.0369?

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### Doug HalseySenior Member

The Bradfield paper actually says "Cd = 0.00369", but as Jehardiman points out, there's the question of what is used for the reference area.

Your value of 0.04 looks suspiciously like the term in the Schoenherr equation. Cf = 0.044 /( Re^1/6) which as you see needs modifying by a function of the Reynolds Number.

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### jehardimanSenior Member

Well if he is only using skin friction Cf, all the more reason for higher Cd at lower speeds. Cf=0.075/[log(Re)-2]^2 (ITTC line) which means the Cf decreases as speed increases. That would make the towed data scatter more plausable due to the wave making humps and hollows.

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### jehardimanSenior Member

FWIW, here are some of the different friction lines...things change depending on which you use, all different slopes and curvature due to different methods of data fitting.

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### Doug HalseySenior Member

The Bradfield method's virtue is its extreme simplicity. I'm sure Dr. Sam was aware of the more rigorous methods (being an engineering professor). In the paper, he writes "To a first approximation, (kCf) can be considered constant over the entire operating range...". I'm surprised its results look so reasonable.

As you mention, the wave making should make humps and hollows in the towed data. I'm not sure how big they should be, but I also would be suspicious of the data itself, since it was obtained by towing behind a powerboat in open water, rather than in a dedicated towing tank.

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### jehardimanSenior Member

Not really much of a surprise, as a tornado cat hull, all things favor small and widely spaced wave making humps: low Cp, low B/L for each hull, extremely low displacement-length ratio, and widely spaced hulls. It would be much different if you looked at a much different cat, like a Lagoon 400.

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### dustmanJunior Member

Could you explain this chart to me, the meaning of each line of data? Is the N line newtons of drag? If so it seems extremely low. This is actual experimental data?

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### DolfimanSenior Member

I tried to address the essence of your specification, and also taken into account this excellent synthesis (attached) by Terho Halme on sailing catamaran design ratios, to propose you (with using Gene-Hull Catamaran) a preliminary design of a Racing Cata 30' Lwl.
The goal is actually to have a numerical base on which to address the specificity of a sailing catamaran, i.e. to investigate various « Cata with heel » configurations and to derive the parameters and ratios of each hull, and in particular the ones of the leeward hull when the windward one is fully flying off the water, in view with the peak performance evaluation. Such parameters and ratios, inc. Lwl/Bwl, Bwl/Tc, Lwl/D^1/3, Sw, Cp, LCB, … is the short list usually involved to estimate the drag components from the existing experimental data. Also output from this "Cata with heel "study is the rigthing moment RM versus the heel angle, to introduce in the VPP.
On this basis, the next 2 steps ahead is the best possible evaluation of the drag components, and the building of a complete VPP tool by also introducing the sail forces and the heeling moment in the process.
This approach is of course more complex than just using a drag overall coefficient, and honestly does not guarantee a better speed evaluation in absolute. But the real and challenging objective is elsewhere, it is the consistence of a tool, able to rightly react to each design iteration and help progress towards the best trade-off solution.

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• ###### Racing Cata 30'_Study with heel.pdf
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### PeakyJunior Member

The OP was really related to finding a sail area. I’m surprised no one has mentioned that this is more dictated by stability factors than a target speed. It is quite unusual to set a sail area based upon an anticipated hull drag.

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### DolfimanSenior Member

I am transposing a VPP built for the Melges 32 to a one for this Cata issue >>> a very first order of magnitude for the sail surface, considering only the moment equilibrium:
- A sailing upwind, with Wind 12 knots
- Boat speed objective : 8 knots
- RM : 15,9 kN.m max (from my previous study in quote # 14)
>>> a sail surface of about 60% Melges 32 one , i.e. ~ 39 m2 can be possible
It remains to demonstrate that the speed of 8 knots is possible….. from the force equilibrium, i.e. a good evaluation of the drag components.

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### jehardimanSenior Member

Sorry for the tardiness, been traveling.
Anyway, if you look at the data/curve provided by Doug, you can see that drag (D) is plotted as a fraction of weight (W) [n.b. this is typical of planning vessel design]. We know the full up weight with crew of a Tornado is ~302kgf so now we have the drag in kgf at various speeds. We then convert the drag to newtons (N), 1kgf=9.8N. We then convert the speed in miles an hour (MPH) to a velocity (V) in meters/sec. Now Cd = D/(0.5*rho*A*V^2). rho is typically 1.029 kg/m^3 and we don't know the reference area (A). Moving all the unknowns to the left side we get a factor of Cd*A, where A may or may not be a constant (long discussion on that in other threads about drag: Skin-Friction Formulas https://www.boatdesign.net/threads/skin-friction-formulas.31280/). If we knew the reference area and if Dr W S Bradfield truly used Schoenherr's/ITTC-57 friction, then the Cd should follow the friction line exactly.

Edit to add, the drag forces are not out of place for such a small light vessel. If we look objectively at it, a drag of 1036N at 8.9408 m/s means you need 9.3kW delivered, which is about 12.3 hp. Ask yourself: would a 18 hp outboard drive a 600 lb skiff at 20 mph?

Last edited: Jul 23, 2019
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### Doug HalseySenior Member

I've found the missing pages in my copy of Bradfield's paper, and determined that he used reference area = 80.6 ft^2 and total weight = 740lbs.

I think that, if he used the friction curves you mention, his Cd will only be an average of some sort since he assumes a constant value.

Bradfield also used his drag equation in an approximate VPP, with results given in Marchaj's Aero-Hydrodynamics Of Sailing.
I used the same values in one of my own VPP's & calculated somewhat higher speeds at most angles. I don't think my results are worth showing here though, since I used generic data for the aerodynamic characteristics, and because of differences in several aspects of our VPP codes.

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### DolfimanSenior Member

Thanks for this document (a serie of slender hull models sharing the same block coefficient Cb ~0,4), which can be exploited in the frame of a sailing catamaran.
I first focused on the residuary drag component of the slender monohull, a key issue in relation with the leeward hull of a racing cata, for which fortunately the paper gives directly the drag values (Fig. 32a to 32d). Thanks to models data also given, it is possible to convert these curves in a more appropriated adimensional form for such a residuary drag Dr, i.e. Dr/Mg (%) in function of Froude Fn, so showing its independance to Reynolds (as "residuary" is mostly the "wave" drag) and directly usable within a VPP. The proposed curves (in page 1 of the analysis attached) are graduated in Lwl/Bwl + a correction factor for Bwl/Tc when different from the pivotal value 2 (Bwl/Tc = 2 is an "attractor value" in the design iteration loops, as it usually corresponds to the minima of the friction drag which is dominant in the decomposition of the total drag). Detailed analysis are in page 2 and over.

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• ###### Residuary drag estimation for a slender monohull.pdf
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### Doug HalseySenior Member

Norm Riise would approve.
Norm Riise - Ahead of the curve >> Scuttlebutt Sailing News https://www.sailingscuttlebutt.com/2013/11/14/norm-riise-ahead-curve/

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### Doug HalseySenior Member

The treatment of residuary drag in his catamaran VPP from the late 60's or early 70's was very much in the same spirit.

Here's how he describes it in his Ancient-Interface paper "Optimized Hull Length For a D Class Catamaran"
and here's the figure he refers to

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