center of flotation calculation and implications?

Agree, but if the designs are of same length and of same static load factor. Otherwise use of these simplified single-number factors is not appropriate for fair comparisions.

 

This is diagram I developed for power catamarans, both displacement and planning. The diargam proved to be useful for preliminary estimations of power/speed requirements at early design stages.

Similar results can be obtained for monohulls.

As one can see, there is dependance on length even at planning speeds.

Of course, for practical design one should not rely on such deagram only, but should perform detailed analysis using Molland and MulerGraf methods at diplacements speeds, and Savitsky method with corrections for planing speeds.

 

Sorry, couldn't find anything under the thumbnail.

 

Try now, it was updated.

 

The displacement speed formula and two of the three planing speed formulas that I had discussed earlier in the thread all have a length factor in them (length on the waterline), so of course there is a dependency on boat size. In the case of the displacement speed formula, the coefficient = 10.665, was given by its originator, Dave Gerr. He based this value on empirical data. I showed how I have used a slightly different coefficient for my own special hullforms, and how that seemed to be valid for boats of similar form and varying lengths and displacements.

In Crouch's formula, where his coefficient varies with boat type, there is no length factor. Plus he uses a square root function where I believe this is a simplification--to match up with the physics of powering, this should probably be a cube root function.

In Wyman's formula, there is a length factor, and again, David Wyman derived the coefficient from empirical data. The neat thing about Wyman's formula is that it appears to be valid for vessels in all powering regimes, whether displacement, semi-displacement, or planing.

Yes, you can use more sophisticated analysis techniques for analyzing the power required for different boat lengths, displacements and speeds, to home in on correct powering answers. The point is your final answer is not going to be too far off from what these formulas provide. Therefore, they are good predictors of powering and performance and useful for comparisons.

Eric

 

Eric, I won't use Crouch and Gerr's formulas for anything then preliminary predictions. Wyman's formula - will check it, but the result will probably be same. There is bunch of formulas for planning craft, actually I have them on same spreadsheet with Crouch

Some methods like deGroot series, NPL, etc. give much better result for semi-displacement craft as they allow separate consideration of frictional and residual resistance. Actually I use at least 3 methods for every design to verify the result.

I understand that Gerr likes to invent methods for his students and readers that do not require any engineering knowledge, but these are not the methods naval architect can rely on, and actually with availability of software or Excel spreadsheets making calculations with use of systematic series takes same amount of time. For estimates - yes, those methods work. Problem with simplified formulas is that unexperienced user gets illusion of simplicity of calculations. In most of books no limits for those formulas are specified, so 'user' playing outside range is just generating mistakes. For systematic series, limits/parameters of series are always specified.

But good side of simplified methods is: once designer is developing parametric model of design (for design study or optimization), those are really useful. Coefficients should be verified before use, anyway.

 

Also to add on previous post: I have noticed that last Mashead reports that Westlawn student used 3 methods for resistance predictions: Holtrop, Gerr and Wyman for his design. (BTW, good design, I like it).

Holtrop/Mennen method is developed for commercial ships forms (like series 64, etc.), it is known to be unreliable for craft with transom sterns, underestimating the resistance [McPherson]. No way it can be used for small craft, but maybe it is availabe from FreeShip so they used it. (If my student does this, I'll probalby shoot him!)

Other methods mentioned are suitable just for estimation... No boundaries specified, no detailed specifiction of appendages and air drag, etc. No way to include actual efficency of propeller - it can vary from 0.45 to 0.70!

Why didn't they take deGroot graphs or Mercier-Savitsky regression? Big question mark (not to the designer but to the school).

 

Use of square root in Crouch's fromula

These graphs show power predictions for our design of 44' powerboat, for range of displacements. Three methods are used: two methods from Wolfson and Savitsky method (modified). As the prototype of hull was tank tested, we know that actual resistance is likely to match Savitsky prediction (orange lines) within 2% at design speed of 40kts and around. As it can be seen SHP-speed curves can be approximated by square functions with high accuracy - see red and pink lines and R2 values.

It is interesting to note that for WHSC line (green) cubic approximations work good and square is not appropriate; but those lines are suitable for heavier craft or craft with semi-planning shapes.

So my conclusions are:
a) for full planning hulls Crouch's formula with square root seems justified;
b) for semi-planning hulls and heavier craft Crouch's formula with square root is not justified but also it is not intended for those hulls.

Please colleagues any comments on this.

 

The purpose of the design ratios and speed estimating formulas is to do precisely as you suggest in preliminary design and design comparisons. A naval architect will usually use other more complicated forms of calculations and analysis, as you suggest, to predict horsepower for the design at hand. These can include the NavCad suite of programs, which I use, which can be configured for many different types of craft. If I have it, that is if the client has paid for it, I can also use model tests which I can align and combine with NavCad for speed and power predictions. I did this on the Moloka'i Strait motoryachts. For planing speedboat predictions, I have found the Holtrop methods in NavCad to be the most reliable.

Again, the document "The Design Ratios" is an attempt to explain what these really are, how are they defined, what do they mean, how are they used, in layman's terms for the benefit of the readers of the forum.

I cannot speak for Westlawn about what they include or don't include in their instruction. In a previous issue of The Masthead, they were kind enough to republish my chapter from The Design Ratios on The "S" Number, so I am greatful for that. I will say that Westlawn is a boat design school, it is not a naval architecture school--for that you have to go to university. There is a certain curriculum that they have to get through in order to make the program appropriate and affordable. I know from sitting on the Advisory Board to the Design Program at The Landing School for seven years--also for boat design, not naval architecture--that there is always more material that should be covered but that can't be covered simply because the school year is not long enough to fit it in. There is only so much material that can be crammed into a given amount of time and cost. It is always an act of compromise.

Eric

 

Holtrop? As far as I know it covers only displacement ships for Fn<0.45, with L/B>3.9. Most of small craft won't fit in the range.

http://www.jmr.unican.es/pub/00603/0060302.pdf

 

Sorry about that. I was speaking from memory on the last job I did, and I had to go back and check the files. Make that the Mercier resistance database for planing craft which is built into NavCad, along with a number of other speed-power prediction methods. Mercier was developed at the Davidson Laboratory at Stevens Institute in 1973 under the direction of Daniel Savitsky. It was closest to the design at hand under analysis--transom sterned round bilged hull form--a 46' lobster style boat. And that was only that particular case. When I use NavCad, I try to match up the best prediction method with the type of craft at hand.

Eric

 

Yes, exactly, I thought You meant Mercier-Savitsky also called 'Savitsky pre-planning'.

Would You please comment graph I posted, showing SHP=f(v^2)? It shows a bit of contradiction with Your paper. I checked other few designs, and the result is similar for planning craft - square.

 

Your graph looks like a spreadsheet calculation with trend lines added to match the data. The trend lines are quadratic (power of two) curve fitting lines that align with the data. That's an acceptable analysis for that particular boat. It won't necessarily be the same for any other boat.
That is, the coefficients in the quadratic trend line will be different for another boat. You see this frequently in trend line fitting--I use it myself all the time. You will not necessarily be able to use this trend line fit for any other boat, so it is not a predictor, necessarily, for other boats.

Note too that Savitsky's method of calculating power versus speed calculates drag as a function of speed squared, and power as a function of speed cubed, so the physics and the math are consistent. How you fit the results of the calculations with a trend line is a totally different matter. It is not invalid, you just have to know what you are doing. If your chart gives you predictable results for that boat, fine.

Eric

 

That's not the point. The purpose for that trendline was to show that power curve for this boat can be fitted as quadratic function of speed, as it was pointed by some posters earlier in this thread. Similar quadratic fit I got for other 2 planning designs I checked randomly yesterday. This seems to add some credibility to using square root in Crouch's formula though You claim it should be cubic function. But seems for full planning designs quadratic function works.

 

Square functions work for limited analysis, and in the case of Crouch, it works too for limited speeds and hull forms. If the speeds are different or the hullforms are different, the Crouch coefficient must change to make its square root function work for those conditions. I never said it did not work, I never stated how accurate or not it was, and I never made any comment on curve fitting quadratic equations through calculated results. I merely stated that Crouch's formula does not necessarily follow the physics of the problem, and if you want to follow the physics of the problem, a cubic function would do it, as in Keith's or Wyman's formulae. Crouch's formula has been used for years, and still is so. If it works for you, fine. I have used it effectively as well. Wyman's formula works also, and the coefficient varies only with speed/length ratio, not with hullform or displacement. If I do an analysis similar to yours, I may very likely fit a quadratic equation through the results in order to predict power required at different speeds for that particular boat, but I would not use that same quadratic equation for any other boat--I'd calculate a new one. There is nothing wrong with that. My point is that Crouch's formula, which is used for calculating power versus speed and displacement is a square function (power of 2), whereas true power calculations are cubic functions (power of 3).

I think we have beat this topic to death.

Eric