Design parameters methodology

[hbr]

Originally Posted by jehardiman

Hbr.

Let us take 100 different "good" hulls that I have speed and powering data on. I can then non-dimensionalize those hulls and their powering on dimensional data (i.e. LWL,LWL^2,LWL^3,V,B,B^2,T, T^2, S, SA, seconds since the beginning of time, etc.) and other non-dimensional coefficients like Cwp, Cb, LCB/LWL, Rn, Fn, moon-phase, etc. I can then, using statistical methods and stochastic methods, come up with a "best" fit set of interlationship curves based on random non-dimesionalized pairings for that data.

There is no real "scientific" basis for the equation and the factors...it is someones informed and overprocessed guess at a curve fit of the data. There has been a lot of this type of pseudo-science since the advent of computers that makes it easy to do.

Get a good book on dimensional analysis, curve fitting, and nomograph development and design (a dying art IMHO). If you are an engineering student, this should have been covered in your very first engineering class.

Thanks a lot for the reply and yes i am trying to find already for a long time a good book about the subject (of course in the context of hull design) but this seems to be not so easy, any tip ???

[hbr]

Originally Posted by PI Design

Where did you find that formula hbr? It seems to be a way of producing a desired 'curve of areas' based on a pre-selected LWL, Cp and LCB. But it is ridiculously complicated and without more information there is no way of knowing what type of vessel it is supposed to be applied to, nor whether the resulting curve is actually optimal.

I have used a formula for curve of areas that I first saw used by Tom Speer on his Basilicus project - I think he got it from a Russian paper. I developed this for use in ship (not boat) design to allow automated hull generation including parallel mid body and transom submergence. It runs in Excel and the resulting hull offsets can be imported to Rhino for further modelling. I will try and post a copy of it on this site when I get time, but it is quite buggy and needs Solver to be installed in Excel. It currently only works for ships (which have no rocker, just a keel cut up) but I started to develop a yacht/dinghy version which allows a rocker profile to be included and more elliptical cross sections (actually cateneries). It isn't finished and I don't have time to work on it at the moment, but hope to complete it one day.

Cheers,

PI

P.S. I started writing this before Jehariman's post appeared. He is quite right, there is no scientific basis for the formula you give. The remarks about over processed pseudo science are spot on.
Knowing a desired Cp, LCB position etc however is not pseudo science but good traditional nav arch, albeit things should never be set in stone.

Many thanks for this guidance, you have pointed me to valuable information and Tom also explained the information. Appreciated a lot !

[jehardiman]

Originally Posted by hbr

Thanks a lot for the reply and yes i am trying to find already for a long time a good book about the subject (of course in the context of hull design) but this seems to be not so easy, any tip ???

Hull design of what? Of ships or boats in general? Tugboats? Small sailboats? Large sailing ships? Displacement motor cruisers? Planing craft? ULCCs?

Many different hull forms, many different selection criteria.

[Guest625101138]

Originally Posted by hbr

.......
Serious now i am going to have a look to your tip : Godzilla.
Best Regards,
Hugo

Hugo
I have attached the in.mlt file for a 1100kg catamaran. This is a text file that is used to input the data at the start of optimising for a catamaran. So you can open it with a text editor like Notepad to look at the contents.

If you scroll down to the line where the "FIRST HULL" offsets are shown you will see the starting hull has been defined by 4 input parameters. This optimisation input file is set up to work with 7 hull shape functions. You can find these in the Michlet manual.

The optimisation speed is 5m/s (say 10kts). Other than this and the displacement, the limits I have set are wide enough to have no other hull constraints. I have set the hull output as 17 stations and 11 waterlines. This gives adequate hull shape resolution.

So if you download Michlet/Godzilla from here:
http://www.cyberiad.net/michlet.htm
Then load the program with the attached in.mlt file in the same folder as the Godzilla.bat and mlt807w.exe you can run the program and watch the hull shape morph into the most efficient.

The output data will be the hull drag versus speed and the hull offset files plus a lot of other hull information. You will need to read the manual to understand what is going on.

The beauty of Godzilla is that you have an analytical approach to calculating wave drag, good empirical curves for viscous drag and an automatic means of modifying hull shape to minimise drag.

Rick W.

[GuestR01312011]

There's a fair bit of research going on here at Uni Southampton on Genetic Algorithms for taking parent hulls and trying to produce a son/daughter form that is better than that of the parent...

[tspeer]

Originally Posted by hbr

Yes, starting form the LWL, the boat characteristics are derived. and as a result the area od the stations are calculated. From drawing point of view the result is excellent.

I think this is an excellent approach. Wave drag depends primarily on the cross-sectional area distribution, and much less on the shape of the sections themselves. So it makes sense to start with the area distribution for performance and then shape the sections to meet other design objectives.

Can not find in the theory books (e.g. Larsson & Elliasson,..) any reference and yes the basic math books are providing the nescessary formula for curves (ellips, circle, paraboloc,..) still i didn t found an example expressed with such a terms.

Here's a similar example. In aerodynamics, for small disturbances that can be approximated by linear supersonic theory, the minimum wave drag is produced by the area distribution of a Sears-Haack body. Water waves are different than shock waves in air, but I suspect that when both are reduced to linear theory, the optimum solutions may be similar. You may be able to confirm this in classical texts on hydrodynamics.

When you get to nonlinear issues, like the breaking of a bow wave; large changes in immersion due to bow wave, squat and trim; and the added resistance from non-wall-shaped sections, then this similarity will break down. Still, it gives you a place to start, and by preserving the area distribution (however derived) as you shape the sections, you preserve the hydrostatic specifications (volume, lcb, Cp, etc.).

Seems difficult to get some feedback and yes the answer that it corresponds with a curve is right. Could anyone be more specific ?

An analytical expression at least starts off "right" as it produces a family of fair shapes. After that, there's no simple expression that will tell you which area distribution is most suitable for your purposes.

I'll echo the advice of others to use Michlet and Godzilla to evaluate your designs. The family of shapes available for use in Godzilla is somewhat limited. But you could use a Godzilla design as a starting point and then modify it, while keeping the area distribution the same.

For example, the area distribution comes to a point at the stern. But that doesn't mean the stern has to be canoe-shaped. Even if you choose an elliptical cross section shape, by sweeping the junction between the ellipse and the topsides up from the waterline, you can create a shape that has a non-immersed transom and flatter run. The immersed portion of the elliptical section will be increasingly flatter and will meet the area distribution requirements. However, the wider sections above the waterline will pick up buoyancy quickly as the stern squats, moving the lcb aft and limiting the squat compared to the wall-sided sections that are used in Godzilla. Of course, the wetted area of the flatter immersed portions is greater than it would be if the sections came to a point at the waterline, but that may be a small price to pay for the other advantages of more volume in the stern above the design waterline.

[hbr]

Originally Posted by tspeer

I think this is an excellent approach. Wave drag depends primarily on the cross-sectional area distribution, and much less on the shape of the sections themselves. So it makes sense to start with the area distribution for performance and then shape the sections to meet other design objectives.

Here's a similar example. In aerodynamics, for small disturbances that can be approximated by linear supersonic theory, the minimum wave drag is produced by the area distribution of a Sears-Haack body. Water waves are different than shock waves in air, but I suspect that when both are reduced to linear theory, the optimum solutions may be similar. You may be able to confirm this in classical texts on hydrodynamics.

When you get to nonlinear issues, like the breaking of a bow wave; large changes in immersion due to bow wave, squat and trim; and the added resistance from non-wall-shaped sections, then this similarity will break down. Still, it gives you a place to start, and by preserving the area distribution (however derived) as you shape the sections, you preserve the hydrostatic specifications (volume, lcb, Cp, etc.).

An analytical expression at least starts off "right" as it produces a family of fair shapes. After that, there's no simple expression that will tell you which area distribution is most suitable for your purposes.

I'll echo the advice of others to use Michlet and Godzilla to evaluate your designs. The family of shapes available for use in Godzilla is somewhat limited. But you could use a Godzilla design as a starting point and then modify it, while keeping the area distribution the same.

For example, the area distribution comes to a point at the stern. But that doesn't mean the stern has to be canoe-shaped. Even if you choose an elliptical cross section shape, by sweeping the junction between the ellipse and the topsides up from the waterline, you can create a shape that has a non-immersed transom and flatter run. The immersed portion of the elliptical section will be increasingly flatter and will meet the area distribution requirements. However, the wider sections above the waterline will pick up buoyancy quickly as the stern squats, moving the lcb aft and limiting the squat compared to the wall-sided sections that are used in Godzilla. Of course, the wetted area of the flatter immersed portions is greater than it would be if the sections came to a point at the waterline, but that may be a small price to pay for the other advantages of more volume in the stern above the design waterline.

Tom,

Took the time to elaborate the case study hullshape, at the end of the cross sectional area distribution you refer to the Saers-haack body. Undrstood that it's relying on circular cross sections. May be i miss a piece of the puzzle but through conic lofting you are trying to map these cross sections within a kind of V shape. Assume that the fixed points are mapped on the so called conic curve?

concerning the conic curvature i am puzzled by the parameter r, can not find this r in the formula's. where is it used in this lofting phase of the case study?

The midpoint between the ends a reference is made to x1... can you help me to understand this better ?

How is this conic lofting linked with the section shaping ?

Section shaping is deviating from the V line segmenting at lofting ? assume that you further fine tune these sections ???
could you please explain me how this works ?

is it correct that Yc1 corresponds with the beam a littlebit under the waterline ?
Is this method already implemented in a kind of calculator (e.g MS excel ?) ??

Best Regards

[tspeer]

Originally Posted by hbr

Tom,

Took the time to elaborate the case study hullshape, at the end of the cross sectional area distribution you refer to the Saers-haack body. Undrstood that it's relying on circular cross sections.

The classic Sears-Haack body does have circular cross sections, however, what is really important is the cross sectional area.

You can measure the wave drag of a hull by measuring the waves over a large area at some distance from the hull. This is done in a tow tank, for example, by having a wave guage in one location and measuring the waves as a function of time as the model runs down the tank. This is equivalent to scanning the waves from ahead to behind the model. A far-field measurement like this loses all the details of the flow at the hull itself, as these get smeared out with distance. But the drag-causing waves are still propagating out from the hull.

This illustrates the basis for area ruling. If it's the cross sectional area that counts, then the designer has the freedom to trade off depth for beam, or to make the sections more V'd, flatter, or rounded. So long as the area of the section is maintained.

May be i miss a piece of the puzzle but through conic lofting you are trying to map these cross sections within a kind of V shape. Assume that the fixed points are mapped on the so called conic curve?

At the time, I did not have a CAD program, so I was doing everything in Excel. The conic sections were a simple way of lofting surfaces, and are provided by many CAD programs (such as Multisurf), along with more sophisticated surfaces like B-spline patches.

There's nothing magical about the choice of conic sections to make up the various segments of the section shapes. I needed to not only calculate the shape given the control points, but I also wanted to be able to calculate the control points based on some required specifications for the curve. That would be much more difficult with a higher-order surface. And, in fact, I now go that route with Multisurf linked to Excel to define B-spline surfaces.

What I was doing was adopting a generic cross sectional shape that could be defined with a limited number of parameters that could be defined independently of the actual size of the section. These parameters were then varied smoothly along the hull to produce a fair shape. I defined them at the forward perpendicular, midships, and aft perpendicular sections, and varied them parabolically in between. The stem shape was defined by extrapolating the hull shape to the center plane, so it was largely defined by the shape of the bow section.

Both V shapes and rounded shapes were accommodated by the choice of parameters. For example, if theta_D=0, one gets a round bottom. If theta_D>0, then the bottom will have a V-shaped bottom with deadrise.

The Mn points lay on the mold line of the hull, and the Cn points were control points at the corners where the tangents from neighboring mold line control points intersected. This made it possible to quickly sketch out what the shape should be.

concerning the conic curvature i am puzzled by the parameter r, can not find this r in the formula's. where is it used in this lofting phase of the case study?

That is a typographical error. It should have been "rho" not "r". That is the parameter that controlled how sharply the curve bent between the end points.

The midpoint between the ends a reference is made to x1... can you help me to understand this better ?

I didn't make that very clear. The figure below should help.

The parameter rho described how much the curve was allowed to "cut the corner". If rho=0, then x5 was coincident with x4. If rho=1, then x5 lay on top of x2. I found this to be an intuitive way of describing the difference between a hard chine and a soft bilge shape.

How is this conic lofting linked with the section shaping ?

Each section was made up of a series of conic section curves. For example, in this section,

the bilge is one curve, with
x1=M1
x3=M2
x4=C1
The topsides are another curve with
x1=M2
x3=M3
x4=C2
and the deck is a third curve with
x1=M3
x3=M4
x4=C3

The underwater section shape actually started with other parameters that qualitatively described the shape. These were
theta_D = the deadrise angle of the section
theta_F = the angle of the topsides from the vertical near the waterline
b/d = beam/depth ratio, which specifies deep, narrow sections vs wide shallow sections
rho = hard vs soft chine shapes
Note that these are all nondimensional parameters that allow the underwater shape to be scaled freely.

The topsides were defined mostly in terms of the freeboard distance. Only the vertical distance was specified because the topsides beam was scaled to the underwater section size.
hM2 = distance above the waterline for the bottom/topsides joint. This allowed an alternate way of flattening the underwater sections by only using the bottom portion of the curve as the immersed volume.
hC2 = the height of the control point above the waterline
hM3 = the height of gunwale or knuckle
hM4 = height of the crown of the deck above the waterline
theta_T was the angle between the deck edge and the vertical. This was used to shape the crown or the knuckle for bell-shaped sections, ala Shuttleworth designs.
wM3 allowed for the specification of flare or tumblehome.

Section shaping is deviating from the V line segmenting at lofting ? assume that you further fine tune these sections ???
could you please explain me how this works ?

The hull design process started by specifying the design parameters at the three key sections (bow, midships, stern). These were all varied parabolically from bow to stern, except for the crown of the deck, M4, for which I used a cubic curve so that I could additionally specify a bubble cabin top and shear at the bow.

By fixing the section beam with a first guess for a given section, the mold line and corner points could all be calculated, and conic section curves provided a precise definition of the entire section shape. The underwater sectional area was then calculated, compared with the specified sectional area, and the beam adjusted to rescale the section to match the specification.

The end result was the entire hull shape was defined by a limited number of design parameters, all of which had intuitive meaning to the designer. Here are all the input parameters required for a hull:

Hull Parameters
Length of Waterline
Displacement
Prismatic Coefficient
Center of Buoyancy

Underwater Section Parameters
Beam/Depth Ratio @ Bow, Mid, & Stern
Tangent of Deadrise @ Bow, Mid, & Stern
Tangent of Entrance Angle @ Bow, Mid, & Stern
Slackness of Bilge @ Bow, Mid, & Stern
Height of Moldline M2 @ Bow, Mid, & Stern

Topside Section Parameters
Height of Corner C2 @ Bow, Mid, & Stern
Slackness of Flare @ Bow, Mid, & Stern
Height of Moldline M3 @ Bow, Mid, & Stern
Width of Flare @ Bow, Mid, & Stern
Slope of Topsides/Deck @ Bow, Mid, & Stern
Slackness of Deck @ Bow, Mid, & Stern
Height of Moldline M4 @ Bow, Mid, & Stern

is it correct that Yc1 corresponds with the beam a littlebit under the waterline ?

If you defined a hard chined hull (rho=0), yC1 would be the half-beam of the chine. For a soft-bilged boat, yC1 is just a control point location, and is not actually a point on the hull at all. However, you are guaranteed that the hull will lie inside of yC1.

Is this method already implemented in a kind of calculator (e.g MS excel ?) ??

I've implemented the technique two ways. The first was entirely in Excel. The second was a combination of Excel and Multisurf.

The Excel version basically worked, but the calculation of the conic section control points would occaisionally blow up. It was also somewhat limited, in that it only calculated the outer moldline. Drawing objects could be superimposed on a plot of a section to position interior components, but they weren't defined quantitatively and had to be redrawn by hand every time the outer moldline changed.

The Excel/Multisurf implementation is much more powerful. Multisurf supports object linking and embedding. So from the same input parameters, Excel computes a first approximation to all the control points for a B-spline surface. Then Excel makes a succession of calls to Multisurf to create the points in a CAD model, create spline curves that are used to extrapolate the control points to the center plane to define the stem, and generate the surface patches. It then calls Multisurf to dice up the hull into sections and compute the hydrostatics. Multisurf returns the hydrostatic results for the whole boat and each section to Excel. Excel then rescales the control points, calls Multisurf to readjust them in the CAD model, and then calls the Multisurf hydrostatics function to get the final results. It's quite fascinating to push the "Update" button in the Excel spreadsheet, and then watch the points and surfaces appear in the Multisurf window as if by magic.

[hbr]

Tom,

Appreciated the information you provided in the feedback.
need time to absorb the information.
on the one hand i enjoyed the elaboration of your hull shape and lofting so far
on the other hand the extra motivation (personal learning point of view) to continue is mainly based on your feedback.

BR
Hugo