Compound Curvature in Aluminum plate

[fpjeepy05]

Example of a developable surface hull with deadrise varying from bow to stern. Blue and green lines are ruling lines. None of the surfaces are flat, cylindrical or conical.
View attachment 149046 View attachment 149047

If the surfaces are not flat, cylindrical or conical, what are they?

 

[TANSL]

They will probably be ruled, generated by straight lines. But ruled surfaces not always are developable.

 

[DCockey]

If the surfaces are not flat, cylindrical or conical, what are they?

Tangent developable surfaces, which can be created by sweeping a line tangent to a curve along the curve. The surfaces in the post above were created from the edge curves by determining untwisted ruling lines between the edge curves and using the Rhino command DevLoft.

From https://link.springer.com/content/pdf/10.1007/s00004-011-0087-z.pdf (see linked document for figures):

There are therefore three types of developable surfaces (excluding a fourth type, the planar surface):

1. surfaces in which generating lines are tangents of a space curve: this type of surface is spanned by a set of straight lines tangential to a space curve, which is called the edge of regression (fig. 1a);
2. surfaces which can be described as a generalised ‘cone’ where all generating lines run through a fixed point, the apex or vertex of the surface (fig. 1b);
3. surfaces which, in the same manner, can be described as a generalised cylinder, where all generating lines are parallel, swept by a set of mutually parallel lines (fig. 1c).

 

[fpjeepy05]

Tangent developable surfaces, which can be created by sweeping a line tangent to a curve along the curve. The surfaces in the post above were created from the edge curves by determining untwisted ruling lines between the edge curves and using the Rhino command DevLoft.

From https://link.springer.com/content/pdf/10.1007/s00004-011-0087-z.pdf (see linked document for figures):

Do the surfaces have tangency at the ruling lines? Are the edges of the surfaces at the centerline coincident with the stem/keel? Are the edges at the chine coincident with the chine?

 

[DCockey]

Do the surfaces have tangency at the ruling lines?

What do you mean by this question? The ruling lines were extracted from the surfaces.

Are the edges of the surfaces at the centerline coincident with the stem/keel? Are the edges at the chine coincident with the chine?

The stem/keel, chine and sheer curves were used directly in the creation of the surfaces. The surface edges are coincident with the curves. The hull is 300 inches long and the maximum deviation of a surface edge from a defining curve is less than 0.009 inches. That deviation could be reduced if needed.

Reason for your questions/skepticism?

 

[TANSL]

The ruling lines were extracted from the surfaces.

I think I do not understand. So, the ruling lines have been obtained from the surfaces and not vice versa?. Strange, very strange

The hull is 300 inches long and the maximum deviation of a surface edge from a defining curve is less than 0.009 inches

How can this deviation be measured? It looks like science fiction. For me a deviation of one per thousand is more than enough.

 

[DCockey]

I think I do not understand. So, the ruling lines have been obtained from the surfaces and not vice versa?. Strange, very strange

The ruling lines shown were obtained from the surface. The developable surface was created by the algorithm in the Rhino V7 command DevLoft. I do not know the details of the internal code of the algorithm but my testing of the command has shown that it creates developable surfaces when used appropriately.

Alternatively I could have determined "no twist" ruling lines between the pairs of curves and then created the surfaces using those curves. The resulting surfaces would be essentially the same.

How can this deviation be measured? It looks like science fiction. For me a deviation of one per thousand is more than enough.

Standard CAD system method for determining deviation between curves. I used the Rhino Deviation command. I assume that AutoCAD has a similar command. Why does it look like science fiction? CAD can be very accurate.

 

[fpjeepy05]

What do you mean by this question? The ruling lines were extracted from the surfaces.

The stem/keel, chine and sheer curves were used directly in the creation of the surfaces. The surface edges are coincident with the curves. The hull is 300 inches long and the maximum deviation of a surface edge from a defining curve is less than 0.009 inches. That deviation could be reduced if needed.

Reason for your questions/skepticism?

It’s hard to envision the hull without being able to spin the model around a look at it. I know what a warped bottom hull looks like and I know it’s not developable. I want to know what this hull looks like in comparison.

If you were to draw a section line at a quarter buttock, would be be able to identify where one surface meets the next or at all edges tangent?

The reason I ask about the keel/stem and chine curves is because they are different curves. If you have two straight lines and two different curve and you make a surface from edge curves the surface will not be developable, unless the non-straight curves are sister curves and are diminishing to a perspective point coincident to the two straight curves.

Coincident and small deviation are similar, but also different.

 

[Mr Efficiency]

Is this a theoretical exercise, or a practical one ? Without any clear indication of what is desired to be achieved, there is little that can be usefully said.

 

[fpjeepy05]

Is this a theoretical exercise, or a practical one ? Without any clear indication of what is desired to be achieved, there is little that can be usefully said.

Im thinking more practical. I want to commission the build an aluminum hull. I want it to be a warped plane hull, but I need to design it so the builder can actually build it. But if I follow DC's suggestion I just want to know that the ever result will look like, and how it will behave.

 

[DCockey]

I know what a warped bottom hull looks like and I know it’s not developable. I want to know what this hull looks like in comparison.

Would you like a 3D CAD file of the hull shape? I can export from Rhino is several file formats including: .3dm, .dxf, .obj, .ply, .skp

By "warped bottom" do you mean only a bottom with variable deadrise and straight sections? If so I agree that such a bottom is not developable. The hull I posted above has curved sections as I described in a previous post:

It is possible to design a variable deadrise boat with developable surfaces but the stations will not be exactly straight. However not all variable deadrise shapes are developable.

If you were to draw a section line at a quarter buttock, would be be able to identify where one surface meets the next or at all edges tangent?

The bottom and side surfaces meet at the chine and are not tangent. The bottom and side each are comprised of 3 NURBS surfaces and the individual surfaces of the bottom and side are tangent with each other and effectively curvature continuous with each other.

The reason I ask about the keel/stem and chine curves is because they are different curves. If you have two straight lines and two different curve and you make a surface from edge curves the surface will not be developable, unless the non-straight curves are sister curves and are diminishing to a perspective point coincident to the two straight curves.

This is incorrect. You are describing a "sufficient" condition for creating a developable surface but not a "necessary" condition. Sufficient and necessary are fundamentally different though frequently confused. The use of "sister" curves is one method of creating a developable surface using traditional 2D drafting methods.

A more general method to determining a developable surface between edge curves is to determine a set of ruling lines without twist between the edge curves, and then create the surface based on those ruling lines. To do so is theoretically possible using 2D manual drafting methods but very tedious and time consuming. However CAD software such as Rhino can make the process relatively quick. I described one method for determining no twist ruling lines between edge curves graphically using Rhino on the Rhino forum. See Developable surface - exact ruling lines from edge curves https://discourse.mcneel.com/t/developable-surface-exact-ruling-lines-from-edge-curves/73928

Another method which requires coding is to determine using iteration sets of points on pairs of edges curves corresponding to the ends of no twist ruling lines, and those sets of points and the equations of the edge curves can then be used to create surfaces.

Coincident and small deviation are similar, but also different.

Numerical calculations ultimately have deviations. The current deviations could be reduced to the order of .0000000000001 which is approximately the round-off error of the digital math used in Rhino but I don't see any practical reason to do so.

 

[DCockey]

Im thinking more practical. I want to commission the build an aluminum hull. I want it to be a warped plane hull, but I need to design it so the builder can actually build it. But if I follow DC's suggestion I just want to know that the ever result will look like, and how it will behave.

My suggestions is to find a designer/builder with experience with warped hulls in aluminum. I've been told by folks with experience building boats in aluminum that the shape can deviate a "little" from precisely developable, but have not seen quantified how much deviation is possible with preforming the plates. My guess is if there was a simple method to do so someone would have described it by now.

I heard a designer who has successfully designed aluminum boats describe how he initially designs using straight sections, and then adds "belly" to the sections to allow plating with flat sheets based on his expeience That is a difficult method for other designers to replicate.

 

[Mr Efficiency]

Im thinking more practical. I want to commission the build an aluminum hull. I want it to be a warped plane hull, but I need to design it so the builder can actually build it. But if I follow DC's suggestion I just want to know that the ever result will look like, and how it will behave.

OK, so what size boat, what kind of service requirements, sea conditions etc ?

 

[fpjeepy05]

Would you like a 3D CAD file of the hull shape? I can export from Rhino is several file formats including: .3dm, .dxf, .obj, .ply, .skp

By "warped bottom" do you mean only a bottom with variable deadrise and straight sections? If so I agree that such a bottom is not developable. The hull I posted above has curved sections as I described in a previous post:

.3dm would be great. I'll re-read your tutorial on McNeel's site and see if I can recreate the ruling lines myself. I'm sure this will clear up a lot of my confusion. I can't tell from the images you posted, but I assume the curvature in the bottom is convex?

Numerical calculations ultimately have deviations. The current deviations could be reduced to the order of .0000000000001 which is approximately the round-off error of the digital math used in Rhino but I don't see any practical reason to do so.

Agreed, the purpose was only for my understanding. A warped hull could be made with flat panels with no bending and .000000001 deviation if the panels were made .0000000001 wide. This is theoretically possible, but not very helpful.

My suggestions is to find a designer/builder with experience with warped hulls in aluminum. I've been told by folks with experience building boats in aluminum that the shape can deviate a "little" from precisely developable, but have not seen quantified how much deviation is possible with preforming the plates. My guess is if there was a simple method to do so someone would have described it by now.

I heard a designer who has successfully designed aluminum boats describe how he initially designs using straight sections, and then adds "belly" to the sections to allow plating with flat sheets based on his expeience That is a difficult method for other designers to replicate.

Go idea or not, I plan to do the designing myself. Builder is a low-tech builder in Louisiana. But the price is right.

I will try to do the calculations I described earlier in this thread and report back as I feel it has the potential the quantify allowable twist.

OK, so what size boat, what kind of service requirements, sea conditions etc ?

28x5ft semi-displacement eco side console fishing boat. Personal use. Mostly calm seas.

 

[DCockey]

.3dm would be great.

.3dm file attached.

I can't tell from the images you posted, but I assume the curvature in the bottom is convex?

Single curvature with one principal curvature zero. Ruling lines are straight.

I will try to do the calculations I described earlier in this thread and report back as I feel it has the potential the quantify allowable twist.

I'll be interested in the results but currently am skeptical.

Builder is a low-tech builder in Louisiana. But the price is right.

Any idea how close the finished boat will be to the design you provide?