1. Junior Member
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## Conic Projection

Dear members,

Does any-one have a suggestion for a source of information about conic projection - the method of designing the forward bottom of a stem and keelson area, and for deciding the amount of round on the forward frames/moulds?

I have John Teale's book on small boat design, and though he covers this, and though I understand each and every word he says, I cannot make it work for me. Tainternet searches turn up lots of complicated maths and cartography, nothing useful for a bodger like me.

Thanks,

Collin

2. ## Re: Conic Projection

FS Kinney's Skenes Elements 8th (1973) edition has a section on it. https://www.abebooks.co.uk/servlet/B...srp1-_-title15

A how it works picture.

3. Junior Member
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## Re: Conic Projection

Thanks Peerie Maa, I'll be getting a copy shortly.

Keep safe,

Collin

4. ## Re: Conic Projection

Originally Posted by CollinR
Thanks Peerie Maa, I'll be getting a copy shortly.

Keep safe,

Collin
Are you designing from scratch or trying to loft an existing design?
If it is a new project and you are comfortable working on a PC screen try Freeship
https://sourceforge.net/projects/freeship/

Lofting an existing design will require a lot of trial and error to find where the generator locus sits. So it may be easier to input the stem-keel and chines into Freeship anyway.

5. ## Re: Conic Projection

So Nick, please expand... the distance of the locus from a fixed point on the hull denotes fineness or otherwise of the bow?

Although I can imagine a drawn out mathematically (and therefore dimensionally) cone to be a reasonable entry and easier to build that an asymmetrical form, is all there is to it hydrodynamically? A rule of thumb to fall within the limits construction materials, build time and method habits?

6. ## Re: Conic Projection

Originally Posted by lupussonic
So Nick, please expand... the distance of the locus from a fixed point on the hull denotes fineness or otherwise of the bow?

Although I can imagine a drawn out mathematically (and therefore dimensionally) cone to be a reasonable entry and easier to build that an asymmetrical form, is all there is to it hydrodynamically? A rule of thumb to fall within the limits construction materials, build time and method habits?
First off it is not a true cone with a circular base. The conic part is that the straight line generators all sweep around a common locus that would be the a[ex of the surface, or can be parallel, and sweep along the CL profile or the chine. On a true cone, the keel profile would be part of a parabolic or hyperbolic curve.
The fullness or fineness is affected by the position of the locus. The farther forward/lower, the finer the bow. The further to the side/higher, the lower the dead rise of the bottom and forefoot. Obviously he keel/stem profile has a profound effect.

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## Re: Conic Projection

developable-surface-boat-designs.blogspot.com

It is a subject I have been playing with for years.

8. ## Re: Conic Projection

Nick's How it Works picture doesn't quite give the whole story for me, nor does Skene. As I was initially a little confused, I decided to mark up the diagram to show how to use the cone to get the actual offsets. The green lines represent one particular mold or frame. The solid blue are the two views of a line on the cone. From these you can lift off the offsets (red). I hope this helps others understand the process as it did me. What is not clear to me is how one chooses the vertex of the cone. It appears that the further forward and higher the position, the softer the sections. And, the further down and out from the center line the harder (straighter) they are. I assume choosing the optimal position is a matter of experience (and experiment).

conic development (1).jpg
Last edited by akitchen; 11-21-2020 at 04:15 PM. Reason: Diagram unclear, added to description.

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## Re: Conic Projection

Peerie Maa, this is the continuing development of a "new" design ("new" as in about ten years from conception!). I tried Freeship, but I will stick to pencil and paper, I can "see" things more easily.

W Grabow, despite the note about Freeship, above, I'll have a look.

aKitchen, you seem to have been in the same place as me, I understand theoretically what I'm supposed to do, but so far when I try to draw it, it all goes to nonsense. Thanks for your additional information, I'll keep trying with more hope of success.

All - keep safe and thanks.

Collin

10. ## Re: Conic Projection

Originally Posted by CollinR
Peerie Maa, this is the continuing development of a "new" design ("new" as in about ten years from conception!). I tried Freeship, but I will stick to pencil and paper, I can "see" things more easily.

Collin
Freeship really is better, easier, than paper and pencil.

• It is less wasteful of your time when iterating the design. You do not need to start over from a blank sheet of paper.
• You can rotate the model on the screen to see it from any direction.
• It has routines that prove the developability of the panels as well as visualising their curvature.
• It will calculate displacement and stability.
• It will output the shape of the developed panels.

11. ## Re: Conic Projection

Originally Posted by Peerie Maa
Freeship really is better, easier, than paper and pencil.

• It is less wasteful of your time when iterating the design. You do not need to start over from a blank sheet of paper.
• You can rotate the model on the screen to see it from any direction.
• It has routines that prove the developability of the panels as well as visualising their curvature.
• It will calculate displacement and stability.
• It will output the shape of the developed panels.
Nick,

I realize that what you say is true. But I'm so old fashioned, I just love the visceral feel of drawing lines with pencil and paper. Funny, because in a previous life I taught computer science.

Andrew

12. ## Re: Conic Projection

Originally Posted by akitchen
Nick,

I realize that what you say is true. But I'm so old fashioned, I just love the visceral feel of drawing lines with pencil and paper. Funny, because in a previous life I taught computer science.

Andrew
Fairy Nuff. Can I suggest that you stick with round bottoms, and do not go down the hard chine conic projection route?

13. ## Re: Conic Projection

Originally Posted by Peerie Maa
Fairy Nuff. Can I suggest that you stick with round bottoms, and do not go down the hard chine conic projection route?
That's my plan. Next project is Doug Hylan's "Siri', and no designing required on my part.

14. Junior Member
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## Re: Conic Projection

My copy of the eighth edition of "Skene" finally arrived today (delayed due to Covid, presumably), what a disappointment! Very little information on conic projection, and the notes on the drawing are barely legible, as well as irrelevant as to the "How do you do it?" question.
On the other hand, there's loads of other stuff of interest, some of which is likely to be directly relevant to my project.
I've been thinking about this some more, and I'm going to try to get the pen and paper method again with what I've now got in my head, and if it works, I'll post up a "How to" guide here in the next few days.

Dwedais"Gwirion", nid "Twp"

15. ## Re: Conic Projection

You might also look up the work of Harry Schoell, and his delta-conic and duo-delta-conic hull forms.

Here's a good article from our host's sister pub:

http://trojanboat.com/wp-content/upl...ll-article.pdf

Kevin

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## Re: Conic Projection

Finally, after days of snarling and hair tearing, I think I've done it. Get yourself a glass of your favourite beverage, and settle down for a long read....

This is how to get the conical developed shape of the forward bottom and frames/moulds of a ply on frame boat (i.e. the correct curve of the forward bottom and the frames/moulds). It does not develop the shapes of the panels themselves. My example is for an 18' x 5' dinghy, with stations 0 (fwd) to 8 (aft), and one chine (i.e. gunwale, topside panel, chine, garboard and keel).

Run through the usual design iterations, until you're reasonably happy with the displacement, LCB, prismatic coefficient, hull balance and all that stuff. Draw the usual 3 views, profile, plan and sections, in pencil. Do not bother with the cross section of the keel/rabbet for now, leave it as a "V" on the centre line, but pencil in the profile of the main keel and any skeg you need. Ink in the station lines, the water line, the buttocks and the chine in profile, plan and sections (you have to start with a known line somewhere, and the chine can be designed on paper with a clear conscience). Draw the hoped for curve of the forward bottom in pencil, in fact, put your ink away for now, unless you're very lucky you'll be redrawing lines several times from now on.

Draw in pencil a vertical line to the right of the plan of the bow (I used about 20mm, 3/4" to the right as a start on my drawing at 1:10). Choose a spot on the line about 1/2 the beam below the centre line of the plan, this is your first guess at the position of the apex of the generator in plan, and is Point "A" in what follows. Draw a line from here to the chine at station 3. This new line will cross the planned rabbet at some point, project a vertical line from here up to the profile view. This vertical line will cross the suggested rabbet at some point. Draw a line from the intersection of section 3 and the chine through this point on the rabbet and on to intersect your vertical line on the right. Use this point (point "B") as the first guess for the apex of generator in profile.

Back to the plan view and draw a line from the intersection of the chine and station 1 to point A on the right. This line crosses the centre line at some point, project from here up to the profile, and then draw a line from the intersection of station 1 and the chine to point B over on the right. This line crosses the vertical you've just drawn at some point. If this point is reasonably close to your hoped for profile, you're in luck and you can carry on with the rest of the work. If it's too far away from the hoped-for profile, you'll have to move your generators, for example, if your derived point is too far above your hoped-for profile, I suggest you move point B down a bit. If you can't see an improvement, you'll have to move A up or down, or the whole line A-B closer to or further from the end of the lines drawing.

If you've got a reasonable match with the first two points in profile, carry on with the rest, using Station 2 and station 0 as above. You should now have 4 points on the forward part of the profile which define a reasonable shape for the forward bottom of your boat. If you want more points, then add half stations wherever you want them. Fair them in with a spline. Don't be too dismayed if they're not quite perfect, there's plenty of places where minor errors can creep in in this process, and there' still a bit of flexibility in the plywood.

Plot the "confirmed" positions of the bottom of each station on the sectional drawing. Sketch in straight lines from the chine to the bottom at each station. Draw in at least one buttock line in plan and on the sectional view.

The line from the intersection of station 4 and the chine to point A crosses the buttock line at some point, project this point up to the profile view. Where a line drawn from the intersection of chine and station 4 to point B crosses the vertical from the plan view you've just drawn is the buttock in profile at that point.

Lines from the other intersections of station and chine to point A are projected up onto the profile view, and where they cross their respective lines from the same intersections to point B in profile gives more points along the buttock. Fair them in with a spline, and take off the heights where each station crosses the buttock. Transfer these points onto the sectional drawing. They should all plot below the sketched straight line between chine and rabbet, by a small amount (these curves will not be very tight on a "normal" sort of craft). Fair them in, and there you have the developed shape of the forward frames for a small boat.

Finish that drink and go and get another, you deserve it!

Dwedais "Gwirion", nid "Twp"

17. ## Re: Conic Projection

Good stuff here, folks. Sorry that I am late to the party; I should have been more attentive.

As I started my career as a pencil-and-paper draftsman, I did a fair amount of conic projections. Modern computer technology has certainly taken a lot of the drudgery out of designing boats, but it IS nice to know how to do it 'the old way'. Over the years I have collected a number of papers on the topic, which I would be happy to share with interested parties. Send me a PM and we'll work out a method to get a copy to you. In my file #2180 I have the following papers:

Multiconic Development of Hull Surfaces - Sam Rabl (The Planimeter, 1958)

Developable Hull Surfaces - Ullmann Kilgore (Marine Technology, SNAME)

A Standard Series of Developable Surfaces - L.W. Ferris (Marine Technology, SNAME) (a mathematical method, not graphical - mmd)

There are a number of other papers, but they are more complicated, more mathematical, and mostly geared towards programming a computer to develop fair planar surfaces.

The Rabl paper is probably the best one for developing a chined hull panel using conic projection. It is clear in both illustrations and prose, and easy to follow along. It is available as a downloadable PDF at https://www.boatdesign.net/attachmen...001-pdf.82878/ Click on this link and it will download the PDF to your computer.

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