William Sutherland's concept of ship hull design, 1711

[trippwj]

This has been a most interesting discussion. I do not have the skills to try and replicate the drawings digitally, but have an interest in how these hull forms evolved.

Let me offer another couple of references which may (or may not) be of interest to the conversation.

 

Let me introduce David Balfour.  According to Bellamy, " One of Christian IV’s principal shipwrights was David Balfour (1574–1634). He was born in St Andrews, Scotland, and we know that he travelled abroad to study mathematics. The first reference to him in Denmark occurs in 1597 when he was awarded contracts to build two galleys. They must have been well received as in 1599 he got his first contract to build a large warship."

 

Why Balfour? Well, there are some archival records of his design process, as well as extant drawings/plans. Below are a couple of images from Bellamy (2006)

 

 

Source:

Bellamy, Martin. 2006. “David Balfour and Early Modern Danish Ship Design.” The Mariner’s Mirror 92 (1): 5–22. https://doi.org/10.1080/00253359.2006.10656978.

 

So we see some use of the design drawing contemporary to the "Newton" manuscript. Of interest for the 17th Century as well may be the 1620-ish Treatise on Shipbuilding as transcribed and annotated by Salisbury in 1958.  While this treatise moves us a bit later than the Balfour works, we are still quite a bit behind the era of Sutherland. Here, then, are three more which are available for review. Obviously Deane's Doctrine is the more famous, with a very nice book published by Brian Lavery. THe other two, however, have not been transcribed but may contain some interesting tid bits.

 

Salisbury, William, and R. C Anderson, eds. 1958. A Treatise on Shipbuilding: And a Treatise on Rigging, Written about 1620-1625. Occasional Publication, No. 6. London: Society for Nautical Research.

 

While this treatise moves us a bit later than the Balfour works, we are still quite a bit behind the era of Sutherland. Here, then, are three more which are available for review. Obviously Deane's Doctrine is the more famous, with a very nice book published by Brian Lavery. THe other two, however, have not been transcribed but may contain some interesting tid bits.

 

Battine, Edward. 1685. The Method of Building, Rigging, Apparelling, & Furnishing His Majesties Ships of Warr, According to Their Rates. https://collections.library.yale.edu/catalog/17268860.

Bushnell, Edmund. 1678. The Complete Ship-Wright. Plainly ... Teaching the Proportion Used by Experienced Ship-Wrights ... To Which Are Added, Certain Propositions in Geometry ... Also, a Way of Rowing of Ships by Heaving at the Capstane ... The Fourth Edition, Etc. 4th ed. R. W. for William Fisher. https://books.google.com/books?id=kWpnAAAAcAAJ.

Deane, Sir Anthony. 1670. “Anthony Deane’s Doctrine of Naval Architecture and Tables of Inventions Etc. - National Maritime Museum.” 1670. http://collections.rmg.co.uk/archive/objects/471544.html.

 

One other set of papers I have not had the opportunity to delve into are those by Thomas Harriott (Manuscript on Shipbuilding and Rigging ca. 1608-1610)

 

Pepper, Jon V. 1981. “Harriot’s Manuscript on Shipbuilding and Rigging (ca. 1608‐1610).” In Five Hundred Years of Nautical Science 1400-1900, edited by Derek Howse, 204–16. National Maritime Museum. https://www.academia.edu/11773314/_III_PEPPER_Jon_V._Harriots_manuscript_on_shipbuilding_and_rigging_ca._1608_1610_.

Pepper provides this recreation of lines from Harriot.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Website for the collections is

 

“The Manuscripts of Thomas Harriot (1560–1621).” 2012. Digital Edition of Thomas Harriot’s Manuscripts. 2012. http://echo.mpiwg-berlin.mpg.de/content/scientific_revolution/harriot.

 

Also see:

Stedall, Jacqueline. 2013. “Notes Made by Thomas Harriot (1560–1621) on Ships and Shipbuilding.” The Mariner’s Mirror 99 (3): 325–27. https://doi.org/10.1080/00253359.2013.815995.

 

 

 

At any rate, one final modern study that may be of interest would be the following:

 

Kenchington, Trevor John. 1993. “The Structures of English Wooden Ships: William Sutherland’s Ship, circa 1710.” The Northern Mariner 3 (1): 1–43.

 

Enjoy!  Hope some of this is useful in your efforts.

[druxey]

Yes, Waldemar, The draught for a 180 ton merchant vessel was first constructed at 1:96 using the 'Propositions'.  You can see the first iteration of the draught. This was based on a 60' 0" keel to the touch, 27' 0" breadth and 10' 6" depth of hold. The model was built at 1:48. The midships floor has no deadrise, but is flat. Changes in radii were later adjusted to occur at the joint lines.

[Waldemar]

 

6 hours ago, trippwj said:

This has been a most interesting discussion.

 

Wayne, I am glad you are comfortable with the subject matter.

 

 

Information on David Balfour and his ships can also be found in the following works, among others:

 

Niels M. Probst, Christian 4.s flåde (1996),
Christian P.P. Lemée, The Renaissance Shipwrecks from Christianshavn (2006),
Martin Bellamy, Christian IV and his Navy. A Political and Administrative History of the Danish Navy 1596–1648 (2006),
Henrik Christiansen, Orlogsflådens skibe gennem 500 år. Den dansk-norske flåde 1510-1814 og den danske flåde 1814–2010 (2010).

 

 

The works you have listed are both very important and interesting, but as I have already written, none of them defines the shape of the bottom curves in a clear way, if at all (and Battine's inventory-like compilation does not deal with the issue of hull shape design at all). This is precisely why Sutherland's work is so informative in this regard.

 

Thank you again for your interest in this thread.

 

 

Edited October 1, 2022 by Waldemar

[Waldemar]

 

10 hours ago, druxey said:

Here are photos of a merchantman's hull, as derived by graphic methods, from the Newton manuscript. Comments?

 

4 hours ago, druxey said:

Changes in radii were later adjusted to occur at the joint lines.

 

Druxey, thank you, but to tell you the truth, I continue to see little connection between the information in the 'Newton' manuscript and the drawing and description you have provided in relation to the bottom curves.

 

By the way, I also just discovered in the concluding remarks of the 'Newton' manuscript that conoidal hulls (i.e. with variable radii for the different frames) were nothing novel already around 1600.

 

 

[druxey]

No, conoidal hulls were not a novelty by 1600, but in the 1660's the cono-cuneus curve used to develop the lower hull below the conoid was. And, I can assure you, I used the Newton ms to develop the draught that I posted.

[Waldemar]

 

4 hours ago, druxey said:

No, conoidal hulls were not a novelty by 1600

 

I am glad that you accept my observation about conoidal hulls as early as 1600.

 

 

4 hours ago, druxey said:

but in the 1660's the cono-cuneus curve used to develop the lower hull below the conoid was.

 

Can you point to any period work on shipbuilding describing or even suggesting the use of "the cono-cuneus curves to develop the lower hull below the conoid"?

 

 

4 hours ago, druxey said:

And, I can assure you, I used the Newton ms to develop the draught that I posted.

 

Druxey, you may have reconstructed the general shape of the merchantman's hull based on the 'Newton' manuscript, and I have no intention of verifying this. But we are now talking specifically about bottom curves, and I don't even see a resemblance to their shapes as described in the manuscript. Your statement: "Changes in radii were later adjusted to occur at the joint lines" is quite incomprehensible. Either way, according to the manuscript, there should be no 'changes in radii' at all.

 

 

[druxey]

No, I think you misunderstood my statement: the joint lines run along junctions of the different arcs.

 

There is no period work (that has yet been uncovered) describing the application of the cono-cuneus curve in the lower part of the hull. Pett was recorded as going to write about this, but he died before he could reveal his 'shipwright's secrets'. These were recently rediscovered by reverse engineering from the 3D scans of a contemporary model.

[Waldemar]

 

9 hours ago, druxey said:

No, I think you misunderstood my statement: the joint lines run along junctions of the different arcs.

 

Well, this further explains nothing. Never mind, I'd better leave such explanations alone now, because I think I have something more interesting.

 

 

9 hours ago, druxey said:

There is no period work (that has yet been uncovered) describing the application of the cono-cuneus curve in the lower part of the hull. Pett was recorded as going to write about this, but he died before he could reveal his 'shipwright's secrets'. These were recently rediscovered by reverse engineering from the 3D scans of a contemporary model.

 

Originally, I did not intend to verify this, but in the end, I too carried out my own reconstruction of the frame shapes of this contemporary model (Restoration yacht). This was in order to form my own view of those cono-cuneus curves.

 

For this, I used first the conventional method of shaping frames known from the Sutherland's work, in the 'as designed' variant (as opposed to the shipyard version using templates). Either way, both of these variants used only simple geometric figures - arcs and line segments for this.

 

In short: if the published 3D scans of the model are to be trusted, it appears that the use of the conventional method as described in the Sutherland's work gives exceptionally good results (i.e. the reconstructed lines are very well aligned with the model frames).

 

Then I compared the reconstruction lines as printed in the publication, based on the cono-cuneus curves with the same 3D scans and the results turned out to be inferior. In this light, while I might have had some doubts before, now the proposal of cono-cuneus curves to reconstruct frame shapes has lost credibility for me.

 

I have called the following composition 'A Perfect Fit' (lines are mine and the 3D scans of the frames profiles were taken from the study A Restoration Yacht's Design Secrets Unveiled: An examination of a ship model with reference to the works of William Sutherland, The Mariner's Mirror 2021, Volume 107, Issue 2). Not all the lines are shown in the drawing, especially the auxiliary ones. However, the most important thing is that it is perfectly possible to geometrically recontour the shape of the model's frames just from the arcs and line segments.

 

 

 

[druxey]

An interesting comparison!

[Waldemar]

 

Hopefully, for some. For me, certainly conclusive.

 

By the way. A monograph on the Restoration yachts by Brian Lavery, Royal Yachts Under Sail, will soon be published. It may even be available in digital format now. Lavery is a trustworthy author, and this monograph is sure to become a standard work on the subject. However, I do not expect him to include an overly detailed analysis of yacht design and construction in this publication, which is after all intended for a wide audience.

 

 

[Waldemar]

 

For those who like theory, the following sketch may be of interest. It explains the principle of the geometrical formation of conoidal hulls in a more elaborate form, consisting of as many as two, actually three, conoids. Naturally, the surfaces of the two upper conoids are tangent to the surface of the lower conoid along two longitudinal lines, as can be seen in the drawing.

 

This was precisely the method used in the design of the Restoration yacht under examination.

 

 

 

 

Edited October 2, 2022 by Waldemar

[trippwj]

On 10/1/2022 at 6:39 AM, druxey said:

There is no period work (that has yet been uncovered) describing the application of the cono-cuneus curve in the lower part of the hull. Pett was recorded as going to write about this, but he died before he could reveal his 'shipwright's secrets'. These were recently rediscovered by reverse engineering from the 3D scans of a contemporary model.

Druxey -

 

I confess up front to not have the breadth of familiarity that you do concerning the designing of hulls. I noted your comment about Pett and, as I sometimes do, I wandered down a rabbett hole (see what I did there??Rabbett???) and came across a small piece, originally dated 1662, entitled Cono-Cuneus, or, The Shipwright’s Circular Wedge in a letter to the honourable Sir Robert Moray.  Since included in Wallis' 1685 A treatise of algebra, both historical and practical

 

The transcribed text of Cono-cuneus may be found here (without figures)

Wallis, John. Letter. 1662. “Cono-Cuneus, or, The Shipwright’s Circular Wedge That Is, a Body Resembling in Part a Conus, in Part a Cuneus, Geometrically Considered,” April 7, 1662. http://name.umdl.umich.edu/A67375.0001.001.

 

European Cultural Heritage Online (ECHO) has an on-line version of Treatise of Algebra, including cono-cuneus (with figures) which can be found here (cono-cuneus begins on page 402):

 

Wallis, John. 1685. A Treatise of Algebra, Both Historical and Practical : Shewing the Original, Progress, and Advancement Thereof, from Time to Time, and by What Steps It Hath Attained to the Heighth at Which Now It Is ; with Some Additional Treatises. https://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/H3GRV5AU/pageimg&start=421&viewMode=index&pn=430&mode=imagepath.

 

If you desire PDF (I know I do - makes the search and selective printing much easier) then that can be found here (note cono-cuneus starts on page 414, with the figures preceding the text. .

 

Wallis, John. 1685. A Proposal about Printing a Treatise of Algebra, Historical and Practical: Written by Dr. John Wallis. Richard Davis. https://books.google.com/books?id=TXpmAAAAcAAJ.

 

I am not sure if there is direct applicability to the lower form of the hull, but his figures would seem to indicate tha is true.

 

 

 

 

 

 

 

 

Edited October 3, 2022 by trippwj
Added figure

[Waldemar]

 

There is "only" one small problem, these cono-cuneus curves do not match the frame scans. That's it.

 

 

[druxey]

The application all depends on the proportions of the c-c curve. They are related to the principal dimensions of the hull. Once the appropriate c-c curve is made, it will apply all the way along the hull below the (single) conoid. In my opinion, the solution is simpler and more elegant than Sutherland's. And that's all I have to add to this conversation.

 

Yes, Wayne, that's Dr. Wallis' contribution via the Royal Society.

[Waldemar]

 

 🙂

 

Mark, may I ask the reason for your "Confused" reaction? You don't like that the cono-cuneus curves don't fit the original model anything to write about them, you don't like that I wrote about it, or something else?

 

 

[jud]

Interesting thread, but like most modern theories' it fails to address the reason for the general shape of the lower hull to begin with. Curved frames add strength, but so does mass, so strength is unlikely to be the primary reason for the general shape of the lower hull. I throw this idea out for thought. Buoyancy and the fact that sailing ships traveled on their heeled over sides more often than level is what caused the shape of the lower hulls to be constructed as they were to maintained a constant buoyancy as the ship heeled over in her travels using the typical rigs of the time. The upper hulls return towards the C/L was dealing with center of gravity and resolves a different need. All the mathematical theories were aimed at obtaining a mathematical constant in hull design that fit the discovered, 'by trial and error', conclusion of the best shape of the lower hull to maintain constant buoyancy as she heeled over. Later sail rigs and much larger hulls with lower Center of Gravities eliminated that need and the basic reason for the shape was forgotten. I have made no scientific study for this theory, it developed after observation and a curiosity of why, over time, but I think it has enough merit to drop it in for consideration and perhaps there has been a study on the subject and someone can bring it to light.

 

[Waldemar]

 

Yes Jud, you are absolutely right. This thread is not so much about why hulls were shaped one way or another, but rather how this was achieved. However, this equally interesting subject can also be successfully pursued in most early works on shipbuilding or naval architecture. And it probably goes without saying that the two issues are indeed very closely linked.

 

 

[trippwj]

11 hours ago, druxey said:

Yes, Wayne, that's Dr. Wallis' contribution via the Royal Society.

Yeah, I feel kind of silly now - I see it listed in the References of your MM article. oops! 

 

 

[mtaylor]

12 hours ago, Waldemar said:

 

 🙂

 

Mark, may I ask the reason for your "Confused" reaction? You don't like that the cono-cuneus curves don't fit the original model anything to write about them, you don't like that I wrote about it, or something else?

 

 

I think that I"m just confused about it and need to do some research.   I realize there's a lot of ways to do lines but since I've never drawn a set of lines...  well, there's that.  Fascinating topic even if I don't grasp everything.

[jud]

11 hours ago, Waldemar said:

 

Yes Jud, you are absolutely right. This thread is not so much about why hulls were shaped one way or another, but rather how this was achieved. However, this equally interesting subject can also be successfully pursued in most early works on shipbuilding or naval architecture. And it probably goes without saying that the two issues are indeed very closely linked.

 

 

The how's are only a drafting method unless the whys are at the core of the solution. Without the whys being paramount and constantly addressed, the fancy curve fitting fails in practice. The how's and the why is one unit reduced to volume and must be addressed as such. Design from point to point and then fit the curve and hold its shape throughout the hull as it is practical to do so.

 

Edited October 4, 2022 by jud

[Waldemar]

 

1 hour ago, jud said:

The how's are only a drafting method unless the whys are at the core of the solution. Without the whys being paramount and constantly addressed, the fancy curve fitting fails in practice. The how's and the why is one unit reduced to volume and must be addressed as such. Design from point to point and then fit the curve and hold its shape throughout the hull as it is practical to do so.

 

We are thinking along similar lines, Jud. Unfortunately, my time is limited, and I now prefer to focus on lesser known or obscure aspects of period ship design. If a broader context is needed, there are a great many works on naval architecture available.

 

 

[Waldemar]

 

On 10/4/2022 at 9:22 PM, mtaylor said:

I think that I"m just confused about it and need to do some research.   I realize there's a lot of ways to do lines but since I've never drawn a set of lines...  well, there's that.  Fascinating topic even if I don't grasp everything.

 

In order to show something concrete again in this thread in as clear a graphical way as possible, and perhaps persuade Mark to design an Elizabethan era ship himself, I present below a relatively easy way to do it. It can be useful for graphical as well as non-graphical and partly graphical methods of ship design. Precisely, it is about achieving the most important and at the same time conceptually most difficult shape of the submerged part of the hull. This is one of the many variants of the moulding method (hauling down/pulling up), giving pre-designed frames along the entire length of the hull.

 

A computer is not necessary as you can draw by hand, but it speeds up the work considerably and improves precision, as can be seen in the accompanying graphics of a comparative nature. This is why the sketch of a merchant ship circa 1600 kindly provided by Druxey will be used as a starting point. For the sake of better comparison, I have retained most of the parameters adopted in the original sketch, apart from a few elements that I have seen fit to modify.

 

 

One must start by establishing the overall proportions of the hull, the shape of the axial skeleton elements and two guides of the most significant importance – the rising/narrowing lines of the breadth and the floor. This is not difficult, but it is best to make use of works on naval architecture, shipbuilding contracts and shipwrecks. However, as I wrote earlier, this is beyond the scope of this thread, as I would also like to do other things in my life besides quoting the contents of other works.

 

Next you need to work out the shape of the main frame. Basically, I used the original design, but added a deadrise so that when the limber holes are cut out, the bottoms are not weakened, and bilge water can flow more easily to the keel and pumps. I have also reduced the radius of the all-important futtock sweep to get larger capacity and to the limits indicated in the 'Newton' manuscript.

 

 

If anyone has read this thread from the beginning and has even a basic understanding of geometry, the attached sketch is self-explanatory. It must be stressed, however, that it is not necessary, or indeed allowed, to use waterlines and diagonals to correct the hull lines, as this will only deform the shape obtained by the historically correct means. There is no mention of the use of these design tools in early English works on shipbuilding (Baker, Newton, Harriot, anon. 1620, Bushnell), and they only begin to appear on plans in the second half of the 17th century.  Properly applied moulding method together with a properly selected main frame shape almost guarantees correct, smooth hull surfaces. Obtained shapes may be not absolutely perfect, but this is an inevitable, inherent limitation of this method.

 

 

 

Hollowing templates lines ('moules') were added in a systematic way along the entire length of the hull. Their shape is described in the 'Newton' manuscript (see my post #57), and the method of application in my post #7.

 

I guarantee that a professorial degree or even an engineering degree is not needed for this. It is also safe to say that most would not be able to cope, at least not immediately. I invite you to experiment for yourself. Enjoy!

 

 

 

 

 

Edited October 10, 2022 by Waldemar

[Waldemar]

 

Back to Sutherland and the Restoration yacht. Below is a sketch showing in detail how the frames of the double conoid hulls were drawn. and all the necessary elements are there. It is difficult to imagine something simpler and efficient at the same time in terms of design method.

 

The stern is constructed in the same way with the difference that the hollowing radii are variable and equal to the corresponding radii of the lower conoid, with the exception of the very last frames, where hollowing radii are equal to the corresponding upper conoid. That's it.