Seeking information on determining load waterline

[JohnE]

How did they balance all of these, in the absence of slide rules, spreadsheets and calculators?

 

My friend, they used logarithms. They memorized the table of logs. A modern sliderule is nothing but a replacement for memorization. They used pen/pencil, paper, and their brains, along with a book of tables, if necessary.

 

This was the age of d'Alembert, Bernouli, Euler, Fourier, Laplace, Lagrange, Gauss, Rolle, and a bit earlier Newton, Descartes, and Fermat. Mathemeticians that we moderns are, frankly, unable to comprehend without an "advanced" degree; and it took 358 years to solve Fermat's last, the proof of which he declined to put in the margin because it was a 'bit' too long.

 

Don't ever make the mistake of thinking these people weren't "accurate" just because they didn't have computers or Exel. They had more practical math sense than I could ever hope to have, and I'm a physicist and naval architect.

 

John

[malachy]

Harris' biography about af Chapman has a very interesting appendix with Chapman´s hand-written calculations for a 70-gun ship, made in 1767.

He calculated:

 

- displacement volume (with two methods, integration of the cross-sectional areas at each station and integration of the areas of each waterplane)

- location of the centre of bouyancy

- centre of flotation

- location of the metacentric heigth above the load waterline

 

Well worth a look if one wants to know how they did things back then

Edited April 3, 2016 by Bava

[lehmann]

At one time, not so far back, "calculator" was not a device, but a profession.

[trippwj]

My friend, they used logarithms. They memorized the table of logs. A modern sliderule is nothing but a replacement for memorization. They used pen/pencil, paper, and their brains, along with a book of tables, if necessary.

 

This was the age of d'Alembert, Bernouli, Euler, Fourier, Laplace, Lagrange, Gauss, Rolle, and a bit earlier Newton, Descartes, and Fermat. Mathemeticians that we moderns are, frankly, unable to comprehend without an "advanced" degree; and it took 358 years to solve Fermat's last, the proof of which he declined to put in the margin because it was a 'bit' too long.

 

Don't ever make the mistake of thinking these people weren't "accurate" just because they didn't have computers or Exel. They had more practical math sense than I could ever hope to have, and I'm a physicist and naval architect.

 

John

 

John –

You bring up some interesting considerations – thank you!

 

One of the aspects that comes out in trying to research this topic, esoteric as it may be, is that there was a distinction to be drawn between the theorist and the builder.  Many of the mathematicians (Bernouli, Euler, Fourier, Newton etc.) were mathematical theorists.  They developed methodologies and approaches to the task, yet were not ship builders themselves.  Nor, for that matter, did they design ships.

 

There was, of course, the mathematically oriented ship builder – people like Deane, Pett, Baker (and Tom Wells) and Chapman.  They not only designed and built ships, but also applied the mathematical theories in their work. 

 

Now we come to the pure ship builder of old.  They had enough mathematical background to determine the measurements of components (often based on simple rations, arcs and so on – see Rees and Steel, publishing someone else’s narrative, for examples), but did not apply the mathematical theories to the effort. 

 

The frustration in English naval architecture can be found in the publications by The Society for the Improvement of Naval Architecture (Society for the Improvement of Naval Architecture. 1791. An Address to the Public, from the Society for the Improvement of Naval Architecture. Instituted 14th April, 1791. https://archive.org/details/someaccountinst00unkngoog.)

 

To promote this important object as effectually as possible, the society purpose to encourage every useful invention and discovery as far as shall be in their power, both by honorary and pecuniary rewards.—-They have in view particularly to improve the theories of floating bodies and the resistance of fluids—to procure draughts and models of different vessels, together with calculations of their capacity, centre of gravity, tonnage, &c. —to make observations and experiments themselves, and to point out such observations and experiments as appear best: calculated to further their deigns, and most deserving those premiums which the society can bestow.

 

But though the Improvement of Naval Architecture in all its Branches be certainly the principal object of this institution, yet the society do not by any means intend to confine themselves merely to the form and structure of vessels. Every subordinate and collateral pursuit will claim a share of the attention of the society in proportion to its merits; and whatever may have any tendency to render navigation more safe, salutary, and even pleasant, will not be neglected.

 

We also find, in 1860, the Reverend Wooley reflecting on the progress and state of mathematics in Naval Architecture (Wooley, J. 1860. On the Present State of the Mathematical Theory of Naval Architecture. In Transactions of the Royal Institution of Naval Architects, I:10–38. The Institution. https://books.google.com/books?id=xR-oHqNU7RIC)

In former times, the constructors of ships in the Royal Navy were restricted to certain relative dimensions of length, breadth, and depth, which in fact gave a small amount of natural stability, and necessitated a recourse to ballast. Sir William Symonds was the first surveyor of the Navy who obtained the power of building ships without those unnatural restrictions, and he gave considerable beam to his vessels, and with it great natural stability, and so was enabled to reduce very materially the quantity of ballast--a very important gain. Whatever may be thought of the form of his vessels in other respects, it cannot be denied that, so far as increasing beam and diminishing ballast are concerned, he effected an immense improvement in the vessels of the Royal Navy.

 

The scientific constructor would do well, however, not to confine his investigations to mere formulae derived from analytical processes, and to inferences drawn from them; but he would derive immense information, and add most materially to the breadth and practical value of his views, by examining from first principles, and in a more geometrical method, the several elements on which stability may be made to depend. In this way he may gain most valuable experience as to the twofold nature of stability which I have already indicated.

 

Interspersed among a multitude of period writings are observations concerning the limited mathematical skills of most ship builders and shipwrights.  Indeed, more recent scholarly research has drawn the similar conclusions (see, for example, Tebeaux, E. 2008. Technical Writing in English Renaissance Shipwrightery: Breaching the Shoals of Orality. Journal of Technical Writing and Communication 38, no. 1: 3–25. http://jtw.sagepub.com/content/38/1/3.)

 

The information was there, but most of those who were in a position to use it and benefit from it were not trained in how to use it.

 

Time for a working hypothesis. 

 

The central question: At what point did shipwrights shift from marking a load waterline based on where they felt it should be to determining where the load water line would be based upon the form and structure of a vessel.

 

The Hypothesis:

 

Early shipbuilders developed their methods and designs based largely on trial and error.  As the size of vessels increased, methods became more formalized in an attempt to maintain the relationship between form (shape), function, and performance.  Systems such as “whole moulding” and “shell first” construction were developed over many years of trial and error, to guide a builder in forming the body of a ship.  No attempt was made to predetermine accurately the immersion of these vessels, but rather institutional knowledge (what had worked for similarly built vessels) guided the builder.

[trippwj]

Having stuck my neck out by making this broad a statement, let me offer some of the reasons behind this assumption.

 

While the processes and methods used to design vessels are as old as the use of ships, for the purposes of this discussion I am going to limit the time frame to about 1400 through 1800.  This period includes a variety of design and construction methods, as well as increasing awareness of the science of flotation and resistance.  The upper end point is very carefully chosen as representing the point where, particularly in Great Britain, there was a paradigm shift about to occur in how the ship builder thought about the form and design of the ship.  Sepping’s bow, diagonal riders, stability calculations, the advent of steam and iron construction – all of this and more influenced a paradigm shift during the first half of the 19th century, worthy of study separate from the earlier periods.

 

The modern approach to designing a ship is generally thought of in terms of measured drawings and plans drawn on paper and then transferred to the mould loft floor. These drawings were used to determine the exact shape of the ship - before the start of building. The drawings were also used to store good designs both for review and reuse.

Neither measured plans nor even the technique for making them existed in the Middle Ages. Ship design, in terms of determining final dimensions, was carried out in the shipyard while the ship was being built. While the overall shape of the vessel was easily envisioned, determining the dimensions of hundreds if not thousands of individual parts that had to be cut from timber and assembled together was the challenge. What methods were used to store the “good” designs and retrieve them for later use?

 

In 1434, Michael of Rhodes sat down to write out the manuscript for which he is remembered. He recorded his full name of Michalli da Ruodo twice in the 440-page text. In his treatise on shipbuilding, he provides two approaches to the challenge of ship design. For the types of ships built in private shipyards, he describes a system based on a proportional approach; for the galleys built in the state-run Arsenal, his approach reflects the recording of actual measurements on paper.

Michael's manuscript contains some of the earliest known ship-design drawings, marking an early stage in the transfer of design from the shipyard to the drawing office. Most of a galley's frames were shaped by proportion, or "moulded." The geometry, however, did not extend all the way to the bow and stern which were shaped by hand, using thin wooden battens, or ribbands, as guides.

 

The shapes of most of a galley's frames were determined by proportion, but the geometry did not cover the shape of the bow or stern. These were determined in the yard, using string to get the proper curve. This drawing was intended to illustrate part of the process. The top diagram provides dimensions relating to the shape of the stempost; the bottom diagram, dimensions relating to the stern.

 

 

Source:

 

Stahl, Alan M., ed. 2009. The Book of Michael of Rhodes: A Fifteenth-Century Maritime Manuscript, Vol. 2: Transcription and Translation. Trans. Franco Rossi. Vol. 2. 3 vols. Cambridge, Mass: The MIT Press.

 

Also see The Michael of Rhodes project. Accessed April 28, 2016. http://brunelleschi.imss.fi.it/michaelofrhodes/index.html.

 

 

[trippwj]

This approach to ship design was fairly common in the 15th and 16th centuries.  Bellabarba (1993) observed that

 

Many ships have been built, right up to our times, using a few measurements and proportions between the main parts, and the 'master's eye' dealing with all the rest. Although this method provided respectable, indeed admirable, results, it did not permit a successful example to be reproduced exactly, nor any mistakes to be corrected intelligently. Any possibility of making progress depended on individual masters' memories and insight and their willingness to share their experience with others (colleagues or successors).

 

With this intuitive yardstick, it was impossible to build a series of identical units which was particularly essential for the fleets of Mediterranean galleys and likewise to prefabricate parts of the hull. But, in contrast, the ancient method of design allowed a hull shape to be reproduced exactly the same as any other one or its characteristics to be subtly varied by means of a set of 'rules' which, in addition to simple measurements (length, height, width, proportions etc.) included indications for defining the hull curves geometrically. These instructions could be memorised and easily communicated, with no need for either drawings or mathematical calculations. This distinguishes the ancient method described here from all the other, more or less contemporary ones, based on mere intuition (the 'master's eye') or the ribbands, which we shall come back to later.

 

The set of 'rules' were numerical instructions which could be used directly in the yard during shipbuilding. So the method could be described as a 'method of rules' as opposed to the more recent method of drawings.

 

Bellabarba, Sergio. 1993. “The Ancient Methods of Designing Hulls.” The Mariner’s Mirror 79 (3): 274–92 . doi:10.1080/00253359.1993.10656457.

 

Loewen (1998) offered a brief description of the process:

 

Three major steps made up the ship carpenter's process of designing a hull. First, he worked out the four basic dimensions of the hull: its breadth, its keel, its length from stem to sternpost and its depth of hold. These dimensions mirrored those used by ship surveyors to gauge a ship's tonnage and, in practice, allowed a carpenter to convert to a merchant's desire to build a ship able to carry a certain tonnage of goods into real measures.

 

Second, within the parameters of the breadth and the depth of hold at midship, the carpenter worked out the shape of the master frame, using as his fundamental elements a series of five tangent lines and arcs: the floor line, the bilge arc, the futtock arc, the arc at the greatest breadth and the tumblehome line. He then devised a master mould from this shape, and marked off the points on the mould at which his lines and arcs touched.

 

Third, using the master mould, he worked out the shape of frames fore and aft of the master frame by means of three systematic adjustments to the master mould, namely: the rising of the floor, the narrowing of the floor and adjusting the aspect of the frame from the bilge upwards.

 

Loewen, Brad. 1998. “Recent Advances in Ship History and Archaeology, 1450-1650: Hull Design, Regional Typologies and Wood Studies.” Material Culture Review / Revue de La Culture Matérielle 48 (1). http://journals.hil.unb.ca/index.php/MCR/article/view/17791.

 

In A Treatise on Shipbuilding: And a Treatise on Rigging, Written about 1620-1625, the anonymous author offers a detailed description of the process of “whole moulding”:

 

'Suppose I would mould out the 20th bend of timber aft:
1st: I strike a ground line upon the foot of the timber and cross it at right angles with a middle line for the depth.
2nd: I set off the rising of that bend from the ground line, at the length it is marked upon the floor mould.
3rd: I seek the depth of that bend, which set off from the rising line I draw a parallel to the gound line for the breadth.
4th: I take the narrowing aloft out of the greatest breadth and at that breadth draw a parallel to the middle line.
5th: I set the narrowing alow upon the middle line of the timber and score out by the mould both within and without the frame of the mould.
6th: I bring down the sine mark of the lower part of the futtock to the haleing down thereof upon the wrong head and score out that part of the futtock.
7th: I bring down the lower end of the upper futtock to the haleing down marked upon the lower part, and score out the upper part of the futtock.
8th: I put up the top timber upon the end of the futtock according to the mark of putting up, that it may fit his breadth at the upper surmark, and score aut by it the top timber mould. And so is the whole bend truly moulded with all his parts'.

 

 

Salisbury, W, 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.

[jud]

I used a simple method for the boats made from 1" X 4" lumber and a saw. Required a Horse Trough, some stones and a careful stacking of those stones onto the deck of my boat, when it dumped them I knew the limit. A very reliable method unless I introduced some wave action and lost my cargo. Needed to  spend some time retrieving stones from the bottom of the trough, for butt protection.

jud

[trippwj]

Harris' biography about af Chapman has a very interesting appendix with Chapman´s hand-written calculations for a 70-gun ship, made in 1767.

He calculated:

 

- displacement volume (with two methods, integration of the cross-sectional areas at each station and integration of the areas of each waterplane)

- location of the centre of bouyancy

- centre of flotation

- location of the metacentric heigth above the load waterline

 

Well worth a look if one wants to know how they did things back then

 

Chapman's work is, indeed, of great interest, and will represent a seperate posting when the time comes - I am working with the Inman translation of his Tractat om skeppsbyggeriet, first published in 1775 to complement the author's Architectura navalis mercatoria.  The plates and figures related to many of the calculations are included, and detailed methods discussed.  Additionally, it is long out of copyright so the figures and text are freely available for quotation and so on.

 

I am working though some of his details and it is quite interesting!  As one tidbit:

 

To construct from hence a scale of burden.

(182.) Draw two lines perpendicular to each other, the one in a horizontal direction, the other in a vertical direction; make on the horizontal line a decimal scale at pleasure to represent lasts, and on the vertical another scale of feet also at pleasure, as is seen in Fig. 50.

Below the horizontal line and at the distance from this superior line of 1.62, 3.24, 4.28, 6.48, 8.1, 9.72 and 11.2 feet, draw parallels thereto.

 

On the scale of lasts, take the quantities, which have been found, in lasts 45.16, 85.89, 120.88, 149.75, 171.45, 184.6 and 189.58; set off these quantities on the corresponding horizontal lines, from the vertical line.

 

Through all the points so determined pass a curve, and you will have a scale of solidity.

 

The horizontal scale is in French tons, English tons, and Swedish lasts.

 

The method of using the scale is this. 

 

The line a b (NOTE 53.) on the sheer plan is the load water-line, the privateer being laden. Suppose that the water-line before it is entirely laden, were cd; then the distances ac, bd are taken, which by the scale of the plan give 4 feet 1 ½  inches and 5 feet 1 ½  inches; these two quantities are added, and half the sum is taken, 4 feet 7 ½  inches.

 

Take this quantity 4 feet 7 ½ inches on the scale of solidity" you will have e g, which must be transferred perpendicularly to the line e f, until it meet the curve in h. From h draw the line hi perpendicularly to f e, or what is the same thing, parallel to e g; this line marks on the scale of lading the weight, which must be put on board to bring down the ship to the line a b, namely, 175 Swedish lasts.

 

(183.) If the ship be quite light, one may in this manner find the lading, which it can take; or if the water-line of a ship ha~. been once observed, supposing another to be found, one may be able" by means of the said scale, to obtain the weight which the ship has taken on board, or of which it has been discharged, to render it so much more brought down, or more raised.

 

[trippwj]

Thought it might be polite to provide the other 3 figures used in the above Scale of Burden for a Privateer.

 

 

 

[trippwj]

The convergence of three separate yet ultimately related concerns resulted in the availability to the shipbuilder of a reasonably accurate method to predetermine the displacement (and thus the LWL) for a ship, whether a war ship or a merchant ship, when fully loaded for the intended purpose.

 

1. The need to accurately determine the carrying capacity of a vessel (particularly a merchant ship) for collection of duties, port fees and so on.
2. The desire to identify the form of a ship which offers the least resistance to the water.
3. The requirement to identify the shape and form of a ship which provides suitable sailing and handling qualities in all conditions, and to handle the intended sails well.

Each of these separate lines of study, coupled with advances in scientific theory and mathematical capabilities, resulted in methodologies that also allowed the shipbuilder to predetermine the displacement from the plans, before construction, rather than having a desired floating level that was dependent on limiting stowage on the ship.

The first concern has already been discussed in an earlier post, with incremental changes in methods leading up to the work of Moorsom in the 1850’s, which relied on mathematical approaches developed in response to the other concerns.

 

Efforts to identify the best form of a ship have been ongoing for more than 300 years, and continue today, although with a much higher level of sophistication.  As various approaches were developed to identify the best form to part the water, efforts were also undertaken to mathematically explain the empirical results. Euler, Bouguer, Beaufoy and Chapman are among those who developed stability (and displacement) theories based on initial work around the form of least resistance. Earlier work by Pardies, Renaud and others attempted to provide a theoretical framework to describe the motion of a ship – why it could sail against the wind, for example, rather than be pushed hither and yon.  This yielded a method to calculate the dérive (drift of ships or lee way) as a point of reference (see figure from Pardies below).

 

 

From Pardies, I.G. 1673. La statique ou la science des forces mouvantes. Sébastien Mabre-Cramoisy. http://echo.mpiwg-berlin.mpg.de/MPIWG:46XPZMX8.

 

 

[trippwj]

Let’s take a moment to consider what, exactly, was meant in point 3 above:

3. The requirement to identify the shape and form of a ship which provides suitable sailing and handling qualities in all conditions, and to handle the intended sails well.

Many treatisers and mariners from the time provided their own description of what these qualities were.  Let’s take a quick look at a few:

From 1792:

 

A ship, whether destined for war or commerce, ought to be able to bear a certain determined lading, and be sufficiently capacious to afford ample accommodations for her crew, with all the contingencies involved in the consideration of their health and comfort. She must carry the cargo with ease to herself; the artillery in a perfectly efficient state, whether space for working the guns, or the height of those guns above the surface of the sea, be considered. She must be so formed that she shall be able to make her passages with velocity when the wind is favourable, and contend with it advantageously when it is unfavourable.

The ship must be capable of being worked with ease, rapidity, and certainty, however adverse the circumstances may be under which the maneuvers are performed; for it will sometimes happen, that the more unfavourable the circumstances are, the more imperative is this necessity for success. She must have great stability, or the power of resisting inclination, and of restoring herself to an upright position when inclined; and this must be so nicely graduated and adjusted, that the perfect safety of the vessel may be insured without any injurious strain being brought upon the masts or rigging by an excess of this resisting power. She must be able to sail over rough seas without any injury from the pitching or rolling motions which will ensue, and without the hazards to the crew, to the vessel, or to the cargo, which would result from a tendency to ship seas when thus situated. Her masts must be so proportioned that they shall be sufficiently strong, taking into consideration the support they derive from the rigging, to resist the strains to which they will be subjected, and that without being so heavy as to diminish unnecessarily the stability of the ship, or require superfluous lading from extra ballast. The masts must be lofty enough to spread an adequate surface of canvass to furnish the propelling power, and, at the same time, be so placed and so proportioned to each other, that this propelling power may be readily converted into a series of mutually counteracting or co-operating forces to insure quickness of maneuvering.¹

 

Let’s jump forward about 30 years to 1829:

Disregarding the fundamental principals of floating bodies, and too hastily giving up as hopeless the attainment of a theory combining experience with established scientific principle, they have contented themselves with ingeniously inventing mechanical methods of forming the designs of ships bodies, which they did not even pretend to prove had any conexion with the properties of the machine, necessary to ensure the qualities conducive to its intended use. For instance, - some invented methods of forming ships' bodies of arcs of circles; others of arcs of ellipses, parabolas, or of whatever curve they might arbitrarily assume.  Taking anyone of these curves as the principle of their design, they investigated, with mathematical accuracy, the means of completing the form of the ship's body in correct accordance with their assumption. They did not attempt to show that these curves possessed any property which would render a ship a faster sailer, a more weatherly, or a safer ship than any other curves which might have been adopted in the construction of the ship's body.²

 

There are many others with similar statements.  What was desired for a ship was that it:

1. Handled the intended sails well (that is, was stable and responsive)
2. Must carry the cargo (or weapons &.c.) intended at the correct draught of water.
3. Should sail well at all points of the wind.
4. Should be a fast sailer.

 

Each of these qualities brings a specific set of design criterion, often at odds with each other.  Designing a stable vessel by increasing breadth often decreases the speed.  Increased ability to sail to windward may reduce the ability to carry the intended cargo at the desired draught. Trial and error design approaches brought the ship near to a desired condition, but as often as not a success in one aspect resulted in a poor result in another.  What Morgan & Crueze (and, indeed, many others during the later 18th and 19th centuries) were trying to accomplish was to apply a mathematical solution to the design of a ship to achieve the best compromise between the competing design requirements.

 

 

 

1.  Society for the improvement of naval architecture London. 1792. Some Account of the Institution, Plan, and Present State, of the Society for the Improvement of Naval Architecture: With the Premiums Offered by the Society, List of Members, and the Rules and Orders of the Society. To Which Are Annexed Some Papers on Subjects of Naval Architecture Received by the Committee. http://archive.org/details/someaccountinst00unkngoog. Page 5 (43 of 128)

 

2.  William Morgan and Augustin Francis Bullock Creuze, Papers on Naval Architecture and Other Subjects Connected with Naval Science Vol. II, vol. II (G.B. Whittaker, 1829), page 3.

[malachy]

Very interesting posts, trippwj! I´m looking forward to the next installment

[trippwj]

Perhaps lost in the past several pages of debate and discussion is the original purpose of my study – how and when did that simple line (Load Water Line) become a pre-determined height for inclusion on the design plans for a ship?

 

I am not sure there is a singular answer, or date, or individual.  There are examples of the presence of the LWL on plans dating back to the times of Matthew Baker (see, for example, his famous drawing of the Revenge, showing the immersed portion of the hull, 16th century).  There are also the pre-construction estimates by the Pett’s (cited earlier, I believe) which verified extremely well post-construction (circa 1630).  HOWEVER, we also have noted designers/constructors such as Sutherland throwing out a waterline of an apparently arbitrary level, and then others (and I must apologize, for in preparing this quick post I neglected to note the reference for that –  I will locate it and add to a latter posting as soon as I am able!) offering the use of the desired waterline as the base line for drawing a ships plan.  An interesting approach, but begs the question of how to guarantee the ship, as fully equipped for service, actually swims at the desired depth?

 

 

I am, perhaps, getting closer to a defensible position, yet not there yet.  Finding the boundary between a true “design” waterline (that depth at which the fully equipped ship will float, identified during the design of the ship) versus the “desired” waterline (that depth at which the ship floats when adjustments in equipping, stores, ballast &c. are made such that the vessel floats at the level intended).  OOOHHH!  Two new definitions added – thoughts on that distinction?

Many thanks -

[trippwj]

I wanted to take a moment to consider the manuscript attributed to Baker. 

 

From Castro, F. 2002. Fragments of Ancient English Shipwrightry. Ship Treatises and Books.

http://nautarch.tamu.edu/shiplab/treatisefiles/ttfragments.htm

The Fragments of Ancient English Shipwrightry is a collection of miscellaneous notes and incomplete plans of ships started by an English shipwright named Matthew Baker (1530-1613) in the 1570s, and continued with notes from one of his apprentices, John Wells, and annotations on mathematics.

Baker was born in 1530, the son of a shipwright of King Henry VIII of England.  There is notice of him traveling to the Levant in January 1551, at the age of 21, probably as a ship's carpenter aboard an English merchantman.  He may have visited Italian and Greek shipyards and collected Venetian and Greek designs of midship frames.  A fairly cultured man with a good understanding of mathematics, he certainly had contacts and was influenced by the Italian shipwrights hired by Henry VIII in 1543.  These Italians appear to have remained in the country for over forty years, earning wages thirty percent higher than their English counterparts.  In 1572 Baker was appointed Master Shipwright of the kingdom.  He worked with other men of knowledge, and his notes reflect the first steps of a trend to change English shipbuilding from the medieval empirical method to the modern standard of paper plans and conceptual models that could be repeated, improved and enlarged.  When he died in 1613, he left the manuscript to his neighbor and protégé John Wells.

 

Baker's notes present a compilation of precious observations, abacus, tables, and drawings, comprising more than 30 geometrically defined midship sections, from the sections of 4 galleasses designed by his father, James Baker, in the second half of the 16th century to the early 17th century midship sections that were in use when new methods to determine the rising and narrowing of the bottom of the vessels in the central portion were fully defined in England.  The part added by John Wells is mostly occupied with calculations of spherical geometry, making extensive use of logarithms from 1617 on.

 

Richard Barker (1985 - “Fragments from the Pepysian Library.” Revista Da Universidade de Coimbra XXXII: 161–78.) provides additional information concerning this manuscript.  Of particular interest for this post is the following:

One of the more intriguing aspects of the numerical work in Fragments is the frequent calculation of sectional areas of moulds below the depth by Baker, usually linked with the product breadth x depth, effectively giving a prismatic coefficient. Taken with Bourne’s Treasure for Travellers on mensuration of ships lines and waterplanes, from which it is perfectly clear that Bourne and his contemporaries knew how to measure displacement tonnage at any selected draught, either as a paper exercise or with the use of models, it is difficult to avoid the conclusion that Deane’s contribution to the principles at least of determining displacement (and thence draught at launching) has been overstated. It appears to rest entirely on Pepys’ record of what Deane told him. Even Deane is not explicit in his Doctrine about his methods in the procedures covered now by Simpson’s Rules, and begs a number of question in his treatment. Just what Baker was doing with prismatic coefficients and immersed (?) areas of sections remains a mystery, but the practice should at least be credited to his era. It is at least possible that the incentive for both Baker and Wells was the search for a satisfactory tonnage rule. Baker apparently changed his method about 1582: Wells was heavily involved in a Commission to investigate tonnage rules in 1626.

 

 

Johnston, S. 1994. Making Mathematical Practice: Gentlemen, Practitioners and Artisans in Elizabethan England. PhD Dissertation, University of Cambridge. http://www.mhs.ox.ac.uk/staff/saj/thesis/

 

A re-creation of the figure from Page 35 pf Fragments:

 

 

The diagram is a simplified version of Baker’s drawing. There are many more inked and scribed lines in the original, as well as numbers for the calculation of areas.

 

In this example of Baker’s procedures for drawing the midship mould, breadth and depth are given as 36ft and 16ft respectively. dg = 1/5 ed. With eh = dg, draw gh. Then draw ec, cutting gh at i. Through i draw mk perpendicular to ed; ek is the floor for this half of the mould. Mark point l on gh such that hl = 2/3 gh. The first centre n is on mk and has its arc passing through k and l. Extend line ln beyond n; the second centre o is found on this extended line and its arc sweeps from l to c. To find the third centre, first mark the other half of the floor with p. The third centre q is at the intersection of oc and pn (extended). Baker then draws the upper futtock in three different ways.

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

 

Page 12:
With Balfour’s contract for the Hummeren in 1623 there came another significant change in that the contract specified the draught of the completed ship. This was a notoriously difficult measurement to predict and along with a vessel’s tonnage, was surrounded by a certain element of mystery and mystique.

 

 

 

[trippwj]

Perhaps lost in the past several pages of debate and discussion is the original purpose of my study – how and when did that simple line (Load Water Line) become a pre-determined height for inclusion on the design plans for a ship?

 

 HOWEVER, we also have noted designers/constructors such as Sutherland throwing out a waterline of an apparently arbitrary level, and then others (and I must apologize, for in preparing this quick post I neglected to note the reference for that –  I will locate it and add to a latter posting as soon as I am able!) offering the use of the desired waterline as the base line for drawing a ships plan.  An interesting approach, but begs the question of how to guarantee the ship, as fully equipped for service, actually swims at the desired depth?

 

 

Well, it took me a bit, but I located the reference.  Rev. Inman, in his 1820 translation of Chapman and added commentary (Chapman, Fredrik Henrik af. 1820. A Treatise on Ship-Building, With Explanations and Demonstrations Respecting  Architectura Navalis Mercatoria Published in 1768. Translated by James Inman. Cambridge: Printed by J. Smith, sold by Deighton & sons. Page 277), offers the following:

 

PREPARATION OF SOME OF THE PRINCIPAL LINES IN THE DRAUGHT.

(10.) Before the constructor proceeds farther, it may be proper to draw the few lines he has fixed on in pencil, and to prepare the paper for the insertion of the other parts of ,the draught.

Draw a straight line for the length of the load water-line from the after edge of the stern-post rabbet to the fore. side of the stem rabbet. At the extremities square up and down perpendiculars to this line; upon which take the draught of water head and stern, and draw a line for the bottom of the false keel. Set up square to this line the thickness of the false keel and next of the keel itself as far as the lower edge of the rabbet; and draw another line parallel to the former...

 

Basing the development of the plan on the LWL rather than the previous standard of a "baseline" would open numerous areas for experimentation.  While it may seem insignificant at first blush, the implications for the layout of the lines (such as the station lines being perpendicular to the waterline and NOT to the keel, as one example) certainly alter the paradigm.  It is quite different from that described by Rees or Steel, as but 2 examples. Note, however, that toward the end of his description of designing a ship, Inman does add the following, on bringing the station lines back perpendicular to the keel (page 295):

 

(41.) Lastly, it may be of considerable importance to form from the draught, now considered as complete, a block model of the vessel it is proposed to build; from which a still more accurate judgment may be formed of the fitness and beauty of the body. And should any defect be thus discovered, farther alterations must still be made; till the draught and the model are perfectly approved of. These different alterations and repeated calculations in some cases may appear very tedious, but they will not appear unnecessary to any person at all skilled in the business of construction. The many obvious reasons for using every means to ascertain the correctness and even nicety of every part of a ship, previous to its being built, need not be mentioned.

The different transverse sections in the construction which follows, in conformity to the method described above" are projected on a transverse plane perpendicular to the load water-line; also the curves are supposed to be drawn on the outside of the planking. Whereas in draughts for building', the sections are perpendicular to the keel, and the curves go no farther than the exterior surface of the timbers. To form one draught from the other, to space the timbers, place the ports, &c. is a mechanical operation, which it would be improper to describe here; this is within the reach of every practical person tolerably acquainted with the use of the drawing pen.

[trippwj]

A brief jump forward – let’s visit the US in 1863, and an interesting little work by a gentleman by the name of John Nystrom. 

 

John W. Nystrom (Swedish: Johan Vilhelm Nyström) (1825–1885) was a Swedish born, American civil engineer, inventor and author. He served as an assistant Secretary and Chief Engineer of the United States Navy during the American Civil War.  In 1863 he published an interesting little treatise (less well known than his writings on numerical systems and mechanics, apparently) entitled A Treatise on Parabolic Construction of Ships and Other Marine Engineering Subjects. Philadelphia : London: J.B. Lippincott & Co. ; Trèubner. http://catalog.hathitrust.org/Record/100209615.

 

Let’s start at the beginning, when Nystrom introduces us to his theory.

The Parabolic Construction of ships was originated by the celebrated Swedish Naval Architect, Chapman, who published a work on the same in the year 1775. Mr. Chapman came on the fortunate idea, that a vessel of the least possible resistance in water, should have the ordinate cross-sections of the displacement diminishing in a certain progression from the dead flat.

 

In order to find out that certain progression, he collected a great number of drawings of ships of known good and bad performances; on each drawing he transferred the ordinate cross-sections to rectangles of the same breadth as the beam of the vessel, placed the upper edges in the plan of the water line, by which he found that the under edges of the rectangular sections formed a bottom, the curve of which was a parabola in the ships of the best known performances.

 

I have labored very hard to find out some theory by which to sustain Chapman's hypothesis, but have not succeeded; found it necessary to start on new hypothesis, namely, that the resistance to a vessel of a given displacement, bounded in a given length, breadth and depth, is proportioned to the square of the sine of the mean angles of incident and reflection. By differentiating and integrating those angles, and finding their maxima and minima, will result in, that the square root of the ordinate cross-sections of the displacement should be ordinates in a Parabola, the principle upon which the Parabolic Construction is herein worked out.

 

Whew!  Sounds difficult.

 

Nystrom then proceeds to offer 26 equations which define the fundamental properties of a ship based on parabolic design and construction.

 

 

[trippwj]

Whilst working my way through various contemporary treatises, some more legible than others, it occurred to me that for the application of the Archimedes Principle to be effective, it was necessary to be able to estimate the actual weight of the vessel before it was constructed.  I took a detour, as it were, to search out some examples where estimates of a ships weight were given.  The four provided below are just representative cases – there are others.  It is interesting to see how the relative proportion of each part of the ship has, surprisingly, remained rather consistent across classes and decades.  For example, in 1754 the hull was 44,6% of the total weight for a 30 gun frigate, and in 1847 (with much more accurate methods used) it was 54.3% of the total weight for a proposed 80 ship.

 

 

Sources:

Murray, Mungo. 1754. A Treatise on Ship-Building and Navigation. In Three Parts, Wherein the Theory, Practice, and Application of All the Necessary Instruments Are Perspicuously Handled. With the Construction and Use of a New Invented Shipwright’s Sector ... Also Tables of the Sun’s Declination, of Meridional Parts ... To Which Is Added by Way of Appendix, an English Abridgment of Another Treatise on Naval Architecture, Lately Published at Paris by M. Duhamel. London, Printed for D. Henry and R. Cave, for the author. https://archive.org/details/treatiseonshipbu00murr.

 

Rees, Abraham. 1819. Article on Shipbuilding in The Cyclopædia; Or, Universal Dictionary of Arts, Sciences, and Literature. Vol. 32. London : Longman, Hurst, Rees, Orme & Brown [etc.]. http://archive.org/details/cyclopaediaoruni32rees.

 

Edye, John. 1832. Calculations Relating to the Equipment, Displacement, Etc. of Ships and Vessels of War. Hodgson.

 

Read, Samuel, Henry Chatfield, and Augustin Francis Bullock Creuze. 1847. Reports on Naval Construction, 1842-44. W. Clowes.

 

 

[trippwj]

Here is a new attempt at a timeline of developments relative to the overall topic.  Would appreciate any recommendations - is it too cluttered or hard to read?  Note I still have information to add for the period after 1707.

 

THANK YOU!!!

 

[Talos]

Whilst working my way through various contemporary treatises, some more legible than others, it occurred to me that for the application of the Archimedes Principle to be effective, it was necessary to be able to estimate the actual weight of the vessel before it was constructed.  I took a detour, as it were, to search out some examples where estimates of a ships weight were given.  The four provided below are just representative cases – there are others.  It is interesting to see how the relative proportion of each part of the ship has, surprisingly, remained rather consistent across classes and decades.  For example, in 1754 the hull was 44,6% of the total weight for a 30 gun frigate, and in 1847 (with much more accurate methods used) it was 54.3% of the total weight for a proposed 80 ship.

 

weights.png

 

Sources:

Murray, Mungo. 1754. A Treatise on Ship-Building and Navigation. In Three Parts, Wherein the Theory, Practice, and Application of All the Necessary Instruments Are Perspicuously Handled. With the Construction and Use of a New Invented Shipwright’s Sector ... Also Tables of the Sun’s Declination, of Meridional Parts ... To Which Is Added by Way of Appendix, an English Abridgment of Another Treatise on Naval Architecture, Lately Published at Paris by M. Duhamel. London, Printed for D. Henry and R. Cave, for the author. https://archive.org/details/treatiseonshipbu00murr.

 

Rees, Abraham. 1819. Article on Shipbuilding in The Cyclopædia; Or, Universal Dictionary of Arts, Sciences, and Literature. Vol. 32. London : Longman, Hurst, Rees, Orme & Brown [etc.]. http://archive.org/details/cyclopaediaoruni32rees.

 

Edye, John. 1832. Calculations Relating to the Equipment, Displacement, Etc. of Ships and Vessels of War. Hodgson.

 

Read, Samuel, Henry Chatfield, and Augustin Francis Bullock Creuze. 1847. Reports on Naval Construction, 1842-44. W. Clowes.

 

Really interesting stuff. I wonder, looking at the table, if some of the difference might be in the construction of the hulls, since the other three examples are all ships of the line. Is there a 32 or 36-gun frigate from the 19th century you might be able to compare it to? That'd be pretty close in class to the 30-gun of 1764.

[trippwj]

Really interesting stuff. I wonder, looking at the table, if some of the difference might be in the construction of the hulls, since the other three examples are all ships of the line. Is there a 32 or 36-gun frigate from the 19th century you might be able to compare it to? That'd be pretty close in class to the 30-gun of 1764.

I'll see what I can find. The 30 gun is actually French, Duhamel du Monceau treatise of 1754, translated and included in Mungo Murray's treatise. I need to fix that in the table!

[AaronCastor]

I know it’s an old thread but it’s been a big help with my own project.

 

I’ve been making a designer tool that you trace over plans and you lay your own waterline rake and location and it knocks out the math for displacement, block coefficient for each segment, and center of buoyancy.  The hull form then feeds into righting arm, speed, stability, and etc.

 

This is work still in progress but the end game is to sail these ships once again across the oceans using recorded weather and realistic sailing characteristics.