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Seeking information on determining load waterline

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Michael

 

I have looked at the plan above and I can not see where the load water line is marked "load water line" or "LWL".  Also, on your copy of the plan, is there a date of the plan?  I am not referring to the title of the plan.

 

Phil

Edited by roach101761
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Continuing on my quest, Ferreiro provides the following information (source: page 340-341 in Ferreiro, L., 2004: Down from the mountain : the birth of naval architecture in the scientific revolution, 1600-1800. University of London, 550 pp. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411610).:

 

In Venice, the Capitulare navium (Maritime statutes) of 1255 established load waterlines according to the age of the ship, using an iron cross fixed to the hull.  One hundred years later, the Republic of Genoa adopted a statute that established freeboards for different routes based on sea conditions; higher for the open waters of the Bay of Biscay, lower for the protected Mediterranean. There was a clear appreciation for the practical requirements of weight control, based on the expected weather and seas conditions and state of the ship, even if there were no means of predicting those requirements during its construction. The actual load waterlines were not marked on the hull, and were rarely marked on drawings in ship manuscripts prior to about 1650, however, most of Matthew Baker's hull elevations in his manuscript Fragments of Ancient English Shipwrightry mark the "swimming line", though there is no text or calculation to support it.

 

So, then, what we have to work from is that there was an awareness in the 13th century of the importance of an identified load waterline, if not a method to determine it during construction.  This would align well with the mass production method of Venetian construction (which is a fascinating topic to delve into - quite a bit of discussion around the concept of "Whole-Moulding" and similarity between the Mediterranean and European approaches, but I digress...)  and somewhat standardized proportions for the rising, narrowing and hauling down, for example.

 

We also see, then, that Mathew Baker (and others) had some ability to pre-determine the "swimming line" during the 16th century.  Richard Barker (1988 - “Many May Peruse Us”: Ribbands, Moulds and Dodels in the Dockyards. Revista da Universidade de Coimbra, XXXIV, 539–559. http://home.clara.net/rabarker/sagres87mmpu-txt.htm). notes that William Bourne ( Treasure for Travelers, 1578) describes the use of models, to scale to measure the displacement of the corresponding ship. He describes waterplanes and load-marks in the process. This may have been purely theoretical on Bourne's part when drafted in 1572 (it was published in 1578).

 

So - I am slowly narrowing the timeframe where initial calculations may have been used to pre-determine the "swimming line" and "draught of water" - but not there yet!  On to more French, Dutch and Italian research works! 

 

 

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Wayne

 

Pulled down my copy of Dean's Doctrine of Naval Architecture, 1670 edited by Brian Lavery copyright 1981,Conway Maritime Press.  I do not know why I did not pull it down a couple of weeks ago.  I guess I presumed you had reviewed it as you mention Dean above, or perhaps I just forgot I had it.  Hard to keep track of my books.  I pulled it down for another purpose today. From reading above you may be reading from a copy of the actual manuscript.  I have only read parts of it today but Lavery's introduction explains exactly what the work consists of and why it was written in the first place.  There is a whole section on "The water-line or greatest depth of water the ship must draw, completely gunned, rigged, victualled,and stored".

 

Through this section and the sections that follow, it is apparent that he is aware, and has the ability to design a ship which will float on the  load water line he designed and fit for its intended purpose.   He explains how he does it but does not give the math.  It kind of reads like he backed his way into the result that proper math would have calculated.   As an example:   You have a pile of 49 objects and you desire to know how many separate equal piles of objects you can make.  Rather than solve with math, you keep physically dividing the pile until you get to 7 piles of 7 objects each.  

 

As to your earlier post in which you were looking for contracts for ships prior to 1750,  Lavery's book contains in its appendix  the specifications of a third rate of 1666 and states that the original before it was amended, was for the Speaker of 1649(renamed Mary in 1660) The designer of the ship was Christopher Pett who drew up the first version of the specification.     Alas it is only a contract specification for a builder.  It does not mention LOL.  This seems logical to me because the builder would not be responsible for its design, only its construction pursuant to the contract. 

 

Phil

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Wayne,

 

For French ships, Boudroit's The 74 Gun Ship gets into a discussion of this in passing.  He describes how the "Surveyor" training started with heavy maths and what was involved in the training.  Part of the drafting of new ships was determining the water line. I'm not sure (it didn't say or I overlooked it) when this practice started. 

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So, to summarize key data thus far, I present this lovely chronological table.  Still a work in progress so no firm conclusions - please let me know if I have missed something germane (which is highly probable....)

 

post-18-0-88558100-1427065402_thumb.png

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I'm from the camp of roach101761:  LWL is a nice to have, easy to draw, but very difficult to predict.  Even assuming the mathematics for determining displacement were used and measuring the area of cross-sections were accurate (having tried it, counting squares to measure areas is not that accurate, and the planimeter wasn't invented until 1814 and not readily available until at least 1854 [Wikipedia: planimeter]) there is the other side of the equation: estimating weights and the distribution of weight (center of gravity).  I've designed a few small boats and the practical problem of estimating the weights of all the parts of even a 14 ft dingy is intimidating.  Specifying the location of the lead fin keel for a modern yacht is downright scary.  For a wooden ship, each piece has an irregular shape that is custom fitted to the preceding framework, so there are no drawings to base calculations.  I think modern ship builders can do this because they use 3D solid modelling and the steel plates, gussets, etc are laser cut.  Even then, major components are still weighed.  Furthermore, with wood, what is the moisture content?  The planking swells considerably after the hull is put in the water, so even if you weight each fitted plank just before attaching it to the frames, your numbers are suspect.

 

Another issue you need to consider is, as I understand it, that early design drawings were to the inside of the planking so that the builder can use them for directly laying out the frames.  My impression is that creating line drawings to the outside of the planking is a relatively new concept, which, I would assume, coincided with the development or acceptance of mathematical methods, which need the external shape.  This, of course, wouldn't apply to lines taken off existing hulls.  

 

Given the large uncertainty in the as-built weight and weight distribution of a large wooden vessel, I suggest that the only method of prediction is how a hull of similar form and construction floated.  Tradition isn't just from a lack of knowledge or an aversion to risk (or ridicule): staying close to successful designs allows builders to build.  The historian of engineering, Henry Petroski, has written extensively on the benefits and risks of the trial-and-error development. Since all ships carry a significant weight of cargo, the final water line for profitability, stability or best sailing trim is determined by the ship's officers.  Hull shapes or construction methods that couldn't do their job likely became evolutionary dead-ends.  In this sense, an interesting study would be to compare, with modern naval architectural tools for displacement, stability and seaworthiness, the design of hulls which were widely used to those that were only built once.  I suspect this happened quite often as construction technology with steel created more design options, which justified the cost of naval architects and marine engineers.

 

Lastly, I wonder if there were intermediate stages between the initial drawing and the final construction that could be used to empirically determine where a ship will float.  Half-hull models could be used to determine displacement; and builder's models could help with center of gravity.  As a research engineer, I like having a prototype to test new features for unintended consequences and to verify my estimates.

 

PS.  I just checked the drawings in Chapman's Architectura Navalis Mercatoria (ANM). (1768)  The lines are all to the inside of the planking.  I also see that Chapman, in Treatise on Shipbuilding, shows the calculation method for a ship's load curves (draft vs displacement).  The curves for many if not all the of the drawings are show in Plates XXIII and XXIX of ANM..  The calculation looks like it's based on Simpson's Rule using the areas of each water line, although I'd have to verify this as the multipliers aren't quite what I would expect.  

 

Also, quadrature methods of numerical integration were know before Simpson derived that general formula that is attributed to him.  Kepler used it long before that, so in German, its known as Keplersche Fassregel.  

Edited by lehmann
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Bruce -

 

Thank you for this - you have summarized quite neatly many of the areas that I am trying to dig into in order to understand this transition to pre-determined draught (I am using draught here as meaning the level on the vessel that she is designed to float when fully burdened.  Measured from the base of the keel) and displacement!

 

I pulled some of your observations from your post and provide some partial responses - I still have a bunch more work to do!

 

           LWL is a nice to have, easy to draw, but very difficult to predict.

 

That is really the basis for my project – at some point, it became Need to know, not just nice to know, and thus a component to the design of a ship.  For example, as the gun port came into use, it became important to have adequate freeboard – to keep the wet stuff a safe distance below the openings into the hull.  While an existing vessel with adequate freeboard could serve as a model for the current generation, ships grew over time and the shape changed, so that what was good before no longer applied.

 

 early design drawings were to the inside of the planking so that the builder can use them for directly laying out the frames.

 

This is true – since the primary purpose was to determine the shape of the frames.  However, since the thickness of the planking was generally known (either “institutional knowledge” or specified in the requirements), adding that to the dimensions was an easy step for the designer. 

 

Given the large uncertainty in the as-built weight and weight distribution of a large wooden vessel, I suggest that the only method of prediction is how a hull of similar form and construction floated.

 

This is a good point, and an area that I am gathering more information on.  Some of the earliest treatise (British) discussing the determination of displacement (and draught) use “plug numbers” to come up with the weight of ships to then try to determine both the ballast required to reach a desired draught and the draught itself.

 

Since all ships carry a significant weight of cargo, the final water line for profitability, stability or best sailing trim is determined by the ship's officers.

 

This has always been an issue – many of the officers during the days of sail had a tendency to over-mast vessels, resulting in poor sailing qualities and reduced stability.  There was also a lot of fidgeting with ballast and stores distribution to alter the trim to that desired by the master – sometimes to the detriment of effective performance.  A good case study would relate to the early American frigates, where the Secretary of War basically threw up his hands and directed that each Captain and Constructor should mast the frigate as they saw fit.  Some performed much better than others….

 

Half-hull models could be used to determine displacement; and builder's models could help with center of gravity. 

 

There was actually an attempt to do this, although it failed miserably since building a model of true scale (not just dimensions, but also weights and trim) was not possible, and model testing was rudimentary and not an accurate indicator of 1:1 build performance.

 

Among the interesting research papers I have come across is one from 2008 entitled "Technical Writing in English Renaissance Shipwrightery: Breaching the Shoals of Orality" by Elizabeth Tebeaux - well worth the read if you get the opportunity!

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Just a couple of notes to show the difficulty the old boys had:

Records:

One of the reasons for having plans instead of just specs was that 10 years later you had a good, duplicateable record of a ships form.  You could then tweak it based on performance.  Slade was a master of tweaking.   A few times the British got caught when they had committed to a large number of ships so that subsequent vessels were being built before the first ones had a good trial.  I'm talking over a couple of hundred years' time.

Balance of rig to hull:

USF Constitution had real problems keeping masts whole until they reduced the ballast and increased the size of the masts.  The balancing out of the rolling motion (from too much ballast) the strength of the masts and the ability of the hull to carry sail took a while to work out.

Use or purpose of a vessel:

Nelson as a junior captain had the task of sailing a French prize to the West Indies.  He had to water from a tender partway there because he didn't have enough stowage.  If he had taken aboard enough water, the ship would have been too deep.  The French design was for quick raids, not long voyages.

You often see something like 'draft aft, draft forward with: 4 months' provision, home waters, foreign waters, 6 months' provision and 3 months' water; they were aware of most of these things but struggled to get the proper compromises in the design.  Even up into the second half of the 1800s they hadn't quite got everything figured out.  I think it was just a lack of maths or calculation capacity.  Titanic was still mostly worked out by arithmetic.  I use that example not because she sank, but because they looked very carefully into her construction so we have some records of the process.

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Perhaps another source for earlier design  (to add to your list, Wayne) is from the so-called "Newton Manuscript': a transcription by Sir Isaac Newton of a treatise c.1600. This gives instructions for designing ships, both naval and merchant. It is given in its entirety in an article in Mariners' Mirror, 1994, Volume 80, No.1. The 67 'Propositions' given describe how to design a ship.

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Replies in blue...

 

           LWL is a nice to have, easy to draw, but very difficult to predict.

 

That is really the basis for my project – at some point, it became Need to know, not just nice to know, and thus a component to the design of a ship.  For example, as the gun port came into use, it became important to have adequate freeboard – to keep the wet stuff a safe distance below the openings into the hull.  While an existing vessel with adequate freeboard could serve as a model for the current generation, ships grew over time and the shape changed, so that what was good before no longer applied.

 

I alluded to this in my comment about the development of naval architecture. As the needs, more cargo, more guns, more sail, etc.,  increased, the rules of thumb could no longer keep up, so the engineering had to be developed to keep the risk tolerable.  Can you show a trend of how the use, not just the knowledge, of navel engineering increased as requirements increased?  Note, that it is difficult to tell whether needs drove new knowledge, or knowledge created opportunities.  

 

 

Given the large uncertainty in the as-built weight and weight distribution of a large wooden vessel, I suggest that the only method of prediction is how a hull of similar form and construction floated.

 

This is a good point, and an area that I am gathering more information on.  Some of the earliest treatise (British) discussing the determination of displacement (and draught) use “plug numbers” to come up with the weight of ships to then try to determine both the ballast required to reach a desired draught and the draught itself.

 

Chapman knew how to develop load curves in 1760's for estimating how cargo weight affected draught.   The basic question is could he predict the weight of a fully equipped vessel with empty holds?  

 

There is also the question of what tolerance would have been acceptable or detected?  Did ship owners require a performance test in terms of how much cargo could be stowed at an determined draught?   Are there records of ship owners taking shipwrights to court?  

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From some modern texts on the design of wooden boats:  

 

Sailing Yacht Design: by Douglas Philips-Bert:  

Weight Calculations.  

     These are not often made for small craft, except when built to rated classes or of an uncommon breed on which there is little data.  With larger craft weight approximations are sometimes necessary, and particularly so when no inside ballast, except a little for trimming purposes, is to be used.  Indeed,  if weight calculations were not so time consuming, it is doubtful if the praises of inside ballast would ever be sung so cheerfully.  With wood construction, however, weights are always approximate owing to the uncertain density of timber, which varies by 20 percent or more depending on green and seasoned states.  Weight calculations are to a large extent common sense and dreary arithmetic, palliated by the intelligent use of approximations.  

    One of them is the cubic number. By its means the structural weight of yacht may be approximated from that of a similar yacht, of the same type of scantlings, but of any size.  The cubic number may be accepted as:

 

( LOA x Max. beam x Depth of hull)

                        100

 

the later quantity excluding the fin keel, and being measured to point of greatest body depth.  The structural weights vary in different yachts in the same proportion as their cubic numbers.  

 

[Detailed calculations]

Planking:  Area multiplied by the thickness...

Frames and Timbers:  The area of the frames will be a certain proportion of that of the planking, the proportion depending on the siding and spacing of the frames.  ....

Keel, Stem, Sternpost and Deadwood:  Approximations are best made when dealing with these members, since their irregular shapes make the calculations of volume difficult.

Stringers, Gunwales, Shelves and Clamps:  The length of these may be measured from the drawings....

Deck:  The area is most simply measured with a planimeter...

Deck Beams:  The siding and spacing of the beams show what proportion they bear to the deck area....Allowances must be made for heavy beams [at masts or hatches], and for hanging and lodging knees.

Joiner Work and Furnishings:  This may be worked out by proportions from similar craft.  The only other method is to consider each item in turn.

 

 

Skeen's Elements of Yacht Design: Rev. by Francis Kinney

Comparative Weights

     To make a rough estimate of the weight of a new boat based on the know weight of an old boat multiply the weight of the old boat by the length of the new boat divided by the length of the old boat.  

 

-----------------------------------------------

 

If the ratios of draught/length and beam/length are similar for the old and new boat, then the two formulas give the same estimate.

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The formula lehmann gives is very close to the ancient formulas used for tonnage (cargo capacity).

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This comes a little late to the table, but I have just come cross a description in A Treatise of Shipbuilding, circa 1620-25, as reprinted, edited and annotated by W. Salisbury and R.C. Anderson (Society for Nautical Research Occasional Publications No. 6, London 1958). It reads as follows (pages 26-27):

 

The next thing to be drawn in this plane of length and depth is the swimming line, which is a principal thing to be regarded for the good qualities of the ship. From that line are set off the decks and ports for the ordnance, higher or lower as we will have them lie to pass; therefore of right there should be marks made on the ship's side to direct the mariner always to keep her in that trim, neither to sink her deeper nor let her swim shoaler. The depth of this line is taken off the midship bend, for where the two upper sweeps intersect each other with respect to the thickness of the plank (which intersection is easily found by drawing a straight line through the centres of the upper sweep and futtock sweep), from thence to the ground line is the true depth of the swimming line. Which depth being marked upon the midship line and upon each perpendicular of the upper rising, draw a straight line from stem to stern. So you have the swimming line desired.

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This comes a little late to the table, but I have just come cross a description in A Treatise of Shipbuilding, circa 1620-25, as reprinted, edited and annotated by W. Salisbury and R.C. Anderson (Society for Nautical Research Occasional Publications No. 6, London 1958). It reads as follows (pages 26-27):

 

The next thing to be drawn in this plane of length and depth is the swimming line, which is a principal thing to be regarded for the good qualities of the ship. From that line are set off the decks and ports for the ordnance, higher or lower as we will have them lie to pass; therefore of right there should be marks made on the ship's side to direct the mariner always to keep her in that trim, neither to sink her deeper nor let her swim shoaler. The depth of this line is taken off the midship bend, for where the two upper sweeps intersect each other with respect to the thickness of the plank (which intersection is easily found by drawing a straight line through the centres of the upper sweep and futtock sweep), from thence to the ground line is the true depth of the swimming line. Which depth being marked upon the midship line and upon each perpendicular of the upper rising, draw a straight line from stem to stern. So you have the swimming line desired.

 

Thank you, druxey.  That is useful - I have been searching (unsuccessfully) for a copy of this book.  Please let me know if you come across any!

 

Thus far I have only been able to gain a small understanding from Barker's narrative published as Barker, Richard. “Fragments From The Pepysian Library.” Revista Da Universidade de Coimbra XXXII (1985): 161–78. http://home.clara.net/rabarker/Fragments83txt.htm.

 

He notes the following, which really keyed my interest!

 

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.

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Hi, Wayne. I was actually given a copy of this Occasional Publication No. 6 last month by a fellow modelmaker. He was dispersing the contents of a deceased model maker's workshop and knew I had an interest in "that early stuff". I'd never come across a copy before and was working my way through the text yesterday.

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Backing off in time, I have been able to find a copy of the Bourne Treasure for Travellers of 1578, and am now testing my vision whilst perusing the same.  Here is the link and a teaser of the first page on ship building.

 

Bourne, W., 1578: A booke called the treasure for traveilers : devided into five bookes or partes, contaynyng very necessary matters, for all sortes of travailers, eyther by sea or by lande. Imprinted at London : [by Thomas Dawson] for Thomas Woodcocke, dwelling in Paules Churchyarde, at the sygne of the blacke beare, 286 pp. http://archive.org/details/bookecalledtreas00bour(Accessed April 26, 2015).

 

post-18-0-65986300-1430319260_thumb.jpg

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I greatly appreciate all of the contributions to date – each has opened a new area to look into, and some have taken me down quite a diversionary path!

 

Going back to where this all began, I began this journey (which is still only just begun) wondering how the ship designers of old determined the height of the load waterline when they were designing the ship.  In looking through various descriptions of the design process in a number of treatises and books from the 18th and early 19th centuries, and then comparing to a small sampling of plans, it appeared that the LWL was not necessarily used to design the vessel, but rather was a goal for how the ship should float.  The majority of the plans used design waterlines along with buttock lines and station lines to transfer the shape of the frames and other timbers to the mould loft floor. A quick (and very simplified)  review of the principal lines used in these plans:

 

Design waterlines – horizontal lines on the Sheer and Body Plan, curved profiles on the half breadth.  Represent fixed distance above the baseline and are usually parallel to the keel.

 

Buttock Lines – curved lines on the Sheer Plan, horizontal lines on the Half Breadth plan and vertical lines on the body plan.  Represent the shape at fixed distances parallel to the centerline of the ship.

 

Station Lines – vertical lines on the Sheer Plan and the Half Breadth Plan, curved profiles on the Body plan.  Represent the shape of the ship at fixed locations fore and aft of the midship frame.

 

The LWL may, but more often did not, match one of the design waterlines.  Since it wasn’t needed to loft the frames, when was it added and how was it determined? 

 

To know the amount of water a ship will draw (that is, how deeply it will sit in the water), the weight of the ship is the primary consideration.  The weight then is used to determine the amount (volume) of water that will be displaced – regardless of the shape of the ship (that is, a rectangular shape will displace the same amount of water as a ship shaped ship at the same weight).  In most references I have looked at covering 1700 to 1850, the British standard was about 64 pounds per cubic foot of seawater.

 

Once the weight and the volume were known, what remained was to determine the level on the ship where the volume below the water matched the volume of seawater.  That may seem simple, but proved far more complex in practice!

 

Determining the weight of a ship was, also, an interesting exercise.  In theory, by knowing the density (weight per cubic volume) of each material used, and then determining the volume of each item used in the construction (bolts, treenails, frames, beams, planks, and so on, with a different value for each type of wood, that also varied with the dryness and changed over time) the builder could determine the light weight.  Then all that was needed was to do the same for the crew (and their personal effects), food, water, masts, spars, blocks, rigging, powder, guns, small arms, lamps, candles, and on and on to determine the fully burdened weight.  Not likely to happen – far too much to even attempt that! 

 

Another method was that of equivalency – for a given class of ship, determine the height at which it floats empty, then load everything that would be needed and see how much it settled.  By determining the difference (how much lower it sat in the water), the additional volume displaced (assuming a fairly simple shape for simplicity in most cases) represented the additional weight above and beyond the ship itself.  From various activities such as this, Sutherland (among others) offered a set of assumptions to use in determining the weight of the vessel empty and fully loaded.  Not totally, accurate, but a starting point! This was a “close enough” approximation, but only for vessels of similar shape and dimensions.  The assumptions fall apart when either is altered more than a small amount.

 

Which, of course, brings me back to the beginning – in the absence of mathematical methods (which the shipbuilders did not like, based on many reports and descriptions from the 18th century – both in France and in Britain), other than “looks about right based on the last one I built”, how would they be able, before launch, to have any certainty that the ship would ride where they intended – whether merchant or war ship?

 

So, there you have it – the “why do this” that is driving me forward!  What have I learned so far?  Much about the development of the science, a bit of the history of the first Royal School of Naval Architecture (Reverend Inmon and John Fincham were key players there), the resistance to these changes during the time of Captain Symonds as the Surveyor of the Navy, and the influence of France, Spain, The Netherlands and Sweden in advancing the understanding of the science (and applying to shipbuilding long before the British).  Also that it appears the Americans were followers for many years with little in the way of contribution to the science until the 19th century.  I have also learnt much about the development of mathematics between the time of Archimedes and the mid-19th century.  Not to mention (well, okay – I’ll mention it) the value of colleagues who can translate other languages!

 

The quest goes on, and the questions continue to accumulate – please feel free to add to the list and, if you can, shed some light on those darker areas that are yet to be illuminated!

 

Many thanks!!!

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This comes a little late to the table, but I have just come cross a description in A Treatise of Shipbuilding, circa 1620-25, as reprinted, edited and annotated by W. Salisbury and R.C. Anderson (Society for Nautical Research Occasional Publications No. 6, London 1958). It reads as follows (pages 26-27):

 

The next thing to be drawn in this plane of length and depth is the swimming line, which is a principal thing to be regarded for the good qualities of the ship. From that line are set off the decks and ports for the ordnance, higher or lower as we will have them lie to pass; therefore of right there should be marks made on the ship's side to direct the mariner always to keep her in that trim, neither to sink her deeper nor let her swim shoaler. The depth of this line is taken off the midship bend, for where the two upper sweeps intersect each other with respect to the thickness of the plank (which intersection is easily found by drawing a straight line through the centres of the upper sweep and futtock sweep), from thence to the ground line is the true depth of the swimming line. Which depth being marked upon the midship line and upon each perpendicular of the upper rising, draw a straight line from stem to stern. So you have the swimming line desired.

 

I was able to obtain a copy of 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.  Here is the method described for laying out the midship bend and determining the swimming line (see the Figure 1 attached below from the document for the points of interest).

Breadth – 36’

Depth = 15’ 6”

Draw parallelogram ABCD

A-B = 36’

A-C and B-D = 15’ 6”

Floor KG= 1/2 the half the difference between depth and breadth = 10’ 3”

Wrong Head Sweep (GN) radius (LG, LN) = 1/3 the depth and the difference between depth and breadth added together = 9’ 8”

Sweep of Breadth or Naval Timbers (BO) radius (MB) = 15:19 of the Wrong Head Sweep = 7’ 8”

Futtock Sweep (ON) radius (PN, PO) is 21’ 8”.  Point P found by taking an arc from M and L.

The desired swimming line, then, is the point where a line from P to M extended out crosses the sweep at O to the outside of the planking.  The height above the baseline (CD) is the draught of water.  Care should be taken by the master to never load the vessel such that she sits below that level.

 

post-18-0-53975600-1432220002_thumb.jpg

 

My next step is to compare this with Barker, R. 1994. A Manuscript on Shipbuilding, Circa 1600, Copied by Newton. The Mariner’s Mirror 80, no. 1: 16–29 and with Barker, R. 1985. Fragments From The Pepysian Library. Revista Da Universidade de Coimbra XXXII: 161–178 to see how the methods relate.  Then it is on to Sutherland and Mungo Murray.

 

Thoughts?

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Thoughts? Good stuff!

 

Thanks, Druxey.  Pondering the implications - we know Baker is said to have shown waterlines on many of his drawings - but not certain the method used to determine.  Perhaps they were as in this example - the maximum draught of water is based on shape, and then the weight of the vessel fully outfitted is limited by that depth.  In other words, you may want 28 guns, but to stay above this point you may only have 20. 

 

Given that Mungo Murray (1754), while discussing the more scientific methods used by Duhamel du Monceau, spends a great deal of ink discussing whole moulding - similar to the approach discussed in the 1620 manuscript above.  This would result in determining the swimming line based on sweeps rather than on any predetermined displacement (weight/volume relationship).  Perhaps, and this is still only a hypothesis, the swimming line (load water line) on many of the early plans were either (1) post construction or (2) desired, based on the whole moulding design method.  The total weight was restricted post-construction to remain within the design criteria, rather than the design criteria based on the intended weight?

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I have been following this thread with interest and enjoying the level of knowledge of old shipwrightry far superior to mine.

Nevertheless I would like to put up for consideration my thougts on the matter.

 

First, I think the load waterline marked on the plan marks the desirable immersion of the ship.

To have the ship float at that immersion (draft) is not overly complicated, although the actions taken to attain it would have 

some effect on the ship's qualities.

If upon launching the draft is noted and then after loading a few tons of ballast the new draft is read we have TPI (tons per inch

immersion).

Knowing the distance to the load waterline we know how many tons we may load.

(of course the TPI increases as the draft increases, but we may consider it as an allowance for the timbers soaking up water.) 

The weights of masts riggin and so on are known, crew weight is approximately known so we are left with provisions and ballast

to play around to get the ship to the load waterline.

If we put on board water and food for 60 days instead of 80, or 100 rounds per gun instead of 120 for example, or reduce some ballast, we eventually

will get it floating at the desired draft.

Of course it will have quite different nautical properties than if things were spot on - less ballast to move around to trim properly, less sail carrying capacity in a breeze, if we err in the other direction and have to add ballast we will have a stiffer ship wich, at the limit, could endanger the masts.

 

Well, this is how I think they would go about getting the ship to the load waterline, and it really doesn't need much mathematics.

I try to keep in mind they were practical people.

 

 

Al the best

 

Zeh

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Just a brief update to reassure you all that I have not forgotten nor forsaking this undertaking!  While I am not close to being able to draw any definitive conclusions, I am still learning and, as time allows, gathering new information.

 

I recently came across an interesting reference - McGee, D. 1998. The Amsler Integrator and the Burden of Calculation. Material Culture Review / Revue de La Culture Matérielle 48, no. 1 (June 6). http://journals.hil.unb.ca/index.php/MCR/article/view/17794

 

The author provides some interesting perspective on how the Amsler Integrator was instrumental in ship builders (and Naval Architects) finally began to actually calculate the immersed volumes to obtain more accurate volumetric data for not only displacement but also stability purposes.  Stability calculations (and, by extension, displacement curves and calculations) were rarely done for Naval (and almost never for merchant) vessels due to the immense number of calculations necessary to produce them, until the introduction of the Amsler Integrator.  From McGee:

 

Arriving at the data for each section was a thing of incredible simplicity. The track for the instrument was laid down on the drawings and the instrument placed in the track. The pointer was placed on the drawing and readings were taken from the vernier scales attached to the cogwheels. The pointer was then used to trace the outlines of the irregular curve or section to be measured. The rollers turned the cogs, and new readings were taken from the scales. The initial readings were subtracted from the new readings. The results were then multiplied by a constant provided by the manufacturer.

 

And that is all there was to it. In a few minutes the operator could know the area and moment of any section in the body, sheer, or half-breadth plans. The operation then had to repeated for the other sections. The resulting tables of areas and moments could then be combined by mathematical means to arrive at the location of the centre of buoyancy of the vessel in question.

 

So – what does this mean for those Load Water Lines (and the swimming line, for that matter)?  Were they “real”, determined pre-build?  Were they added after launch and fitting out?  Were they conjectural – representing the desired outcome, subject to the actual results when the ship was built???

Edited by trippwj
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Wayne, judging by the number or failures to achieve the desired height above waterline for the port sills, I would guess your last situation was fairly common, '...conjectural – representing the desired outcome, subject to the actual results when the ship was built.'

I don't think the math was yet up to predetermining such things.  You could still have waterlines used in the design process, as parallels, Deane in 1670 was beginning to introduce them a bit, but the success or failure of matching desires to results were still in the lap of the gods.

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Having done displacement calculations by hand using Simpson's rule, I can attest to the tedium and the chance of error.  The use of a planimeter (integrator) makes a world of difference.  However, as I've mentioned before, knowing the displaced volume is only the first, and easiest, part of the calculation (estimation) of the load water line: the second is the weights of the ships components (framing, planking, spars, anchor chain, etc), which could easily have a 20% error band.  A planimeter could be used with the volume calculations of frames, assuming you have drawing for each component, etc, but there's still significant uncertainty in the density of wood.  And, if you want to calculate the stability, you'll need to estimate the center of gravity of all those components as well.  With a 3D drafting application, this can now be done, but by hand it would be a nightmare, even with the Amsler intregrator.    Up until the time of building steel or aluminum hulls with 3D drafting, weights were likely estimates with revisions based on the designer's experience with similar ships.  I'll bet that even today, each component is weighed before it is added to the construction as a check on the calculations.     

 

So, in your researches, you'll only have a definitive answer if you see both the displacement and the weight calculations.  

 

The second aspect is the captain's prerogative for the amount and location of ballast, supplies, water, cargo and armament to achieve the best sailing trim, stability, profitability or defense.   However, as the weight of these items becomes large relative to the weight of the hull, the errors in hull weight become less significant in the load water line determination.  That may be a clue for your research:  what is the relative weight of the hull to the weight of these other components?  If the hull weight is a large percentage then the weight calculations are critical for both determining the water line and the success of the vessel in its intended purpose.  If the hull weight is a low percentage, then ship can be loaded until the desired water line (trim) is achieved.   In my travels through the many treatises on ship design, I don't recall seeing any hull weight calculations or even comments on it, so I would assume that, in general, the hull weight is a low percentage and the water line could be determined by the captain.  This would also remove the need to calculate displacement and allow builders supply vessels based on previous similar designs and rules of thumb.   Note that there would be a rapid evolutionary process here:  builders that supplied ships that were not successful didn't get more commissions or relegated to building traditional hulls. 

 

A third aspect for tracing the development of the mathematics of ship design would be to look at when design changed.  As calculation methods are developed to the point where the designers trust them, they will begin to push the design envelope.  In ship design, I suspect that most significant developments resulted from new knowledge in structural strength, and more recently, in hydrodynamics, but there may have been some new hull designs that were dreamed up as designers saw that they could do "what-if" calculations with some certainty that they wouldn't be judged as indulging in folly.  As happens today, the envelop is usually pushed hardest by the military, racers or some commerce where speed or endurance are critical.  

 

Bruce

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Having done displacement calculations by hand using Simpson's rule, I can attest to the tedium and the chance of error.  The use of a planimeter (integrator) makes a world of difference.  However, as I've mentioned before, knowing the displaced volume is only the first, and easiest, part of the calculation (estimation) of the load water line: the second is the weights of the ships components (framing, planking, spars, anchor chain, etc), which could easily have a 20% error band.  A planimeter could be used with the volume calculations of frames, assuming you have drawing for each component, etc, but there's still significant uncertainty in the density of wood.  And, if you want to calculate the stability, you'll need to estimate the center of gravity of all those components as well.  With a 3D drafting application, this can now be done, but by hand it would be a nightmare, even with the Amsler intregrator.    Up until the time of building steel or aluminum hulls with 3D drafting, weights were likely estimates with revisions based on the designer's experience with similar ships.  I'll bet that even today, each component is weighed before it is added to the construction as a check on the calculations.     

 

So, in your researches, you'll only have a definitive answer if you see both the displacement and the weight calculations.  

 

The second aspect is the captain's prerogative for the amount and location of ballast, supplies, water, cargo and armament to achieve the best sailing trim, stability, profitability or defense.   However, as the weight of these items becomes large relative to the weight of the hull, the errors in hull weight become less significant in the load water line determination.  That may be a clue for your research:  what is the relative weight of the hull to the weight of these other components?  If the hull weight is a large percentage then the weight calculations are critical for both determining the water line and the success of the vessel in its intended purpose.  If the hull weight is a low percentage, then ship can be loaded until the desired water line (trim) is achieved.   In my travels through the many treatises on ship design, I don't recall seeing any hull weight calculations or even comments on it, so I would assume that, in general, the hull weight is a low percentage and the water line could be determined by the captain.  This would also remove the need to calculate displacement and allow builders supply vessels based on previous similar designs and rules of thumb.   Note that there would be a rapid evolutionary process here:  builders that supplied ships that were not successful didn't get more commissions or relegated to building traditional hulls. 

 

A third aspect for tracing the development of the mathematics of ship design would be to look at when design changed.  As calculation methods are developed to the point where the designers trust them, they will begin to push the design envelope.  In ship design, I suspect that most significant developments resulted from new knowledge in structural strength, and more recently, in hydrodynamics, but there may have been some new hull designs that were dreamed up as designers saw that they could do "what-if" calculations with some certainty that they wouldn't be judged as indulging in folly.  As happens today, the envelop is usually pushed hardest by the military, racers or some commerce where speed or endurance are critical.  

 

Bruce

 

Weight estimates have been available for many a year.  For example, Sutherland (Sutherland, W. 1711. The Ship-Builders Assistant : Or, Some Essays towards Compleating the Art of Marine Architecture. London: printed for Mount, Bell, and Smith. http://echo.mpiwg-berlin.mpg.de/MPIWG:12RWTM5U)provides several examples of weight for various types of ships.  Likewise, Mungo Murray (Murray, M. 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) provides more detail on weights (both above and immersed).  There are many more dating from about the middle of the 18th century such as Rees, Morgan and Creuze and so on.  The weight calculations, however accurate, were present.

 

In the case of Murray, he calculates the weight of the hull plus furniture (masts, blocks, pumps, cables, anchors) for the Renomee (Frigate of 30 guns) to be about 52% of the total weight for the ship when fully provisioned and crewed (see summary table below).

 

post-18-0-76568600-1453811475_thumb.png

 

Of these components, the next largest weight component after the hull and furniture is provisions (not a great deal of freedom to not load these), followed by the ballast (the only true variable that the Captain has some control over, albeit not very much!).

 

The open question, of course, remains the same - did the shipwright of old actually use the information to determine the load water line?  I have some theories, but that would be getting ahead of myself. 

 

Keep the suggestions coming - each drives me back to the source documents to see what they contain, and I find new stuff each time!

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Wayne, judging by the number or failures to achieve the desired height above waterline for the port sills, I would guess your last situation was fairly common, '...conjectural – representing the desired outcome, subject to the actual results when the ship was built.'

I don't think the math was yet up to predetermining such things.  You could still have waterlines used in the design process, as parallels, Deane in 1670 was beginning to introduce them a bit, but the success or failure of matching desires to results were still in the lap of the gods.

 

Joel - I somehow suspect that you're probably right, at least into the mid-19th century.

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Two examples:

Vasa was ballasted to the point where the gunports were in danger, but needed a lot more to be stable.

Consitution was ballasted conventionally, but most of that was removed before she achieved her best sailing ability.

If I recall correctly, both were armed as (roughly) 50 gun 24 pounder ships.

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Wayne,

 

I've read that the French were very heavy into the mathematics in ship design.  The designer was able to determine the various waterlines but with how much accuracy I'm not sure.  I'll have to go back and re-read Boudroit's History of The French Frigate 1650 - 1850 which is where I saw this to grasp the fulll scope.

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I read that the French intellectual investigations into ship design didn't actually make it into the ships themselves and remained a mostly theoretical endeavor.  The British had the same experience and shortly cancelled the academics.

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