Seeking information on determining load waterline

[mtaylor]

You're probably right, Joel.  I'll have to go re-read.  I know the maths were large part of the training for designers but not much more at this moment.  Been a few years since I read that book.

[jbshan]

Mark, I'm not sure where I found it, but perhaps in one of the ship of the line series by Lavery.

[trippwj]

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.

 

Mark -

 

The French were, in some ways, far ahead of the British in the science of ship design.  For example, it was at the request of the Admiralty that Pierre Bouguer expanded on the use of trapezoids to determine tunnage and displacement.  Regrettably, after a period of embracing the mathematical design (vice geometric - parabolas, arcs etc), there was a change in regime which altered the acceptance of science for a time, but not nearly as serious a disruption as the British.  For some interesting discussion (not necessarily easy to pull out, since it is part of a broader narrative on Ships and Science) see  Ferreiro, L. 2007. Ships and Science the Birth of Naval Architecture in the Scientific Revolution, 1600-1800. Cambridge, Mass.: MIT Press. http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=173439.

 

 

 

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.

 

Good point, Joel, though not quite accurate - the French were successful at making the transition.  See Ferreiro, L. 1998. Organizational Trust in Naval Ship Design Bureaus France, Great Britain, and the United States. Acquisition Review Quarterly. https://www.academia.edu/1573277/FRANCE_GREAT_BRITAIN_AND_THE_UNITED_STATES. for a brief overview. (extract below):

 

Pride of place goes to France for forming the first professional corps of naval constructors. The Génie Maritime, as it was known (génie means both engineer and genius), was formed in 1765, and was marked by a rigid system of application into the corps, including the training in shipyards and education in  engineering, and a formal system of advancement based on technical merit. The Génie Maritime became the model for the naval construction corps of many countries, including Spain, the Netherlands, Japan, and Britain. The constructors of the Génie Maritime operated autonomously, each in their own shipyards, until 1895, when ship design was centralized into one bureau.

[trippwj]

The Royal School of Naval Architects

 

When considering the British implementation of formal study, there is a clear and (in my opinion) destructive conflict between the “traditional” (that is, shipwrights who came up the old way with no formal education), the “empirical” (that is, the Captain of a Ship knows more than any civilian possibly could) and the “scientific” (the incorporation of mathematical and scientific methods to understand resistance, stability and so on) approaches to Naval Architecture.  At different times, each was dominant.

 

The rise of the Scientific method coincided with the leadership of Sir Robert Seppings as Surveyor of the Navy (1813 – 1832), and the decline (for lack of a better word) into strict Military rule with the resignation of Seppings and the appointment of William Symonds.  Symonds' "empirical" school of shipbuilding came into conflict both with the "scientific" school led by the new class of professional naval architects and the first School of Naval Architecture, and the "traditional" school led by Master Shipwrights from the Royal Dockyards.

 

The following is an extract from Anonymous. 1847. Review of the Course Pursued by the Shipbuilding Department of the Admiralty between the Years 1832 and 1847, Etc. [With Diagrams.]. R. White Stevens. https://books.google.com/books?id=GrNWAAAAcAAJ.

 

On reviewing the history of the Civil department of the Navy, we find by a report to the House of Commons, 16 July, 1806, very important observations relative to the then existing state of the dock yards, and a plan proposed for training up for the public service an  educated class of persons who “should form the plans of our ships of war, consistently with scientific principles,”—the commissioners stating that a want of proper foresight and due consideration in our shipbuilders must finally lead to much danger to the country. They further state, in regard to the Shipwrights’ apprentices, “that they rise to the direction of the construction of ships, on which the safety of the empire depends, without any care being taken to give them the least instruction in the science of Naval Architecture.“

 

This led, in 1811, to the establishment of a School of Naval Architecture at Portsmouth, previously ratified by the King in Council, in 1809, for introducing properly qualified men into the service.

 

Notable members from the School of Naval Architects (1811 to 1832) include:
Reverend James Inman
James Peake
William Morgan
Augustin Francis Bullock Creuze

[trippwj]

Meaning no insult to Sir Anthony Deane, I wanted to take a moment to elaborate somewhat on earlier methods of determining the burthen of a ship.

 

William Bourne published a rather difficult to read (due to the typeface, see earlier post in this thread) treatise called 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. 

 

Richard Barker has provided a transcription (and modernized the language) of the sections related to measuring ships.  His transcription may be found here: http://home.clara.net/rabarker/Bourne2m.htm

 

Bourne describes two methods - in the first, the vessel is grounded, and the physical dimensions taken.  His alternative method is described as "an easier way than rehearsed above, by the Art Statical, to know the true weight of any ship, with all her lading, and all the rest of her furniture".  Here is a very brief excerpt - I encourage you to read the full description.

 

And now I caused the mould to be made for every foot, but a quarter of an inch, so that for the 50 feet long the mould was made 12 inches and a half, and for the 20 feet broad, but 5 inches, and for the 12 inches deep, but 3 inches. And that being filled with water, the water being weighed, did contain in weight 3 pounds and 2 of 73 parts [sic: probably derived from the ratio of Troy to Avoirdupois pounds as 60:73. 1/30 Troy pound, 2/5 of a Troy ounce, is 0.438 ounces Avoirdupois. Bourne presumably experimented with a set of Troy weights] of a pound, and that is scant half an ounce, and the true contents of the weight of the water. And then from that you see that the proportion of the length of the mould, is but 12 inches, and one of 2 parts; that is, but the 48[th] part of the length of the ship. Therefore multiply it in this manner 48 times 48 and that makes 2304 and then multiply it by 48 again, and then it makes 110592. Wherefore now multiply 110592 by the weight of the water, that is to say 110592 times 3 and 2 of 73 parts. And that makes 334620, so that you may conclude that the ship weighs 334640 pounds.

 

And now to know how many tons the ship weighs, by dividing by 2240 as declared above, and so further as rehearsed above. And furthermore, you may cause in the proportion of the mould of lead or tin, to be certain parallel lines, to be made but a quarter of an inch asunder, as many as you like, and then you may know by those lines what weight the ship is of, when she is not laden. And also, if you wish, you may know how many tons more in weight, will load the ship, as often as you do know how many feet or inches the ship lacks from her load mark.

 

 

[trippwj]

Still working on how best to visualize the parallel yet disjointed development of the science and implementation into shipbuilding.  Not sure this really tells the story - I am thinking that it may be better graphically to keep the science on one side of the timeline and the application on the other.  Your thoughts?

 

[JohnE]

Hi Wayne.

 

Are you still looking at how les anciens put their load lines? I've been slogging through some French stuff from 1690 to 1790 and have some bits of something-or-other on "ligne d'eau en charge" and/or "ligne de flottaison". 1690 reference is an "instruction" for double banked ship-frigates and fregates legere. 1790 reference is Vial du Clairbois. In between is Pierre Morineau. Didn't want to blundger your thread if you have moved on from this.

 

[ed] btw, this is tehcnically only for French practice on frigate-type vessels, although much of the practical "sense" is applicable elsewhere.

 

John

Edited January 28, 2016 by JohnE

[trippwj]

Hi Wayne.

 

Are you still looking at how les anciens put their load lines? I've been slogging through some French stuff from 1690 to 1790 and have some bits of something-or-other on "ligne d'eau en charge" and/or "ligne de flottaison". 1690 reference is an "instruction" for double banked ship-frigates and fregates legere. 1790 reference is Vial du Clairbois. In between is Pierre Morineau. Didn't want to blundger your thread if you have moved on from this.

 

[ed] btw, this is tehcnically only for French practice on frigate-type vessels, although much of the practical "sense" is applicable elsewhere.

 

John

Hello, John - As I am regrettably only bilinqual (English and Yankee), any aid in understanding the French (or Dutch, Spanish, Italian etc. ) contemporary reference works would be greatly appreciated!

[jbshan]

Isaac Newton (listed on your chart) was trying to find the 'ideal body' for a ship or other object in water.  Like Einstein's search for a further law of relativity, he never found it.

[druxey]

Don't forget the 'anonymous' of c.1600 whose manuscript of Propositions Newton copied out!

[lehmann]

If I may summarize Bourne's method: take the lines of the hull and build a scale model, in this case, 1/48 scale, measure the volume of water displaced by the model then multiply by 48 cubed and the density of water.

 

Do you have any indication this method was used? I suppose it is one use of half hull models.

 

I recall reading that this method is somewhat error prone, with the main problem being that the wooden model absorbs water.

 

It reminds me of another way to measure measure area: trace the shape onto paper on cardboard and weigh it. Also weigh a piece with a known area. Area of the irregular shape calculated by simple ratio.

[JohnE]

There’s a lot of contextual stuff involved in this. Thought I might start with some thoughts on the 1690s and then post on the 1750s and beyond. I believe Jean Boudriot has slogged through the same stuff (and much more) and come the same conclusions; that this was inferential, subjective, and highly dependent on the coup d’oeil and skill of the designer.

 

Beginning with the 1680-90 period, There were “instructions” issued that set out rules, many of which had already been in use for some time. These “regulations” were cast as His Majesty’s desires, but one assumes they were articulated by the staff of Monsieurs Colbert, through Choiseul. The text includes the following:

 

“Two-decked frigates shall have as their greatest breadth outside plank (dehors des bordages) and at the midship bend (le maître), no more than a quarter of the length. … The depth of hold of the vessel shall be fixed at one half the breadth at the midship bend (le maître), counting from the keel to the “fix” point of the “span” of the gundeck (ligne du 1er pont), in a straight line. … With regard to the height of breadth, or breadth extreme (ligne du fort), His Majesty desires that it shall be precisely observed henceforth to place the height of breadth directly at the waterline (ligne de flottaison en charge).”

 

In 1680-90, French ships were built to a box rule of proportionality. Gundeck position was determined by the proportional mathematics of the rule. But the relative height of gundeck above ligne en charge and/or ligne du fort was determined by a “designer’s rule” as to how far off the water the guns were to be carried. Sill height above deck was given by the “regulation” so one simply moved straight down, from ligne du 1er pont, the requisite amount, and drew a horizontal line which became the reference for the load line (or line of max breadth).

 

They had a subjective appreciation of the problem, and the solution was practical, determinable and repeatable geometrically, although not particularly scientific. It was up to the designers to draw midship sections that would accommodate gundeck heights (from depth of hold values) and give a “ligne du fort” that accommodated a desired height of sill.

 

Given the extent of French proportionality and dimensionality rules for virtually everything else, I find the lack of anything related to waterline placement to be very significant. It infers that there was no generally accepted rule. His Majesty “desired” that the load and max breadth lines coincide, but this made no reference to different hull shapes. Clearly, geometric design wasn’t able to comport with reality at the extremes, so launching a vessel would very often result in either a loud “Bien” or a more subdued “Merde”.

 

Just my humble opinions.

 

John

[trippwj]

If I may summarize Bourne's method: take the lines of the hull and build a scale model, in this case, 1/48 scale, measure the volume of water displaced by the model then multiply by 48 cubed and the density of water.

 

Do you have any indication this method was used? I suppose it is one use of half hull models.

 

I recall reading that this method is somewhat error prone, with the main problem being that the wooden model absorbs water.

 

It reminds me of another way to measure measure area: trace the shape onto paper on cardboard and weigh it. Also weigh a piece with a known area. Area of the irregular shape calculated by simple ratio.

 

Bruce -

 

I have seen an additional 2 or 3 treatisers whom mention this method, though none seem to actually have used it.  The challenge becomes one of actual scale equivalence - scaling length, breadth and depth is fairly easy.  Scaling density (specific gravity) and weight is not quite so linear.  The weight doesn't scale directly proportional (since the density does not change) when the physical dimensions are scaled. 

 

It may be useful to accurately model the below water hull form and then measure the displacement when it is submerged (irregardless of the mass involved), then scale this volume to seawater at a 1:1 scale.  Unfortunately, I suspect that the level of accuracy (how small an amount of volume can you measure) plays a role - even a small amount missed at 1:48 scale can become much more important at 1:1 scale. 

[trippwj]

Don't forget the 'anonymous' of c.1600 whose manuscript of Propositions Newton copied out!

 

Indeed!  As "anonymous" pointed out (transcription courtesy of R. Barker) -

 

61. The height of the ship above water must be in proportion unto that part of the ship under water &c the height of the ship in the mid-ship must not exceed the depth under water & the height of the stern must not exceed the height of the depth twice & the height of the forecastle must not exceed the depth once & 1/3.

 

Not particularly scientific - more a rule of thumb based on existing practice and experience?

[JohnE]

The 1740-1790 period was very interesting because this is when certain “modern” scientific principles took hold. Once again, the period texts give no rule, regulation, instruction, for a consistent, determinable, placement of the “load waterline”.  Once again, I believe this is a significant omission. The period extends from Pierre Morineau to Vial du Clairbois and includes Spain’s Romero Landa. Interestingly, at various times during the period, Spain was leading-edge in certain aspects of Naval Architecture and ship design.

 

Morineau followed the earlier paradigm and often put the load line coincident with height of breadth for his corvettes. In fregate and vaisseau designs, the ligne en charge was set at his “height of sill” definitions and the height of breadth fell where it may. Actually, it was the other way around, but “chicken or egg”. Ligne en charge “shall be no lower than a twelfth part (pouce par pied) of breadth below ligne du fort”. So again, LwL was subjective and depended on designer’s choice of section curvature. But LwL was not determinative.

 

The Spanish system, as late as 1790 (and maybe longer), was to use well known principles for buoyancy to do their designs. They launched the ship and made careful records of her “lightship” draught, fore and aft. They loaded her out (with moveable ballast) and made iterative sea trials to determine her best sailing trim. They made careful recordings of draft fore and aft under “best” conditions, and poof, a Load-Waterline.

 

Romero Landa, Reglamento de Maderas Necesarias para la Fábrica de los Baxeles del Rey,

Madrid, 1784 [Prof. Francisco Fernández-González, Escuela Técnica Superior de Ingenieros Navales, Madrid]

 

Even today, Lwl is a dynamic quantity. Every racing sailor knows that some boats like to go “butt-up” and some like “butt down”, and it all depends on aspect to the breeze. I would only ever give something a design “lightship” float mark for any of my designs, because the practical reality is so completely different.

 

John

[rybakov]

Well, nice to see that I wasn't completely off about a way of determining the load waterline.

On the other hand there are some questions that process and John's commentary raise:

  Is the designed LW an ideal LW or a do not exceed LW, sort of a Plimsol marking?

  I would assume that a ship statically trimmed to an even keel would be sailing trimmed by the head,

  Is that desirable or usual?

  so is that drawn line that important or is it there just to give an impression of how the ship would look

  in the water, referring to John again.

 

Meanwhile I keep watching, learning and having something to think about

 

 

Thank you all

 

Zeh

[JohnE]

My personal opinion is that load lines are not all that important in an objective sense, but rather serve as a designer’s reference points.

 

Four Spanish third-rate sister-ships built between 1785 and 1789; two at Ferrol, two at Cartagena.

San Ildefonso: Empty – not known. Best Trim – 24’ 3” aft, 22’ 8” forward.  San Francisco de Paula: Empty – 19’ 5” aft, 14’ 0” forward. Best Trim – 24’ 8.5” aft, 22’ 9.5” forward. San Telmo: Empty – 19’ 2” aft, 13’ 5” forward.  Best Trim – 24’ 4” aft, 22’ 10” forward. Europa: Empty – 18’ 10” aft, 14’ 3” forward. Best Trim – not known. [Francisco Fernández-González]

 

Capitain de Vaisseau Pigue Villemaurin recorded trials of Cornelie: Lightship – not known, Best Trim – 17’ 3” aft, 15’ 4.5” forward.  Sill height recorded at best trim – 6’ 5.5”, after six recorded runs at different trim lines. [personal copy, Devis de la fregate de Republique, la Cornelie].

 

Inferring that the actual load line was a dynamic, after-the-fact, quantity.

 

According to Boudriot, when French 74s were disarmed for yard work, “everything” was removed except the ballast, lower masts and bowsprit. “In the disarmed condition, a 74 would float 8 pieds above water amidships (water to port sill distance) as opposed to the loaded condition where the gundeck sills were 5 pieds above the waterline”. Again inferring that the nominal load line depended on the desired height of the gunports. It was a dynamic, after-the-fact, quantity.

 

In my humble opinion.  John

[trippwj]

Well, I’m back.  I have taken a brief detour into the realm of tunnage admeasurement, not simply for my personal education, but because it is so closely intertwined with the development of accurate determination of displacement for a vessel.  I won’t bore you with a history of tunnage admeasurement – that is very well covered in numerous other more detailed studies (See attached bibliography)

 

Tunnage References.pdf

 

Saulisbury (1966a) offers the following very concise description of admeasurement:

Some sort of tonnage measurement, based on some arbitrary and artificial unit of capacity or weight, was necessarily closely connected with the development of merchant shipping. Warships could be described satisfactorily by the number of men or guns carried or by the number of oars or men required to propel them, and even today some small craft can be classed by such 'natural' units. Ships designed to carry cargo, however and particularly those driven by sails-needed altogether different treatment. In default of statutory enactments, an artificial unit which was to be generally acceptable had to evolve by usage alone, and this demanded a state of economic activity in which large quantities of a common commodity were frequently shipped over a wide area.

 

Many of the references (see attachment) address the inaccuracy of the methodology used – essentially, the maximum breadth was a key factor, the length of keel for tunnage was a derived measurement (that is, it was not a measurable length but rather derived from other values, of which more below), and the depth of hold was, likewise, generally derived from the breadth.  The result was that two vessels having the same breadth and length (whether on gun deck or between perpendiculars) would have the same tunnage, with no account of the shape of the ship.  A sharp vessel with large deadrise would have the same tunnage as one with a flatter bottom and full body.  While this was good for the collection of customs duties, it was not equitable across vessels nor a true reflection of cargo capacity.
For a model builder, some important considerations arise –

1. The Length of Keel provided in many references works (such as Winfield) are not always able to be identified as actual length of keel or length of keel for tunnage – two very different values!
2. Period documents are not always clear as to which methodology is used to determine the tunnage, and in many cases (as we shall soon see) the value is not able to be recreated based on available data.
3. Methods for determining the tunnage changed many times over the more than 300 years of interest, varying not only by nation but also by region. 

Some terminology may be of use before I look at a few of the methods used to admeasure tunnage.
Admeasurement: The measurement of cargo capacity, usually in volume (tuns)
Ton/tonnage: The term "ton" can describe both weight and volume, so to avoid confusion, ton and tonnage will be used for weights and displacements.  
Tun/tunnage: These terms will be used for volumetric measures (admeasurement).

[trippwj]

There are several dozen potential ways that have been identified by Salisbury (among others) for measuring tunnage.  For the sake of simplicity and illustration, I am only going to highlight a few of them.

Mr. Bakers Old Rule (from about 1582):
The old way, which was established in Queen Elizabeth's time, and never questioned all King James time, is this: The length of the keel, leaving out the false post, if there be any. Multiply by the greatest breatdh within the plank, and that product by the depth taken from the breadth to the upper edge of the keel produceth a solid number which divided by 100 gives the contents in tons, into which add one third part for tonnage, so have you the tons and tonnage.
K = Length of keel excluding false post
B = greatest breadth within plank
D = depth from B to upper edge of keel
Divisor = 100

 

Naval Papers of Peter Pett (about 1650)

Take the Length from the inside on the Upper Deck between the Stem and the Sternpost, and the greatest Breadth from Outside to Outside: likewise, the Depth from the underpart of the Beam of the Upper Deck to the floor by the side of the Keelson. Multiply the Length by the Breadth, and that by the half Breadth, except the Depth exceed the half Breadth, then you are to multiply by that and divide the quotient by 110.

K = Inside on upper deck between stem and stern post
B = greatest breadth outside to outside
D = depth from underpart of beam to floor by side of the keelson or ½ B, whichever is greater
Divisor = 110

 

The Massachusetts Rates and Duties Act. (In The Acts and Resolves of the Massachusetts Bay (Boston, 1869-1922), I, pp. 207-8.) (from about 1695)
... the breadth at the main beam within board, the depth to be accounted half the said breadth, and the length three times so much as the breadth, after the usual manner of multiplying, and dividing the product by one hundred.
K = 3 x B
B = width at main beam within board
D = ½ B
Divisor = 100

 

An Act for Making a Convenient Dock or Basin at Liverpool (1709)
Take the length of the keel of every ship or vessel so much as she treads on the ground and the breadth to be taken within board by the midship beam from plank to plank and half that breadth shall be accounted for the depth ... Then the tonnage will be (L x B x D)/94… any custom practice or usage notwithstanding.
K = Length of keel treads on ground
B = width at midship beam within board
D = ½ B
Divisor = 94

13 Geo. III, c. 74 (pg 1) (The Smuggling Act.) The' Old Rule', adopted for general use in all later Acts until the 'New Measurement' of 1836. (1772)
The length shall be taken on a straight line along the rabbit of the keel of the ship, from the back of the main-post to a perpendicular line from the fore part of the main-stem under the bowsprit; from which subtracting three fifths of the breadth, the remainder must be esteemed the just length of the keel to find the tonnage; and the breadth shall be taken from the outside of the outside plank, in the broadest place in the ship, be it either above or below the main wales, exclusive of all manner of doubling-planks that may be wrought upon the sides of the ship; then, multiplying the length of the keel by the breadth so taken, and that product by half the breadth, and dividing the whole by ninety four, the quotient will be deemed the true contents of the tonnage. According to which rule the tonnage of all such ships and vessels shall be measured and ascertained, anything in the said recited act of the sixth of George I, or any other act or acts of parliament, to the contrary notwithstanding.
K = Along rabbet of keel from back of main post to perpendicular from forepart of main stem below bowsprit, minus 3/5 B
B = greatest breadth outside to outside exclusive of doublings
D = ½ B
Divisor = 94

U.S. Stat. L, vol. I, p. 55. United States Tonnage Law, passed 1st September 1789. Known as 'Custom House Measurement'. (1789)
The length was measured from the fore part of the main stem, to the after part of the sternpost, above the upper deck. From this, 3/5 of the beam was deducted in order to obtain the Length for Tonnage. The breadth was measured at the broadest part above the main wales. The depth varied. In single decked vessels the depth was measured from the underside of the deck plank to the ceiling in the hold. In ships with two or more decks, the depth was taken to be half the breadth.

K = the fore part of the main stem, to the after part of the sternpost, above the upper deck minus 3/5 B
B = the broadest part above the main wales
D = Single decked: underside of deck plank to ceiling in hold.  Double decked = ½ B
Divisor = 95

Joshua Humphreys, War Department Papers  TNB06 (1793) http://wardepartmentpapers.org/document.php?id=9527 
In the first place to find the length of straight rabbet forward you take 3/5 of the beam as usual from that point to the after part of the stern post allowing its width for measurement not to exceed 1/12 of the beam. That length being determined you then multiply it by the length of beam & that product by the height of the gundeck beam amidship on the top of the beam added to half of her waste amids which last product divide by 95 which will give the number of ton required.
K = length of straight rabbet forward minus 3/5 B to after side stern post
B = width at midship beam within board
D = top of gun deck beam to floor plus ½ B
Divisor = 95

 

The following are provided in Steel’s Vade Mecum (1805)

THE GENERAL RULES OBSERVED FOR MEASURING THE TONNAGE OF SHIPS IN THE KING'S AND MERCHANTS’ SERVICE, ARE AS FOLLOW.
Let fall a perpendicular from the foreside of the stem, at the height of the hawse-holes*, and another perpendicular from the back of the main post, at the height of the wing transom. 
From the length between these perpendiculars, deduct three-fifths of the extreme breadth+, and likewise as many 21/2 inches as the wing transom is high from the upper edge of the keel, and the remainder is accounted the length of the keel for tonnage.
Then multiply the length of the keel for tonnage by the extreme breadth, and that product by half the extreme breadth; then, dividing by 94, the quotient will be the burthen in what is denominated Builder's Tonnage.
Or, Multiply the length of the keel for tonnage by the square of the extreme breadth, and divide the product by 188, the quotient will be the burthen in tons.

K = length from foreside stem at hawse holes to back of main post at wing transom minus 3/5 B minus 2 ½ “ per height of wing transom above upper edge of keel.
B = extreme breadth outside to outside
D = ½ B
Divisor = 94

 

* In the merchant-service, this perpendicular is let fall from the foreside of the stem, at the height of the wing transom, by reason of the hawse-holes being generally so very high, and their stems also having a great rake forward.
+ By the extreme breadth, is meant the breadth taken from timber to timber outside, with the thickness of the bottom on each side added; or, which is the same thing, the thickness of the bottom on each side added to the moulded breadth.

 

RULES BY MR. PARKYNS, LATE OF HIS MAJESTY's YARD, CHATHAM.
RULE I. For Sharp Ships, particularly those of the Royal Navy, 
Take the length on the gun-deck, from the rabbet of the stem to the rabbet of the stern-post, or between the perpendiculars. Then take 23/24 of this length, and call if the keel for tonnage:
To the extreme breadth add the length of the gun-deck, or length between the perpendiculars; then take 1/23 of this sum, and call it the depth for tonnage,
Set up this depth from the limber strake; and, at that height, take a breadth also from out to outside of the plank at dead-flat, and another breadth between that and the limber strake; add together the extreme breadth and these two breadths; take one-third of the sum, and call it the breadth for tonnage.
Multiply the length for tonnage by the depth for tonnage, and the product by the breadth for tonnage, and divide by 49. The quotient will be the burthen in tons nearly.
K = Length on gun deck (between perpendiculars) x 23/24
B = at height D above limber strake take breadth outside to outside.  Add to extreme breadth plus breadth at limber strake divide the sum by 3.
D = extreme breadth plus LBP x 1/23
Divisor = 49

 

Rule II. For Ships of Burthen, or Commercial Ships, in general,
Take the length of the lower deck, from the rabbet of the stem to the rabbet of the stem-post; then take 31/32 of this length, and call it the keel for tonnage.
To the extreme breadth add the length of the lower deck; then take 3/55 of the sum, and call it the depth for tonnage.
Set up this depth from the limber strake; and, at that height, take a breadth also from out to outside of the plank at dead-flat. Take another at two-thirds of this height, and another at one-third of the height. Add the extreme breadth and these three breadths together, and take one fourth of the sum for the breadth for tonnage.
Multiply the length for tonnage by the depth for tonnage and the product by the breadth for tonnage, and divide by 36.6666 or 36 2/3 and the quotient will be the burthen in tons.

K = Length on lower deck (between perpendiculars or LBP) x 31/32
B = at height D above limber strake take breadth outside to outside at dead flat.  Take second at 2/3 this height and a third at ½ the height.  Add to extreme breadth plus these three breadths and divide the sum by 4.
D = extreme breadth plus LBP x 3/55
Divisor = 36 2/3 (36.6666)

 

[trippwj]

The next step in the process, then, is to look at how these various measures compare when looking at a single vessel.  I opted, for convenience sake, to work with the design specifications for the 36 gun frigates from Joshua Humphreys, primarily because I had a good detailed set of specifications available.  Note that the actual vessels “as built” differed from these specifications, but for my purposes here that was not important.

 

 

The calculations here are preliminary – I still have some additional tweaking to do, but they serve to illustrate how broad the tunnage can be when the different admeasurement methods are used.

K = length of Keel for tunnage
B = Beam (maximum breadth)
D = Depth of Hold for tunnage

 

 

 

[Mark P]

Dear Wayne;

 

You have put a serious amount of time and effort into researching all this,  with many interesting contributions from others added in,  and it is fascinating stuff.  I had no idea that Matthew Baker was calculating such things as described in this thread.

 

As has been said earlier in this thread,  it would appear that Deane's role in all this has been somewhat aggrandised by Pepys.

 

And with regard to your last post,  it would be a rather unfortunate merchant who had his customs dues calculated by Mr Humphrey's method.  He appears to be considerably off the mark.

 

Would you mind if I printed off this thread to read in more leisurely circumstances?

 

All the best,

 

Mark P

Edited March 28, 2016 by Mark P

[trippwj]

Dear Wayne;

 

You have put a serious amount of time and effort into researching all this,  with many interesting contributions from others added in,  and it is fascinating stuff.  I had no idea that Matthew Baker was calculating such things as described in this thread.

 

As has been said earlier in this thread,  it would appear that Deane's role in all this has been somewhat aggrandised by Pepys.

 

And with regard to your last post,  it would be a rather unfortunate merchant who had his customs dues calculated by Mr Humphrey's method.  He appears to be considerably off the mark.

 

Would you mind if I printed off this thread to read in more leisurely circumstances?

 

All the best,

 

Mark P

 

By all means, feel free to print it off and peruse at your leisure!

 

I keep going back to that Humphreys calculation and pondering why the tunnage is so great.  Here is a direct paste from his 1793 letter to Samuel Hodgdon:

 

Dec 16, 1793

Dear Sir

I think it necessary to inform you in what manner the tonnage is calculated that I have made the estimate from.

In the first place to find the length of straight rabbet forward you take 3/5 of the beam as usual from that point to the after part of the stern post allowing its width for measurement not to exceed 1/12 of the beam. That length being determined you then multiply it by the length of beam & that product by the height of the gundeck beam amidship on the top of the beam added to half of her waste amids which last product divide by 95 which will give the number of ton required.

    I am respectfully yours &c

Joshua Humphreys

 

It is that additional factor (1/2 her waste amidship) that results in the dramatic increase in tunnage.

 

I pulled up another description from him dated 1804 (in response to an inquiry from the auditor of the navy concerning builders measure in Philadelphia in 1799).  In this letter, he does NOT include that addition to the depth of hold!

 

'Dear Sir

I shall with pleasure endeavour to explain the Mode of ascertaining the Tonnage you require I hope it will be satisfactory.

The rule for ascertaining of Tonage of Vessels Carpenters Measure in this Port in the Years 1799 & 18oo was as follows-

 

Breadth of Beam was ascertained from the outside to outside of the timbers - or the Moulded Breadth at dead flat or widest part of the Ship or from

inside to inside of the plank or Wales at the same place, which is the same thing. When the length of Beam is so found you take three fifths of its length which is allowed for the rake of the Stem, let the rake be what it may either more or less - but the rake is generally less- In order to assertain the point of straight rabbet on the Keel, you must set 12 inches before the rabbet of the Stem at the height of the Gundeck from that point let fall a line at right Angles with the rabbet of the Keel then Measure from that line 3/5 of the Beam & wherever that distance terminates on the Keel is the point called straight rabbet & from which to the rabbet of the stern post is the length of Keel for Tonage Carpenters measure of this Port - then Multiply the length of the Keel so found

by the Breadth of the Beam as above & that product by half the length of the Beam- which last product divide by ninety five which will give the Number

of Tons required. (transcription provided in M. V. Brewington. 1941. Notes: Tonnage Rules in 1799. The American Neptune: A Quarterly Journal of Maritime History and Arts I, no. 3: 295–296. http://phillipslibrarycollections.pem.org/cdm/compoundobject/collection/p15928coll3/id/939).

 

 

 

When I change the depth of hold to 1/2 the beam, the calculated tunnage is much more agreeable - 1080 & 68/95 tuns carpenters measure.

 

Mr. Humphreys was an interesting character, and regrettably his working notebook (compilation of all sorts of tidbits around shipbuilding &c.), while containing a great deal of information, is NOT chronological, in the sense that it traces events in order, but rather a sequential listing of information in the order it was entered.  For example, the first entry is a transcription of the British 1719 Establishment, followed by a description of some method of ascertaining tunnage (NOT either of the two above given), then followed by more of the 1719 Establishment.  This is then followed by an entry titled "Navy Office, August 1st 1737 Dimensions", and about 20 pages later "An abstract of numbers, natures, lengths & weight of cannon according to several rates of ships as proposed at a meeting of Flag Office and established by His Majestic Council on the 6th of July, 1716."

[mtaylor]

Since this is a "working notebook" it might be that the earlier version of his calculation was his equivalent of thinking out loud.  

[lehmann]

The estimation of load water line and tonnage (displacement or cargo capacity) is just that - an estimation to as a check on the designer's intention that the vessel could fulfill its role.  Nowadays, we understand the physics, the mathematics have been simplified (even without the aid of computers to do the repetitive number crunching), and we have accurate measurements to prove everything.   At the time there were many unknowns and uncertainties, but the the designer still needs some assurance he can be proud of the design, or at the least, not be sued.   These various formulas are nothing more than first approximations that included some basic factors that were easy to measure mixed with a few fudge factors that make the numbers fit with "experience" or a consensus of opinion.  The ease of measurement is important in that different people would get the same results and those who didn't have access to more sophisticated measurement tools were not left at a disadvantage.  

 

As an engineer, I still do a "back of the envelope" calculation like this as a reality check of a computer model analysis.   You may not realize that some rules in standards, such as the National Building Code, are still based on a consensus of experts when the theoretical and experimental data does not provide sufficient information.  

 

The fudge factors would, I assume, vary depending on region, or predominant ship design.  Factors that "work" for shallow draft coastal boats don't work for deep water clipper ships.  However, customs and insurance officials like to have a common formula that can be easily and uniformly applied by their inspectors.  The question arises, who chooses which rule to use?  Ship owners pick the lowest when charged for customs and insurance, and the highest when impressing a customer.  The same is done now in all aspects of business, even if standards organizations are tasked with choosing an evaluation method: there are always factions trying to influence the choice.   It also reminds me of the rating formulas for racing yachts, which resulted in some strange looking boats.   I recall reading somewhere that tonnage rules also produced some un-seaworthy distortions as owners found hull shapes that maximized actual cargo capacity relative to the rated tonnage.  As with all business performance measures, there will always be someone who "games" the formula, resulting in an unintended consequence.

 

My conclusion is that tonnage rules are a different animal than displacement calculations for load waterline or trim.  The tonnage rules have a strong connection to politics and influence.   On the performance side, it may be possible with computational fluid dynamics programs to choose the best displacement and trim for best sailing qualities, but I doubt anyone has figured out the hull design that is the best compromise for all sea conditions, cargoes and sail trim: maybe the designers of the America's Cup boats get the closest to this ideal. Even with computer models, there are still several model ship testing basins used for experimental validation.  There is still a lot of evolution in ship design and that the key to evolution is survival - physical and economic.   The main difference between 2016 and 1816 is that designers have the tools to avoid the failures.  I'm not sure a modern designer, forced to work with wood and hemp, could design a better ship than their predecessors developed by trial and (lots of) error. 

[mtaylor]

Bruce,

I think I agree.  It's sort of like in certain states in the US that for taxation purposes there's a formula for HP of an automobile.  It has zip to do with real world measurements and (in this case, autos) it's seldom the same from State to State.  

[trippwj]

Bruce -

 

You bring up some excellent points! 

 

 

The estimation of load water line and tonnage (displacement or cargo capacity) is just that - an estimation to as a check on the designer's intention that the vessel could fulfill its role.  Nowadays, we understand the physics, the mathematics have been simplified (even without the aid of computers to do the repetitive number crunching), and we have accurate measurements to prove everything.   At the time there were many unknowns and uncertainties, but the the designer still needs some assurance he can be proud of the design, or at the least, not be sued.   These various formulas are nothing more than first approximations that included some basic factors that were easy to measure mixed with a few fudge factors that make the numbers fit with "experience" or a consensus of opinion.  The ease of measurement is important in that different people would get the same results and those who didn't have access to more sophisticated measurement tools were not left at a disadvantage.  

 

Indeed, the tunnage quoted was only an estimate of the cargo capacity for any vessel.  It was not so much a check on the design as it was a means to try and both standardize how cargo capacity was defined and simplify the collection of customs duties.

As an engineer, I still do a "back of the envelope" calculation like this as a reality check of a computer model analysis.   You may not realize that some rules in standards, such as the National Building Code, are still based on a consensus of experts when the theoretical and experimental data does not provide sufficient information.  

 

Quite familiar with the standards setting organizations – have done work with a few over the years.  Consensus based standards are just that – based on best available information, a consensus is reached to establish standards (NOT legal requirements, though they are often incorporated into law or regulation) concerning a specific domain, such as Emergency Management (NFPA 1600) or the National Electrical Code.

 

The fudge factors would, I assume, vary depending on region, or predominant ship design.  Factors that "work" for shallow draft coastal boats don't work for deep water clipper ships.  However, customs and insurance officials like to have a common formula that can be easily and uniformly applied by their inspectors.  The question arises, who chooses which rule to use?  Ship owners pick the lowest when charged for customs and insurance, and the highest when impressing a customer.  The same is done now in all aspects of business, even if standards organizations are tasked with choosing an evaluation method: there are always factions trying to influence the choice.   It also reminds me of the rating formulas for racing yachts, which resulted in some strange looking boats.   I recall reading somewhere that tonnage rules also produced some un-seaworthy distortions as owners found hull shapes that maximized actual cargo capacity relative to the rated tonnage.  As with all business performance measures, there will always be someone who "games" the formula, resulting in an unintended consequence.

 

Actually, the divisor (“fudge factor”) were based initially on a known relationship between the volume of a wine tun.  The change in divisors over time related to both attempts to better account for the useable volume for cargo as ship forms changed and, particularly in the UK, a desire by Parliament to improve the measurement while not changing the total registered tonnage when applying the new methods – that was actually a key component to setting the divisor, even in the mid-19th century when the Moorsom System was implemented.

 

Tunnage rules were, in most cases, a legislated not regulatory matter.  They were set in law (by Parliament in the UK and Federal law by the Congress in the US).  One of the reasons that they were set in law was so that each customs collector had the same information to basis the collection of duties.  In the same manner, the ships were competing on a more level ground when they were measured and described in the same way.  Note that the actual cargo capacity of a ship (or sloop or brig or schooner) was nearly always different from that on the register.  By the 1700’s, admeasurement had gone from being a simple accounting practice used for business, to an administrative tool used by governments to bring some standardization into customs collection as well as for establishing charter rates of ships hired by the Navy, although it wouldn’t be until the mid 19th century that these rules actually became “standard”! In Great Britain, there were separate rules used by the Navy Board, Parliament and the various Customs houses in the port cities.  In the US, there were differences between the legislated “Customs House” rule and the “Builders Measure” used in different cities.  One of the key reasons for the difference was that a builder had access to the ship plans and could clearly measure the various lengths and dimensions – the ship was out of the water.  The Customs surveyors had a vessel in the water where it was not practical to obtain the real measure of the keel or the depth of hold, so simplified approaches were used.  The builder got paid, in general, per ton builders measure.  The freight and duties were based on customs house rules.

 

My conclusion is that tonnage rules are a different animal than displacement calculations for load waterline or trim.  The tonnage rules have a strong connection to politics and influence.   On the performance side, it may be possible with computational fluid dynamics programs to choose the best displacement and trim for best sailing qualities, but I doubt anyone has figured out the hull design that is the best compromise for all sea conditions, cargoes and sail trim: maybe the designers of the America's Cup boats get the closest to this ideal. Even with computer models, there are still several model ship testing basins used for experimental validation.  There is still a lot of evolution in ship design and that the key to evolution is survival - physical and economic.   The main difference between 2016 and 1816 is that designers have the tools to avoid the failures.  I'm not sure a modern designer, forced to work with wood and hemp, could design a better ship than their predecessors developed by trial and (lots of) error. 

 

For constructors, the emphasis on cargo tunnage as the measure of the ship (even for warships) meant that they had little reason to think in terms of displacement tons when measuring their ships. This fact partly explains the long delay in many countries in adopting displacement tonnage as a unit of measure, as both constructors and owners (including admiralties) continued to apply the simpler admeasurement rules and avoided the more exact measures required for correctly calculating displacement.

 

There is evidence that some British constructors were estimating load waterlines by the 1630s, although it was probably not common practice. For example, see the examples in this post http://modelshipworld.com/index.php/topic/9892-seeking-information-on-determining-load-waterline/?p=296187

And this one
http://modelshipworld.com/index.php/topic/9892-seeking-information-on-determining-load-waterline/?p=300218

 

Ferreiro, among others, makes the point that displacement calculation as a matter of routine was unique, perhaps, in that usually the need to accomplish something drives the development of a methodology.  In the case of displacement, and the subsequent stability calculations, the need to calculate the curves and so on was driven by the development of the capability – which, to a certain degree, was driven by the financial interest in accurate determination of cargo capacity. 

Much of the theory related to displacement was driven as well by interest in determining the best forms for a ship to “divide the water”.  A great deal of effort was expended in model basin testing to try and derive the best shape – and some interesting detours into false premise and failed designs followed, as well as some successes.

 

We know that there were successful efforts to identify the swimming and LWL as far back as the 1600’s.  We have the plan for the Danish ship Elephanten (1705) built and designed by Olaus Judichær showing clearly marked waterlines (see facsimile in Ferreiro, Ships and Science). We have the contracts and information by the Pett’s, and also by Deane.  We have the LWL beginning to routinely show on plans by the mid-1700’s in British ships.  By the late 1700’s we have Humphreys and other American designers discussing the design draught for their ships.  What we also have, though, is a clear indication that while it was possible, it was not routinely done.  In 1791, we find the establishment of The Society for the Improvement of Naval Architecture in Great Britain.  Among their early awards, was the following:

 

The Societv offer a Premium of Twenty Guineas and the Silver Medal for the most ready and accurate method, by approximation or Otherwise, for determining the tonnage of vessels and ships of every description, from an admeasurement of all the principal dimensions.

 

Among the contributions was one by Chapman discussing the Swedish methodology.  It is an interesting and worthwhile read.

 

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.

 

We also have, slightly later, Steel (1805) bemoaning the fact that displacement is not calculated:

 

By this rule, all vessels, whether their bodies be extremely full or. extremely sharp, will appear to be precisely of the same burthen or capacity, if the length of keel and extreme breadth be similar. Thus, the sharpest cutter will seem to carry as much as the fullest merchant-ship of the same length and breadth extreme. This method is, of course, exceedingly detrimental to that principle which promises velocity; as the ship which is narrowest above, and widest and deepest below, will measure least in proportion to her real capacity; the very reverse of which is necessary for fast sailing.

 

In order to ascertain the true burthen of a ship, we ought to find the place of the light-water line, and thence calculate the number of cubic feet below the line of floatation: as the product, deducted from the number of cubic feet contained at the load-draught, would shew the real capacity by which the tonnage may be computed: and, if the difference be multiplied by the weight of a cubic foot of sea water, 64 3/8 lbs., the product, divided by 2240 (the number of lbs. in a ton), will give the true burthen in tons.

 

Or, in other words, by deducting the weight of the ship at her light-water mark from her weight when brought down to the load-water mark, the remainder will be the tonnage.

[trippwj]

Several times during our discussion the point has been made that design waterlines were just that – the desired draught for a fully loaded ship.  Indeed, that was the intent, but it was also a critical design element. 

 

By the 18th century, a warship was designed with a desired number and weight of guns on a specified number of decks.  This primary design criterion brought with it a host of other specifications – the intended crew size and composition (as well as the accommodations for officers &c.), the weight in powder and shot for the typical mission profile, the quantity of spares and materials for repairs, the victualling and water, and on and on.  It also, based on the weight of gun, drove the scantlings to support the guns and facilitate their use.  While the weight of all of these could be estimated (see earlier posts), they were far from firm – there was always variability.

 

The ship designer needed to consider these factors, along with the form of the vessel for best sailing and handling, to ensure that when fully loaded the vessel maintained a safe freeboard (well defined by the 1700’s as 3 to 5 feet from LWL to lowest gun port).  I suspect that it was the increased focus on the builder delivering a ship which achieved an appropriate compromise between these various factors (handling, speed, draught of water and ability to carry intended weapons and supplies) which ultimately forced the shipbuilder to actually determine the displacement and determine whether the ship design could achieve what was desired.  While there was a certain amount that could be done to mitigate the draught by adding or removing ballast, this had implications for the handling and seaworthiness of a ship – the ballast was intentionally there to bring the center of gravity (even if not understood as such) lower and improve the roll and pitch – to keep her from becoming crank, as it were.  Too little ballast resulted in a top heavy ship that rolled excessively.

 

The same holds true for merchant ships – the ballast was much more variable (and there are many documented cases where ballast was added or removed for specific cargos), but the builder (and owner) wanted to maximize the cargo capacity for a given set of tunnage admeasurement rules, while ensuring adequate speed, handling and (of some great importance for some routes) keeping the overall draught of water within a given limit (particularly for bays or harbors with shallow entries or bars).  At the same time, the merchant wanted to use a small a crew as possible, so the types and nature of the rigging was also a major consideration. 

 

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

[trippwj]

this is dated 1839 but it adds a little insight to how it was done back then. if this is printed in 1839 i suspect the practice was in use well before then

 

Thanks, Dave!

 

Interesting side bar:  Lord Barham set up a Commission of Revision which reported in 1806, among other things, that there should be a deeper study of the principles of ship design. It was recommended that the best apprentices in the Royal Dockyards should be given special instruction in Naval Architecture and related subjects. The first School of Naval Architecture was set up in Portsmouth in 1811 but, following a change of Government, was abolished in 1832.  Inman and Fincham were among the faculty.  Indeed, at that same time Robert Seppings was replaced as Surveyor of the Navy by William Symonds.  Seppings, you may recall, published two significant treatises on ship building - On the Great Strength Given to Ships of War by the Application of Diagonal Braces and On a New Principle of Constructing Ships in the Mercantile Navy. 

 

Quite the uproar over appointing a non-shipbuilder but rather a Naval officer (and purely political patronage appointment)  to the position of surveyor of the navy!

[pollex]

Re: DWL & LWL

     It is always fascinating to read extracts from the logs of 18th & early 19th century

ships of the British Royal Navy, where Captains were urged to report (in as much

detail as possible), the ship's best point of sailing, the draughts and the loading of

stores & ballast. These extracts are found in books by Gardiner & Lavery, etc. and

show how important the Admiralty considered them for reviewing present ships and

future designs.

     I'm convinced that the mathematical reckonings for DWL & LWL were known

as early as the beginning of the 1600's by Phineas Pett & Co. but were kept as the

secret "black magic" by which they presented designs and estimates preferred to

their competitors.  Later, as mathematics became a more public knowledge say

after 1750,  design theory added to practical build experience.  Regards, pollex (Calgary)

[lehmann]

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

 

Welcome to the risky world of engineering and architecture. The capabilties of theories and math only go so far and at some point judgement is needed. This still applies in the age of super-computers. Remember that with more knowledge we want to take advantage of it. It also means we soon realise there are more unknowns to deal with. However, decisions have to be made. Some universities teach "design" which try to systematize the process, but these methods usally come up short because the methods of weighting the various factors are too linear.

 

In reality, each design that gets built is an experiment. This point cannot be over-emphasized. Some succeed and some fail, but hopefully someting is always learned. The trick is to know how much the new theories can be "stretched" and still be valid in an untested condition, at which point the system breaks down and a new or modified theory is needed. Too many successes lead to over-confidence in the theory, which often leads to dramatic failures. If you're interested, an engineering professor named Henry Petrosky has documented this through a history of engineering failures. The basic truth is that we learn through failure, not success, because successes don't unusally get near the limits that define a theory. For example, Seppings wouldn't have created diagonal bracing unless previous builders hadn't pushed the limits of ship length to the point where premature hogging occured. Going further, Seppings' method would sooner later have reached its limits and failures would start to appear. However, builders switched to steel construction.....

 

Or, to tie this this back to where it started, judgement comes from experience- experience comes from poor judgement.

Edited March 30, 2016 by lehmann