The Keel

The width and depth.

“Haare langte (gelijk geseid is,) is na de langte van ‘t Schip: grosso modo mag men daar voor een tiende Deel minder reekenen; maar tot desselvs Breedte, dwers-Scheeps, moet men voor yder 7 Voeten, Schips langte, 1 Duim nemen. De Diepte mag met dito Breedte gelijk, of een weynig minder wesen, na dat het Hout wil uitleeveren”. (p. 54, l. 14) (Her length is according to the length of the ship. As a rule of thumb one may count on one tenth less of the overall length of the ship but the width, athwart, has to be 1 inch for every 7 feet ships length. The depth may be equal to the width or a bit less as the tree allows to give.)

The width and depth are the two dimensions of a piece of timber in profile or cross section and one usually measures the width and depth at one of the (face) ends of a piece of timber assuming these measures run constantly over the total length of the piece.In normal circumstances timber, which is delivered or produced at the shipyard, has a rectangular profile i.e. square edged, apart from the complete tree trunks, compass timbers and hogs which are used for production. Cornelis uses different terms to describe the measurements of the profiles of the construction parts and often interchangeably, depending on the construction part. As for the keel: the athwart measure is described with ‘width’ and ‘depth’ is used for the height of the sides or flanks, in Dutch ‘wangen’ (cheeks).For each 7 feet vessel length one inch width is prescribed, the depth is allowed to be:

“een weynig minder wesen, na dat het Hout wil uitleeveren” (p. 54, l. 18) (a bit less than the width as the tree allows to give).

The depth coincides with the width or is slightly less, depending on the size of the tree. Remarkable: one would rather expect a provision where the emphasis is on the depth to be optimally cut from the available tree since it determines the stiffness in longitudinal direction but Cornelis describes the exact opposite. The moment of inertia for a piece of timber with a rectangular profile corresponds with the formula M= (WxD3)/12 where ‘W’ stands for width and ‘D’ for depth. This formula clearly indicates that the stiffness in the vertical plane of the keel depends essentially on the depth.

Nicolaes mentions the width and depth of the keel together with the exact spot where to expect these measurements: “De kiels dikte is ¼ meerder als de binnen-kant van de steven, en de breedte is 1½ breeder als de steven, namentlijk, op den hals 1/3 van vooren, daar ‘t Schip het wydste is...”. (p.105, c.1, l. 6, 1690) (The depth of the keel is ¼ times more than the inside of the stem and the width is 1½ times wider than the stem namely at the ‘hals’, 1/3 from fore where the ship is at its widest).Nicolaes uses the athwart measurement of the back of the stem as a reference for many measurements as we saw in chapter 2 so to establish the width of the keel we need to find the measure for the back of the stem of a 155 feet ship. Nicolaes gives a ratio to establish the thickness of the stem: “...deeze dikte vindt men uit de lengte van ‘t Schip: by voorbeelt, 10 voet lengte, 1 duim dikte”. (p.105, c.1, l.16, 1690) (...one derives this thickness out of the length of the ship for example, 10 feet length, 1 inch thickness). Cornelis gives exactly the same rule:

“De dikte vande Steven is, op yder 10 Voeten, Schips Langte, 1 Duim, of wat meerder, soo de Scheepen niet heel groot sijn”. (p. 57, l. 29) (The thickness of the stem is 1 inch for every 10 feet ships length, or a bit more in case the ships are not very large.)

This ratio will give the keel a width of 1,5 x 15,5 inches = 23,25 inches, 0,60 m¹.

In the certer for a 155 feet ship Cornelis gives the stem a thickness of 1 foot and 5 inches so 16 inches, 0,41 m¹. If we apply Nicolaes’s rule this yields 1,5 x 0,41 = 0,62 m¹ for the width of the keel so both measurements are almost equal.Grebber does not mention the thickness of the keel nor the thicknesses of stem and stern.Apart from this rule, Nicolaes sets the measurement of the width for a keel of a 180 feet ship at 2½ feet, (p.110, c.1, l. 55, 1690) and mentions this to be a measurement which emerged after lessons many

© Jaap Luiting, 2015

The Keel

master shipwrights had learned. From this measurement he derives a set of measures for the width of the keel for ships from 80 to 180 feet.In this row we can find the width for the keel of a 155 feet ship: 23½ inch, 0,60 m¹ which is exactly the width we found using his prescribed ratio.If we compare the rules of both authors we can establish the width of the keel as described by Cornelis is a bit less than the width Nicolaes’s rule yields.

According to Cornelis the depth is allowed to be;

“een weynig minder wesen, na dat het Hout wil uitleeveren” (p. 54, l. 18) (a bit less than the width as the tree allows to give),

so he doesn’t give a rule but assumes the depth equal to the width or slightly less depending on the size of the tree. The decision if the tree yields enough depth is due to the discretion of the master shipwright. Nicolaes states the depth “is ¼ meerder als de binnen-kant van de steven”, (is ¼ more than the inside of the stem). In this case 1,25 x 0,40 = 0,50 m¹. Using this rule you always end up with a horizontal rectangle as cross section with a ratio W:D = 1 : 0,83. A reason to emphasise the width isn’t mentioned but one may assume this was construction related. To be able to mount the futtocks on the keel an adequate amount of width was needed to lay them on the keel and to place and mount the bolts. Another construction part Nicolaes mentions is the ‘zaathout’ or ‘kolzem’ (kelson) which had a width which exceeded the width of the keel pure for construction purposes: “Het Kolzem is breeder als de kiel, om dat het spoor daar in gemaakt, en de wagers daar in gehecht moeten wezen: het werdt met bouts aan de kiel vast geklonken: het dient tot stevigheit van 't geheele Schip, en magh te recht een binne-kiel genaamt worden: het heeft veeltydts voor een lasch”. (p. 334, c. 1, l. 48, 1690) (The kelson has a greater width than the keel to be able to make the step mast and mount the inner planking, it is riveted with bolts to the keel and is meant to give sturdiness to the whole ship and is rightfully called inside-keel; in most cases it has a joint fore.)Nicolaes gives a definition of this ‘wageren’: “Wageren. Planken binnewaarts tegen de scheeps inhouten aan slaan”. (p. 621, c. 2, l. 35, 1690) ( Wageren. Mounting planking inside the ship against the frames) and this inner planking is attached not only to the frames of the ship but also connected to the kelson. To be able to place and rivet the bolts through kelson, futtocks and keel the keel must have had a considerable width too. For his virtual pinas of 134 feet Nicolaes gives the width and depth of the keel: 2 feet (0,57 m¹) width and 16 inches (0,41 m¹) depth, a bit more width than his own prescribed ratio on page 110 (1690) where the keel of a ship of 135 feet has a width of 21 inches.For the inner side of the stern Nicolaes gives a thickness of 13,25 inches (p. 110, c. 2, l. 57, 1690). If we apply this ratio the width turns out to be 1,5 x 13,25 = 19,88 inches, 0,51 m¹ and a depth of 1,25 x 13,25 = 16,56 inches, 0,43 m¹. These calculated numbers differ from the given ones, a difference for which Nicolaes does not account for.

For our 155 feet ship we assume a square profile: an equal width and depth and Cornelis’s formula yields a massive width and depth. In the certer of our 155-foot ship, the width and depth of the keel are not specified but the certer, for a 154 feet ship built in 1667, specifies a width and depth of 22 x 22 inches, 56,6 x 56,6 cm¹ which matches exactly Cornelis’s formula (154/7=22). For a ship of 155 feet this comes down to 155/7 = 22.14 inches or 57 x 57 cm¹. The oak trees able to provide such a piece of timber are also massive. Moreover, the tree has to be as straight as possible with a branch-free rootstock; the part where the keel will be cut out of the tree. To cut a size of 57 x 57 cm¹ square without being backsided the upper part of the rootstock needs to have a diameter of about 97 cm¹ taking into account an average of 8 cm¹ sap-wood and bark, which will have to be removed, and assuming the tree is reasonably round, not egg-shaped or elliptical in cross-section.

© Jaap Luiting, 2015

The Keel

Cross section rootstock.

Backsided timber.

In most cases, a certain amount of backsided timber is acceptable, subject to the discretion of the master-shipwright.

© Jaap Luiting, 2015

The Keel

Another thing is the tapering of the keel. More about this later but the mentioned width and depth concerns the profile before the keel tapers in forward and backward direction. In other words, the width and depth of the keel fore and aft are of a lesser size than the specified width and depth. This is the reason Nicolaes mentions a specific place, the ‘hals’ (the neck), where the keel is expected to have this specified width and depth.

Already mentioned is the stiffness in longitudinal direction. Since all measurements are linearly related to each other every relation between these figures will show as a straight line in a graphic assuming there is no development in this ratio. For instance the relation between the surface defined by the width and depth of the keel, which is a general indication for stiffness, related to the surface of the width and depth of hold of the ship itself.In the next table both figures are listed.

© Jaap Luiting, 2015

The Keel

Author No. Type YearWidth in meters

= W

Depth in meters

= D W x D in m2

Width keel specified in meters

= Wk

Depth keel specified in meters

= Dk

Wk x Dk in m2

Van Yk 1 Ship 1629 6,51 2,32 15,10 0,39 0,39 0,15

Van Yk 2 Ship 1629 11,27 5,87 66,16 0,59 0,59 0,35

Van Yk 3 Square sterned 1634 5,10 1,98 10,10 0,33 0,39 0,13

Van Yk 4 Ship 1659 10,47 4,84 50,68 - - -

Van Yk 5 Ship 1662 8,21 3,63 29,80 0,41 - -

Van Yk 6 Ship 1664 10,19 4,81 49,01 - - -

Van Yk 7 Ship 1666 11,32 5,30 60,00 0,62 0,62 0,38

Van Yk 8 Ship 1667 10,76 4,89 52,62 0,57 0,57 0,33

Van Yk 9 Ship 1668 6,23 3,11 19,38 0,36 0,36 0,13

Witsen 1 Pinas Virtual 8,21 - - 0,57 0,41 0,23

Witsen 2 Ship 1627 7,36 3,26 23,99 0,39 0,39 0,15

Witsen 3 Ship 1628 7,43 3,33 24,74 0,41 0,36 0,15

Witsen 4 Ship 1628 7,64 3,40 25,98 - - -

Witsen 5 Ship 1628 7,71 3,47 26,75 - - -

Witsen 6 Ship 1628 7,93 3,54 28,07 - - -

Witsen 7 Ship 1630 10,47 5,24 54,86 0,59 0,51 0,30

Witsen 8 Ship 1637 7,93 3,68 29,18 - - -

Witsen 9 Ship 1639 8,14 3,68 29,96 0,51 0,41 0,21

Witsen 10 Ship 1640 7,86 3,26 25,62 - - -

Witsen 11 Ship 1640 8,28 3,82 31,63 0,49 0,41 0,20

Witsen 12 Ship 1641 7,64 3,54 27,05 - - -

Witsen 13 Ship 1641 8,21 3,68 30,21 0,49 0,41 0,20

Witsen 14 Ship 1642 7,93 3,47 27,52 0,41 0,37 0,15

Witsen 15 Ship 1660 8,31 3,54 29,42 0,51 0,44 0,22

Witsen 16 Man of War 1664 9,63 4,25 40,93 0,57 0,51 0,29

Witsen 17 Man of War 1667 12,46 5,38 67,03 0,67 0,62 0,42

Witsen 18 Man of War 1669 11,32 5,24 59,62 0,62 0,57 0,35

Witsen 19Grebber

Appr. 1650

Virtual 10,97 4,39 48,16 - - -

© Jaap Luiting, 2015

The Keel

W x D of ship and keel plotted against each other.

The tendency is very clear: the measurements vary but they are arranged around a straight line which means, with some deviation, all measurements are linearly related to each other based on the same ratio. The fact all measurements are subject to this ratio means there is no indication this ratio changed in the time span the certers include, they only vary within limits. So the only thing worth investigating is if there is a change in the ratio between certain measurements over time. This topic has been partly addressed in chapter 2 and in this chapter concerning the rakes of stem and stern and will be later on. The question of the relation of the measurements of construction parts with regard to the longitudinal stiffness and stiff- and sturdiness in general is a moot point and the structural integrity of a wooden ship in different situations is a quite complicated matter beyond the scope of this analysis. But one thing is very clear: in the 17th century they assumed a lineair increase of the measurements of all the construction parts depending on the ships length would be sufficient to deal with the demands needed to maintain the structural integrity of the ship as a whole and Cornelis as well as Nicolaes stress this to be an important circumstance.

Concerning the width and depth: Cornelis mentions the vertical height of the keel to be secondary to the width and so does Nicolaes who actually defines the initial profile of the keel as a horizontal rectangle. This definition is very probably related to requirements of construction rather than the issue of stiffness in the longitudinal direction. Emphasising the width in combination with the mentioned tapering however is not beneficial to the vertical stiffness of the keel.

© Jaap Luiting, 2015

W x

D k

eel i

n sq

uare

met

ers

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

W x D ship in square meters0 10 20 30 40 50 60 70