Transcript
The Stem
The shape. This section deals with the shape of the stem. With ‘shape’ is meant the profile of the stem in side view. Cornelis gives two drawings each illustrating how to establish the profile of the stem. The first drawing, ’Num. 3’, shows a stem with a height larger than the rake.
Construction drawing ‘Num. 3’ of the profile of the stem. Cornelis van Yk.
Between page 58 and 59.
Cornelis describes the procedure as follows:
“De Bogt en het vallen van dese Steven is, veeltijds; na dat het Hout wil uitleveren, of ook na de Meester dat goed agt. Dog om op alderley Hoogte, en vallen, een goed Beloop van een Steven te trecken, soo kan ‘t volgende Voorbeeld werden in agt genomen. ‘k Heb dan een Steven nodig, diede Kiel 12 Voeten langte aan brengen, en 20 Voeten hoogte opwerke. Vrage hoedanig sal de Bogt wesen? Hier toe beschrijft eerst de Kiel A, B. Op dese trekt regthoekig B, C, ter hoogte van 20 Voeten. Op dese haald C, D, voor ‘t vallen 12 Voeten. Trekt nu de vallende D, E. Deeld dese in 2 gelijke Deelen, als in F. Trekt van daar de Regthoekige F, G. Verlengt nu C, D, tot daar sy G snijd. Steld in ‘t Snypunct de Passer, en opentse tot in D, of E, en den Omtrek sal goed wesen: soo als in ‘t vervolg, by de Figuur Nummer 3 te sien is. Wat nu wyders de Winthouwer, de Klos boven inde Steven, mitsgaders het Slemphout aangaat. Den Bouwmeester sal dese, uit de verlengde D, C, of G, F, ligtelijk na believen inschrijven konnen”. (p. 57, l. 45 ) (The curve and the rake of this stem is, mostly, so as the tree will deliver, or so the Master deems fit. But to be able to draw a fair course of the stem at diﬀerent heights and rakes, the following example can be observed. I need a stem who brings 12 feet length to the keel and with a height of 20 feet. Question is how the curve will be? To this end one describes the keel A, B. On these one draws perpendicular B, C, with a height of 20 feet. From this (line) one draws C, D, for the rake of 12 feet. Now draw the oblique D, E. Divide it in 2 equal parts, as in F. Draw perpendicular to this line F, G. Lengthen now C, D, til it intersects in G. Set the compass in this intersection and open it till D, or E and the outline will be good, as can be seen in figure number 3.
Jaap Luiting © 2017
The Stem
Concerning the ‘Winthouwer’ (the chock up in the stem or cutwater), and the apron. The Master Shipwright will draw these with the lengthened D, C, or G, F, plain as desired.)
Making this geometric construction yields the following procedure. The basis for the reconstruction is provided by a height of 20 feet height, 5,66 m. and a rake of 12 feet, 3,40 m..
First the keel ‘AB’ is represented as a straight line. On this line point ‘B’ is chosen to draw a line equivalent to the height of the stem.
From this point a line perpendicular to the straight line ‘AB’ is drawn with a height of 20 feet, 5,66 m.. This is point ‘C’.
From this point ‘C’ a line perpendicular to this line, 12 feet long, 3,40m., is drawn forward which yields point ‘D’.
From this point ‘D’ a line is drawn to the first point ‘B’ which yields ‘E’. This line ‘DE’ is divided in two equal parts which yields point ‘F’.
From point ‘F’ a line is drawn upward perpendicular to line ‘DE’ above point ‘C’.
Line ‘DC’ is lengthened til it intersects the line from point ‘F’ in point ‘G’.
This point ‘G’ is the center point of a circle with radius ‘GD’ or ‘GE’. Part of his circle is drawn from ‘D’ to ‘E’. and the whole construction is represented by the following picture.
If we superimpose this reconstruction and the drawing the following picture emerges. The reconstruction is drawn in red.
Reconstruction of the procedure superimposed on drawing ‘Num. 3’.
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The Stem
To scale the picture the height ‘bc’, 20 feet, is used. It is immediately clear the ratio ‘bc’/‘cd’ is not correctly drawn. Point ‘f’ is also not the exact middle of line ‘de’ while the line ‘fg’ is not perpendicular to the line ‘de’. The strange thing about this circle cut is that Cornelis mentions this to be a ‘good outline’ for the (inner) profile of the stem but the constructed profiel doesn’t run alongside the inner profile of the drawing. So this drawing is quite confusing as the circle cut doesn’t define the inner profile nor any other profile of the drawn stem.
We can make the same construction for the second drawing. In this case the rake is larger than the height. The procedure given by Cornelis is basically the same drill as with drawing ‘Num. 3’, only with other measurements.
Construction drawing ‘Num. 4’ of the profile of the stem. Cornelis van Yk.
Between page 58 and 59. “Gesien hebbende hoe ‘t sig toedraagt, als de Hoogte vande Steven meerder dan haar vallen is; soo moet dit Voorbeeld aanwysen hoedanig datmen handelen sal, als het vallen meerder dan de Hoogte is. ‘k Heb dan een Steven wiens Hoogte 12, en vallen 18 Voeten is, vrage hoedanig sal de Bogt wesen? Beschrijvt wederom de Liny A, B. Op dese trekt als vooren, de regtstandige B, C, ter Hoogte van 12 Voeten. Van dese haald C, D, voor ‘t vallen 18 Voeten. Beschrijvd wyders de vallende D, E. Dese deeld in twee gelijke Deelen, als in F. Van daar haald de Regthoekige F, G. Verlengt eyndelijk, E, C, tot daar sy G snyd. Stelt in ‘t Snypunct de Passer opentse tot in E, of D, en doet als vooren. Siet de Figuur Numero 4. En al schoon aan dese trek wel iets diend veranderd, soo kan sulks op de verlengde B, C, door de Passer, na believen, ligtelijk geschieden”. (p. 58, l. 15) (Having seen what happens when the height of a stem is more than its rake, this example must show how to act when the rake is more than the height. I have a stem which height is 12 and its rake 18 feet, question how the curve will be? Draw again a line A, B. Draw on this line, as before, the perpendicular B, C, with a height of 12 feet. From this one gets C, D, for the rake, 18 feet. Draw furthermore the Jaap Luiting © 2017
The Stem
oblique D, E. This line divided in two equal parts, as in F. From there one gets the perpendicular F, G. Lengthen finally, E, C, till its intersects G. Set the compass in the center point, open it till E, or D, en do as before. See plate number 4. And if something has to change in this course, this is easily accomplished at the lengthened B, C, through the compass, at pleasure.)
The basis for this reconstruction is provided by 12 feet height, 3,40 m. and 18 feet rake, 5,10 m..
The keel ‘AB’ is represented as a straight line. On this line a point is chosen to draw a line equivalent to the height of the stem.
From this point, later named ‘E’, a line perpendicular to the straight line ‘AB’ is drawn with a height of 12 feet, 3,4 m.. This is point ‘C’.
From this point ‘C’ a line perpendicular to this line, 18 feet long, 5,10 m., is drawn toward aft which yields point ‘D’.
From this point ‘D’ a line is drawn to the first point which yields ‘E’. This line ‘DE’ is divided in two which yields point ‘F’.
From point ‘F’ a line is drawn perpendicular to line ‘DE’ beyond the height of line ‘CD’.
Line ‘EC’ is lengthened til it intersects the line from point ‘F’ in point ‘G’.
This point ‘G’ is the center point of a circle with radius GD or GE. This circle cut is drawn.
Reconstruction of the procedure superimposed on drawing ‘Num. 4’.
When we superimpose this construction and the drawing the same thing happens as with drawing ‘Num. 3’: the drawn circle cut doesn’t match in any way the inner profile of the drawn stem. An explanation for this can be that according to Cornelis the determination of this profile is a start, a guide towards the final shape and not an absolute requirement. According to Cornelis because:
“De Bogt en het vallen van dese Steven is, veeltijds; na dat het Hout wil uitleveren, of ook na de Meester dat goed agt. Dog om op alderley Hoogte, en vallen, een goed Beloop van een Steven te trecken, soo kan ‘t volgende Voorbeeld werden in agt genomen”. (p. 57, l. 45 ) (The curve and the rake of this stem is, mostly, so as the tree will deliver, or so the Master deems fit. But to be able to draw a fair course of the stem at diﬀerent heights and rakes, the following example can be observed.)
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The Stem
There are more intriguing details in both drawings. In drawing ‘Num. 3’ point ‘b’ is situated at port side at the upper side of the keel while the stem itself seems to be standing beside the keel at starboard: the upper side of the keel is completely visible. Furthermore the perspective is a bit odd: the front or forefoot of the keel is not visible while the front of the stem is.
In drawing ‘Num. 4’ the keel and stem seem to be connected and in extension of one another but the origin of line ‘bc’ is now on the starboard side. This could be the reason the line representing the profile is partly rendered as a dotted line because it runs at the side of the stem which is not visible contrary to the profile line in ‘Num. 3’.
Another peculiar thing is the fact in both cases the keel is straight, lying level while the stem is standing upright. In drawing ‘Num. 4’ a shipwright is standing in front of the stem using a plumb. Apart from the scale of the shipwright with regard to the stem one might ask, to what end? A plumb, drawn like this, can be used in this occasion for two reasons. The first is to check if the stem is standing upright and not leaning sideways towards port or starboard. This is a check that can be done when a ship is lying level ànd on a slope. In this case the line of the plumb need not necessarily be attached to the top of the stem, however, the longer the line, the more accurate the check. The second reason is the check of the rake. On a level plane this should be possible but on a slope this is not possible. The main reason for this is the slope itself since a slope can’t provide a useful reference plane for a plumb.
This makes the interpretation of these drawings diﬃcult when you don’t know what the intentions of the makers exactly were. Drawing abstract construction lines together with a rendering of the ‘real’ profile was something the makers of these illustrations, Jan and Caspar Luiken, were not accustomed to.
But the way Cornelis presents these drawings allows us to draw two provisional conclusions: first, the base of the inner profile of the stem is a circle cut and second, the ends of the diagonal line between the rake and the height provide the two points through which this circle cut is drawn.
This relation between the length of this diagonal line, the circle cut and the radius of the circle provides us with a control method on these measurements.
Before we continue with the profile as described by Cornelis it is interesting to look at what we can find in Nicolaes’s books. Nicolaes doesn’t give a detailed description how to construct the profile of the stem in his days but he starts by describing how the profile of the stem was established around 1520 in the Netherlands, so in shipbuilding before his time.
“De voorsteven schoot meest altijt uit, met een kringsche rontheit, en een derdendeel van de kiels lengte na vooren toe; zijnde de hoogte van het schips bovenste overloop. Uit het hooft van de kiel wierd een linie opgehaelt, tot de gegevene hooghte: het derde van kiels lengte, weinig min of meer; welkers toppunt voor het middelpunt dient, daer de steven werd uitgetrokken. Dees middelstip, doch, wierd een weinig hooger of laeger genomen, na gelegentheit van het gebouw; om dat zijn hooge of laege stant het stevens vallen bepaelt. (…..) Het middelpunt evenwel, daer de steven uitgetrokken wierd, behield men altans in een recht opgaende linie, van wat gestalte de schepen ook mochten zijn. Een vaste regel was het, dat ’t uitschieten van de steven noit min mochte zijn, als vijf zesten van de hoogte tot d’ overloop, en noit meer als dees hoogte, en een zesten”. (p. 47, c. 2, l. 7, 1671)
(The stem almost always protrudes, with a circular roundness, and at one third of the keels length towards fore; being the height of the ships upper deck. From the forefoot of the keel a line is taken, up to the given height: one third of the keels length, a bit more or less; which top is the center, from which the stem is derived. This center, will be taken a bit higher or lower, according to the size of the structure; because this determines the stems rake.
(…..) The center point however, from which the stem is derived, was kept on a perpendicular line, no matter what shape the ships have. A fixed rule was the protruding of the stem may never be less then five/sixth of the height to the lower deck, and never more then this height and one/sixth.)
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The Stem
Construction of three stem profiles. Nicolaes Witsen. Plate 18, 1671.
The drawing Nicolaes uses to illustrate this came by in the section about the rake. If we analyse this piece of text together with this illustration we can draw lines according to the description Nicolaes gives. The keel is visible as a straight green line. The forefoot of the keel is the place where a line perpendicular to this green line is erected. On this line the center point of the profile of the stem is located. If we divide the length of the keel in three parts we have the length of this line which is the height of the upper deck and at the same time the rake of the stem because the center point for its profile is located on this line. If we draw a circle with the origin of the perpendicular as center point and 1/3 of the keel length as radius this blue circle intersects the perpendicular line at point ‘a’. If we use the points marked by Nicolaes on this perpendicular line this yields the two red circles with centre points at ‘b’ and ‘c’.
The last sentence Nicolaes writes about the rake is interesting: he says the rake may deviate from the height but no more than one sixth, plus or minus, of the height of the upper deck. If we show only the profiles and their center points the picture becomes much clearer.
Jaap Luiting © 2017
The Stem
Three constructed profiles according to plate 18 of Nicolaes Witsen.
At the left superimposed on the original drawing, the plain profiles at the right.
The first thing that stands out is the fact the profiles with center points given by Nicolaes, ‘b’ and ‘c’, are fairly accurate. Another thing is these profiles are designated as the profiles from stems with the least and the most inclination. Nicolaes also describes the allowed extremes for the protruding rake of the stem: never less than five/sixth of the height to the lower deck, and never more than this height and one/sixth. If the center point for the circle cut is always situated on the perpendicular line this will result in a profile falling backwards in the case the rake is smaller than the height because you have to extend the curve above the center point as can be seen at profile ‘b’. This is according to Cornelis an unwanted circumstance:
“En alhoewel dit Stevens vallen weinig schijnd; nogtans zo men agt geevd dat de Scheepen agter gemeenlijk veel dieper dan voor in ‘t Water sinken, sal dit agter overhellen dan ook merklijk doen meerder schijnen. Op dit agter nedersacken moet in ‘t toeleggen van de Voorsteven ook agt werden gegeven, op datmen die aan ‘t boven Einde niet te Krom, en binnen de LootLijn maake, ‘t welk een Misstand soude geagt werden”. (p. 60, l. 4) (However this rake of the stern seems small, when one should pay attention to the fact the ships aft sinks much deeper in the water, this leaning backwards will seem much more. With regard to this sinking down aft one must give attention to the setting of the stem also, so one makes this at the top end not too curved and inside the perpendicular which can be considered an abuse.)
For that matter, the design method of Cornelis can be considered an innovation because this method is adaptable to a diﬀerent height and rake instead of the center point of the profile being located on the perpendicular line. Still, Nicolaes mentions the fact the rake and height can diﬀer:
“Wanneer men de Steven van een Lastdrager toestelt, magh men die wel 2 voet hooger maken als het vallen, of ook wel 3 en 4 voet, mede wel wat krommer als in 't gemeen”. (p. 168, c. 2, l. 52, 1690)
(When one makes the stem of a freight carrier, one may make it 2 feet higher as the rake, or also 3 and 4 feet, and a bit more curved as usual.)
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The Stem
If we compare height and rake both from Cornelis and Nicolaes we see they diﬀer considerably. The data from our 155 feet ship in red.
Author
No.
Type
Year
Height stem in meters
Rake stem in meters
Height/Rake
Van Yk
1
Ship
1629
5,02
5,66
0,89
Van Yk
2
Ship
1629
9,27
9,63
0,96
Van Yk
3
Square sterned
1634
3,40
5,38
0,63
Van Yk
4
Ship
1659
7,36
7,36
1,00
Van Yk
5
Ship
1662
5,89
6,23
0,95
Van Yk
6
Ship
1664
7,88
6,23
1,26
Van Yk
7
Ship
1666
8,78
6,79
1,29
Van Yk
8
Ship
1667
7,93
7,93
1,00
Van Yk
9
Ship
1668
4,61
4,25
1,08
Witsen
1
Pynas
Virtual
7,08
7,36
0,96
Witsen
2
Ship
1627
5,03
5,95
0,85
Witsen
3
Ship
1628
5,24
5,66
0,93
Witsen
4
Ship
1628
5,24


Witsen
5
Ship
1628
5,24
4,81
1,09
Witsen
6
Ship
1628
5,95
4,81
1,24
Witsen
7
Ship
1630
7,93
7,79
1,02
Witsen
8
Ship
1637
7,08
5,66
1,25
Witsen
9
Ship
1639
6,94
5,52
1,26
Witsen
10
Ship
1640
5,66


Witsen
11
Ship
1640
6,87
6,51
1,06
Witsen
12
Ship
1641
6,51
4,95
1,32
Witsen
13
Ship
1641
6,94
6,72
1,03
Witsen
14
Ship
1642
6,37
5,66
1,13
Witsen
15
Ship
1660
6,65
5,95
1,12
Witsen
16
Man of War
1664
7,22
5,10
1,42
Witsen
17
Man of War
1667
8,49
6,23
1,36
Witsen
18
Man of War
1669
8,21
6,23
1,32
Witsen
19
Grebber Appr. 1650
Virtual
7,36
7,36
1,00
Jaap Luiting © 2017
The Stem
Because Nicolaes doesn’t give a clear description how to determine the profile like Cornelis does we can’t consider how he deals with these diﬀerences. In the last quote he only mentions some absolute figures, not even ratios.
If we want to get to know something about how Nicolaes describes the profile of the stem in his days we will have to look closely at the pictures and how they are described.
Nicolaes shows on plate 50 how the height and rake of a stem are measured.
Drawing ‘Q’, plate 50, Nicolaes Witsen, 1671. Nicolaes gives an explanation of this drawing ‘Q’.
“Om vorder dees Voorsteven te maken, zoo leght men de stukken op malkander, als gezeght is, en ziet of daar na begeerte bogt in is, zoo ja, dan leght men een stok van a tot b, 't geen de hoogte van de Steven is, gelyk te zien is op de plaat by letter Q, en een andere stok van c tot b, dat het vallen van de Steven is; daar na neemt men een winkelhaak en houdt die aan de binnenkant van de stokken by b, en als het daar in de winkel is, tekent men by c en e het kinnebak in de winkel, als van d tot c, dat de lip op de kiel is, en als het getekent is van d tot c, en van c tot e, zoo blyft dat het vallen van de Steven. De bouts in de lasschen van de Steven werden van boven en van onderen in geslagen”. (p. 168 , c. 2, l. 35, 1690)
(Moreover to make this stem, one lay the pieces on top of each other as mentioned en looks if this yields a curve as desired, if so, one lays a pole from ‘a’ to ‘b’, which is the height of the stem, like shown on the plate with the letter Q, and another pole from ‘c’ to ‘b’, which is the rake of the stem; after that one takes a square and holds this at the inside of the poles at ‘b’, and if it is square, draws at ‘c’ and ‘e’ the ‘boxscarf’ in the square, as from ‘d’ to ‘c’, which is the lip at the keel, and as drawn from ‘d’ to ‘c’, and from ‘c’ to ‘e’, so it stays the rake of the stem. The bolts in the joints of the stem are hammered in from below and above.)
In this drawing ‘Q’ the line ‘ab’ represents the height and the line ‘bc’ represents the rake. This is, as we have seen, diﬀerent from the way Cornelis measures the rake but here the question is how the profile of the stem is established: does Nicolaes start with the inner or the outer profile? Nicolaes doesn’t mention this. Trying to answer that question we have to look at two descriptions of the stem he gives in chapter 9. But before we can have a look at these descriptions we have to Jaap Luiting © 2017
The Stem
keep in mind the fact Nicolaes uses a ‘model’ ship as an example, a virtual Pinas, about which he states the following at the beginning of chapter 8:
“Hier toe laat een Pynasschip, (by gedachten gebouwt) lang over steven 134 Amsterdamsche voeten, en in al zyn deelen ontleedt, tot voorbeeldt dienen (…..)”. (p. 94, c. 1, l. 29, 1690)
((To do so let a Pinas ship, long over stem and stern 134 Amsterdam feet, be an example. Which is (built in mind) dissected in all its parts.(…..)).
So one would expect this ship is the central object in descriptions where he mentions clear ratios and derived measurements except where he explicitly mentions these measurements are from another ship like in the certers. Chapter 9 however, starts with an enumeration of ship parts and their proportions while measurements are derived for a ship of 100 feet length. This enumeration lasts from page 104 to 110 (edition 1690) and on page 110 he starts again with an enumeration but now for his virtual Pinas of 134 feet length. In general in the first part, where he uses this 100 feet ship as an example, Nicolaes gives ratio’s and ways of deducing measurements from one another whereas in the part about the 134 feet ship, mere measurements are given. Nicolaes doesn’t mention why, but the first of the two descriptions of the stem is located in the part of the 100 feet ship and the second one in the part of the 134 feet ship. As we have seen in chapter 2 of this book the given measurements for this 134 feet pinas diﬀer considerably from the ratios given in the part where this 100 feet ship is used as an example. For instance the ratio of the length and width of the 134 feet Pinas is extreme: this ship is one of the narrowest of all the ships Nicolaes presents, while the ratio of the 100 feet ship exactly matches the ratio given in Grebber’s table. Nevertheless Nicolaes says about his 134 feet Pinas:
Het schip hier in gedachten gebouwt is noch van de wydste noch van de naauwste slagh; welke maat met voordacht is genoomen, om zoo wel een Oorloghals een Koopvaardyschip te vertoonen. (p. 330, c. 2, l. 19, 1690)
(The ship built here in mind is nor the widest nor the narrowest kind; which size is chosen deliberately, to be able to represent a warship as well as a merchant ship.)
The reason for this strange contradiction is obscure. More about this in chapter 1 and 2 of this book.
The following table compares some of the given measurements. Measurements in feet/inches and meters. The rake of the 100 feet ship is not given and therefore calculated using the ratio Nicolaes gives in the next description: 28/29 x the height of the stem. These calculated measurements are in red.
Main
100 feet
134 feet
L:W:H
Length
Wide
Height
Feet/ Inches
100’
25’
10’
Meters
28,31
7,08
2,83
Feet/ Inches
134’
29’
13’
Meters
37,94
8,21
3,68
4:1:0,4
4,62:1:0,45
Keel
Stem
Stern
Wide
Height
Height
Rake
Thick
Height
Rake
15”
12,5”
18’
17,38’
10”
18’10”
3’
0,39
0,32
5,10
4,92
0,26
5,35
0,85
2’
16”
25’
26’
13,25”
24,25’
4’
0,57
0,41
7,08
7,36
0,34
6,87
1,13
Part of the description for a stem for a ship of 100 feet long is as follows:
“Tot de hooghte van deeze steven addeert, of brengt t'zamen, de holte, het opzetten, en dat daar boven zyn moet, als 't kot, de bak, enz. by voorbeeldt, 10 voet hol, 2 voet opgezet, hier neemt men ook wel 3 voet toe, 6 voet verdek aan boort, komt 18 voet tot de hoogte van de steven. Een Fluit valt minder, en een Fregat meerder. Als men de hooghte van de steven neemt, moet men te vooren weten of het Schip een bak zal hebben, of niet: zoo daar geen bak op gemaakt zal worden, dan moet de steven zoo veel laeger zyn als de hooghte van 't kot is. Of men neemt twee elfde parten van de lengte over steven, tot de hooghte van de steven, in de winkel. Andere neemen Jaap Luiting © 2017
The Stem
mede hier toe elf zestigste parten van de lengte. Tot het vallen van de voorsteven neemt men, of kan men neemen, 28/29 deel van de hooghte van de steven, in de winkel. Het kot voor is ten minsten hoog 31⁄2 voet. De voorsteven heeft bogt 5 voet”. (p. 105, c. 1 l. 21, 1690)
(For the height of this stem add, or bring together, the height (of the ship red.), the rising of the decks, and what has to be above, like the cable stage, the forecastle, etc. for example, 10 feet height, 2 feet rise, for this one also takes 3 feet, 6 feet for the upper deck at the gunwale, makes 18 feet (5,10m.) as the height of the stem. A ‘Fluit’ has a lesser rake, and a frigate more. If one takes the height of the stem, one has to know in advance if the ship carries a forecastle, or not: if there is no need for a forecastle than the stem needs to be as less high as the height of the cable stage. Or one takes two eleventh parts from the length over stem and stern, as the height of the stem, in the square. Others take for this eleven sixtieth part from the length (of the ship red.). For the rake of the stem one takes, or one can take, 28/29 part of the height of the stem in the square. The cable stage fore is at least high 3 1/2 feet. The stem has curve 5 feet.)
The first three sentences are a description much like Cornelis gives about establishing the height of the stem. But the last sentences contain some interesting remarks. Concerning the given ratios with regard to the height of the stem related to the length of the ship, if we consider the height of the stem, 18 feet, as 2/11 part of the ships length, this length turns out to be 18/2 x 11 = 99 feet, if we consider this 18 feet to be 11/60 part of the length this length turns out to be 98,18, both close to 100 feet.
If we scale the line ‘ab’ on drawing ‘Q’ at plate 50 to this height of 18 feet the rake turns out to be 5,06 m. If we use the ratio Nicolaes gives this should be 28/29 x 5,10 which is 4,94 m.
Stem of plate 50 with superimposed in red height, rake and profile. Nicolaas Witsen
The height and rake in this drawing are almost equal. If we choose three separate points on each profile curve, beginning with the top, and let these three points define a circle, what will happen?
We evenly distribute these three points while trying to place the first and last point as far away from each other as possible while in the process keeping a match with the profile.
Jaap Luiting © 2017
The Stem
Profiles and matching circles of drawing ‘Q’, plate 50, Nicolaes Witsen.
We see that both profiles match a certain circle over a substantial length, only downward they start to deviate as can be expected at a point where you have to make a connection with the keel. If these profiles match the part of a circle, it is interesting to look where the center points of these profiles are located. It turns out these center points are in the vicinity of the extension of the diagonal green line. If we remove the circles and add letters to the drawing we are able to make a clear description.
Measuring the height of the curve of the stem of drawing ‘Q’, plate 50, Nicolaes Witsen.
Jaap Luiting © 2017
The Stem
The height and rake form rectangle ‘ABCD’. In this rectangle diagonal ‘BD’ is drawn and extended upward towards ‘E’. The blue line is drawn between the ends of the inner curve. The intersections
of the diagonal line with this blue line are marked ‘F’ and ‘G’. The length of the line ‘FG’ represents the highest point of the inner curve and in this case the length of line ‘FG’ is 1,46 m. In the description of a stem for a 100 feet ship Nicolaes mentions the following:
“De voorsteven heeft bogt 5 voet”, the stem has curve 5 feet (1,42 m.).
The way the height of a curve of a piece of wood is measured.
What is meant by this word ‘curve’ and how is it measured? In carpentry it is customary to measure the height of a curve from a large piece of wood on the inside from the line strung between the extreme ends of this curve. The following picture shows this using a three dimensional rendering of drawing ‘Q’. The blue line is strung between the ends of the inner profile. From the midpoint of this line and perpendicular to it the height of the curve is measured represented by the green line. If we use the exact midpoint of this blue line you will find at that point the highest point of this curve because the curve between this points is a (near) circle cut.
The height Nicolaes gives is 5 feet, 1,42 m. If we measure line ‘FG’ in the drawing this yields 1,46 m. which is an indication Nicolaes measures the height of the inner curve of the stem. This might also be an indication Nicolaes constructs the inner profile first. Another thing is measuring the width of the stem at a certain point. Measuring the width of a curved piece of wood is always done perpendicular to the tangent at that point on the curve which is the same as measuring the width in the direction of the radius of the circle in this case line ‘BE’.
Jaap Luiting © 2017
The Stem
If we have a look at a second drawing of a stem from Nicolaes we can do the same as for drawing ‘Q’.
Profile of a stem, plate 47, Nicolaes Witsen.
Matching circles and profiles of the stem from plate 47.
Jaap Luiting © 2017
The Stem
Rectangle ABCD formed by the height and rake of the stem of plate 47 and its extended diagonal.
Nicolaes Witsen.
The height of the stem on plate 47, line ‘BC’ is again scaled to 18 feet, 5,10 m. which yields a rake of 5,63 m. So here the rake is larger than the height, contrary to his given ratio for a 100 feet ship (height : rake = 1,04) but more congruent with the given measurements for his 134 feet ship although the ratio height : rake of this stem is smaller: 5,10/5,63 = 0,91 and 7,08/7,36 = 0,96 for the 134 feet pinas.
The center points of the circle cuts are again in the vicinity of the diagonal line and both profiles are an almost perfect match with the drawn circles. The length of line ‘FG’ is 1,37m. This is slightly less than 5 feet partly because the blue line is not drawn between both ends of the curve and partly because the ratio of height and rake diﬀer from drawing ‘Q’. In fact, the direction for measuring the height of the curve should be a bit more downward if this line should start from the midpoint of the blue line.
But all in all it seems plausible to conclude both inner and outer profile of the stem in Nicolaes’s case are circle cuts with a probable deviation at the ends according to the size and shape of the tree and the requirements of the joints.
Another thing is the way the width of the stem is measured. As said measuring the width of a curved piece of wood is always done perpendicular to the tangent at that point on the curve. To that end the diagonal line can be used, also in a practical way, to check how much curve the trees yield while rearranging the pieces of wood. By using a fixed point like a block of wood with a nail you can use a line with a designated length attached to this nail to look for the best way to make a stem out of the two pieces as Nicolaes says:
“Om vorder dees Voorsteven te maken, zoo leght men de stukken op malkander, als gezeght is, en ziet of daar na begeerte bogt in is.” (p. 168 , c. 2, l. 35, 1690)
Jaap Luiting © 2017
The Stem
(Moreover to make this stem, one lay the pieces on top of each other as mentioned en looks if this yields a curve as desired)
What you need to know is the length of this line i.e. the radius of the desired curve which is derived from the height and rake en the two points defined by the end of the rake and the origin of the height being the end and beginning of this curve, just like in the case of the method Cornelis demonstrates. The oblique line or the hypothenuse between height and rake is the line that contains the center point of the profile. By lengthening or shortening this line the center point changes and so does the curve. Together with manipulating the two pieces of wood one works towards a satisfactory result due to the discretion of the master shipwright.
Still, the question if Nicolaes starts with constructing the inner or outer profile remains unanswered which is peculiar because the upperouter corner is one of the points to which the length of the ship is measured which is an important circumstance.
As said there is another description of the stem but written for the 134 feet Pinas:
“1. De voorsteven,hoog 25 voet, valt 26 voet. Het vallen van de steven meet men uit het kinnebak, tot de hangende streep of perpendiculaar van de boven kant der steven.
2. Binnen dik 131⁄4 duim, voor dik 9 duim, onder breedt 3 voet, boven 2 voet, binnen 5 voet bogt. 3. 't Kinbak lang 8 duim.
4. 't Lasch lang 6 voet, het eindt dik 31⁄2 duim, 't lasch geklonken met vier bouts. 5. De lip op de kiel lang 5 voet 5 duim, het eindt dik 4 duim. De voorsteven is de richtsnoer daar men alle grootte in een Schip uit trekt: deeze vindt men uit de lengte van 't Schip”. (p. 110, c. 1, l. 10, 1690)
(1. The stem high 25 feet, rake 26 feet. One measures the rake of the stem from the forefoot of the keel to the perpendicular of the upperfront side of the stem.
2. Thick inside 13 1/4 inches, fore thick 9 inches, below wide 3 feet, above 2 feet, height of the inner curve 5 feet.
3. The box scarf long 8 inches.
4. The joint long 6 feet, the end thick 3 1/2 inches, the joint riveted with four bolts.
5. The lip on the keel long 5 feet, 5 inches, the end 4 inches thick. The stem is the guidance while one derives all measures for a ship there from, one finds this from the length of the ship.)
Is it possible to make a reconstruction of the profile of the stem for this 134 feet pinas on the basis of what we know now but without knowledge of the construction method of the profile? The data from this paragraph who are important:
Height: Rake: Width above: Width below: Height inner curve: Lip on the keel:
25 feet, 7,08m.
26 feet, 7,36 m.
2 feet, 0,56m.
3 feet, 0,85m.
5 feet, 1,42m.
5 feet 5 inches long end at its end 4 inches thick, 1,54m. long and 0,10m. thick.
The keel of this 134 pinas is midships 2 feet wide and 16 inches high. Nicolaes doesn’t give a height fore. The width is equal to the thickness of the stem which is 13,25 inches. If we apply the same ratio width/height to the width/height of the keel fore this would yield 9,64 inches. This is also the case in his description of the 100 feet pinas where Nicolaes does not give a height of the keel fore. Lets assume the height of the keel is 10 inches, 0,26m.. We also don’t have the length of the part of the stem which extends the underside of the keel. In the first two examples this length was 0,12 x the rake (drawing Q) and 0,175 x the rake (plate 47). Lets assume this length is 0,15 x the rake which yields 1,10m. This point gives us a place to measure the width of the stem below. Nicolaes doesn’t give the width in the middle.
Furthermore it is important to realise this is a ship ‘built in mind’. So there are no practical limitations why a measurement should deviate from the desired or mentioned ratios.
If we make a reconstruction with these data the following picture emerges.
Jaap Luiting © 2017
The Stem
Constructed profile 1 of the stem of a 134 feet pinas.
First we draw the height and rake, make the rectangle ‘ABCD’ and draw the extended diagonal line ‘EB’. If the inner and outer profiles are circle cuts we need at least three points to be able to draw them by absence of a construction method and subsequently the absence of a radius. The first is point ‘L’ while ‘CL’ is the width above, 0,56m. The second is point ‘G’ since ‘FG’ is the height of the inner curve, 1,42m., measured to the blue line which is strung between the ends of the inner curve. The third point is ‘I’, the point that emerges when the width below, ‘IJ’ is adjusted on line ‘DJ’. Line ‘JK’ is the length of the extension of the keel. The first circle determining the inner profile is drawn through these three points. For the outer profile we have just two points, ‘C’ and ‘J’ because the width in the middle is not specified. Nicolaes mentions the derivation of the width for the 100 feet pinas:
“1. De voorsteven, in de midden drie maal breeder als de dikte, onder en boven breeder”. (p. 105, c. 2, l. 11) (The stem, in the middle three times wider as the thickness, below and above wider.) The width above, 0,56 m., can be considered a very skimpy measurement if you compare this to three times the thickness: 3 x 13,25 inches is 39,75 inches, 1,02 m. If this stem should be wider above and below than three times the thickness, this 0,56 m. is an impossible measurement. Even the width below is less wide than three times the thickness of this stem. We will draw the circle which determines the outer profile in such a way the third point is located on line ‘EB’ and establish ‘by eye’ a fairly decent profile. This yields point ‘H’. The two circles are provided with their respective center points.
One thing is immediately clear: the mentioned height of the inner curve yields a stem with a much lesser curved profile compared to both drawings in Nicolaes’s books and the stem for the 100 feet Jaap Luiting © 2017
The Stem
pinas. If the curve had a height in relation to the curve height of the 100 feet pinas this curve height had to be around 7 feet instead of 5 feet. The consequence is, the center points of the circle to produce these curves, are lying far more removed from the rectangle formed by the rake and height. Just from a practical perspective this is highly improbable.
We can make a second attempt with one change which corresponds with drawing ‘Q’: the curves of the profiles do not completely match a circle cut over their entire lengths.
Constructed profile 2 of the stem of a 134 feet pinas.
For the construction of the inner profile we use the same three points only we draw the blue line in a diﬀerent way, not from the innerupper corner of the stem towards the end of the joint with the keel but towards point ‘I’, where we expect the end of the circle cut just like in drawing ‘Q’. Subsequently we give the inner curve a height of 5 feet, line ‘FG’. If we draw a circle through the points ‘L’, ‘G’ and ‘I’ the profile is much more in line with the previous examples Nicolaes presented. Also the center point is much closer to the rectangle ‘ABCD’. The same is true for the outer circle drawn through points ‘C’ and ‘J’, again trying ‘by eye’ to get a fair course of this profile, yielding point ‘H’. The only thing we have to do is to fair the line between point ‘I’ and the end of the joint on the keel. If we measure in this construction the length of ‘F*G’ this yields 2,1 m., close to the earlier mentioned expected height of the curve of 7 feet, 1,98m..
We can regard the first profile of the stem as highly improbable and in contrast to all what we have seen earlier. The second one is much more in line with the other examples Nicolaes presents. If we keep profile 2 and discard the rest of the construction and superimpose the profile of drawing ‘Q’, scaled to the height of the stem of the 134 feet pinas, the result is as follows.
Jaap Luiting © 2017
The Stem
Profile of drawing ‘Q’ in black, profile of the 134 feet pinas in red.
The profile of drawing ‘Q’ is drawn in black, the constructed profile of the 134 feet pinas is drawn in red. Clearly visible is the strange pinched top of the stem for the 134 feet pinas. All in all, Nicolaes provides not enough information to be able to construct a credible profile for a stem for this 134 feet pinas mainly because the method by which this profile is designed lacks. Together with the strange measurements given for this stem in particular the height of the inner curve and the width at the top make these measurements a quite peculiar example for a model ship, ‘built in mind’.
So, until other information is available, we regard the information to construct this stem as inconclusive.
Jaap Luiting © 2017
The Stem
Returning to the way Cornelis describes the profile of the stem, he gives a list of some stems made by masters of his time.
“Siet hier eenige Voorbeelden van VoorStevens, sodanig die by verscheide Meesters sijn gemaakt. (Table insert) By dese Lijst kan men wel zien, dat de Proportie van alle dese SteevensDeelen, juist niet even regelmatig tegen den anderen staan: maar als men agt geevt, dat het eenen Schip een Dek heeft gehad en ‘t andere niet; ‘t eene voor hoger als ‘t ander is geweest; zoo konnen deze verschillen eenigsints vereﬀend werden. Alleenlijk munt meest uit, dat een Schip 101 Voeten lang, een VoorSteeven maar van 8 Duimen dik, soude gehad hebben; dog geloov dit abusive aangeteekend te zulle wezen”. (p. 58, l. 30)
(See her some examples of stems, as made by diﬀerent Masters. (Table insert) In this list one can see that the proportion of all these stem parts, are not placed regularly against each other: but when one pays attention the one ship has a deck and the other hasn’t; the one fore was higher than the other; so these diﬀerences can be somewhat explained. Most striking is, that a ship 101 feet long, would have had a stem of just 8 inches thick; I believe this to be erroneously written down.)
Length ship
Height ship
Length stem in the square
Thickness stem
Rake stem
Feet
Meters
Feet
Inches
Meters
Feet
Inches
Meters
Inches
Meters
Feet
Meters
85
24,06
11
0
3,11
16
3
4,61
9
0,23
16
4,53
93
26,33
7
6
2,14
16
3
4,61
10
0,26
18
5,10
101
28,59
7
6
2,14
14
0
3,96
8
0,21
20
5,66
113
31,99
9
0
2,55
17
0
4,81
11
0,28
22
6,23
132
37,37
12
9
3,63
20
10
5,92
13
0,33
18
5,10
140
39,63
14
6
4,12
27
9
7,88
15
0,39
22
6,23
144
40,77
15
0
4,25
29
0
8,21
16
0,41
30
8,49
154
43,60
17
3
4,89
28
0
7,93
16
0,41
28
7,93
155
43,88
17
0
4,81
27
9
7,88
16
0,41
22
6,23
160
45,30
17
0
4,81
27
0
7,64
16
0,41
27
7,64
160
45,30
16
0
4,53
28
0
7,93
16
0,41
30
8,49
177
50,11
19
0
5,38
31
0
8,78
17
0,44
33
9,34
Table with measurements of the stem. Page 58. Cornelis van Yk.
Jaap Luiting © 2017
The Stem
The interesting thing is in this table some ships are mentioned who are not present in the list of certers in chapter 24. We can use these and the already mentioned certers to analyse the height of the stem with regard to the height of the ship. More about this in chapter 8 about the hull.
If we look at the selected certers from Cornelis we can make a construction of the profile of the inner curve. The table with measurements is as follows. Measurements in meters. The last column is the ratio of the height and rake of each set of measurements, referring to the height as ‘1’, so we are able to compare the curves. The profiles of number 3 and 7 are the two extremes. We can put them together with the profile of a stem with the same height and rake like number 4. The constructions yield the following profiles.
Page
Built
Length ship
Height stem
Rake stem
Ratio height:rake
1
Schip
145
1629
28,73
5,02
5,66
1:1,13
2
Schip
157
1629
48,69
9,27
9,63
1:1,04
3
Spiegelschip
154
1634
22,65
3,40
5,38
1:1,58
4
Schip
126
1659
45,30
7,36
7,36
1:1
5
Schip
128
1662
37,37
5,89
6,23
1:1,06
6
Schip
131
1664
43,88
7,88
6,23
1:0,79
7
Schip
156
1666
47,56
8,78
6,79
1:0,77
8
Schip
147
1667
43,60
7,93
7,93
1:1
9
Schip
143
1668
24,06
4,61
4,25
1:0,92
Heights and rakes of the 9 ships from the certers from Cornelis van Yk.
Three constructed profiles using the method of Cornelis van Yk.
Point ‘x’ is the center point of the circle cut.
Jaap Luiting © 2017
The Stem
If we look at the data Cornelis gives in the certers we can make a reconstruction of the profile of the stem for a 155 feet ship. In this certer the following measurements are given:
“De Voorsteven was by de Bogt om  gemeeten lang En in de Winkelhaak, tot den binne Hoek Hadde Bogt Breed, onder In ’t midden Boven Viel voor over (p. 131, l. 12)
37 voet  2 duim 27 voet  9 duim 7 voet  0 duim 3 voet  9 duim 2 voet  8 duim 3 voet  5 duim 22 voet  0 duim”
(The stem was long measured along the curve And in the square, till the inner corner Had curve Wide, below In the middle Above Fell forward
10,53 m. (line ‘aec’)
7,88 m. (line ‘ab’)
1,98 m. (line ‘de’)
1,08 m.
0,77 m.
0,98 m.
6,23 m. (line ‘bc’))
Cornelis mentions, just like Nicolaes, the width is derived from the thickness:
De Breedte, in ‘t midden, is tweemaal hare Dikte, onder en boven breeder, na ‘t Fatsoen, en het Oog vande meester. (p. 57, l. 31)
(The width, in the middle, is twice her thickness, below and above wider, according to the shape, and the Eye of the master.) In this case this would mean a width in the middle of 15,5 x 2 = 31 inches is 0,80m. which is close to the given measurement.
If we use the height and rake for the construction as explained by Cornelis we can make the following drawing. Line ‘ab’ is the height, 7,88 m., line ‘bc’ is the rake, 6,23 m.. The profile is drawn through the points ‘a’, ‘c’ and ‘e’, the line ‘adc’ is the chord towards which the height of the curve ‘de’ is measured.
Construction of the inner profile of a 155 feet ship by using the points ‘a’, ‘c’ and the chord ‘de’.
Jaap Luiting © 2017
The Stem
Does this circle cut ‘aec’, constructed by drawing a circle through the points ‘a’, ‘c’ and ‘e’ match the given measurements? In a construction like this the radius of the circle cut ‘xc’, the angle α and the length of circle cut ‘aec’ have a fixed ratio depending on the given height and rake. The construction in the computer yields a length of 11,06 m. for line ‘aec’ while using 1,98 m. for line ‘de’. Cornelis gives a length of 10,53 m. for ‘aec’ and 1,98 m. for ‘de’.
With a given chord ‘de’ according to the given measurement, the length of the constructed curve ‘aec’ is slightly longer than the length Cornelis gives. There can be a number of reasons or a combination of them what can cause this. Point ‘a’ for instance could be a point higher on the curve ‘aec’ due to a shortage of wood. The profile ‘aec’ could be out of shape, i.e. is not an exact circle cut but deviates also due to the yield of the two pieces of wood. But the measurements of the reconstruction are close to the ones given by Cornelis in his certer. Because of this and the fact the lengths of chord or curve can’t be brought closer to one another without substantially altering and deviate the one or the other, we will use this profile to define the inner curve of the stem which is the basis for the outer curve using the given widths. But before we do that it is important to realise the choice for this inner profile has a significant consequence: the center of the drawn profile shifts from ‘x’ to point ‘x’’, highlighted in green. This will cause a slight falling backwards of the upperinner profile of the stem, with regard to the perpendicular, as is clearly visible at the drawing. The green highlighted center ‘x’’ yields the red curve, the center marked with ‘x’ the blue curve. The blue curve represents the profile the construction method of Cornelis would yield. This blue curve shortens chord ‘de’ with approximately 235 mm..
Shifted center of the inner profile of the stem.
It is very well possible this deviation is due to the available pieces of wood at the time this ship was built. This is remarkable because this means more curve instead of less, the opposite one would expect.
Jaap Luiting © 2017
The Stem
Cornelis gives three measurements:
Width above Width in the middle Width below
0,98 m.
0,77 m.
1,08 m.
If we measure these widths in the direction of the radius of the circle cut of the inner profile (i.e. perpendicular to the tangent at that point) this yields three points through which the outer profile of the stem is drawn. The way this is done is shown in the next picture.
Construction of the outer profile of a 155 feet ship. Cornelis van Yk.
Jaap Luiting © 2017
The Stem
The width above, 0,98m., is measured in the direction of line ‘xc’ and is presented by the blue line ‘cg’. This yields the first point ‘g’. The width in the middle, 0,77m., is measured in the direction of line ‘xe’ and is presented by line ‘eh’ which yields point ‘h’. The place to measure the width below is not clearly defined. In this case we chose to lengthen line ‘xf’ with this width, 1,08 m, and draw a circle with this radius till it intersects the extended line from the underside of the keel taking into account the height of the shoe. Part of this circle is shown in blue intersecting the lower black line which represents the extended underside of the keel (the keel doesn’t taper in height in this case). This width below is represented by line ‘fi’ and yields point ‘i’. The points ‘g’, ‘h’ and ‘i’ are points of the outer profile of the stem and need to be connected with a curve. It is not necessary these three points are connected by a circle cut but experimenting with the way to draw this curve showed if you connect these three points with a circle cut it is part of the green circle with the black cross as center point. This center point is located in the vicinity of the extended line ‘xh’. This could be a coincidence but very probably isn’t. The fastest way to draw a curve through three points while looking for the amount of wood you have is by using a center point on the extended line ‘xh’. The center point is not exactly located on this line but it is close. If the objective was to create an outer profile which does not fall backwards, also when one takes into account the ship has trim by the stern this center point has to be above the center point of the circle cut of the inner profile which it is. Furthermore we will see they had some problems with this stem which will be addressed in the section about the joints. So we regard this determined profile as provisional.
We also know the keel extends 0,99m. in front of point, ‘a’ (see for this the section about the rake). So we can draw the profile of the keel together with the stem profile. The extension of line ‘ac’ intersects the extended curve of the outer profile and for the time being we will regard this as the top of the stem though it is too high up. Due to the fact the length of he inner curve was according to the measurements of Cornelis shorter than the reconstructed one we will assume the upper inner corner is the most they could get from the available pieces of wood and the problems occurred at the base of the stem as we will see in the section about the joints. All this yields the next picture of a provisional profile of the stem for a 155 feet ship.
Provisional profile of a stem for a 155 feet ship. Jaap Luiting © 2017