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Post by jules on Feb 15, 2021 12:59:06 GMT
Hello Philemon, Let's get back to the first question of the 6th of February. How was the shape of the bottom of the ship controlled when building according to the method Witsen describes? First of all I think it is important to mention that the chine (knikspant) you describe as a result of Witsen's method was never there in the first place. We know several wrecks which have been built according to this method that do not show the chine. To give a couple of examples: Vasa, E81 and wreck B&W5 in Christianshavn. Here is a representation of B&W5 from Lemée's book, page 186: But, the figure Z you show from Witsen's book actually shows a chine. The chine in this figure Z is the result of a drawing method in which Witsen uses only one arc and one straight line. When we look at the figures directly above figure Z, the figures W and V, we see that two arcs and a straight line are used to make the shape, and as a result of this there is no chine. And this agrees with what he describes in his text, two arcs and a straight line, and this is what we see in the wrecks described above. Why Witsen decided to use a single arc in illustration Z? Good question. It certainly is easier to draw only one arc, but it is not what he actually describes in his text and shows in other figures. Over time it resulted in a lot of confusion. That the chine was not wanted is clear from from a remark he makes on page 48, I: "Nu bevint men, schepen met kringstukkige deelen de sterckste te zijn, waer van in dien tijt het tegengestelde wierd gelooft. Hierom bouwden zy hun schepen plat, en hoekigh buitewaerts." (Now we know ships have to be round to be strong, they believed the opposite, so they built their ships flat and with chines.) And Witsen also describes how you could prevent the chine while working according to his method, page 67, I: "Wanneer het schip wijder is als de proportie of even-maet hier gegeven, dan laet men de laeste vlackgangh wat rijzen, als anderzints wel zoude geschieden, op dat met de kimme wel moge over-een-komen, en niet zy gelijk een trogh." (When the ship is wider than the proportion given here, one raises (tilts) the last board of the bottom a bit more as otherwise, so it agrees with the bilge, and is not like a trough." It is clear from this that chines were not wanted when building according to Witsen's method, and that a ship with a chine was considered to be misshapen in Witsen's time. For the control of the shape of the bottom posts placed on the floor of the wharf were used as supports for the bottom boards. The boards themselves were fixed to eachother with temporary clamps which were nailed to them. These clamps could have been straight or could have had an angle, so the boards would make an angle to each other according to the angle of the clamps. The boards were also held in position by pincers. These pincers could be equiped with parts to keep the boards at an angle as well. The use of these three supports was enough to keep the bottom in a stable position when the first frame parts were placed in the bottom. This method is of course very well explained by Witsen, but also by Vos and Lemée. Here is a drawing of Vos, page 69, fig. 4. I hope this answers your first question; more to come, Jules
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Post by philemon1948 on Feb 15, 2021 15:27:22 GMT
Hello Jules, Thanks for your fast reply. This is getting interesting. Let me try to give a reaction as good as I can. I use your own sentences to start my description to prevent any confusion. It almost immediately starts to get complicated so I will try to do one sentence an/or subject at a time. “First of all I think it is important to mention that the chine (knikspant) you describe as a result of Witsen's method was never there in the first place.” I am much more wary to make these bold statements. That this chine, I didn’t know the word by the way, did not show up in wrecks is no proof it didn’t existed. To generalise on the basis of three wrecks seems to me a little too far off. If you look at the drawing Witsen presents and we both use to make our point (plate 52, figure W, from the edition of 1671) there is something strange going on. Witsen himself presents this drawing as a way “hoe men de verdeeling op ’t papier maeckt, eer men de Scheepen aenlegt”, how one makes the distribution on paper before one starts to build the ships. Whatever you may think of this, this looks very much like designing before building. But if these drawings were used and how, I don’t know. But there is another thing. Witsen uses an example ship, ‘by gedachten gebout’ built in mind, as the basis for the presentation of his material. Chapter nine in Witsen’s book starts with an enumeration of all kinds of ship parts and how to derive them by using ratio’s, in many cases using the length of the ship as basis. Witsen often uses the inside thickness of the stem as basis but this measurement is also derived from the length of the ship. The derivation of the measurements of these structures is done using an example ship, 100 feet long over stem and stern, 25 feet wide and 10 feet hold. After 6 pages Witsen starts again giving measurements but now for his 134 feet example ship. All the given measurements Witsen gives for his 134 feet ship differ from the ones given for this 100 feet ship. And quite significant. All but one, which is the hold of the bilge. And that is exactly the measurement where something strange happens in drawing ‘W’. In the description on page 151 (1671) Witsen describes how to draw this drawing ‘W’. If you look closely to the ratio width and height you see that this ratio is exactly 1:0,4. This profile represents the main frame of the ship. The ratio is exactly according to the given ratio for the pinas of 100 feet length and according to Grebber’s table. But the ratio of the main measurements of Witsen’s example ship show something completely different. If you make a reconstruction for this main frame using the ratio and measurements Witsen gives, you get lost. Because you can’t find point ‘h’, the centre for the circle cut with which the profiel of the bilge is defined. This is due to the fact Witsen doesn’t tell how you can find point ‘g’. The width of the bottom can be reconstructed so point ‘f’ can be determined more or les accurately. Maybe you are more succesfull in reconstructing the main frame for Witsen’s example ship but I couldn’t do it. The fact the measurements of Witsen’s example ship deviates abnormally from the ratio’s supplied by Witsen himself gives rise to the question how reliable Witsen’s data really are? For me, this is the main enigma concerning Witsen’s books. Together with the often cryptic way Witsen writes I decided to try another approach. Is it possible to prove the things Witsen writes are consistent? Or, to put it another way, can you build a ship from scratch using Witsen’s data on scale 1:1? My provisional answer is: no. To be continued. Attachments:
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Post by amateur on Feb 15, 2021 16:37:37 GMT
Hi Philemon, IN reaction to your remark that yuo lack more precise data on the stern of the Wasa. I guess you are aware of the drawings taht the Vasa-Museat issued in the 70-ies (and that were uploaded in the forum by Fred Hocker) warshipvasa.freeforums.net/thread/216/vasa-drawings-ship-48-scaledrawing 3-B gives a longitudinal cross-section of the hull, from which you can see the stern (I assume that the measurements, and constructin details were taken from the ship itself) Jan
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Post by amateur on Feb 15, 2021 17:16:35 GMT
Hi Philemon,
Point g is derived from what Witsen describes on page 67 (facsimile 1671 edition), under the tilte 'Van de KImmen': de holte op de hals is 1/3 van de total eholte op de hals' [i.e 1/3 ot the distance a-b in de drawing]. van de wijdte op de kimmen, 10 voet lange van 't schip doet de kimmen 1 duim nauwer zijn als de gehele wijte, zo dat de oplange 10 duim uithangen over 't boeizel. [i.e. at a ships length of 134 voet, point g is 13.4 duim inside the total width.]
What I find quite unclear in Witsen is whether or not he refers to the total width when speaking of thes 10 duim, or to the distance to the centerline of the ship (ie 5 duim, half a foot, o5 10 duim at earch side, so a full foot - give or take a duim) The drawing suggests a full foot at each side A second point I can't discover in the description of W, is what he uses as radius to find point h: the figure suggests that it is the point halfway e and f, but that is not what he describes, and in the figure point h is not completely on this line. A third thing I can't quite understand is how you can be sure that the listing of measurements on page 67 and the description of the frame are in accordance with each other. Is the drawing used to derive the measurements, or is it the other way round?
It was Hoving who somewhere wrote that you actually do not need this profile to construct a ship, and tha Witsen tries to give his work a kind of 'scientific look', in order to look like the english texts who are very much focussed on the mathematical construction of frames and frame parts. {I quote from memory, so maybe I do injustice to what Hoving wrote}
Jan
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Post by philemon1948 on Feb 15, 2021 17:20:46 GMT
Hello Jules, To show how mind-boggling the information provided by Nicolaes Witsen sometimes is, I would like to present the following example. Recently I finished reconstructing the stern construction as described by van Yk. In this stern construction you can find (at least) two gates for the guns who are set up at the ships rear end. The jambs used to define these gates together with the underside of the wing transom and the upper side of the first transom are called in Dutch ‘tuimelaars’. This term is nowhere to be found in Witsen’s book. Witsen gives a complete picture of the whole stern construction at plate 49, the first attachment to this post. This plate lacks these ‘tuimelaars’. According to the captions of all the plates who are related to the shipbuilding trade, Witsen has made these plates himself i.e. he made at least the drawings. How is it possible a structure which is so present in the whole of the ships architecture is omitted in the drawing which should show this complete stern construction? While according to many other plates in Witsen’s book, these gates were certainly present as can be seen at plate 39, also made by Witsen himself, the second attachment in this post. To be continued. Attachments:
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Post by philemon1948 on Feb 15, 2021 17:25:39 GMT
Hello amateur,
I will look into your post with regard to the hold of the bilge and see if I can use that for a renewed attempt to reconstruct the main frame of Witsen's example ship. I will keep you posted.
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Post by philemon1948 on Feb 16, 2021 8:56:41 GMT
Hello Jules, Before I pay attention to the three wrecks you mention I would like to stay with Witsen for a while longer. As you might have guessed, my interest for this subject is not from yesterday or the day before that. I am trying to make a reconstruction of the 155 feet ship Cornelis van Yk describes in chapter 24 of his book. I use Witsen’s books for comparison and for retrieving information if van Yk doesn’t provide this. I came across many curious things in Witsen’s books. I am trying to retrieve a consistent story from what Witsen presents which is not so easy. I want to show you some pictures. The first picture in the attachments is the hull, pictured just before launch. I try to decipher what I see and I see here a very striking transition between the lower part of the hull and the upper part. And this runs over the entire length of the ship. All pictures of the hull in Witsen’s book show this feature and this is one the most profound. It doesn’t seem that the bilge here ‘zagt en eenparig omgaat’, gentle and gradually turns, as van Yk states. I can’t see it any other way but as a sudden change in direction, a chine. Attachments two and three, cross sections of the hull, show exactly the same thing. For the rendering of the hull, you might argue, that it is a bit awkward, or a bit clumsy manufactured. Or maybe the man who translated the drawing in copper made a mistake. But to see this chine appear in so many drawings cannot be dismissed als an accidental mistake. If you do not agree with me, you will have to find a convincing explanation what Witsen is showing at these plates. That does not mean a curved bilge isn’t possible. Every shape is possible but can you find evidence for it? And my original question was, how do you control the bevel of the planking when you make a curved shape without the help of the already erected frames? Even if only the bilge is curved and the bottom of the ship isn't, you encounter that problem. With only the bilge curved, this problem of establishing the bevels is however greatly diminished. But I still wonder, if they did it like this, what their method was? Furthermore you try to prove your point by presenting three wrecks. So the evidence comes from an outside source i.e., maritime archeology. Lets have a look at these wrecks. To be continued.
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Post by jules on Feb 16, 2021 11:13:40 GMT
Hello Philemon, Please allow me to take this step by step. I can of course not reply to all your posts in one time. So let me first go back to your answer to my first reply. Please give me some examples of the chine in real life Dutch shipbuilding. I gave you 3 examples of real ships without chines, now it's your turn. Point is, if you're not willing to accept there is no chine, you will not be able to design your main frame. Witsen's main frame of his pinas is a special case. Please have a look at the drawing below: On the left side of the drawing you can see what happens when you use a radius of three quarters of the width, like Witsen suggests: the radius goes through the end of the bottom of the ship. There is simply no way to make a second radius fit between the straight line of the bottom and the 3/4 radius of the side of the ship. So, what we have to do is use the three coordinates Witsen gives for the lower hull, and draw a fluent line through these three pionts. See my suggestion on the right of my drawing. When we use the 'normal' coordinates for these three points from Grebber's table, drawing a main frame is much easier than in Witsen's special case. I think this same special situation, the end of the bottom exactly at the radius of the 3/4 width, also explains why we find the chines in Witsen's illustrations. As said before, he only uses one radius in these illustrations, while he describes two. For the reliabilty of Witsen's data. Witsen is the first to give an enormous ammount of information for one ship: his pinas. For me it is quite clear that all of this data is real data, measured on the actual ship being build. Next to the information Witsen provides for his pinas, Witsen provides us with a large set of design rules the shipbuilders of his time used. But these rules were mostly rules of proportion for the ship parts, not so much for the ship design, the ship's shape. The rules Witsen gives for the ship design can also be found in the table of Grebber: proportions for length, width and depth. For keel, stem and stern, transom beam, and some coordinates for designing the main frame: end of the bottom, end of the bilge, greatest width at the required depth. That's it, for the rest it was only the shipbuilder who could make the adaptations to the ever changing requirements of the customer. To the question if the design of the main frame that Witsen shows was actually used in Dutch shipbuilding, I would like to refer to Rembrandt's painting of a shipwright, Jan Rijcksen, who has a drawing with that design in front of him. So yes, the method was used. To the question if it is possible to build a ship with the data Witsen provides, I would like to ask you which data you mean: the data Witsen provides for his pinas, or the data Witsen provides as general rules. For the first data set, the pinas data set, I would say yes, it is possible to make a good reconstruction. Witsen provides a lot of coordinates to determine the shape of the hull, and by using these coordinates a good hull can be build. Mister Ab Hoving showed this of course, by building his pinas model. For the second data set, the general rules data set, it is not so easy to make a good hull reconstruction. The amount of information, the small number of coordinates, simply leaves too much room for interpretation. You can come up with a lot of hull shapes that would fulfill these requirements. It also gives the shipbuilder a lot of freedom, and that is probably what was intended. As you have already noticed, the data in the Van Yk contract for a VOC-ship is not the same as the data we find in a warship for the King of Sweden, though both are build in the same period of our history. Changing the requirements changes the design. That's how it was, and that's how it is. Kind regards, more to come, Jules Attachments:
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Post by philemon1948 on Feb 16, 2021 12:08:44 GMT
Hello Jules,
You present a reconstruction of Witsen’s main frame. I made this too, several years ago, for both Witsen’s 100 feet pinas and his 134 feet pinas. I will dust these off a little bit and try to present them and compare it with what you have done. As I said earlier, I don’t believe the 134 feet example ship of Witsen was a pinas. If you look at the ratio of the main dimensions for Witsen's 100 feet pinas, these are 4:1:0,4, exactly matching Grebber’s table. If you look at all the certers presented by van Yk and Witsen you see this ratio of the length versus the width varies between about 3,9:1 to 4,4:1 for warships and merchant ships. The ratio for the 134 feet pinas is 4,62:1:0,45. This is by far the narrowest pinas Witsen presents, if it is a pinas. 4,62:1 looks more like the ratio of a flute. Furthermore Witsen states: “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 Oorlogh-als een Koopvaardy-schip te vertoonen”, ‘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’. Whatever you think, that is a very strange remark.
To be continued.
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Post by jules on Feb 16, 2021 15:44:38 GMT
Afternoon Philemon,
I have a suggestion. If I understand correctly, the ultimate goal of your quest is to reconstruct the 155' ship from Van Yk's book. I 'did' this ship as an exercise years ago, and a lot of questions came up. Probably the same questions you have now. So here is the suggestion. I think it would be a good idea to just grab the contract for this ship and try to reconstruct it here together. All possible questions will rise automatically and everybody can chip in to answer them. If you think this could be a good way forward, I suggest you make a new thread and we'll start straight away. We will leave this thread open, so we can try to answer the more general questions here.
What do you think?
Jules
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Post by philemon1948 on Feb 17, 2021 11:24:09 GMT
Hello Jules,
That sounds interesting but I think it is beyond the scope of this forum. And if you want to discuss the geometry of a whole ship such as the 155 feet ship van Yk describes, including the considerations about design concepts, you are in fact discussing a whole book. And I think a forum like this is not a very suitable platform to do that. What I find interesting, if it is possible to discuss certain aspects I don’t understand. For instance the strange inconsistencies I find in Witsen’s books. I already mentioned some of them. Or what van Yk states about the rabbet in the keel. We can start with your presentation of the reconstruction of the main frame of Witsen’s ship. I can, step by step, like a thread within a thread, show you my reconstruction and you can comment on that or ask questions. I made this reconstruction about 5 years ago and concluded the construction Witsen describes doesn’t work the way he intended. But I am not infallible and can always overlook things. So to be able to reason with someone else who studied the same subject, is always very useful. Persons like that are very scarce.
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Post by jules on Feb 18, 2021 12:01:35 GMT
Hello Philemon,
I think it would certainly be possible to try to do a reconstruction of the Van Yk 155' ship here, but it's up to you of course.
If I understand correctly you are still not sure how they controled the shape of the hull while building according to the Witsen method. As I tried to explain before, they were able to determine the shape of the bottom by supports in the form of posts, angled clamps and big pincers.
Mister Vos built the bottom of his Zeven Provincien with these simple but efficient tools in the 1990s. He describes his findings very well in his book of 2014.
The design aspect is a different matter. For determining the shape of the bottom, the shipbuilder must have made a design on forehand. This design was of course determined by the requests of the customer. This customer could be, for example, the VOC or the Admiralties.
What is important to understand is that the design did not depend on the way the ship had to be build. The design could be transformed into a ship independently of the building method that was used to build the ship. To say it differently: the design could be transformed into a ship by using Van Yk's frame first method, or Witsen's bottom first method. Let me explain.
The coordinates system Witsen used to register the shape of the hull of his pinas, became a much used system in the 1690s. It is very well documented for the VOC and the Admiralties. As you most certainly know both these organisations consisted of several departments, and each department had to build its own ships. Let's take the example of the VOC. The VOC consisted of different 'chambers'. When the VOC wanted to build new ships, they organised a meeting of all the master shipbuilders of the different chambers, and determined the 'certer', the contract, for the new ships. Usually a ship that had functioned well in the past was taken as an example. And here it comes, the design of this ship, its hullshape, was registered by the use of coordinates. The coordinates of the example ship were known, and could be used to build the same ship once again. Usually however, the design was changed by slightly adapting the coordinates to the new wishes of the gentlemen of the VOC. When the new coordinates were fixed, the master shipbuilders of the different chambers were able to build a ship from this information. And, they could do so independent of the ship building method they used. For example, the master shipbuilder of the Amsterdam chamber, Pool, could, working according to the Witsen-method, transform this information into a ship.
But, there's more. We know that during one of these meetings the master shipbuilder of Amsterdam, Pool, did not bring his set of coordinates of a good ship he had built in the past, but the drawing of that ship. From this it is clear that ship hulls were not only registered by coordinates but also by drawings.
From all this it is clear how hull shapes were registered in the Netherlands in the 1690s. The length of the ship was devided into 10 equal sections, and for each section the coordinates were given in tables.
But, you are trying to reconstruct the hull of a ship of the 1660s, without having these coordinates. And that is a big challenge, open to interpretation and misconceptions.
As you may know I'm working on a reconstruction of Gouden Leeuw of 1666. And, of course, I had the same problems as you are having: not enough information from the two main books from the era: Witsen and Van Yk. So what I did was visiting all possible archives in the Netherlands to find the missing link: the notebook of the shipbuilder who built Gouden Leeuw, which, ideally, would contain the coordinates for Gouden Leeuw, or its drawing. After searching for years, I had to give up. I am pretty sure this notebook, or any other, can not be found.
I am still working on the reconstruction of Gouden Leeuw, but for me it is clear that my reconstruction will always stay my personal interpretation of all the information that is available. And that information is simply not enough to be absolutely sure of my reconstruction. Life is a bitch...
And that's why we have to be very greatful of what Witsen registered for his pinas, and that he had the means to publish his registrations. It's a shame though that he chose a rather abnormal ship as an example. Its proportions are completely out of the range he himself gives as a standard. If only he would have chosen another ship as an example; Gouden Leeuw would have been the best choice of course.
Regards,
Jules
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Post by philemon1948 on Feb 18, 2021 12:41:19 GMT
Hello Jules,
What you say is very intriguing. This information has to settle a bit. A surprise is the fact, and you mentioned this also earlier, that Witsen gave coordinates to be able to establish the hull shape. Where can I find these coordinates? I am more at home in van Yk's book than in Witsen so I could have overlooked these. Furthermore,van Yk gives a method to establish the shape of the sheer strake for several ships including the 155 feet ship. The sheer strake is quite fundamental for establishing the hull shape. But it is true I think you need more information. For the fact that Witsen's example ship deviates to such an extent with regard to his own ratios I don't have an explanation. I will get back to you soon and think again about the reconstruction of the 155 feet ship although this has nothing to do, directly at least, with the Vasa.
PS, I think I have found the passages you address as coordinates. Page 81, 82 1671?
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Post by philemon1948 on Feb 19, 2021 7:10:12 GMT
Hello Jules, The things you have said created a lot of thoughts. I am very intrigued by what you say about the shape of the main frame and the hull shape. In general I don’t agree with what you say about the chine. You say about the chine it wasn’t there in the first place and you present two ways to prove that. The first are the profiles of three wrecks amongst which the Vasa. But to me that is no proof. The hull shape with a rounded bilge without a chine as seen in this wrecks is proof of the fact they were capable of building a shape like that. But that does not mean the chine is not present in the designs as Witsen presents them. You are familiar with plate 52 from Witsen edition 1671 (first attachment). At the top the constructed profile of the main frame. When you examine this drawing superficially there seems to be a smooth transition from bottom to bilge. Beneath this profile Witsen presents two cross sections. They both do have a chine. The first simple conclusion is that these drawing contradict each other. They are inconsistent. That is not the only inconsistency in Witsen’s books. You mentioned already the measurements of his example ship which are completely different compared to the general ratios and descriptions for building a ship Witsen presents. Another one are the missing gun ports in the stern construction, not shown, not mentioned, while other, mere general drawings, show they were there. And a very strange and grave one is that Witsen does’n mention trim by the stern where you would expect him to do so, when he describes the sternpost. Some drawings show these ships had indeed trim by the stern. Witsen does mention trim by the stern, only not in the chapters where he describes the construction of his ship. And when he does mention trim by the stern he does this in a way which is in itself contradictory. These inconsistencies can be noticed quite plain and objectively. To find an explanation is another matter. When you look more closely at drawing ‘W’, the construction of the main frame, things are starting to look different. If you use the method Witsen describes to construct this main frame, which can’t be done completely as Witsen describes, you will end up with a profile with a chine. Per definition. And I will prove that to you by drawing this profile using Witsen’s method in the coming posts. When I encounter something like these strange inconsistencies and try to find an explanation, very often my old physics teacher pop’s up in my mind. He once told me that if you want to explore things and report it in such a way this information can be useful to others, you have to be very aware you don’t create your own illusions. Try to see the things as they are, not how you want them to be. That is easier said than done. Often I came across certain passages in van Yk’s book and couldn’t figure out what he was saying. The reason I couldn’t understand some of his writing was often some unconscious bias. You automatically assume things and you are not even aware of the fact you make these assumptions. A beautiful example of that can be found in Witsen’s first edition of 1671. In the facsimile edition a portrait of Witsen can be found (attachment 2). The caption beneath this portrait states this represents Witsen when he was 36 years old. Witsen was born in may 1641, so when he published his book in 1671 he must have been 29 or 30 years old. How is it possible this book contains a portrait when Witsen was 36 years old? The explanation is very simple. At first I couldn’t figure it out because I assumed books were printed and sold the same way as we do it now but that is not the case. So I am very aware of the ever present possibility you make assumptions which are not correct. For that reason I am very grateful Witsen included a glossary in his book. Apart from all kinds of sayings and understanding he mentions which are now lost, he gives definitions and explanations which can provide clues and explanations for some of these inconsistencies, both in van Y’s and Witsen’s book. Attachments:
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Post by jules on Feb 19, 2021 11:31:11 GMT
Hello Philemon,
You say the examples I gave of the wrecks form no proof. Let me remind you again that these wrecks were all build according to Witsen's method: bottom first. I am still waiting for your proof of hulls with chines though.
I hope that we can agree on the fact that Witsen's pinas is not the best example of the proportions that were normally used in Dutch shipbuilding. You proving to me that Witsen's pinas had a chine, certainly does not imply that all ships build with the bottom first method had a chine. Even when we look at the evidence Witsen himself gives for the chine, you have to admit that we can only find the chine in the drawings he uses to explain the building method. Not in the drawings he uses to explain the general design of the ship; we then see the rounded transition of bottom and bilge. And, very important, this is supported by his text: two arcs, not one.
What you are doing is isolating a couple of drawing from Witsen's book, which have nothing to do with design, and draw conclusions about design from these drawings alone. You are not accepting the proof for the contradictory that is in that same book. Look for example at the technical drawing of the 'Noorts-vaerder' in Witsen's book (plate LX, opposite page 160). This is a real design drawing for an actual ship type, and it shows the rounded transition. For two cases actually, Witsen even gives the design changes that have to be made for a ship that has to sail to another region.
And please, accept proof that is outside Witsen's book. Wrecks are very important sources. Look in art: look at the hull shapes of the keeled ships in Nooms' etches. Look at the preserved contemporary design drawings. To the best of my knowledge, all show round shapes, not angled shapes. So please do what your physics teacher told you, and do not just quote him. Keep an open mind for all proof, not just the proof you decided to use to prove your thesis. And please refrain from suggesting that I am biased.
Regarding the trim (stuurlast) that Witsen does not seem to mention. Again, Witsen does not talk much about design. He mainly talks about a building method, and gives a lot of formulas for the design of ship parts, not the actual design of the ship. As mentioned before, in Witsen's book design limits itself almost to the rules which are reflected in the table of Grebber that Witsen reproduces. That trim was present in the design during Witsen's time and location, Amsterdam, is clear from the technical drawing he reproduced as plate XLIV: 'Het Schip op tzy' (the ship from the side). In this drawing we see that the waterline is not parallel to the keel, indicating trim. And it is also clear from the contemporary journals I read in the archives that trim was used in Amsterdam ships.
Regards,
Jules
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