Deck beams and their curvature - questions (?)

[druxey]

If one begins with a sheer line along the crown (centerline) of the beams, there will be unfairness at the ship's side with constant round up as described above. I do not think that this is true if one begins with a fair sheer line at the ship's side. Any comments. anyone?

[CDR_Ret]

Not to beat a dead horse, I thought it would help to illustrate Phil's explanation to show that constant-camber deck construction actually works.

 

Crothers et al claim that an upper edge of a cambered deck beam is a segment of a huge circle—too large to lay out on a lofting floor. So that is why the graphical approximations for a circle segment shown in earlier posts were developed. The following image shows a line of circles of equal diameter arranged along a vertical, rectangular plane. The edges of the circles adjacent to the rectangle represent the edge cambers of a series of deck beams arranged along a straight sheer centerline. This will be the basis for "constant camber." Now, please bear with me. All the following images were derived from a Sketchup model.

 

If you connect the edges of the circles in such a way to create a surface on both sides of the reference centerline rectangle, this represents a cambered surface with no sheer. In Sketchup, you have to create a bunch of small rectangular faces to produce the surface, which I didn't illustrate at this point. However, taking a side view of the constructed cambered surface, it would look like this:

 

The vertical edges within the surface are the included edges of the circles, or camber curves. The horizontal edges form the faces of the cambered surface. Note that these latter edges are all parallel with the straight centerline sheer—a geometrical certainty in a cylindrical surface.

 

Let's remove the portions of the circles not included in the cambered surface to reduce clutter.

 

This is a plan view showing the surface. (The deck/hull centerline is left-to-right in this view.)

 

Again, the longitudinal lines that connect the individual deck beams (the horizontal lines) are parallel to the centerline of the vessel.

 

Here is a perspective of the cylindrical cambered surface looking aft along the centerline. Obviously, the curvature of the camber is exaggerated for this discussion:

 

Now, getting to an actual vessel deck, lets assume the centerline in the profile view is a generic curved sheer line. Then we reconstruct the same surface from that starting point. Again, the vertical rectangle with the curved edge represents the profile view of the centerline plane of the hull deck.

Here, the cambered beam edges are arranged along the centerline sheer. Now, we create the cambered surface by connecting the nodes visible in the image with line segments (this is a process in Sketchup).

 

This results in the "saddle" shape that Phil mentioned in his post.

 

If we look at the profile view of this surface, we see that the longitudinal lines in the surface are all parallel to the centerline (sheer) curve. These lines could represent deck plank edges. They neither converge or diverge from the sheer profile in a constant-camber situation.

 

So, how does this look in a real-world application where the deck beams are constrained by a hull? Let's take a hull-shaped "cookie cutter" and create a deck from this saddle shape that fits into a hull. I stretched out the cambered surface in the longitudinal direction to provide a more realistic proportion of length-to-beam.

 

After cutting out the hull shape on one side, eliminating the parts of the surface outside the cookie cutter, and duplicating, reflecting and joining the two halves of the surface, this is what we have in perspective:

 

Ignoring the facets, which are artifacts of the digital program, this surface represents a sweet and fair moulded deck. All deck beams have the same camber.

 

Again, a profile view of this surface shows that all longitudinal lines on the surface are parallel to the centerline sheer.

 

Note that the lower edge in this image is the outboard deck sheer line from which the rail line can be projected. However, to be perfectly honest, David (Druxey) reminded me that ship designers started with a sweet and fair rail sheer line, then established the positions of the outboard ends of the deck beams below that, and then from this  information, developed the centerline sheer line as dictated by the widths of the deck beams and their camber. This is correct, but working the process in reverse of what was presented here still yields a fair curve without having to create separate cambers for each beam.

 

I hope this illustrated explanation will help visualize what several of the contributors to this topic have been saying. Constant-camber geometry likely applied to vessels at least from the mid-1800s on, if not earlier, so modelers experienced with earlier vessels may be justified in having a different view of this issue.

 

Cheers,

Terry

 

 

 

 

 

Edited July 12, 2021 by CDR_Ret

[Dr PR]

Jaeger,

 

No apology necessary. I have seen the term "camber" used for both the longitudinal )fore-aft) curvature of the deck and the transverse (side to side) curvature.  I have also seen the term "sheer" used for the longitudinal curvature of the deck at the centerline (the modern use of the word) and for the curvature of elements on the sides of hulls (sheer strake) and the line where the deck intersects the hull sides. Unfortunately, many people are familiar with only one use of a word and assume it has the same meaning for everyone, everywhere and at all times.

 

I have also seen plans showing the fore part of the deck near the hawse openings angled down (but not the other decks). I assume (but do not know for sure) this is to cause water coming in the hawse openings to be confined to the bow area. But this downward dip can be created with constant camber deck beams. The centers of the beams just have to follow a downward curve of the centerline sheer line toward the bow.

[Dr PR]

Tom,

 

Excellent presentation! And I certainly agree that modern construction methods are different from those used in the past, and cannot be used for accurate reconstruction of ancient ships. After all, shipbuilding has progressed by learning from mistakes of the past.

 

I wasn't trying to say older ships were constructed with constant deck camber. I just disagree with those who say they couldn't have been built with constant camber.

 

The difference between the "constant camber" method and the "variable camber" method described in your post is interesting. It all depends upon which "sheer" line is the controlling factor. In the constant camber method the "sheer line" is the longitudinal (fore-aft) curvature of the deck at the centerline (crown sheer line). All transverse (side to side) deck beams are positioned with their top center on this centerline sheer line. The location of the line at the intersection of the deck surface and the hull surface is not predetermined, and is just the result of the shape of the two surfaces. Likewise, the vertical distance between the centerline sheer line and the hull-deck intersection line is coincidental.

 

In the variable camber method an arbitrary "sheer line" (rail sheer line) where the deck surface and hull surface intersect is drawn on the profile plan. Another line is drawn for the curvature of the deck at the centerline (crown). The vertical distance between these two lines determines the curvature of the camber for each deck beam. The curvature for each deck beam would have to be calculated.

 

I have to wonder why anyone would have used the variable camber method? It is a lot more trouble to produce and the resulting deck would be less "fair" (could be wavy) and not better structurally than the simpler constant camber method. My guess is that ship designers had not yet developed the drafting methods necessary to determine the intersection of the deck and hull side for the sheer plan.

Edited July 12, 2021 by Dr PR

[Dr PR]

Caarles,

 

I do not follow your description in post #29.

 

In my perspective drawing in post #24, there is no incidence of the center of any of the red deck beams coincident with the black curve. There are no cases where the red camber lines, the red vertical lines and the black curve intersect.

 

The drawing shows the case where the center of the deck camber curves intersect the straight green longitudinal "sheer line" at the point where the vertical red lines intersect the green line. The black line is just the coincidental intersection of the deck surface with the hull sides (not shown) projected upon the vertical centerline plane (not shown).

 

It would be possible to create a different deck surface using the same constant camber deck beam curves just by lowering each camber curve to where the center point of the camber curves is on the black curve where the vertical red lines intersect the black curve. In this case the black curve would be the centerline sheer line of the deck (modern usage of the term sheer line). This deck would be "saddle shaped."

[Dr PR]

Terry,

 

Thanks for the drawings - you saved me the trouble! They illustrate the ideas perfectly. And they show quite clearly that with a constant camber deck the resulting "rail sheer line" where the deck and hull surfaces join is a smooth fair curve.

 

There is a potential problem with the "saddle shaped" deck as shown in your drawing. Of course the curvatures are quite exaggerated, but even with milder curvatures there would be a problem laying constant width wooden deck planks on this surface. If they were placed side by side at the center of the surface (longitudinal and transverse center) they would splay apart at the ends.

 

But this would be a problem only if the individual deck planks ran the full length of the deck. In practice the planks were much shorter, and each run would be created with multiple planks. This would make it easy to bend the planks to the curvature of the deck surface. I have walked the decks of several ships built this way and the plank curvatures are so small they aren't noticeable.

 

In steel hulled vessels the deck plates were cut to fit the curvature.

Edited July 12, 2021 by Dr PR

[druxey]

In wooden ships of the 18th century, the downward curve of a deck at the bow (the camber!) was related to the position of the hawse holes. The primary reason was that if the hawse holes were to come in a deck lower, freeboard would be insufficient and present a hazard. If the holes were high enough to come in at the deck above they would interfere with the headwork. The compromise was to locate the holes 'just right' and lower the forward end of the deck so that it came just below the level of the holes. The bonus was the drainage.

 

Some ships had sloping hawse chutes instead to improve headroom for part of the deck below.

[Dr PR]

I had another thought on this subject. The variable camber design was not limited to ancient vessels. The (relatively) modern barrelback runabouts of the early 1900s were designed with a drastically different camber from bow to stern.

[Charles Green]

My boat building experience is limited to the making of racing canoes.  No decks there, not on the ones I was involved in, so while in that endeavor the deck-beam, camber question never reared its head.  My experience with model ship building is limited to 18th century ships-of-the-line.  At model scale, their relatively straight sides and minimal deck shear make this issue inconsequential.

 

Early on, Andy Davis (Wooden Boat #165), now a naval architect, was involved hands-on in the making of dozens of commercial vessels with deck beams made to a constant camber and encountered the deck distortion this method produces every time.  I contacted him recently and he allowed me this quotation:

 

"There is no controversy, just geometry.  Applying curves cut with a constant curvature to a random, three dimensional curve in space (e.g., the sheer) will not form a "fair" surface.  The change in surface curvature increases with curvature of the base curves; hence, the error for a historic, bluff bow merchant ship with large camber will be greater than for a modern racing yacht with little camber.  Prior to modern methods for developing a deck surface, the only way they had to do it was with deck constant curvature beams...maybe it is therefore historically correct.  No modern fiberglass yacht builder would construct the deck using single camber deck beams. 

 

I stand by the accuracy of the article."  

 

 

In post #32, the white cookie-cutter shape, and immediately below it, the three dimensional drawing of the deck surface it is a projection of, raises a question in my mind. 

 

A piece of paper, cut to the shape of the cookie-cutter, flexible as it would be, would not fit on the three-dimensional deck surface.  Not unless it were elastic.  The area of the 2D projection is less than the 3D surface.  The 3D surface could not be built from material cut to the shape and size of the cookie-cutter.  Though both drawings represent the same object, they aren't the same.  For construction purposes, are they relevant to each other?  Do these drawings assume elastic properties that building materials do not possess?  

 

  

      

[CDR_Ret]

Charles,

 

My reference to a "cookie cutter" is literally what I meant. Think of a quasi-cylindrical tube with a cross-section in the shape of the plan view of a hull, which is the white, boat shape in the image. The cutter intersected the camber surface along the z- or vertical-axis, so the result is a true, three-dimensional shape in all dimensions.

 

Crothers claimed that mid-1800s ship decks were constant camber. My post was intended to simply refute the claim that a constant cambered surface could not produce a fair deck surface.

 

As with many areas of creative human endeavor, making absolute claims about how something can be done simply doesn't hold true because someone always comes up with an effective alternative.

 

Terry

 

 

[Jaager]

17 minutes ago, Charles Green said:

Prior to modern methods for developing a deck surface, the only way they had to do it was with deck constant curvature beams...maybe it is therefore historically correct.

Hmmm,   I wonder why he would see it this why?   The old guys had to develop a multitude of unique curves and make wooden patterns that defined each one for the frames.

There were many fewer deck beams per deck,  Making an individual camber pattern for each one would have been no problem.  In order to get beams that matched the specifications on the profile plan, i.e.  a constant difference in height at the side and at its crown for each beam,  a unique curve for each is necessary.  As you have shown, a constant camber produces sheer curves for the two locations that converge.

 

Using a CAD program can perhaps get a user into entertaining aspects of design - that is the primary purpose of that software after all.   For historical wooden ships,  the function is to replicate as precisely as is practical.  There is no design involved.  Perhaps using a constant camber may have worked, but available evidence suggests that it did not.  Doing it would have been quicker and less expensive, so I suspect it was tried.  Methods used were a craft secret, and not a university degree learned skill.  It was probably tried more than once.  Having to redo a deck and reshape the beams probably a profound negative lesson for each master shipwright who tried it.

[Mark P]

Good Evening Charles;

 

Thanks for your post, which gives a modern point of view, and sounds reasonable enough. The degree of distortion of the fair curve in the sheer of the deck, which would only be noticeable at the extremities, most notably the bow with its rapid narrowing in width, would be dependent upon the amount of round-up required on each deck: the greater the round-up, the greater the distortion.

 

I suspect that the practice in earlier days may well have been that all the deck beams in the midships, and probably going right into the stern, were cut with a constant camber. Coming into the bows, except where a downward curve to shed water may have been desirable, the amount of round-up could then have been increased to provide a fair sheer, which would have been a fairly simple exercise for any competent craftsman. 

 

Re the query concerning 'elastic' properties, this is only truly valid if we are talking about a monolithic deck covering, for example a large sheet of ply. As decks were made up of individual planks, all shaped to fit against each other, there is more than sufficient elasticity provided by the construction method used. 

 

Below is a photograph of the poop deck of the Victory during restoration, taken from Peter Goodwin's book, The Construction and Fitting of the Sailing Man of War 1650 - 1850. The deck beams all appear to be arcs of circles, and to be of a constant camber, demonstrated by the fact that all the edges appear to be parallel. The best proof of this, of course, would be to ask someone who worked on her, which I may be able to do.

 

The actual amount of curvature does not appear to be very extreme, and it must be borne in mind that the poop deck of a sailing warship had the greatest amount of round-up of any of the decks; so all other decks would have a lesser camber than is shown here.

 

All the best,

 

Mark P

 

 

Edited July 13, 2021 by Mark P

[CDR_Ret]

"Once again into the breach" (Henry V-Shakespeare)

 

Because of the persistent view that a constant-camber deck couldn't produce a fair deck, but one with unfair areas in its surface, and because my last attempt to demonstrate that this was not the case was apparently derived from a non-standard approach to ship design and construction, I decided to experiment and see what the outboard-sheer-line-in approach would produce. I had no preconceived notions on this approach, but it seemed that if the outboard sheer line was fair, then it makes geometrical sense that using constant cambers in attached deck beams would also be fair, since corresponding points on the adjacent beams would fall into a curve parallel to the outboard sheer.

 

Many mentions have been made how constant-cambered decks weren't the case in 16th, 17th, and early-to-mid 18th century ships, and I can understand how that is likely due to the relatively low length-to-beam ratios and quite pronounced sheer lines in those eras. But ships became stretched out in the latter 1700s and through the 19th century, so there was less imperative to hand-tool the deck camber, I would think.

 

So, here goes. Using Sketchup again, I created a generic, non-circular curve in three-space and attached it to a vertical plane that corresponds to the centerline of a fictitious hull. The curve represents the outboard deck sheer of the vessel.

Outboard sheer line in perspective.

 

Plan view of the outboard sheer line.

 

Profile view of the outboard sheer line with the centerline plane behind (looking to port).

 

As before, I created a deck camber edge from a segment of a large circle, then placed its center point on the centerline plane. I also added horizontal and vertical guidelines to ensure each camber template was correctly placed longitudinally and on center. These identify deck beam "stations."

Cambered deck beam template and positioning guides.

 

Next, I dragged the camber template down until its edge intersected the outboard deck edge. This was repeated using duplicate copies of camber templates at each beam station line.

Duplicating camber templates and positioning them at the outboard deck sheer line.

 

Completed deck skeleton.

 

As in the previous example in Post #32 of this topic, I "connected the dots" to create the faces forming the cambered surface. (I deleted the curves on the far side of the plane so I didn't have to create 2 million facets, only 1 million...)

Cambered surface created from the camber templates.

 

 

 

You may see where this is leading. Again, to create the deck surface as confined by the outboard sheer line, I created a "cookie cutter" from the outboard sheer line to intersect with the cambered surface. Sketchup allows you to create cutouts of 3D objects using other objects that intersect the one of interest. The cookie cutter's surface is parallel to the z-or vertical-axis of the model.

Outboard sheer line turned into a cookie cutter.

 

After creating the intersection with the cambered surface, I deleted everything but the surface of interest.

 

Intersection that represents the outboard sheer line in the cambered surface.

 

Deleting the surface outside the outboard sheer line, duplicating the half-surface, mirroring it, and rejoining the two half-surfaces yields a fair, cambered deck. All cambers are the same.

Completed cambered deck surface.

 

Finally, taking a look at the orthogonal profile view of the deck, we can see that, while the centerline sheer is smooth, there is a distinct flattening there in the middle, which probably would not be considered "fair" overall. The longitudinal lines in the deck that could represent deck plank edges are no longer parallel to the centerline sheer. This doesn't indicate a problem in form or function, however.

Profile view of a constant-camber deck created by referencing the outboard deck sheer line.

 

So, while this method of constructing a deck might introduce some unfairness in a deck, it doesn't seem to be a significant problem. Recall that the camber round up was exaggerated in this example. With a camber of only 6 or 8 inches, viewing the flattening evident in the above diagram over a length of several hundred feet would be indiscernible, I think.

 

Snide comments about resorting to digital programs to support one's point aside, I don't see any other way to easily and economically illustrate the concepts we are discussing without otherwise resorting to actual plans of actual ships that were built in a particular way. Then what does that prove, except that it worked in that instance?

 

I can't speak about cambers in the forward areas of a ship departing from a fair sheer because I haven't researched those. If anything, those exceptions probably prove the rule. If someone could present an example of such a case, I would appreciate it so I can visualize that situation. I can't conceive of shipwrights having to create numerous deck beams, all with different cambers in order to provide a fair deck in "ye olde days," but perhaps that was the case. It certainly doesn't make geometrical sense to me.

 

Terry

 

 

Edited July 14, 2021 by CDR_Ret

[druxey]

I must say that I'm with you, Terry, having first wrestled this exact problem (manually drafted!) back  about 1969. I rapidly came to the conclusion of 'one round up fits all' - at least in 1:48 scale. The trick was to start, as stated before, using the sheer at the side, not creating one first the centerline.

 

'Nuffsaid!

[CDR_Ret]

Thanks David.

 

I think everything has been said that can be said. I appreciate everyone's contribution from multiple points of view and I learned a lot, personally.

 

Terry