lehmann

I just saw the picture in the first post.  By coincidence, I have the same setup on my mill, but it's on a full size knee mill, not a table-top.   I do research for the sawmill industry on saws, and this setup will be used in an experiment I'm doing.   To give some scale, the saw is 7.25 inches diameter.  
 
I also use it for woodworking - it's a great overhead router, although the spindle speed is a bit low.  Like it for woodworking, because I don't have to build templates to do repeated or precise slots, holes, etc.  On the other end of the scale, I have the "sensitive drill chuck" for drilling a #80 hole.
 
One of the nice things about having full size machines is that I can build the table-top machines myself.  Hopefully, later this week I'll share some pics of a small table saw that fits on a Taig lathe.
 

I just saw the picture in the first post.  By coincidence, I have the same setup on my mill, but it's on a full size knee mill, not a table-top.   I do research for the sawmill industry on saws, and this setup will be used in an experiment I'm doing.   To give some scale, the saw is 7.25 inches diameter.  
 
I also use it for woodworking - it's a great overhead router, although the spindle speed is a bit low.  Like it for woodworking, because I don't have to build templates to do repeated or precise slots, holes, etc.  On the other end of the scale, I have the "sensitive drill chuck" for drilling a #80 hole.
 
One of the nice things about having full size machines is that I can build the table-top machines myself.  Hopefully, later this week I'll share some pics of a small table saw that fits on a Taig lathe.
 

I've been playing with the free version of DelftShip (www.delftship.net) for creating hull designs.  I've done quite a few designs by hand but I've never been able to see how I could create a faired hull with 2D CAD: it would be too cumbersome.  
 
As an test, I created a model of a 30 m "frigate".  Although I didn't use all the tools for fairing the lines, it only took my about three hours to create this design.  I found the tools for pushing and pulling the hull into shape reasonable intuitive.
 
I've attached some of the output files:
Lines drawing Table of waterline offsets (program can also output a point-cloud file) Hydrostatic data Resistance data - it looks like the hull speed is about 9 knots.  Perspective renderings The program can also use a table of offsets to create a model.
 
I didn't add decks, wales or ports, but the program is capable of this.  I did manage to add the keel, masts and a bowsprit, however. 
 
I'm not sure the ship modeller will find this too useful, but there is an interesting feature for laying out the panels of the develop-able surfaces for chine boats. 
 
Those who research hull design, especially how it affects speed, cargo and armament capacity, and perhaps seaworthiness, could find it useful.  I wonder how Chapelle's "Search for Speed Under Sail" would have benefited from being able to quickly do resistance analyses.
 
If anyone wants the Delftship project file, please contact me: this forum won't all me to attach it.  
FrigateResistance.pdf
FrigateHydroStatics2.pdf
FrigateHydroStatics.pdf
FrigatePerspective1.pdf
FrigatePerspective2.pdf
FrigateOffsets.txt
FrigateLines.pdf

Larry,
 
There are two ways to import a set of lines:  One, is to create a table of offsets.  The second is to trace the lines from a scan. To do this DelftShip has the option to put a scanned image in the background.  I think this was just to make a pretty picture, by, for instance, putting a picture of the lines behind the 3D model (see the picture below).  However, I converted the pdf of the lines drawing of my frigate into a jpg, which DelftShip can import.  What I ended up with is an overlay of the jpg image under the program's working set of lines.  In this case, I just imported the profile and buttock lines.  
 
Have a look at the attached file.  You'll see the working lines with the control grid that is used to control the hull shape.  The scanned lines are in the background and slightly offset from the working lines so you can see them.  I had to scale the scanned image a little, but the proportions were not distorted in the process.  To start the process, you'll need to create the basic profile and the spacings of the sections, buttocks and waterlines to match the lines in scanned image.  This will allow you to properly scale the image.
 
The one limitation is that only one view of the lines can be imported, as I did, unless you want to import the all views in one image that you then drag it around depending on the view you're working on.  
 
Overall, this looks like a viable method for re-creating a set of lines.  
 
Bruce
FrigateTracedProfile.pdf

Larry,
 
There are two ways to import a set of lines:  One, is to create a table of offsets.  The second is to trace the lines from a scan. To do this DelftShip has the option to put a scanned image in the background.  I think this was just to make a pretty picture, by, for instance, putting a picture of the lines behind the 3D model (see the picture below).  However, I converted the pdf of the lines drawing of my frigate into a jpg, which DelftShip can import.  What I ended up with is an overlay of the jpg image under the program's working set of lines.  In this case, I just imported the profile and buttock lines.  
 
Have a look at the attached file.  You'll see the working lines with the control grid that is used to control the hull shape.  The scanned lines are in the background and slightly offset from the working lines so you can see them.  I had to scale the scanned image a little, but the proportions were not distorted in the process.  To start the process, you'll need to create the basic profile and the spacings of the sections, buttocks and waterlines to match the lines in scanned image.  This will allow you to properly scale the image.
 
The one limitation is that only one view of the lines can be imported, as I did, unless you want to import the all views in one image that you then drag it around depending on the view you're working on.  
 
Overall, this looks like a viable method for re-creating a set of lines.  
 
Bruce
FrigateTracedProfile.pdf

From some modern texts on the design of wooden boats:  
 
Sailing Yacht Design: by Douglas Philips-Bert:  
Weight Calculations.  
     These are not often made for small craft, except when built to rated classes or of an uncommon breed on which there is little data.  With larger craft weight approximations are sometimes necessary, and particularly so when no inside ballast, except a little for trimming purposes, is to be used.  Indeed,  if weight calculations were not so time consuming, it is doubtful if the praises of inside ballast would ever be sung so cheerfully.  With wood construction, however, weights are always approximate owing to the uncertain density of timber, which varies by 20 percent or more depending on green and seasoned states.  Weight calculations are to a large extent common sense and dreary arithmetic, palliated by the intelligent use of approximations.  
    One of them is the cubic number. By its means the structural weight of yacht may be approximated from that of a similar yacht, of the same type of scantlings, but of any size.  The cubic number may be accepted as:
 
( LOA x Max. beam x Depth of hull)
                        100
 
the later quantity excluding the fin keel, and being measured to point of greatest body depth.  The structural weights vary in different yachts in the same proportion as their cubic numbers.  
 
[Detailed calculations]
Planking:  Area multiplied by the thickness...
Frames and Timbers:  The area of the frames will be a certain proportion of that of the planking, the proportion depending on the siding and spacing of the frames.  ....
Keel, Stem, Sternpost and Deadwood:  Approximations are best made when dealing with these members, since their irregular shapes make the calculations of volume difficult.
Stringers, Gunwales, Shelves and Clamps:  The length of these may be measured from the drawings....
Deck:  The area is most simply measured with a planimeter...
Deck Beams:  The siding and spacing of the beams show what proportion they bear to the deck area....Allowances must be made for heavy beams [at masts or hatches], and for hanging and lodging knees.
Joiner Work and Furnishings:  This may be worked out by proportions from similar craft.  The only other method is to consider each item in turn.
 
 
Skeen's Elements of Yacht Design: Rev. by Francis Kinney
Comparative Weights
     To make a rough estimate of the weight of a new boat based on the know weight of an old boat multiply the weight of the old boat by the length of the new boat divided by the length of the old boat.  
 
-----------------------------------------------
 
If the ratios of draught/length and beam/length are similar for the old and new boat, then the two formulas give the same estimate.

Replies in blue...
 
There is also the question of what tolerance would have been acceptable or detected?  Did ship owners require a performance test in terms of how much cargo could be stowed at an determined draught?   Are there records of ship owners taking shipwrights to court?  

I'm from the camp of roach101761:  LWL is a nice to have, easy to draw, but very difficult to predict.  Even assuming the mathematics for determining displacement were used and measuring the area of cross-sections were accurate (having tried it, counting squares to measure areas is not that accurate, and the planimeter wasn't invented until 1814 and not readily available until at least 1854 [Wikipedia: planimeter]) there is the other side of the equation: estimating weights and the distribution of weight (center of gravity).  I've designed a few small boats and the practical problem of estimating the weights of all the parts of even a 14 ft dingy is intimidating.  Specifying the location of the lead fin keel for a modern yacht is downright scary.  For a wooden ship, each piece has an irregular shape that is custom fitted to the preceding framework, so there are no drawings to base calculations.  I think modern ship builders can do this because they use 3D solid modelling and the steel plates, gussets, etc are laser cut.  Even then, major components are still weighed.  Furthermore, with wood, what is the moisture content?  The planking swells considerably after the hull is put in the water, so even if you weight each fitted plank just before attaching it to the frames, your numbers are suspect.
 
Another issue you need to consider is, as I understand it, that early design drawings were to the inside of the planking so that the builder can use them for directly laying out the frames.  My impression is that creating line drawings to the outside of the planking is a relatively new concept, which, I would assume, coincided with the development or acceptance of mathematical methods, which need the external shape.  This, of course, wouldn't apply to lines taken off existing hulls.  
 
Given the large uncertainty in the as-built weight and weight distribution of a large wooden vessel, I suggest that the only method of prediction is how a hull of similar form and construction floated.  Tradition isn't just from a lack of knowledge or an aversion to risk (or ridicule): staying close to successful designs allows builders to build.  The historian of engineering, Henry Petroski, has written extensively on the benefits and risks of the trial-and-error development. Since all ships carry a significant weight of cargo, the final water line for profitability, stability or best sailing trim is determined by the ship's officers.  Hull shapes or construction methods that couldn't do their job likely became evolutionary dead-ends.  In this sense, an interesting study would be to compare, with modern naval architectural tools for displacement, stability and seaworthiness, the design of hulls which were widely used to those that were only built once.  I suspect this happened quite often as construction technology with steel created more design options, which justified the cost of naval architects and marine engineers.
 
Lastly, I wonder if there were intermediate stages between the initial drawing and the final construction that could be used to empirically determine where a ship will float.  Half-hull models could be used to determine displacement; and builder's models could help with center of gravity.  As a research engineer, I like having a prototype to test new features for unintended consequences and to verify my estimates.
 
PS.  I just checked the drawings in Chapman's Architectura Navalis Mercatoria (ANM). (1768)  The lines are all to the inside of the planking.  I also see that Chapman, in Treatise on Shipbuilding, shows the calculation method for a ship's load curves (draft vs displacement).  The curves for many if not all the of the drawings are show in Plates XXIII and XXIX of ANM..  The calculation looks like it's based on Simpson's Rule using the areas of each water line, although I'd have to verify this as the multipliers aren't quite what I would expect.  
 
Also, quadrature methods of numerical integration were know before Simpson derived that general formula that is attributed to him.  Kepler used it long before that, so in German, its known as Keplersche Fassregel.  

I found "Treatise on Rope Making - Description of the Manufacture, Rules, Tables of Weights, etc." by Robert Chapman  (Master Ropemaker of HM Dockyard, Deptford), 1869.
 
The topics start with harvesting hemp, twisting fibres, spinning, tarring, amount of yarn.threads for various sizes and types of cable, sizes of hearts, weights of cables by length, It even covers manufacturing costs, by operation, including management (officers)
 
Although published in 1869, the English seems older (it is a revised edition), and there is a lot of jargon that will take a while to decipher.  The method of showing calculations is not easy to follow.  Not an easy read, and not a place to find quick answers.  
 
 
Download of pdf, eBook and other formats from the Smithsonian.  
 
http://library.si.edu/digital-library/book/treatiseonropema00chap
 
This is probably a candidate for posting in the References list.
 
 

I was beginning to think about getting/making the correct size ropes and cables for my project.  It occurred to me that if I want a certain size finished cable then how do I select the diameter of the strands used in the cable?.  There doesn't seem to be any data or formula available for this.  I guess most ropewalkers have developed their own by trial and error.
 
I started making a drawing of a 3 strand rope to see the relationship if the strand were assumed to stay circular.  I then took the 3 strand rope and used that to make a larger 3 strand cable (now made of 9 strands).  Have a look at the drawing in the attached  pdf.  
 
I then tried to figure out how the helix angle (lay angle) of the rope affects this.  As a quick simplification I assumed that this reduced the diameter by the cosine of the angle.  Based on my model, a rope made up of three strands of diameter d and a helix angle of A will have an outside diameter of 2.155 x d x Cos(A).  Or, for a 9 strand rope,  [2.155 x Cos(A)]2  = 4.64 x Cos2(A).
 
Theory is good, but it needs a reality check, so I measured some ropes and string around the shop.  The rope measurements and the calculated results are tabulated in the attachment.  It turns out the formula works quite well.
 
The numbers I have are for fairly large size ropes, not model size.   If some one could measure some of their home made rope, or try to use the formula to make a given rope size, that would be a good test.  Also, if anyone had access to actual cable (say a 6" hauser), that would be very interesting.  
 
I can update the table or refine the formula as needed.
 
If this works, I could try stroud layed 4 strand rope.
 
Bruce 
RopeSizeData.pdf

More engineering calculations:
 
Based on the data in http://www.thenrg.org/resources/articles/The%20carronade.pdf, the muzzle velocity of a 32 lb carronade is 750 ft/sec.  Assuming that the explosive force, and therefore the acceleration, is constant, then the average muzzle force is 70,000 lbs.   A lot of this force will go to accelerating the mass of the barrel, but for the moment assume all of this force has to be counter-acted by the elevation screw (which would happen is the slide stuck, or the breech rope were too long and the fighting pin hits the end of the slot).   From the geometry of the 1812 design I described above, then the load on the elevation screw is about 25,500 lbs.  The drawings specify a root diameter of the screw as 1.25" (outside diameter = 2.125"), resulting in a stress of 20,000 psi.  The yield strength of wrought iron is in the range of 23,000 to 32,000 psi. It they used a heat treatable (hardenable) or cold worked steel, which was available, the the yield strength is in the 60,000 psi range.  
 
Since I've greatly over-estimated the load, a screw could survive with a good safety margin in "regular" use.  
 
Bruce

More engineering calculations:
 
Based on the data in http://www.thenrg.org/resources/articles/The%20carronade.pdf, the muzzle velocity of a 32 lb carronade is 750 ft/sec.  Assuming that the explosive force, and therefore the acceleration, is constant, then the average muzzle force is 70,000 lbs.   A lot of this force will go to accelerating the mass of the barrel, but for the moment assume all of this force has to be counter-acted by the elevation screw (which would happen is the slide stuck, or the breech rope were too long and the fighting pin hits the end of the slot).   From the geometry of the 1812 design I described above, then the load on the elevation screw is about 25,500 lbs.  The drawings specify a root diameter of the screw as 1.25" (outside diameter = 2.125"), resulting in a stress of 20,000 psi.  The yield strength of wrought iron is in the range of 23,000 to 32,000 psi. It they used a heat treatable (hardenable) or cold worked steel, which was available, the the yield strength is in the 60,000 psi range.  
 
Since I've greatly over-estimated the load, a screw could survive with a good safety margin in "regular" use.  
 
Bruce

More engineering calculations:
 
Based on the data in http://www.thenrg.org/resources/articles/The%20carronade.pdf, the muzzle velocity of a 32 lb carronade is 750 ft/sec.  Assuming that the explosive force, and therefore the acceleration, is constant, then the average muzzle force is 70,000 lbs.   A lot of this force will go to accelerating the mass of the barrel, but for the moment assume all of this force has to be counter-acted by the elevation screw (which would happen is the slide stuck, or the breech rope were too long and the fighting pin hits the end of the slot).   From the geometry of the 1812 design I described above, then the load on the elevation screw is about 25,500 lbs.  The drawings specify a root diameter of the screw as 1.25" (outside diameter = 2.125"), resulting in a stress of 20,000 psi.  The yield strength of wrought iron is in the range of 23,000 to 32,000 psi. It they used a heat treatable (hardenable) or cold worked steel, which was available, the the yield strength is in the 60,000 psi range.  
 
Since I've greatly over-estimated the load, a screw could survive with a good safety margin in "regular" use.  
 
Bruce

More engineering calculations:
 
Based on the data in http://www.thenrg.org/resources/articles/The%20carronade.pdf, the muzzle velocity of a 32 lb carronade is 750 ft/sec.  Assuming that the explosive force, and therefore the acceleration, is constant, then the average muzzle force is 70,000 lbs.   A lot of this force will go to accelerating the mass of the barrel, but for the moment assume all of this force has to be counter-acted by the elevation screw (which would happen is the slide stuck, or the breech rope were too long and the fighting pin hits the end of the slot).   From the geometry of the 1812 design I described above, then the load on the elevation screw is about 25,500 lbs.  The drawings specify a root diameter of the screw as 1.25" (outside diameter = 2.125"), resulting in a stress of 20,000 psi.  The yield strength of wrought iron is in the range of 23,000 to 32,000 psi. It they used a heat treatable (hardenable) or cold worked steel, which was available, the the yield strength is in the 60,000 psi range.  
 
Since I've greatly over-estimated the load, a screw could survive with a good safety margin in "regular" use.  
 
Bruce

I looked at the drawings for the carronades provided on the CD from the USS Constitution Museum.  They provide two designs, one from the 1927-31 rebuild and another that is "1812 Era" (1985 drawing).  The first drawing shows two wooden "t-nuts" that fit in the slot in the skid and hook under the skid.  Each t-nut is attached to the slide with four 1.25" bolts. There is 1/2" clearance between the bottom of the skid and the hook edge on the t-nut.
 
The 1812 design just shows a 3.75" fighting bolt that runs in the slot and goes through a large (8" diameter) ring that runs under the base. There is no other block in the slot to stop the slide from rotating on the skid shown on the drawings.  
 
I did some engineering calculations to estimate the forces on the various components of the 1812 design. (I'll post them later).  Assuming the thrust force from the barrel is 1000 lbs, then:
     Compression force on the elevation screw: 350 lbs
     Tension (lifting) force on the fighting bolt:  260 lbs
     Force of the back edge of the slide on the skid:  540 lbs
 
There's a lot of friction between 1) the end of the slide and between the skid and 2) the fighting bolt ring that slows the recoil: assuming a friction coefficient of 0.5 (wood on wood and metal on wood), then the friction force is (0.5)(540+260) = 400 lbs.  Most, if not all, of this force will be transferred to the pivot pin next to the gun port.  (I wonder if this means more energy goes to the ball since the barrel recoil velocity must be smaller.  Also, since the recoil is absorbed over a period of time, it should mean less impact on the hull when the breech cable tightens up.)
 
As Jud showed in his drawing, the elevation screw is threaded into the cascabel, so when the screw is not 90 deg to the top of the sled then there is a bending torque on the screw.  However, since the bottom of the screw is just sitting on the surface, there is some friction involved, which reduces the bending forces by about 60%.
 
Going back to the original question of why there there is only one pin in the slot.  If the fighting bolt (pin) is not exactly under the bore then there will be torque that will twist the barrel sideways (looking from above).  This will happen also if the blast force is not symmetric to the bore or the friction between the underside of the slide and the top of the skid were not the same on either side of the slot (actually, this would be outright unstable), so I would think it would be a good idea to have a second slide in the slot.  
 
There are, however, several reasons why the slide will recoil straight back:
that the moment of inertia of the barrel is so large that it would take a lot of torque to make it turn as it recoils. there is a lot of friction between the breech end of the slide and the skid, which will limit rotation of the slide. the force of the explosion acts on the breech, so as long as the fighting bolt (pin) is out-board of the breech, then this force will push the barrel straight back.   These factors also apply to army artillery mounted on two wheels - they recoil straight back.
 
I have to think this out some more, but I think it's important that the center of mass of the barrel is inboard of the fighting bolt.  Overall, it looks like getting the geometry right does most of work, and friction helps to take care of the imperfections.
 
 
Bruce

I looked at the drawings for the carronades provided on the CD from the USS Constitution Museum.  They provide two designs, one from the 1927-31 rebuild and another that is "1812 Era" (1985 drawing).  The first drawing shows two wooden "t-nuts" that fit in the slot in the skid and hook under the skid.  Each t-nut is attached to the slide with four 1.25" bolts. There is 1/2" clearance between the bottom of the skid and the hook edge on the t-nut.
 
The 1812 design just shows a 3.75" fighting bolt that runs in the slot and goes through a large (8" diameter) ring that runs under the base. There is no other block in the slot to stop the slide from rotating on the skid shown on the drawings.  
 
I did some engineering calculations to estimate the forces on the various components of the 1812 design. (I'll post them later).  Assuming the thrust force from the barrel is 1000 lbs, then:
     Compression force on the elevation screw: 350 lbs
     Tension (lifting) force on the fighting bolt:  260 lbs
     Force of the back edge of the slide on the skid:  540 lbs
 
There's a lot of friction between 1) the end of the slide and between the skid and 2) the fighting bolt ring that slows the recoil: assuming a friction coefficient of 0.5 (wood on wood and metal on wood), then the friction force is (0.5)(540+260) = 400 lbs.  Most, if not all, of this force will be transferred to the pivot pin next to the gun port.  (I wonder if this means more energy goes to the ball since the barrel recoil velocity must be smaller.  Also, since the recoil is absorbed over a period of time, it should mean less impact on the hull when the breech cable tightens up.)
 
As Jud showed in his drawing, the elevation screw is threaded into the cascabel, so when the screw is not 90 deg to the top of the sled then there is a bending torque on the screw.  However, since the bottom of the screw is just sitting on the surface, there is some friction involved, which reduces the bending forces by about 60%.
 
Going back to the original question of why there there is only one pin in the slot.  If the fighting bolt (pin) is not exactly under the bore then there will be torque that will twist the barrel sideways (looking from above).  This will happen also if the blast force is not symmetric to the bore or the friction between the underside of the slide and the top of the skid were not the same on either side of the slot (actually, this would be outright unstable), so I would think it would be a good idea to have a second slide in the slot.  
 
There are, however, several reasons why the slide will recoil straight back:
that the moment of inertia of the barrel is so large that it would take a lot of torque to make it turn as it recoils. there is a lot of friction between the breech end of the slide and the skid, which will limit rotation of the slide. the force of the explosion acts on the breech, so as long as the fighting bolt (pin) is out-board of the breech, then this force will push the barrel straight back.   These factors also apply to army artillery mounted on two wheels - they recoil straight back.
 
I have to think this out some more, but I think it's important that the center of mass of the barrel is inboard of the fighting bolt.  Overall, it looks like getting the geometry right does most of work, and friction helps to take care of the imperfections.
 
 
Bruce

I looked at the drawings for the carronades provided on the CD from the USS Constitution Museum.  They provide two designs, one from the 1927-31 rebuild and another that is "1812 Era" (1985 drawing).  The first drawing shows two wooden "t-nuts" that fit in the slot in the skid and hook under the skid.  Each t-nut is attached to the slide with four 1.25" bolts. There is 1/2" clearance between the bottom of the skid and the hook edge on the t-nut.
 
The 1812 design just shows a 3.75" fighting bolt that runs in the slot and goes through a large (8" diameter) ring that runs under the base. There is no other block in the slot to stop the slide from rotating on the skid shown on the drawings.  
 
I did some engineering calculations to estimate the forces on the various components of the 1812 design. (I'll post them later).  Assuming the thrust force from the barrel is 1000 lbs, then:
     Compression force on the elevation screw: 350 lbs
     Tension (lifting) force on the fighting bolt:  260 lbs
     Force of the back edge of the slide on the skid:  540 lbs
 
There's a lot of friction between 1) the end of the slide and between the skid and 2) the fighting bolt ring that slows the recoil: assuming a friction coefficient of 0.5 (wood on wood and metal on wood), then the friction force is (0.5)(540+260) = 400 lbs.  Most, if not all, of this force will be transferred to the pivot pin next to the gun port.  (I wonder if this means more energy goes to the ball since the barrel recoil velocity must be smaller.  Also, since the recoil is absorbed over a period of time, it should mean less impact on the hull when the breech cable tightens up.)
 
As Jud showed in his drawing, the elevation screw is threaded into the cascabel, so when the screw is not 90 deg to the top of the sled then there is a bending torque on the screw.  However, since the bottom of the screw is just sitting on the surface, there is some friction involved, which reduces the bending forces by about 60%.
 
Going back to the original question of why there there is only one pin in the slot.  If the fighting bolt (pin) is not exactly under the bore then there will be torque that will twist the barrel sideways (looking from above).  This will happen also if the blast force is not symmetric to the bore or the friction between the underside of the slide and the top of the skid were not the same on either side of the slot (actually, this would be outright unstable), so I would think it would be a good idea to have a second slide in the slot.  
 
There are, however, several reasons why the slide will recoil straight back:
that the moment of inertia of the barrel is so large that it would take a lot of torque to make it turn as it recoils. there is a lot of friction between the breech end of the slide and the skid, which will limit rotation of the slide. the force of the explosion acts on the breech, so as long as the fighting bolt (pin) is out-board of the breech, then this force will push the barrel straight back.   These factors also apply to army artillery mounted on two wheels - they recoil straight back.
 
I have to think this out some more, but I think it's important that the center of mass of the barrel is inboard of the fighting bolt.  Overall, it looks like getting the geometry right does most of work, and friction helps to take care of the imperfections.
 
 
Bruce

You may want to recheck the reference to 9".  I suspect it refers to circumference, not diameter (because it's easier to measure).  Also, from what I've read, when converting from circumference to diameter, the practice was to just divide by 3, not 3.1416.
 
Bruce

I think the main reason for the tear-out (fuzzies) is that you're using a rip tooth for cross-cutting.  The rip saw tooth is basically a square chisel that tears, more than cuts, grains. A cross-cut tooth needs to have a angle on the tooth face and ideally on the top as well.  This design creates a high point on one corner of the tooth that cuts/scores the wood fibres.  
 
I haven't seen any small circular saw cross-cut saws being offered for sale anywhere (is Jim Byrnes listening?), but you can re-sharpen a rip saw with a small triangular file.  It's not difficult. See http://www.vintagesaws.com/library/primer/sharp.html for hand saws, but the same idea holds for filing circular saws. 
 
The second possible reason for tear-out that the feed is too fast. This obviously creates a larger bite for each tooth and larger forces on the wood grains.  At the end of the cut, these grains are unsupported, so they bend rather than get cut.  This the reason that zero-clearance saw throats and miter guides are used - to support the fibres at the end of the cut.  To make use of this, I would have fed the piece from the other side so that the long (outboard) edge would be against a sacrificial extension on the miter.  As you've done it, each step of the profile is unsupported at the end of the cut.
 
The third reason is related to the size of the tooth relative to the depth of cut.  Each tooth has to have enough volume in the triangular section (called the gullet) to hold and carry all the sawdust that is produced at the tooth tip.  As the feed or depth of cut increases there is more sawdust to be stored in the gullet.  If the gullet gets too much sawdust then it will be under pressure so that at the end of the cut the sawdust pressure will blow the final fibres out before they are cut. Generally, smaller teeth (more teeth in a saw) have smaller gullets, which is one of the reasons fine-tooth saws can't be fed fast.  
 
As a last point, I would have made the profile to run across the grain, then ripped with the grain.  Phillip Reed shows this in his book "Period Ship Modelmaking". As you've done it, the carriage cheeks are very fragile and the surface is rough, which means a lot of sanding or a lot of paint.   
 
Bruce

I think the main reason for the tear-out (fuzzies) is that you're using a rip tooth for cross-cutting.  The rip saw tooth is basically a square chisel that tears, more than cuts, grains. A cross-cut tooth needs to have a angle on the tooth face and ideally on the top as well.  This design creates a high point on one corner of the tooth that cuts/scores the wood fibres.  
 
I haven't seen any small circular saw cross-cut saws being offered for sale anywhere (is Jim Byrnes listening?), but you can re-sharpen a rip saw with a small triangular file.  It's not difficult. See http://www.vintagesaws.com/library/primer/sharp.html for hand saws, but the same idea holds for filing circular saws. 
 
The second possible reason for tear-out that the feed is too fast. This obviously creates a larger bite for each tooth and larger forces on the wood grains.  At the end of the cut, these grains are unsupported, so they bend rather than get cut.  This the reason that zero-clearance saw throats and miter guides are used - to support the fibres at the end of the cut.  To make use of this, I would have fed the piece from the other side so that the long (outboard) edge would be against a sacrificial extension on the miter.  As you've done it, each step of the profile is unsupported at the end of the cut.
 
The third reason is related to the size of the tooth relative to the depth of cut.  Each tooth has to have enough volume in the triangular section (called the gullet) to hold and carry all the sawdust that is produced at the tooth tip.  As the feed or depth of cut increases there is more sawdust to be stored in the gullet.  If the gullet gets too much sawdust then it will be under pressure so that at the end of the cut the sawdust pressure will blow the final fibres out before they are cut. Generally, smaller teeth (more teeth in a saw) have smaller gullets, which is one of the reasons fine-tooth saws can't be fed fast.  
 
As a last point, I would have made the profile to run across the grain, then ripped with the grain.  Phillip Reed shows this in his book "Period Ship Modelmaking". As you've done it, the carriage cheeks are very fragile and the surface is rough, which means a lot of sanding or a lot of paint.   
 
Bruce

Google has a 360 interactive "scan" of all the decks.  The's a link to another from the museum website
 
https://www.google.com/maps/views/view/streetview/us-highlights/uss-constitution-deck/Jjoh75kl7doAAAQZN_qRbA?gl=us&heading=317&pitch=74&fovy=75

You might be interested in this link that provides the specs for a lot of the materials purchased for the restoration of the Constitution in 1993 - 1995.
 
The rope specs are quite a ways down the page but there none the less.  Theses are obviously real sizes not scaled.  I'm not sure it is specific enough for your effort.
 
http://www.maritime.org/conf/conf-otton-mat.htm
 
You might also want to look at this which might be closer to what you are looking for 
 
http://www.digitalhemp.com/eecdrom/HTML/EMP/02/ECH02_18.HTM

I was beginning to think about getting/making the correct size ropes and cables for my project.  It occurred to me that if I want a certain size finished cable then how do I select the diameter of the strands used in the cable?.  There doesn't seem to be any data or formula available for this.  I guess most ropewalkers have developed their own by trial and error.
 
I started making a drawing of a 3 strand rope to see the relationship if the strand were assumed to stay circular.  I then took the 3 strand rope and used that to make a larger 3 strand cable (now made of 9 strands).  Have a look at the drawing in the attached  pdf.  
 
I then tried to figure out how the helix angle (lay angle) of the rope affects this.  As a quick simplification I assumed that this reduced the diameter by the cosine of the angle.  Based on my model, a rope made up of three strands of diameter d and a helix angle of A will have an outside diameter of 2.155 x d x Cos(A).  Or, for a 9 strand rope,  [2.155 x Cos(A)]2  = 4.64 x Cos2(A).
 
Theory is good, but it needs a reality check, so I measured some ropes and string around the shop.  The rope measurements and the calculated results are tabulated in the attachment.  It turns out the formula works quite well.
 
The numbers I have are for fairly large size ropes, not model size.   If some one could measure some of their home made rope, or try to use the formula to make a given rope size, that would be a good test.  Also, if anyone had access to actual cable (say a 6" hauser), that would be very interesting.  
 
I can update the table or refine the formula as needed.
 
If this works, I could try stroud layed 4 strand rope.
 
Bruce 
RopeSizeData.pdf