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Formula for the thickness of rope on any scale ship


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On my last 2 scratch build ships I have guessed the thickness of the different types of rope used. Now that I am working on the Fluit, the Zeehaen, I think that guesstimating the thickness of rope is out of the question. 

 

Is there a formula one uses to figure out how the thickness of rope is calculated? 

For example :

x = scale of the ship

y = real size of the ship

z = thickness of rope

 

Taking in account the year and nationality of the ship (1639, Dutch), or this does not matter? 

 

I know the scale is important which for the Zeehaen is 1:37.5.

 

Thank you in advance. 

Marcus 

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How I approach this:

Most all rigging tables are for circumference.  We tend to use diameter.  Circumference divided by 3.14 = diameter.

Any size dowel - sand it really smooth, mark a 1 inch interval in the dowel, and give it a shellac coat. 

Wrap the line in a tightly packed coil around the dowl.  The number of revolution within the 1 inch interval is the diameter of the line.

 

From the appropriate rigging table,  find the line data.  Divide it by 3.14 and by what ever your scale is.  This is the number to match to   1 divided by the number of rotations.

 

In the Steele era, the tables have a huge variety of rope sixes, more than I can match using the limitations of linen yarn, I got yelled at, but given scale effects, I opt for the closest model line that is below the table number.

 

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If this was a British vessel, the ratios of the ropes all wind back to the masts which wind back to the size of the ship.   Lacking better information, these ratios for all the lines on your vessel can be calculated if you choose to use the information for British ships.   You can use Lees' Masting and Rigging tables as well as look at the chart available here at MSW prepared by Dan Vadas which was based on Lees ratios and will give you the rope circumference of every line.  Be aware though that Dan's information is the same as Lees for ships after 1711 but he used the wrong formula for the length of the main mast for earlier ships thus all subsequent sizes for spars ropes, etc. are not accurate.  Still, at model scales the rope sizes may be quite close to what you need.

Allan

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Thanks for all the suggestions. 

@Justin P.  I do not know the diameter of the real rope. I wish I did because than my job would be much easier. 

 

 

@Jaager  Love the simple explanation and will give it a go. 

 

 

@allanyed No British vessel, I built only Dutch ships. There is much more info on rigging British ships than on Dutch ships. 

 

Marcus 

 

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Next question.

How do you determine what is the right size of line? Historic Ship Models by Wolfram zu Mondfeld cover standing rigging sizes from 16th through 19th century on page 272 and 273 and running rigging on page 308 and 309. 

 

How do I read this information? 

40%, 16%, etc. What do the percentages mean? 

 

Thanks 

Marcus 

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I'll have to look at my Mondfeldt  later, but meanwhile here is something that may help.

 

At a scale of 1:37.5 your scale rope will be easier to determine than some smaller scales.

 

Most of the tables you find will be in inches rather than metric, so you may find yourself with another level of conversion,

however, to determine the size ( diameter ) of the scale line I am working with I wrap the line around a dowel of about  8mm diameter for 10 turns. The diameter of the dowel doesn't matter in this case . Make sure the 10 turns are touching but not compressed.  I then measure the length created by the 10 turns.  You then dive the distance by ten, and you will have the diameter of your scale line.

Example:   10 Turns of your scale line = 8.5mm.   Divide by 10 = .85mm.   The diameter of your line is .85mm =  approx. .03 inches.

Obviously, if you are using very small line, like for ratlines and lanyards, you may want to use 15 or twenty turns and divide by the appropriate number..

 

I use a calculator like this:  Length calculator  , for my conversions..

 

Depending on your resources, getting  scale rope in the exact size you need may be a challenge.

You will have more control if you are making your own rope, but it will still take a lot trial and error to get the sizes you are satisfied with.

 

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Do you have the book (including Cd) of the Tasman-ships?

There is a rather extensive rigging table on the CD. (At least, I guess that is were mine came from). Essentially the system in Dutch ships is comparable to that of the English: rope size (actually: weight) relates to the size of the mainmast (or the mainstay). You can 'rescale' the table in the book. Gives a reasonable outcome. (At least, I am still rather content with the result :) )

 

Jan

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57 minutes ago, amateur said:

Do you have the book (including Cd) of the Tasman-ships?

There is a rather extensive rigging table on the CD. (At least, I guess that is were mine came from). Essentially the system in Dutch ships is comparable to that of the English: rope size (actually: weight) relates to the size of the mainmast (or the mainstay). You can 'rescale' the table in the book. Gives a reasonable outcome. (At least, I am still rather content with the result :) )

 

Jan

LOL, I have the book and cd and I am building the Zeehaen from that book. I am looking at the table and you are correct, it is extensive. How embarrassing, I should have checked this out. (goes and hide in the closet) 

 

I am still interested in how to read the rigging tables in Montfeld's book. 

 

Marcus 

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  • Solution

It's so easy to get bogged down by the minutia within this hobby, especially newcomer/amateur/average members.

There is a wealth of examples of models on this forum, made by folk who know and always will know far more than you will ever get the opportunity learn.

I don't think my suggestion here will be very popular in certain circles. However, here goes....

Study these models made by what I may term 'academics' of the subject. Rigging, for example, has dimensions that were empirically developed over hundreds of years. The 'academic' modeller has the resources and invested time in its study and application.

By studying 'academic' models including their rigging intelligently it's possible to get a sense of what's right, and by your own efforts find out what looks wrong. Generally, it's all about proportion; the relative thickness of one piece of cordage to another.

My opinion (for the little it may be worth) is for all practical use, most ships could be rigged by however many bits of 'sting' get the job to look right to the average modeller.

Then you will have learned to value the respect of others examples.

And the time you have borrowed from them will allow you to fix that shelf or get that slow puncture repaired properly and safely.

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@shipman

 

You are a far braver man than I am, but I guess I am exposing myself  to unpopularity as well; but how bad can it get?

 

I am fully with you when it comes to " how it looks "..

 

" Establishments " were established so that government contracts would have a basis for going forward, and being audited at a later time.

Civilian contractors would also need to meet similar requirements.

 

They didn't want to be billed for 2 inch cable when half inch cable would have got the job done..

The size of the rope depends on the job being done, and in many respects is intuitive; this applies to the blocks as well, however, the size of the rope will determine the size of the block..

 

I may be oversimplifying, but maybe someone else will have more to say.

 

I think if the builders here take a good look at the models; good ones and bad ones,  they will get a good sense of what looks right..

 

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I used to obsess over rigging tables and scantlings and their relative time periods.  I still do up to a point.  But the baseline is that the physics of the forces of wind and water has never changed. 

The strengths of natural fibers and wood has not changed either.  So using Steele or a similar turn of the 19th century source will at least get you sizes for the various rigging components that would have worked and any minor variations from an earlier time or different nation would be outside our range of being able to discern them.  If it is known that an earlier time was prone to over engineering because their materials manufacturing was not up to spec, factor that in.

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1 hour ago, flying_dutchman2 said:

I am still interested in how to read the rigging tables in Montfeld's book. 

 Mondfeldt says that the thickness  (diameter ) of the mainstay shall be .166% of the diameter of the main mast at the deck .  ( which deck? )

The percentages in the tables are  a percentage of the mainstay as measured.

 

So if the diameter of the main mast at the deck is 2'6" ( 30" ) then the main stay should be .166 x 30 = 4.98 ".   The bowsprit gammoning should be 40% of this = .40 x 4.98 = 1.992 ", and so on.

 

Obviously you can't proceed without the main mast measurement, and the confidence that it is correct.

 

Someone else would have to establish if Mondfeld has a reliable basis for making these claims.

 

I think someone could give this a go on a few ropes and see if it looks good as discussed above..

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Or, more simply, the circumference of the main stay is 1/2 diameter of the main mast at the deck.  (Watch the diameter/circumference.  Any period documentation of rope sizes are talking about circumference, which is easy to directly measure vs. diameter which is not (or requires dividing by pi)). 

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The only way to get 100% accuracy on any rigging is to have a piece of paper with a certified dimension written on it. Which is why Steele et al are so relied upon. Then it's a direct scale element. I accept that.

 

As numerous as Naval vessels were, they must have been considerably more civilian vessels which had no official 'establishment' tables to follow until very late into the sail era. They used what did the job.

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@shipman

Thank you for the wise words. Actually, I obsess about everything and after that, I take it in stride. It is only a hobby. I am not doing any life threatening work. You would figure I would be good at it as it is my favorite exercise of building a ship. 

 

@Gregory and @ah100m

Thanks for mathematical formulas and I heard from others that Mondfeld is wrong in many ways. 

I do like the diameter of the "mainstay" formula and thanks to giving me examples with how you got to the answers. 

 

Marcus 

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I have been puzzling over rigging dimensions also. I read every reference I could find and entered all the formulas into a spreadsheet.

 

Basically all rigging diameter is based upon the mast diameter. For the lower mast this is the diameter at the partners. This diameter is almost always calculated relative to the ship's beam (widest part of the hull).

 

From the mast diameter the circumference of the main stay is calculated, and almost all other rigging dimensions are based upon the size of the main stay. Mondfeld's calculations are in error as pointed out above. The main stay circumference is 0.166 times the mast diameter, or 16.6% of the mast diameter. This number agrees closely with Lees and other references that I have found.

 

But the common rigging dimensions given in period references are for the circumference of the rope, not the diameter! But all the thread and scale rope is measured by diameter.  So you have to divide the circumference by pi (3.14159) to get the diameter.

 

To simplify all of this I have created an Excel spreadsheet that includes the formulas from Lees supplemented by Mondfeld's formulas. Just enter the model's main mast diameter into the green cell (C3) and all the circumferences and diameters will be calculated automatically. If you don't use spreadsheets I have included a PDF "print" of the spreadsheet that shows all of the formulas and gives example dimensions for a topsail schooner with a 20 foot beam.

 

 

CAUTION: Schooner masts and spars were smaller and lighter than those of square rigged ships. Schooners did not carry as heavy a load of sails and spars as a square rigger. The masts were typically 4/5 the diameter of square rigger's masts (this took a lot of reading through a lot of references to pin down the relationship!). Thank Harold Underhill for providing this insight. This is borne out by the actual mast dimensions recorded by Mariester in the early 1800s for real schooners as published in Chapelle's "The Baltimore Clipper."

 

However, the relationships to main mast diameter and main stay circumference used in the spreadsheet is the same for about all ships. Small boats may be different.

 

If you want a spreadsheet or PDF that lists all of the rules for mast and spar dimensions for square rigged ships and topsail schooners, with references and examples taken from period ships go to this link:

 

 

******************************************************************

 

Finally, I have attached the working spreadsheet for my current model, a topsail schooner with a 19.9 foot beam. It is tailored to my needs, but it can be used for any model with a few modifications.

 

Note: The cells with green background require you to enter the appropriate values for your model.

 

This spreadsheet includes calculations from Lees, Monfeld, Fincham, Rankine, Cock and Hedderewick  (the last four were actual period ship designers) for just about everything - masts, spars, standing rigging and running rigging, for square riggers and schooners. Just enter the values in the green cells for things like the ship's beam, line of flotation, etc. If you don't understand the terminology or the measurement read through all of my thread linked to above.

 

Note: Rankine, Cock and Hedderewick calculations are for topsail schooners. Lees and Mondfeld calculations are for square rigged ships.

 

Columns A through W give calculations based upon each rule set, so you can see the differences and similarities. Columns X and Y contain the values I used for my model calculations. Just plug in the actual ship dimensions used for your your model Columns AB through AH calculate the dimensions to use in your model. Enter your model's scale "N" in cell AG2. Column AI then scales these to 1:N. Then using these values as references check them over to see if they really are about right for the model you are building.

 

Then in columns BD and BE enter the actual scale dimensions of the model you are building for hull length on deck, hull length between perpendiculars and beam. Then presto! Column BH  (green cells) lists the size of everything on the (schooner) model for spars, standing rigging and running rigging.

 

If you are building a square rigger you may want to add additional calculations - based upon the original calculations at the left side of the spreadsheet - for extra spars, etc. Note: Mast and spar diameters are for the widest part only. You will have to figure out the taper and such.

 

Then the spreadsheet calculates the appropriate block sizes to be used with the rigging diameters.

 

I have listed all the dimensions of Syren's ropes, blocks and hearts so you can figure which are appropriate for your model, And then you can enter the appropriate rope diameter/lengths and figure how many packages of Chuck's rope you need in columns BQ through BV, and you can enter the type and number of blocks and packages of blocks you need. The costs of each package are listed so you can calculate the total order you need from Chuck in column BW.

 

I hope you find this information useful. If you need anything else you are on your own.

 

Mast spar and rigging calculations.xlsx

Edited by Dr PR
Updated spreadsheet
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Phil

Great job on the spread sheets!!!!   I have no idea if these are appropriate for the Dutch fleet but lacking other information these could be a big help for Marcus and many others of us.   If the Dutch ship on this thread is set up with similar sizes as the British, your spread sheet looks to be very close.   For other sizes and eras it should be noted  from what I can find in Lees other multipliers should be used.  The 2.23 multiplier applies to all rates  from 1773 to 1794.  This is very close for the 1639 time frame of Marcus' ship which would have been 2.24, at least for British ships.  Calculating the mast height, depending on time period and rate,  was sometimes  based on  the beam, keel length, lower deck length and depth in the hold.  Differences, depending on rate and era could be as much as 8 feet or more for the same size ship.  

Allan

  

 

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Posted (edited)

Phil,

 

On 2/28/2021 at 3:37 AM, Dr PR said:

And then you can enter the appropriate rope diameter/lengths and figure how many packages of Chuck's rope

Note that Chuck has posted here at MSW that Syren is no longer  making and selling rope.

Allan

Edited by allanyed
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