Math expert needed

[J. Dillon]

I'm math deprived amongst other things. :(

Planing to put cox combing on my tiller but need to know how long a length of 1/8" line to use.
This decorative piece of rope work needs three strands of equal length. In a trial run I did determine the math side of the problem.

It takes 46" of 1/8" line to make 1 5/8" of cox combing on a cylinder 1 7/8" dia.

How much 1/8" line will it take to make 4" of cox combing on a cylinder 1 1/4" dia. ? :confused:

The nearest correct answer will merit my putting the same knot on your tiller. :D

Correct answer determined by actual putting the cox combing on my tiller.
;)
JD

[Tim Sweeney]

Howdy,
Assuming the amount of line is proportional to the surface area of the cylinder (tiller) my guess is that you'll need 75.487 inches of line for your tiller. How about some pics when it's done? I need to learn some ropework.

[mmd]

75-1/2"

[Banjo]

Ahh, the old 'How Long is a piece of string' question. smile.gif

[Donn]

The nearest correct answer will merit my putting the same knot on your tiller. Not with my tiller, you won't! :D

[J. Dillon]

Thanks guys. I'll post a picture of the finished tiller.

Come on Donn your tiller might looke cute, I'll even add a turks head. ;)

JD

[Paul Scheuer]

I dont think it works to scale the diameters. The half hitch in each turn takes a certain length. it will be the same no matter what the diameter is.

You need to wrap the same test length without the knots to determine what length it takes to cover. The difference in what it takes for that vs what it takes with the knots will tell you how much line per turn you need to leave for knots. (It will be the same for any diameter).

Why not do a trial on the atual tiller. Better to be too liong than too short.

[George Roberts]

64-3/4"

How expensive is 1/8" line? Buy 100' and cut off what you don't need.

(added 1/8")

[ 12-18-2003, 10:27 AM: Message edited by: George Roberts ]

[Paul Scheuer]

What knot do you intend to use ? Or how do you intend to interlace the half hitches ? Of the several I've seen, some are more appropriate for grips. The one I used, where the hitching stands up almost a full diameter of the cord, is a little hard on the hands. There is one that ends up with the three cords laying flatter. Seems like there was a WB article in about '82 on the subject. I'll check.

A tip from the Ben Der, Dun Dat department. Do all of your hitching in one sitting. A slight change in the tension will show up. I can still see where I stopped for the night.

http://www.imagestation.com/picture/sraid50/pc59a7708f32c4acc806b72243fe3b935/fca9b225.jpg

edited for the typo.

[ 12-18-2003, 01:12 PM: Message edited by: Paul Scheuer ]

[Matt J.]

Like I need another project (one of the winter frames on Rarus cracked one of the boards on the the companionway sliding hatch :( ... anyway my problem)

How do you do that? Is it in the Marlinspike Sailor book? That looks great. I'd like to put something like that on the wheel for Rarus (the spoke which, in vertical position, indicates no rudder). It sure beats having to hang over the stern to check rudder position.

[Donn]

Paul :cool: I gotta learn how to do that. When I find an appropriate traditional wheel to replace Loon's destroyer wheel, I want to do what Matt said. Right now, I use electrician's tape.

[Paul Scheuer]

At this point I've forgotten just where the best reference is. I just noodle until it looks right.

To do turk's heads on a wheel, you need a four strand turk's head so that you can get two strands on each side of the spoke. I don't like the looks of a three strand anyway. I start with the knot on my hand and transfer it to the work when all the bights are in place and I've chased it at least once. To go over a spoke, you need to continue the tucks on the working end, while you unravel the tail end.

Some time ago I did a sketch showing how to get started. I'll see if I can find it.

[Meerkat]

Completely off topic, but Paul: your "Een Der, Dun Dat" made me think of a great name for a law firm: "Bendare, Dundat and Ouch". ;) :D

[Paul Scheuer]

http://www.imagestation.com/picture/sraid67/p5ecf3ac2fe02506b075b59b8511cb297/fbd47f32.jpg

[Donn]

Thanks Paul. Looks like good evening lap work.

[Matt J.]

By "chase" do you mean to start taking out the slack and tightening things up?

BTW, very good illustration. I once looked at a Brian Toss illustration, and got frustrated. Yours looks like I can follow it.

[NormMessinger]

By chase I think he means to follow the privious strand round and round until the proper number of strands have been laid in. Then the work of taking up begins.

If it takes x inches to lay up a inch on a piece y in diameter would it not take 2x inches to back up a piece 2y in diamenter even though you are wrapping the circumfrence rather than the diamenter. Cirkumphrence is proportional to diamenter and should phactor out. So...! I can't spell either.

[Paul Scheuer]

Basically true, Norm, although "strand" has a unique meaning in truk's heads. If you look at the sencond to last diagram, the four elements between the thumb and index finger are called strands (even though the are the same piece of cord). "chase" is a term I use to mean follow the existing weave.

My comment on the length of line need for cock's combing was a very small, picky point having to do with the fact that when you tie a half hitch on a larger diameter piece, you use the same amount of cord per knot and the knot doesn't take up a proportionally larger segment of the circumference.

[Steve Paskey]

I'm betting Paul is right: scaling the cylinder works if you're just wrapping cord around the tiller, but the knots are essentially the same despite the smaller diameter.

As others have noted, scaling the cylinder gets you 75.487 inches. How much more for the knots? Hard to say, but probably not much.

Based on an arcane formula that I won't disclose here, I'm putting my money on 78-1/4.

[CDRDuck]

77.7 a lucky number of course!

[Paul Scheuer]

Follow up - The Cockscombing (Ringbolt hitching) article was in issue 40, p92, by Brion Toss and Malcolm Wehncke.

They show the grip friendly hitching as a "zig-zag pattern" made by by hitching all strands to the left then all strands to the right.

They also show what looks like an easy to follow set of diagrams on a three legged turk's head tied on a wheel at the spoke.

Of course, they also reference The Ashley Book of Knots.

[Bill Perkins]

Here are some variations as presented by Ashley.

http://www.imagestation.com/picture/sraid93/p8053d3f06dd35d77aab1afd752e371c6/fa404c9d.jpg

http://www.imagestation.com/picture/sraid93/pd3a05eef4e01641bbb67ae0153eec483/fa40497e.jpg

He preferred the term Ring Bolt hitching ,dismissing the term cockscombing as a needlework term that had been recently applied to rope work .The hitches were used to fill in the gaps that would be left on the longer outside circumference of a ring if you simply seized it . Those who find this lump problematic on tillers might want to look at the wide standing Turks heads and coachwipping that were typically used for graspable cylindrical shapes .

I'll use Steves' calc of 78 1/4 in. but add the 1/4 in extra I think will be required over the mathmatical ideal . So,put me down for 78.5 in.

[ 12-20-2003, 04:09 PM: Message edited by: Bill Perkins ]

[J. Dillon]

Well it took 78" to do 4 3/4" of 1/8" line to make the coxcombing on my ole tiller. I had previously put a turks head on the knob end and will put another on the opposite end where the coxcombing finished off.

Will post a picture when it it all done as well as a combination hiking stick and tiller extension.

Thanks all for the very close estimates and I don't know who it makes the winner.
smile.gif
JD