Monday, 22 August 2011

Elliptical Tube Rolling

    Unlike an ordinary penny farthing [1], a geared facile has untapered upper fork legs of an elliptical section. I have previously made tapered forks for a penny farthing by slicing two sections from a much larger diameter tube and welding down either edge. If done carefully this is an entirely satisfactory method and produces the sharper edge common on earlier bicycles. More prone to cracking where the head tangs insert into the legs though, a very high stress riser point. Since all the tubes on a geared facile, except the handle bars, are elliptical I need a way to reliably produce elliptical tubing of predetermined dimensions.

Ellipses are tricky things. Very elegant mathematically though.

For example, Everbody knows how to calculate the circumference of a circle or a tube but the calculation for the circumference of an ellipse is non trivial. Fortunately I am unable to accurately use a hacksaw to the 4th decimal place so a common approximation will suffice. I have been using this online calculator. Even though it has bugs.

The front upper fork legs have a major dimension of 1.6" and a minor dimension of 0.7" [2]. This results in an approximate circumference of 3.88". In theory then, if I start with an initial tube of diameter 3.88/Pi and squish it, I should end up with an elliptical tube of the correct dimensions. 3.88"/Pi is 1.235" which is very close to the standard tube size of an inch and a quarter. Now, New Zealand is a metric country and I'm unable to buy 1 1/4" tubing but I can get 31.75mm tubing quite easily. I got mine from here, which is an easy bike ride from my house.

    Tube wall thickness is another consideration since the tube must be able to take my weight without bending or fatiguing but must be thin enough to be squishable and light enought to provide a decent ride quality. The wall thickness was the one dimension I was unable to measure on the original so I referred to my books instead. On my original racing penny the tubing is 0.028" (22 bwg ~ 0.7mm) but this is fragile and provides a very whippy, exciting ride.

Paul N. Hasluck writing in 1897 describes how to make a front driver and recommends the dimensions as 18 bwg for a 'normal' 13 stone man (83kg) and 20 bwg for a light weight racer under a lighter man. 18 birmingham wire gauge is 0.049" and 20 bwg is 0.035". I obtained samples from 0.028" up to 0.095" (~ 0.7mm - 2.4mm) and duly squished them. I have chosen 0.049 as per Mr. Hasluck's recommendation for the more sturdy rider.

So how to accurately squish this 1.25" x 0.049" chromoly tubing?

Some years ago I bought a machine designed to slice thick leather straps into two thinner leather straps, I have no use for thinner leather straps but it was cheap, very well made and I knew I could use it for one of those 'future projects'. The machine has two rollers for gripping the leather and a geared down manual handle for winding the leather between the rollers. The gap between the rollers is adjustable.

I made a set of replacement aluminium rollers with bronze bushes, each roller has half of the desired elliptical profile cut into it. By starting the rollers far apart and gradually decreasing the gap I figured I could roll the tubes to the correct profile.

 In practise this worked very well if I pre squished the tube slightly so that the rollers had a slightly wider contact patch to grip on to start with. The tubing was pre squished by marking a line down the tube and squishing it in sections in a big vice. As soon as the rollers would grip I starting the rolling process, occasionally taking the tube out and turning it over to reduce bending. Since the desired ellipse has high eccentricty (very flat) it meant a lot of squishing, this proved to be very hard physical work.

Chromoly is extremely tough steel to manipulate and twice I needed to have a sit down and a nice cup of tea during the process. The forces involved here are high as I found out to the detriment of my left thumb nail. As the tube begins to conform to the shape of the rollers it begins to produce a pleasing low whistle as it is rolled, this increases in pitch as the end of the tube is approached. However, it is important not to roll to the extreme end of the tube as it can (and will) fly out as it goes past that point where it is no longer contained by the rollers. I don't need a left thumb nail anyway.

There is a small amount of spring back in the final shape but the the resultant tube conforms very closely to the machined profile. There is also a slight tendency for the tubing to twist as it is rolled, the pre squishing mitigates this to a certain extent and as the fork legs are only 21" long the error is managable.

I'll look at the lower fork legs next which start elliptical and taper to a smaller circular circumference.

In other news, now that the snow has gone I'll have to go to work all week instead of getting in some quality shed time. Sigh.

[1] Pun intended. I rather think I'm going to refer to the standard design ordinary bicycle as a penny farthing for the remainder of this blog. When the PF was the standard design it was simply knowen as a bicycle and only later when the new fangled safety bicycles came along was it given the moniker 'ordinary' to distinguish it from the usurpers. The are people who object to the name penny farthing and feel it is derogatory. I personally don't care either way, I use penny farthing because it is commonly understood and less pompous. The American term high wheel also has merit but is not commonly understood outside of the states. The german and french equivalents, hochrad and grand bi resp. are more or less translations of the american term.

[2] This ellipse has an eccentricity of 0.899, which is high. I have nothing to say about that.

Edit - more elliptical tube tube rolling adventures here and here

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