Weaving is Math (Or, Why my head hurts)

Last time I confirmed that the loom was actually a loom, not an LSO (Loom Shaped Object).  Really, I have two standing issues with it.

First, the tensioning system is idiosyncratic, to say the least.  That's going to have to wait on some more parts before I can do anything about it, and it works well enough for now.

Second, the shed borders on too small for the shuttle I've been using, a standard Leclerc closed-bottom shuttle.  This is the higher priority, since it's slowing me down and making it less pleasant to use the loom.  There are two obvious solutions here:  Make the shed bigger, or make the shuttle smaller, with bonus points for doing both.

Getting a smaller shuttle is relatively simple, so I ordered a Glimakra #6:  it's the same length as my Leclerc shuttle, but about 1/4" smaller in height.  It's definitely an improvement, but it doesn't hold as much yarn, which means more time winding bobbins.  I like the way it feels, and I'll probably get more quills for it, but it's not perfect.

So how do I make the shed larger?  To figure that out, I needed to figure out what decided the size of the shed, in more detail than "the heddles".  (OK, I could have just bought larger heddles and tried, but re-threading isn't my favorite activity, and my time at the loom is limited.)  After poking at the loom for a while, I realized the maximum shed is the distance between the top of the heddle eye on a shaft being lowered and the bottom of the upper shaft bar on a shaft being raised.  After a not-very-good sketch and some thought (and some time spent trying to both step on a treadle and see the shafts from the side), I realized that that's basically 1/2 the length of the heddle, less the height of the shaft bar.  In my case, the shaft bars are around an inch high, and the heddle are 10 1/2".  So about 4 1/4" at the shafts.  So I have a starting point! 

Of course, the shed tapers from there to the fell (the edge of the woven bit), and the shuttle needs to pass through the shed at the reed, not at the shafts, but that's OK.  After a refresher on trigonometry, I figured out what information I needed, and found a triangle calculator online.  What it boils down to is that, given the maximum height and the distance from the fell, I can figure out the angle the shed opens to.  Given the angle of the shed, I can figure out the height at any given distance from the fell.  Also, I can give myself a headache trying to remember how you calculate tan(angle).  Based on my measurements, here's what I found out:

With a maximum shed of 4.25" at 16" from the fell, the angle is about 7.56 degrees (times two, because math, and because I'm treating the shed as a pair of right triangles).

With an angle of 7.56 x 2 degrees, and the reed at 7" from the fell, the shed at the reed is about 1.85", and the shed at 5.625" (where the corner of my shuttle falls) is about 1.5".  Since the shuttle is about 1.375" high, yeah, it's pretty close.  And as soon as the fell gets closer, the corner of the shuttle starts rubbing on the top of the shed.

So a shorter shuttle will help: losing a quarter inch of height will make it work a lot better.  But what about the heddles?  Well, to shorten it down:

With 12.5" heddles, the maximum shed at the reed is about 2.3".  At the edge of my old shuttle, it's about 1.84".

So it gains me about 1/3" at the edge of the shuttle, which is honestly pretty dramatic.  I haven't quite decided what to do yet, but it's clear that going to larger heddles will be an improvement at that end of the shed.  But what's the downside?  Well... there are two downsides.

First, I'll need to re-hang everything and redo the tieup.  That's time consuming, but not a show-stopper.  It would probably take me about a day, which isn't all that bad in the grand scheme of things.

The second issue is bigger.  One of the things determined by the length of the heddles is the distance between the upper lamms and the lower shaft bar, and that's already not a huge space.  I'm reasonably sure it would work, but I can't actually tell for certain without testing it.  That means I'd have to buy some longer heddles not knowing if they'd work, test, and if it does order more.  I'd also be stuck with a whole bunch of heddles that I've already cut apart, which isn't a huge loss, but is still annoying.

So for right now, I'm going to stick with the smaller shuttle, and see how it works.  I've got another yard and a half of my test piece, so I'll keep experimenting with that and see how I like it.  By the time I've done another yard, I should know whether this is sustainable.

And since I try to avoid total walls of text, here's a picture of the new shuttle in use!