Hopefully I am posting this to the right spot...
I have had my Macomber for a few years and would like to know how to use the second cloth beam. Does anyone know the reason for the second cloth beam? Is it for making a doubleweave fabric? Are there resources for learning more?
Double back beam
Generally one uses that second beam if you are needing to tension part of your warp differently. In my experience I've needed my second beam when I was weaving a structure that would require different tensions in different areas of the warp. I did a series of lampas pieces a while ago and they needed 2 beams because the ground weave advanced and "took up" differently than the patterns on top of it. In the photos here you can see several different weave structures and effects in the detail.
Not needed for regualur
Not needed for regualur doubleweave no, pique doubleweave yes. But have you ever wanted to turn an overshot draft? Your tabby is weaving the ground cloth in plain weave and the pattern is a twill floatng on top, so there is different take up. You can use the second to carry pile yarns that need to be slack enough to allow you to draw up loops with dowel rods. When you want to weave areas with no pile, you can put tension on those same yarns for a spell, then release tension to continue with pile loops. Good for striping and when weaving hems. Sometimes they can carry stuffers for warp cord to enhance the rolling and keep the cloth from collapsing or pique (a doubleweave) to weave the pattern where the pique warps surface. There is not always pattern by color when weaving pique, it can be from defelection due to different tensions. See some pique cloth in Strickler's book woven with 2 warps and 2 wefts, but all the same yarn and color.
Another example would be that if you wanted to use plain weave selvedges with a twill or satin pattern. I also think that you have two warp beams, not cloth beams, but everyone seems to know what you are talking about.
Probably meant warp beams. My Macomber has both a sectional warp beam and a plain warp beam. I usually use one or the other (plain for short warps, sectional for longer warps) but I also occasionally use them both together. A second warp beam, together with a Macomber supplemental back beam, makes warp striping easy. I put the base color on the main beams and the contrasting color(s) onto the supplemental beams and threading becomes easy peasy!