A Simpleton's Differential Cut UQ*
*subtitle : A quant makes an underquilt
Last spring I made my first quilt, a down one for spring, summer, and fall, differential cut. Sewed through baffles because it wasn't going to be too thick, and I was following dimensions on the JRB quilts (w.r.t. chamber height, amount of down, and corresponding temperature range).
I got more ambitious this time, to make a thick winter quilt, again a differentially cut one. Thank goodness there are a number of postings on HF that describe what others have done. I am enormously grateful for postings on quilt-making by Coffee, mikeinfhaz, schneiderlein, warbonnetguy, and some others whose HF personas escape me at the moment.
I don't think I offer much to the state of the art, just some experience, and application of the differential cut principle to the bridge hammock. 'cause this simpleton isn't trying to do what youngblood, JRB, or WBG have done with differentials going in more than 1 dimension. This is a differential cut UQ for a bridge hammock (but if I'd put that in the title, would you have clicked on this thread??? Hmmm...)
Basic dimensions : 60" long, 36" at the head, 30" at the foot. The tapered shape is just taking advantage of the fact that I'm wider at one end---I don't need so much insulation below my hips; it also takes advantage of the fact that in a bridge hammock the quilt remains aligned in one direction, as does the body laying in it.
I made the baffle chambers along the long dimension, to limit the possibility of down shift from sides to center, and to escape the need to differentially shape the interior baffle pieces. I was aiming for something that loft-wise approximates the JRB Mt Washington quilt. The JRB website lists it as having a 3" baffle with 4" loft. I stuck my finger in the wind and guessed at a 3.5" finished baffle height for me.
Now we come to the fun part. The inner shell dimensions (modulo seam allowances and the like) are set. How wide and how long ought to be the outer shell?? The sensible ones among us use analog, involving hammock models and wire to capture shapes. Those of us who see this as an opportunity to use greek letters and conic cross-sections assume some shape and base our calculations on that. You know which of these approaches I'd use...
So I'm imagining what a hanging quilt looks like if we take a cross-section, and imagining that the cross-section of the inner and outer shells are both arcs on perfect circles, perfectly nested, with a uniform distance of the baffle height between them. Now we know that the length of the arc on the inner shell is 36", the question then is what is the length of the arc of the outer circle (i.e., width of the outer shell)? Remember now that the circumference of a circle is 2 pi r where r is the radius of the circle. Illustrated
To come up with a radius I'll imagine a straight line from the mid-point of my spreader bar to the bottom of the hammock. I computed that as 16" or so when I made my hammock so I could use r=16". But I'm a cautious sort, and I figured out that if I mis-calculate the radius and choose one that is too large I can end up making the outer shell too narrow and cause some compression. So I deliberately choose a radius a little smaller, r = 14".
Here's what assigning a value to r buys me... I know that the arc length 36" is some fraction of 2 pi r, indeed it is precisely f = 36/(2 pi r) of the circumference. And whatever the arc length of the outer shell is, it is the same fraction of the arc length of its circle . To wit
f = L / (2 pi (r+b))
where L is the length I want to figure out, f I computed above, r is the radius as before, and b is the baffle height. Well shucks, that means the only thing I don't know in this equation is L, and so I can shuffle things around to get
L = 36 * (1+b/r)
Hoowhee! Don't you just love math? That sure is a pretty reduction. In fact, when you think about what it is saying, it just means that the projection of an arc length on the inner body to the outer body is just a multiplicative factor of (1+b/r). We use this immediately to determine the spacing of baffles on the outer body as a function of the spacing on the inner body.
I picked 6" baffle width on the inner body (at the head), mostly because I'd done that before and knew I could get my hand up into the chamber to empty out a bag of down. Given b=3.5 and r=14, that makes the baffle spacing on the outer body 6"*(1.25) = 7.25".
But I have this trapezoidal shape...if I use 6" spacing at the head, I get 6 chambers. At the foot end the baffle spacing on the inner body is 30/6 = 5", which means at the foot end of the outer shell the baffle spacing is 5*1.25 = 6.25". So I'm just about ready to lay out baffle lines on my fabric, except the careful reader will have noticed my studious avoidance of computing the outer body dimensions. This because I have two problems. The first is easy...how much longer ought the outer shell be? Easy because I imagine just needing to add the baffle height to bring the outer shell to the level of the inner shell, and then extra for folding over the edges and closing things off. So make that 60" + 2*3.5 + 2*1 = 68". Maybe a little longer for insurance.
Now for the width. You see, when that quilt hangs, at the top edge there isn't going to be a straight projected edge from inner body to outer body---there's nothing to make a "corner" there in the way the baffles make corners on the interior. Doing the natural thing to compute the arc length of the outer shell at the topmost chambers is going to lead to overestimating (I think) what is needed in that chamber.
So I did a hack. I basically imagined a straight line from where the inner shell ends to half-way where the outer shell body lies on the outer chamber, see below. To a first approximation, the length of that line is 5", which makes the length of the outer shell on these last chambers 3.625+5 = 8.625 inches. There being two of these chambers, and four chambers where the outer shell needs 7.25 inches, we have a width (excluding what's needed on the edge to connect, to make a channel), of 4*7.25 + 2*8.625 = 46.25". That's at the head. To get the dimensions at the tail I just scale this width by 30/36, to get 38.5" at the foot. I added 2" on each side to allow for a double rolled hem, and then a doubling back of the fabric to create a channel.
I add 1 inch seam allowance everywhere on the inner body.
So at last we have the dimensions : inner body a trapezoid that is 62" long, 38" wide at the head, 32" wide at the foot. Outer body a trapezoid that is 68" long, 50.25" at the head, and 42.5" at the foot. The baffles are 60" long and 4.5" high unfinished (allowing 0.5" allowance for sewing to the shells. Schneiderlein's trick of using a hemming foot to roll the mesh and attach to the shell all in one go is highly recommended).
From here, for a while, you do what other quilt makers have done as far as marking where the baffles will go on both bodies (starting with a baffle line down the center of both bodies, working out from that). The only wrinkle here is I have a trapezoid, so you mark the baffle spacing at the head and at the foot and then mark a straight line between them. I thought I'd be clever and mark the baffle line on the outer body with a marker that has a very light tip. The outer body is mom-90. Lesson learned : marker leaks through mom-90 and so there are spots on the outside of the outer shell where you can find marker leak-through (I was able to mitigate the worst of this by sewing the baffles on with black thread, fooling the eye if not covering the bleed-through).
'Nuther lesson learned. You gotta do something with the 3.5" high ends of the baffles at the head and foot, where the outer shell comes down to meet the inner shell. Now that "do something" might actually be "do nothing", which means those ends aren't rigorously sealed and in principle down could move between chambers at the head and tail ends. So it occurred to me after I'd sewn in the baffles without doing anything with these ends that with a little forethought I might have made a right turn in the outer body fabric and sewn the ends to it. Couldn't do it though once the inner and outer shells were already mated by the baffles. So I ended up jury-rigging little extra pieces of mesh that I attached to the mesh ends by hand, then bent over and glued (with fabric glue) to the outer body. Having learned one painful lesson already, I did check to ensure that the fabric glue does not also leak through mom-90. It does not.
Now for the $$ question...how much down goes in this thing? I need to compute the volume of an interior chamber, and the volume of an exterior one. The interior one is easy...consider the difference of the area of a circle with radius r and one with radius r+b : pi * ( (r+b)*(r+b) - r*r ) = pi * (2*b*r + b*b). We're interested only in a fraction of that, the fraction of 6/(2 pi r) (ratio of inner shell arc length to total inner circle circumference) : 6*b + 3*b*b/r = 23.625 sq in. Same calculation at the foot end (where 5" replaces 6" in the above) : 20.125. To get overall volume of the chamber we take 60" times the average of the cross-sectional areas at the ends to get 1312.5 in^3. I was using 800 fp, so before overfill, that means 1312.5/800 = 1.64 oz. Figure a 20% overfill to make that a nice round 2 oz per interior chamber. Because of the hack, the exterior chambers have about 75% of the cross-section of the interior ones, so we'll give them 75% of 2 oz, i.e., 1.5 oz. So we're looking at 11 oz of down total.
Now 99% of you skipped over all that detail looking for pictures. Others of you slogged through it. Your patience is now rewarded. Or perhaps, your pain is over.
You get a lot of "extra" loft when the quilt is laid this way because the outer shell is not being pulled...think about it...over each chamber that 7.25 of outer shell is vertically over the 6" of inner shell, and the down pushes it up well beyond the height of the baffles.
Here you can see a marker leak-through:( Here also is the little tuck that is needed at each chamber to bring 7.25" of width down to 6" for sewing. The black fabric is not actually the inner body...the edges were a bit ragged and un-even on the inner and outer bodies so I ginned up a cover so that you all would never know.
At each corner I put in a tab loop of doubled over 1/2" grosgrain. The original intention was to use this to suspend the quilt, but I ended up using them differently. Along the long edges I put in a channel and worked 1/8" shockcord through. Coming out of a channel the shock cord passes through the toggle, then goes through the tab loop, and back (to form a loop of shock cord to attach to a hammock corner) through the tab loop and again through the toggle. This allows one to use the toggle to adjust tension.
The channel is made of the outer shell doubled over.
I used sil as the inner body, to form a built-in vapor barrier. The main reason for this is that the lower portion of my DIY hammock sock is also sil, and I just don't want moisture getting trapped in the quilt when I'm in the sock...which is where I go in the winter time! I seam-sealed the stitching lines of the baffles, on the outside.
Now, doesn't that look like a semi-circle? :cool: The loft is just a little over 4".
Finally, here we see how the shock cord connects to the corners of the hammock. It does a nice job of pulling the underquilt in to the body of the hammock while keeping the tension up to keep the bottom of the quilt in contact with the hammock body.
In the times I've been out with the quilt...20 degrees---toasty warm.
-2 degrees---cold butt syndrome, otherwise OK. -2 degrees with assist from downmat...heavenly.
someone will ask...this weighs 18.5 oz with all the cord and toggles and such. In case you missed it the first time, 11 oz of that is down. By way of comparison with the JRB Mt. Washington quilt, this has very close to the same loft, 61% of the overall volume, has 66% of the weight, with 73% as much down. Of course, you use the Mt. Washington quilt on hammocks that this one won't serve, and you need to stick something under your feet in mine. Still, the point is that the bridge shape allows one to make a quilt that delivers similar performance warmth-wise with a significant reduction in weight and bulk.
Quilt looks nice and warm. I'll just go ahead and agree with all that math stuff and be thankful that there is somebody out there that understands all that and allows me to stay toasty warm.
The pictures helped, but still...ouch!
It's one thing to figure that all out.....and yet another to actually make it! Beautiful Grizz!
Honestly, thanks for sharing your thought and construction process...It already answered a couple of nagging questions I had.
...and the quilt looks smashing!
What no video, I feel cheated. I'll just have to come see it in person at Mt Rogers.
It would give Shug a run for his money, for sure.
Looking great Grizz! Very nice. I don't know how you find the time to make all this gear, especially at this time of year. Hoping to get the "grand tour" of it all up at Mt. Rogers.
WOW Grizz! Great quilt!!
Thanks for posting about it. Even the math part wasn't too bad. :D ;)
Very nice looking quilt, Griz.
Awesome writeup, Grizz (and beautiful quilt).
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