I recently decided to make a down quilt for myself, and was having a hard time finding resources on baffle design, even very basic things like shape. So I did my best to figure it out myself, and compiled what I learned here. I'm not sure how much of this is common knowledge, but I feel like there is at least some new stuff here. I kept my focus on long tubular baffles, not karo step or anything like that (at least for now). I use the term "box baffle" throughout to refer to the cross section of a tubular baffle with two sides, not the alternate baffle system similar to karo step. As a reminder though, I have made exactly 0 quilts to date, whereas many on this forum have a lot of experience with this. Take everything here with a grain of salt. Still, I hope others find it useful, or that it at least raises some interesting points.

1. Why Use Baffles?

The point of baffles is to hold the down in place and prevent it from shifting and distributing itself unevenly. Box baffles do this by both restricting the number of directions the down can move, and by applying constant force on the down from the fabric so that the down locks itself in place. In a completely un-baffled quilt, the down can move just about anywhere -- pick such a quilt up by one edge, and the down will all move to the opposite edge. Do the same to a properly designed baffled quilt, and the down will not move at all.

2. Basic Shape

Naively, one might think that this is what box baffles are shaped like:

badbaffle.png

That is, that they are rectangles capped with semicircles or arbitrary circular arcs, the exact shape of which left up to the designer.

In general, this is not the case.

A box baffle properly filled with down will take the form of specific type of shape, and only that type of shape. The shape in question is what I will refer to as a truncated circle:

goodbaffle.png

It is what it sounds like, a circle with a part on either side cut off and replaced with vertical walls. This isn't to say youcannotmake a baffle shaped differently; in fact doing so is trivial. But no other shape will be stable.

The reason has to do with how much area can be enclosed in a given perimeter. Imagine for a second that you sewed yourself a rectangular prism, we'll say 1"x1" with some arbitrary length. You calculate the volume, and fill it with the equivalent volume of down. When you finish up, you realize that you do not have a rectangular prism, but some sort of deflated circular tube shape. You can force it into a prism if you try, but it will never stay that way. You decide to fill it with more down, and eventually you get to the point where your deflated tube becomes a regular tube, with a circumference of 4".

Baffles work a similar way. You can cut and assemble the fabric for whatever baffle shape you want, but once you put it together it will be different -- how much different depends on how unreasonable your desired shape was. Further, if you add enough "overfill", the baffle shape will eventually become a truncated circle, as a truncated circle encloses the most area for a given perimeter (taknig the two "rigid" baffle walls into account). This also means that, if you design a quilt with a different baffle shape and no overfill, your quilt will functionally be under-filled, and thus experience more down shifting and have a less stable thermal performance.

This is not to say alternate baffle shapes are necessarily wrong. Sometimes, there is even reason to use these shapes despite these disadvantages. For example, using more widely spaced baffles cuts down on weight, and so may be worth the performance hit in some applications. Plus, other forces can get involved to help maintain certain baffle shapes, like gravity (like our "deflated tube" earlier) keeping down shifting managable, if not at an absolute minimum. Further, in applications like underquilts, being under-filled does not matter very much. It is just important to keep these trade-offs in mind when you decide on a baffle shape.

It is also important to note that the differences we are talking about are usually pretty slight. In practice, the shapes most people choose for their baffles are reasonably close to the ideal, usually within 5 or 10%. Their quilts just come out with slightly different dimensions than they were expecting, and perform slightly worse. Its not a huge difference, there is just no reason to settle for it unintentionally.

A side note: Differential baffles work the same way, but instead of vertical walls they have angled walls (like a trapezoid). The total curve of the quilt is determined by the sum of the angles, making it very easy to model.

3. Shape and performance

Lets assume you want minimize down shifting. That means we've narrowed down the category of shape for the baffle, but there are still some variables to play with. The first is the baffle height,h, which I will use to refer to the height at the center of the baffle. It is equal to the diameter of the circle used to design the baffle. The other variable is the baffle width,w, which I use to refer to as the distance between the baffle walls.

The first thing to note is thatw≤h. This means that thinner quilts will necessarily have smaller, more closely spaced baffles. This increases the weight of fabric needed relative to the volume down, and reduces down's weight savings relative to synthetic insulation (which is available in sheets that do not have the same baffle requirements). Just something to keep in mind when optimizing for cost, though I think it is well agreed upon that anything meant for 40ºF or below is worthwhile for down.

If we setw=h, then we have sewn-through baffles. They are sometimes used in thinner quilts. The idea is that they save both weight and money, the trade-off being cold spots on the edge of the baffles. They do definitely save money, as installing baffles uses more materials and is more time intensive. However, they do not actually save weight.

The reason has to do with how heat works. Naively, one would guess that a sewn-through baffle ofw=h=2 would perform the same as a rectangle ofw=2 andh=π/2. After all, both shapes use exactly the same amount of insulation, and so should block the same amount of heat. The average thickness is the same for both shapes. However, you can't just average thickness like that to find thermal performance. In fact, the sewn-through baffles will allow about 19% more heat through overall! The reason is that heat is lazy, and will preferentially travel through where the material is the thinnest. It isn'ttoohard to figure out exactly how much extra heat escapes. Warning: things are going to get mathy.

Some background on how thermal performance is measured. As consumers of quilts, usually all a manufacturer tells us is the "temperature rating", which is somewhat arbitrary. Where I most commonly encounter actual units expressing thermal resistance is home insulation, for which R-values are typically provided. Since they are what I am most familiar with, I will use R-values throughout this post. Here is the US, R-values are expressed in (h*°F*ft2)/BTU, and are often provided per inch of material depth. The numbers themselves don't have much intuitive meaning, but they are easy to compare. Something that is R8 blocks twice as much heat as something that is R4, and if you put two R4 rectangles on top of each other you get an R8 rectangle. Using the National Institute of Standards and Technology Heat Transmission Properties of Insulating and Building Materials Database, I was able to determine that duck down has an R-value of approximately 3.93 per inch of down. I've heard goose down performs about 12% better, and that fill power doesn't matter for performance, but I'm not sure if either of those things are true. In theory, R-values should be easily (and linearly) convertible to a temperature rating, but I will leave that as an exercise for the reader.

To find the mean R-value for some assemblage of material, one needs to take the mean of the R-values weighted by there areas. But not the geometric mean, which is the kind of mean that we are used to (and would make the previously mentioned rectangular and sewn-through baffles equivalent). Since R-values represent a rate, we need to take the harmonic mean weighted by the areas instead, which is the inverse of the sum of the inverse R-values.

While the harmonic mean works great for discrete shapes, our baffles are curved. That isn't a problem though, all we need to do is take sum up the R-values from arbitrarily small slivers from under the curve to find an approximate area... wait a second, that's the definition of the antiderivative! That's right baby, it's calculus time, and we're breaking out the integral! I bet this isn't where you were expecting this to go. Don't run away yet though: I know not everyone is as excited about math as I am, but the good news is that we get a pretty simple equation at the end.

Since we are dealing with circles, the maths are actually pretty easy. The equation for a semicircle in the plane centered at 0,0 is:

CodeCogsEqn.gif

For our baffles, we can determine the R-value by multiplying that equation by our R-value per inch value (3.93), doubling it (as we have a full circle instead of a semicircle), inverting it, taking the antiderivative over the length of our baffle, dividing by the length of the baffle, and then inverting again. Using ourwandhvalues, we get the integral:

CodeCogsEqn(1).gif

Thankfully, that works out to be equivalent to the much simpler

CodeCogsEqn(3).gif

Now we can use this equation we can use to determine the performance of our baffles. Plugging inw=h=2 for our sewn through baffle, we get that the R value is almost exactly 5, compared to the rectangle which would have an R value of 3.93*π/2, or about 6.2. That's where we get the 19% difference in performance! Of course reality would never work out quite so precisely, as even the fabric has enough of an R-value to cut that percentage to 15% or so. Even considering that, that is enough of a difference that a blanket with smaller box baffles can match the performance using less fabric and down, and thus being lighter than the stitch-through baffle (still more time consuming though).

So now we know the baffles with the best performance are the ones with a smallw, relative to theh. But if you make the baffles too narrow, then you'll be using too much fabric, bringing up the weight again. That means the baffles must be neither too wide or too narrow, relative to the height. So how do we determine the lightest possible baffle for a given R-Value? Tune in later this week for part two: Optimizing Baffles.

Edit: Clarified my use of the term "box baffle"

Edit 2: Fixed final equation to be topped with w*3.93, not 2*3.93, and to use w in place of l.

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