# Thread: On the Design of Baffles, Part I: Shapes and Performance

1. ## On the Design of Baffles, Part I: Shapes and Performance

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:
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 you cannot make 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 that wh. 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 set w=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 of w=h=2 would perform the same as a rectangle of w=2 and h=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't too hard 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 our w and h values, 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 in w=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 small w, relative to the h. 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.

2. Well, it is an ambitious task to try and summarize as you have done, always worth voicing your thoughts and understanding ...

Some thoughts on the post
Part 2: most of the points you raise assume that the top and bottom pieces of the quilt are cut the same .... if you look up the quilt calculator by CatSplat and the subsequent "enhancements" by (darn forgot, but it is on the worksheet) this is pretty well addressed and it outlines some design considerations and even has predicted weights/temp ratings etc ... I suspect the majority of the quilts here are designed with that sheet or a derivative of it.

I totally agree that the intended shape is rarely the actual final shape, not only due to the fact that fabric is a flexible media (we like to talk about shapes and stuff, but cloth doesn't usually listen), but also the impact of actually hanging the quilt (or draping), the stresses will change the shape considerably

Part 3
"The first thing to note is that wh. 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"

Not sure if this is poorly worded or maybe just not correct .... I would think baffle spacing (width) doesn't really have much to do with the height of the baffle, as the line suggests ... the second line suggests the fabric weight required for a thinner quilt increases and again, i don't believe this is correct. The weight of both the down and fabric required decreases as the baffle height is reduced, but I suspect that ratio of fabric to down does increase ... but that isn't really surprising and if you substitute synthetic for down the same will be true, as the effective baffle height is reduced the ratio of fabric to insulation will increase. Making this comparison is also open ended in that it will also depend on the Fill Power of the down selected, as the FP decreases, the weight ratio of fabric to down, will be affected less due to the higher weight of the down.

As for Part 3, I am staying tuned for the next installment ... I am a little worried that there is a lot of lab and not a lot of "outside" in the thinking, but I am just designing 2 more quilts and am up to see if I can leverage on the thinking.

Brian

3. Minor note on the "straight walls" thing: there is an exception. If you have compartments that you want to have differently filled for some reason, then the shape will converge to some other curve in between the straight lines here and continuing the circle, depending on the ratio of fill densities.

4. Originally Posted by Cruiser51
Well, it is an ambitious task to try and summarize as you have done, always worth voicing your thoughts and understanding ...

Some thoughts on the post
Part 2: most of the points you raise assume that the top and bottom pieces of the quilt are cut the same .... if you look up the quilt calculator by CatSplat and the subsequent "enhancements" by (darn forgot, but it is on the worksheet) this is pretty well addressed and it outlines some design considerations and even has predicted weights/temp ratings etc ... I suspect the majority of the quilts here are designed with that sheet or a derivative of it.
This is true, the only thing I said about differential cut quilts is the quick note I made at the end of section two. I ran across a version of Catsplat's spreadsheet in my research, and it included a rudimentary temperature rating estimate (based on average baffle height, but that's close enough for the methodology anyway). Their idea of cross-section shape is interesting: they modeled it as a rectangle topped with an ellipse. It gives a shape that "feels" right, but is entirely arbitrary as far as I can tell. Add enough down and it will become a version of the trapezoidal truncated circle that I describe in my note.

Underquilts are kind of a special case when it comes to modeling though. The way gravity acts on them and the fact that they remain undisturbed in use allows them use a wider variety of baffle shapes and still remain essentially stable, and thus Catsplat's calculator works pretty well. Hypothetically, one should be able to use a much boxier (thus more even and better performing) baffle shape, but this is still an area of active research for me.

I totally agree that the intended shape is rarely the actual final shape, not only due to the fact that fabric is a flexible media (we like to talk about shapes and stuff, but cloth doesn't usually listen), but also the impact of actually hanging the quilt (or draping), the stresses will change the shape considerably
Indeed. One of the advantages of the truncated circle shape I describe is that it is much more resistant to these forces -- any force would necessarily reduce the volume available to the down, compressing it. That means the down will exert a counter force resisting it, limiting deformation -- and one can easily overfill the baffle to further increase resistance, without changing the shape of the baffle in the absence of these forces.

For other shapes, forces could change the shape of the baffle without reducing the volume, and sometimes can even increase it. This means the down won't really resist these forces, making the eventual shape much less predictable. Even overfill on its own will end up changing the shape, which is typically not desirable.

Part 3
"The first thing to note is that wh. 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"

Not sure if this is poorly worded or maybe just not correct .... I would think baffle spacing (width) doesn't really have much to do with the height of the baffle, as the line suggests ...
It does for a truncated circle shape. The widest you can go is equivalent to the width of the circle, and the width of the circle is equal to the height of the baffle (at the center).

the second line suggests the fabric weight required for a thinner quilt increases and again, i don't believe this is correct. The weight of both the down and fabric required decreases as the baffle height is reduced, but I suspect that ratio of fabric to down does increase ...
You are correct that it is the ratio that increases, and that is what I meant to convey with the wording "increases the weight of fabric needed relative to the volume down"

but that isn't really surprising and if you substitute synthetic for down the same will be true, as the effective baffle height is reduced the ratio of fabric to insulation will increase. Making this comparison is also open ended in that it will also depend on the Fill Power of the down selected, as the FP decreases, the weight ratio of fabric to down, will be affected less due to the higher weight of the down.
My comparison to synthetic insulation was specifically concerning the sheet kind, like Climashield APEX. This kind of insulation can't shift or settle like down can, so you can use much wider "baffles" compared to down or loose synthetic insulation without worrying about cold spots, and thus save on some fabric/thread weight. And I did not mean to imply that there is a necessarily a point where using synthetic insulation would actually reduce weight (Hypothetically, there is, but its probably at a point so thin that nobody would build it anyway). I was just pointing out that the weight savings of down relative to synthetic get less and less as the quilts get thinner and thinner, so synthetic is most worth considering for thin quilts.

As for Part 3, I am staying tuned for the next installment ... I am a little worried that there is a lot of lab and not a lot of "outside" in the thinking, but I am just designing 2 more quilts and am up to see if I can leverage on the thinking.

Brian
Honestly, that's my biggest concern too. That's why I'm glad I can get feedback from the community to make sure I'm not off in some fantasy land. I appreciate people taking the time to question my different assertions.

Originally Posted by bluesam3
Minor note on the "straight walls" thing: there is an exception. If you have compartments that you want to have differently filled for some reason, then the shape will converge to some other curve in between the straight lines here and continuing the circle, depending on the ratio of fill densities.
You are absolutely right, and this is definitely something that one should keep in mind when using differential filled baffles.

5. This is the CatSplat link to posts and discussion that followed, in case you didn't find that: https://www.hammockforums.net/forum/...ght=calculator

As far as the baffle spacing, I think we may have a confusion of terms .... when I say baffle width I mean the actual distance between baffles .... so I may have a 2" high baffle (quilt thickness) and a baffle spacing of 5" (distance between baffles) .... I could also have a 1" baffle with a spacing of 10", no relationship between those other than that is the design, not saying anything about performance , just that they are not really related.

Brian

6. https://1drv.ms/b/s!Apygyt54yYPwrnwpJrIVOByjm3B7

A PDF of something along these lines I did a few years back if it helps you any.
Yes you got a bit too mathy for this carpenter but overall we are on a similar page I think.

And yes- there is a point where synthetic outperforms down. Specifically at roughly 50* down quilts vs a Primaloft Gold if one factors in the baffle weight and calculates based upon finished weight of the quilt as your measuring stick.
If you leave the lab and go into the real world... one might also consider humidity creep or even individual cluster overlap as well as further reasons to dismiss down in very low loft use. Personally, unless I were in the very dry west I wouldn't carry a piece of down gear rated to less than 40*. Above 40* I would prefer to use synthetic for performance reasons as real world spec differences (weight, pack size, etc) become negligible or even tip in favor of QUALITY synthetic. Inferior synthetic gear is still inferior gear.

Some thing to consider from a carpenter:
Your shell does have both weight and structure.
1-So that limits somewhat the freeform shape a SINGLE baffle could take if you consider the baffle shape cross section of the full quilt.
2-Gravity and shell tension will limit the down's expansion somewhat as well.
3-Differential cut or the finished shape of a quilt IN USE (vs sitting on a flat table) will also be a factor.

Point being- your baffles are not rectangles, but they are not free flowing shapes drifting to circles either.
Overfilling them will cause them to deform to a circular shape... shrinking the width of your quilt... though one could design for it as I believe you noted you'd get more thermal bridging at the baffle if your baffles get too circular.

Your ideal design holds a uniform thickness and density of down into the shape you will use the piece of gear.

Underfilling a top quilt is less of an issue than underfilling an UQ.
In the top quilt gravity will put the down close to the heat source... and of course heat rises to fluff the down as well.

In the UQ, gravity can pull the down away and cause thin layerl of air to form. As you noted- heat is lazy and will not simply pump downward into your UQ but will rise along the underside of the hammock and out. I find that you can 'blow' the top quilt calculations or fill amount much more readily than on the UQ and your loft charts should not be equal when discussing the two very different pieces of gear.

There have been some discussions on the detriment of overfilling (increased density) but those impacts are debatable... and perhaps you could even make an argument for a very densely filled UQ with 2" baffles vs an 'ideal' filled UQ with 3" baffles. So overfill isn't really a performance breaker or concern about functionality... though it may harm your wallet, pack size, and gram weenie.

Quilts are pretty easy if you don't worry too much about cost, weight, or specific temperature limit.

Getting a 40* quilt that performs at exactly 40* for the lowest possible cost and weight (for a given fill power) is a truly fine art that could occupy a lifetime's worth of study.

But spending \$20 and 2 ounces more to carry a 30* quilt for 40* temps is not too challenging.
Nor is getting really close and spending \$10 and an ounce to be sure.
As many a crappy trim carpenter will tell you- 'Do your best and caulk the rest'.

There is no such thing as 40*.
A poem by Just Bill

40 in spring is not 40 in fall.
40 and windy is not 40 and calm.
40 and happy is not 40 and sad.
40 when raining is not 40 when sunny.
40 and 40 years old is not 40 and twenty years old
40 when dehydrated or tired is not 40 when well oiled and rested.
40 with a belly of cold spring water is not 40 with a belly of hot chocolate.

40 is a number and means nothing to the trees.
40 has meaning only on paper and requires no degrees.
40 in the laboratory and testing chamber is found often with great ease.
Spend enough time outside them and you will soon see; 40 is nothing but words on the breeze.

7. Originally Posted by Cruiser51
This is the CatSplat link to posts and discussion that followed, in case you didn't find that: https://www.hammockforums.net/forum/...ght=calculator

As far as the baffle spacing, I think we may have a confusion of terms .... when I say baffle width I mean the actual distance between baffles .... so I may have a 2" high baffle (quilt thickness) and a baffle spacing of 5" (distance between baffles) .... I could also have a 1" baffle with a spacing of 10", no relationship between those other than that is the design, not saying anything about performance , just that they are not really related.

Brian
It could be we are talking about different things. Just to be sure, I have included a diagram showing what I am talking about:
bafflewh.png
Blue is the baffle, while the dashed line is the limiting circle. The width value can be whatever you want and the shape will still work, so long as it stays within the circle. The top and bottom of the baffle are composed of the parts of the circle that fall between the baffle walls. The circle is not allowed to be stretch or deformed in any way for my baffles, as then the area to perimeter ratio would no longer be maximized. Of course, other baffles can be designed so that they are wider than they are tall, but if you add enough down to them they become that truncated circle shape.

Originally Posted by Just Bill
https://1drv.ms/b/s!Apygyt54yYPwrnwpJrIVOByjm3B7

A PDF of something along these lines I did a few years back if it helps you any.
Yes you got a bit too mathy for this carpenter but overall we are on a similar page I think.
That's a nice PDF you threw together! We do seem to be on the same page, you basically just end a step before I do. You correctly note that adding overfill to a typical baffle increases "bulge" until it it reaches a "balance point". What I have done is shown the shape of the baffle at that balance point — in other words, the shape that encloses the most area for a given perimeter provided two straight walls. It is the shape that all other baffles will reach, given enough down. I'm just designing the baffle to be that shape from the get-go.

And yes- there is a point where synthetic outperforms down. Specifically at roughly 50* down quilts vs a Primaloft Gold if one factors in the baffle weight and calculates based upon finished weight of the quilt as your measuring stick.
If you leave the lab and go into the real world... one might also consider humidity creep or even individual cluster overlap as well as further reasons to dismiss down in very low loft use. Personally, unless I were in the very dry west I wouldn't carry a piece of down gear rated to less than 40*. Above 40* I would prefer to use synthetic for performance reasons as real world spec differences (weight, pack size, etc) become negligible or even tip in favor of QUALITY synthetic. Inferior synthetic gear is still inferior gear.
That is good to know! I'm glad someone sat down and did the working out. I guess that's why I don't see much down gear rated for temperatures above 40ºF.

Some thing to consider from a carpenter:
Your shell does have both weight and structure.
1-So that limits somewhat the freeform shape a SINGLE baffle could take if you consider the baffle shape cross section of the full quilt.
2-Gravity and shell tension will limit the down's expansion somewhat as well.
3-Differential cut or the finished shape of a quilt IN USE (vs sitting on a flat table) will also be a factor.
You are right on all counts. 1 I decided to ignore, just because I figured the effects would be pretty small and hard to measure. 2 is the trickiest part, and the one that I am trying to tackle currently. As for 3, differential baffles are actually easy to model with these baffle shapes. I have not touched upon it at all yet, but it is the likely subject of a Part III. If I can get some solid answers, 2 would be included in that as well.

Point being- your baffles are not rectangles, but they are not free flowing shapes drifting to circles either.
Overfilling them will cause them to deform to a circular shape... shrinking the width of your quilt... though one could design for it as I believe you noted you'd get more thermal bridging at the baffle if your baffles get too circular.

Your ideal design holds a uniform thickness and density of down into the shape you will use the piece of gear.
This is the one place you are wrong -- no matter what value you choose for a width or height, my baffles are already fully circular, as far as the down is concerned. As I said before, my shapes are already at the "balance point", as you put it. And while uniform depth and density is ideal in some sense, what I am trying to accomplish is to get as close to that as possible while minimizing weight, a slightly different problem... but there will be more on that in Part II.

Underfilling a top quilt is less of an issue than underfilling an UQ.
In the top quilt gravity will put the down close to the heat source... and of course heat rises to fluff the down as well.

In the UQ, gravity can pull the down away and cause thin layer of air to form. As you noted- heat is lazy and will not simply pump downward into your UQ but will rise along the underside of the hammock and out. I find that you can 'blow' the top quilt calculations or fill amount much more readily than on the UQ and your loft charts should not be equal when discussing the two very different pieces of gear.
We are actually both right on this, what matters is the degree of underfilling. My point was meant to be for a small amount of underfill, relative to what you call the balance point. Most baffle shapes are underfilled in this sense, by a few percent. For an underquilt, gravity helps compress the shape in a way that reduces area overall, allowing the down to completely fill the shape and avoiding that performance reducing air gap that you mention. Underfill by too much of course, and then you get that gap.

There have been some discussions on the detriment of overfilling (increased density) but those impacts are debatable... and perhaps you could even make an argument for a very densely filled UQ with 2" baffles vs an 'ideal' filled UQ with 3" baffles. So overfill isn't really a performance breaker or concern about functionality... though it may harm your wallet, pack size, and gram weenie.
I've actually done out the math on this, but I'll be brief since this topic is worth its own post. First not-so-well-known fact, each oz of overfill performs about 33% worse compared to that same oz at full loft (at least until you overfill by 250% or so). So if you wanted to increase performance by 8%, you'd have to add 12% more down. This needs to be compared to the weight gain from extending the baffles ~8% and adding ~8% more down instead. How worthwhile this is depends on fabric weight, and fill power, baffle shape, and how big of a performance increase you want. As a general rule it is more worthwhile to overfill smaller baffles for performance gains than larger ones, and even then only to increase performance by a few percent. As far as I can tell, the breakeven point is above the 40ºF rating for reasonable values of those variables, so you should never overfill purely for thermal performance.

Quilts are pretty easy if you don't worry too much about cost, weight, or specific temperature limit.

Getting a 40* quilt that performs at exactly 40* for the lowest possible cost and weight (for a given fill power) is a truly fine art that could occupy a lifetime's worth of study.
Eh, it took a few days...

In all seriousness though, if your willing to throw away enough variables it's easy enough. Deciding to discard outside forces like gravity and tension, and focus on minimizing down shifting gets you to the truncated circle shape. Minimizing weight from there for a given R-value is just the matter of plugging in some values and doing some multivariable calculus, and will be the subject of Part II. It's not quite real life, but it is closer than everything else I have found, so it should be useful. The bigger problem is the 40ºF thing, as your lovely poem points out.

But spending \$20 and 2 ounces more to carry a 30* quilt for 40* temps is not too challenging.
Nor is getting really close and spending \$10 and an ounce to be sure.
As many a crappy trim carpenter will tell you- 'Do your best and caulk the rest'.
Yeah, I have a bit of a problem when it comes to optimization. I just enjoy doing the maths too much. For all this effort, I think I'm able to save an ounce or so on a 40ºF — better than I was expecting, but still not much.

8. My apologies as I misspoke slightly: my use of 'you/your' meant to mean more of a general sense of the baffles in anyone's particular design rather than the baffles you personally laid out.
I think that misled you slightly and caused some confusion.

For example:
"Your ideal design holds a uniform thickness and density of down into the shape you will use the piece of gear."

If I had said "An" ideal design rather than 'your' I believe we are on the same page mainly.
You mentioned synthetic batts being nearly ideal earlier in that they are easier to work with vs. loose fill.

Really if one is looking to optimize... and generally agrees with a loft chart (or converted to R-value) for a given target rating:
The goal should be to deliver that loft uniformly with the least material.

I believe that was the point cruiser was driving at in discussing baffle spacing (width) and what I was getting to regarding the whole quilt rather than a single baffle in isolation.

If height is the driver that dictates warmth in the finished quilt... we need to choose a width that creates the least amount of deformation possible to maintain uniform loft. This is balanced against the need to use the least amount of shell material.

Generally speaking (in real world) the lower the loft the tighter the baffle spacing.
If you wanted a 2" thick piece of gear one might think to increase the baffle spacing to 10" and eliminate baffle material.
Because we all agree that the 2"hx10"w rectangle would quickly deform towards a circle... we'd have to keep pumping in down to keep it filled and our average height would quickly rise beyond our goal of 2" thick at the center. A 2 to 1 ratio is decent starting place, but many push that 2"hx 4"w to 2"x5".

In some sense what you are modeling is a typical down puffy jacket. A mid weight model frequently has a 3/4" high by 1" wide baffle design.
The next level up would be a 1" x 1.5" baffle spacing.

A few tricky variables are missing that make what you are trying to do difficult, so in some sense you've thrown out a few variables already.

Lets consider a baffle as a balloon:
Or ideally as a soap bubble which would want to form a perfect sphere as that is the ideal volume to surface area shape.

Adding down is like blowing up the balloon... which might be measured in PSI of air or in this case a variable we don't know.
PSI- Expansion power of down fill (based upon fill power) is one; tied tightly to real world fill power vs laboratory conditions.

From there- we might note that we require additional PSI to inflate said balloon based upon the material properties of the balloon itself. If the balloon is very thin or very thick, if it's under tension already or not. So the actual weight of your shell material will allow or limit the expansion power of the fill to achieve it's ideal shape.

In theory we have Cubic inches of volume per ounce but that is calculated under a specific conditions test in a specific vessel.
In a long tube shaped baffle there is less resistance over the length of a baffle as opposed to in cross section. So in real life we often find that a well filled baffle will do a better job of eliminating dead spots in the LENGTH of the tube rather than expanding in cross section. In cross section we can discuss the x and y axis expanding... but in the z axis there is almost zero resistance to expansion present... certainly much less than in x and y.

So in reality, even in a single baffle condition, we find that we don't really have a spherical balloon but what we have is the relatively fixed diameter hot dog shaped balloon that gets longer, not fatter as it is inflated. It takes exponentially more force to increase the diameter of this type of balloon as opposed to filling it's length. You must inflate to the maximum length before you even begin to have enough volume of air to attempt to build enough pressure to increase diameter.

How would one calculate this I am not sure.
Again we have not even considered things like shell material weight, gravity, humidity, etc.

It is true that the rectangular baffle does deform... but within limits. Much like that first puff of air into a balloon animal balloon does alter it's shape from a listless shell into a tube... However once going the balloon grows in length, not diameter. At some point though... you would have to increase PSI... or in our case density of fill to a point where it becomes inefficient to do so.

It is this balance of cross sectional baffle shape in the x and y axis we shoot for so that the length of our baffle (z axis) is fully filled with no cold spots. We want to get in just enough down so that we puff up a bit past a true rectangle that is filled end to end... but not so much that the density increases and down fill is wasted. That is why it's a bit unrealistic in the real world to achieve the more dramatic perfectly circular shape. I think at best you could think of cutting out your baffle from a football rather than a basketball.

Again... we are still isolated to a single baffle.

Let us go to two baffles... or ten. Each of these competing or pulling against each other for the adjoining shell material if one is looking at an outer and inner shell joined by strips of baffle material.

If your 5" wide baffle deforms to 4" wide... it needs to pull a half inch from each adjoining baffle to do so.
Yet each of those baffles is fighting for the same thing. In much the same way if one were to push enough circles together they are forced into a honeycomb shape no matter how much you'd like each individual cell to remain a circle.

Not that could not be overcome with enough fill as we are only building one layer of cells thick... but if efficiency is the name of the game it's not ideal to create this condition.

If 10 baffles at 5" wide make up your 50" wide quilt (and we agree you need 50" wide to cover you)...

If these baffles deform to 4" we now need 12.5 baffles to cover the same 50"

Without getting fancy- we need more shell material and more fill to do this.

It is wrong to calculate a simple 2"x 5" rectangle.
And eye opening how down is needed for as little as 1/8" in depth and width due to deformation towards a circle.
However I'd argue that it is also wrong to keep pumping in down once you've achieved a full chamber.

Many here have not understood this concept and tried making a 50" wide quilt only to find it ended up 45" wide after they kept shoving in an extra bit of down into it 'just in case' and inadvertently overfilled the bag.

Just as many do the opposite and figure down for a non-expanding fixed geometry 2" x 50" rectangle and wonder why they have a listless and useless piece of gear.

Understanding fill, overfill, and overstuff is the lifetime of work. Not necessarily the geometry or calculus or thermal calculations. The nuts and bolts of it... the material properties and realities that would require decades of study to quantify or identify into something useful... or even measurable.

I joked on a bridge thread not long ago that I like science, rules, ratios, and math too.
But a good bit of 'voodoo' is often needed as well. Or perhaps better stated a bit of art or bad poetry.
I'm smart to a point- but a bit of intuition, artistry, and simple craftsman's instinct for how things really work is needed to get you from a sweet idea on paper to a satisfied customer in the woods.

I'm all for optimization... nothing the natural world likes better really.

'Mitakuye Oyasin' is what the earth has to say on the subject and remains the most useful.
'We are all one, we are all related' is roughly what that translates to.

All things in balance more or less.

Don't mean to shart in your cheerios. Sleeping gear needs more science applied to it, but that science does have some limits and dead ends to it as well. Or perhaps you've cracked it and it's flown over my head.

My comments are not to discourage you, but to point out a few of the holes so you can plug them if you're able.

9. This is a most interesting discussion and I am intrigued by the reasoning as I have been trying to design an UQ for a while now. I find it odd that the diagrams used so far are all depicted with the width of the baffle being depicted equally spaced at the inner shell and the outer shell. This may work fine for an UQ being used on a bridge hammock but not so good for use on a GE hammock- reason being that (when in use) the inner shell is a smaller radius and the outer shell is a larger radius, therefore shouldn't the spacing of the baffles (w) be less/ closer together on the inner shell and further apart on the outer shell to maintain a given loft which in reality is the objective? Another consideration is that in use the inner shell will not be ballooning out/up because it will in fact be up against your backside and therefore be flattened or actually depressed into the baffle chamber area which will decrease the available area volume in which the down is located? I'm no engineer but I like solving problems- such as this and if I have not thought this out properly please correct me- that way we all learn.

10. Originally Posted by ylnfrt
This is a most interesting discussion and I am intrigued by the reasoning as I have been trying to design an UQ for a while now. I find it odd that the diagrams used so far are all depicted with the width of the baffle being depicted equally spaced at the inner shell and the outer shell. This may work fine for an UQ being used on a bridge hammock but not so good for use on a GE hammock- reason being that (when in use) the inner shell is a smaller radius and the outer shell is a larger radius, therefore shouldn't the spacing of the baffles (w) be less/ closer together on the inner shell and further apart on the outer shell to maintain a given loft which in reality is the objective? Another consideration is that in use the inner shell will not be ballooning out/up because it will in fact be up against your backside and therefore be flattened or actually depressed into the baffle chamber area which will decrease the available area volume in which the down is located? I'm no engineer but I like solving problems- such as this and if I have not thought this out properly please correct me- that way we all learn.
One problem at time

But you are quite correct and that was the differential cut mentioned by Cruiser or my comments about 'in use' shapes.

It helps to look at a flat quilt first (or mild curve).

As far as flatness goes:
A top quilt in a hammock is about as flat as it gets- no real shaping needed.
A top quilt on a back sleeping ground dweller or bridge user is pretty close to flat and folks like Enlighted Equip don't differentially cut their top quilts to keep costs down.

An UQ on a flat bridge is for sure a curved shape, and should have a differential cut.

A top quilt on a side sleeping ground dweller or bridge user is about roughly as curved as a gathered end UQ; both of which are 'U shaped' Most if not all folks who make these professionally shape the quilts in some way.