Measuring deflection of an untreated foam sample26th September 2022
I’ve been looking at thisbike camper ideasome more. I realized that it tickles my brain because it’s sort of aninsoluble problem. There’s so many axes to simultaneously optimize, andmany conflict. For example, strength vs. weight for towing, cost vs.not-spending-a-ridiculous-amount-on-a-silly-idea, large sleeping spacevs. drag while towing, etc. As a bonus, it’s also 100% un-useful andimpractical which always makes things more fun!
Standard little “foamies” are built from XPS (pink/blue rigidinsulation), Titebond II glue, canvas cloth, and coats of exteriorpaint. Depending on the size and shape, there’s generally additionalsupport pieces made using traditional wood, aluminum, or steel.
For a bike trailer in particular though, and preferably non-ebike, I’dlike to really emphasize the “lightweight” axis while still keeping itusable.
So! I’m learning what I assume is some first-year engineering. That is,Real Engineering that involves atoms, not the pretend software-stylethat largely concerns itself with trolling on Twitter1 while waiting forthe linker.
(I apologize in advance if I use engineering terminology improperlyand/or butcher your discipline, please feel encouraged to sendcorrections.)
XPS rigid insulation (foam) has very good compression strength, and soit’s a great material if any forces applied to it are spread out. Butthe surface isn’t very tough (sort of squishy on top, and pieces easilychip off), and it’s quite flexible and will yield and crack very easilyunless it’s extremely thick. So, the good points:
Another material used in place of fibreglass or canvas (by RC planemakers, I believe) is kraft paper. This is moderately thick paper,pretty much like a brown paper shopping bag from the grocery store.
When this is stuck to the foam, it gets surprisingly much more rigid. SoI’m attempting toDo A Science to get a guess as to whether a trailermade out ofonly foam, paper, glue, and paint would be durable andlightweight enough to be useful.
The first round of tests are intended to get an idea of how the tensilestrength is improved. I did this by setting up pieces of 3” by 24” foamthat’s 1” thick.
The kraft paper is first wetted down, a layer of glue applied to thefoam surface, the paper laid, then more glue applied to the top of paperand then rolled in. For the multiple layer samples, the lower layers areallowed to fully dry (24h+) before doing the next layer.
This all results in a delicious foam and paper sandwich.
How does this affect the tensile strength? Imagining that you’re pushingdown on the middle, the sandwich helps because the paper doesn’t stretch(very much). This means that the bottom side of the foam can’t getlonger and the top side can’t get shorter (at least until the sandwichbreaks in some way), so it makes it less bendy.
To measure how well this works, the test pieces are laid across a gap asif they were a bridge and put a weight on the very middle of the span,measuring how much it bends (deflects).
Measuring deflection of an untreated foam sample
Measuring deflection of a foam sample covered in kraft paper
Starting with untreated, measure the distance from the table to the foamwith and without one and two pound weights added. This is also donetwice flipping the sample over, and taking the average because the foamtends to have a natural bend one way or the other.
I repeated these measurements with various samples:
In all cases, the covers are attached with Titebond II glue, inparticular for the fibreglass – it’s not using resin or epoxy, it’sjust glued on too.
Here’s the raw deflection data.
| Nominal | 1 lb | 2 lb |
|---|---|---|
| 3.5405 | 3.0680 | 2.6805 |
| 3.5115 | 3.0980 | 2.7355 |
| Nominal | 1 lb | 2 lb |
|---|---|---|
| 3.3840 | 3.3425 | 3.3100 |
| 3.6470 | 3.5475 | 3.4795 |
| Nominal | 1 lb | 2 lb |
|---|---|---|
| 3.9165 | 3.8750 | 3.8220 |
| 3.1490 | 3.0895 | 3.0415 |
| Nominal | 1 lb | 2 lb |
|---|---|---|
| 3.6415 | 3.5830 | 3.5195 |
| Nominal | 1 lb | 2 lb |
|---|---|---|
| 3.5790 | 3.5295 | 3.4810 |
| 3.5340 | 3.5115 | 3.4740 |
| Nominal | 1 lb | 2 lb |
|---|---|---|
| 3.4040 | 3.3635 | 3.3425 |
| 3.7310 | 3.7085 | 3.6910 |
There’s two measurements for each type, testing with both sides upbecause there’s a curve. “Fibreglass B” is missing because I did such abad job of fibreglassing that the bubbles on that side made itimpossible to measure. Also note that there’s substantially moreaccuracy implied by the number of digits after the decimal point thanthere really was.
Now, taking the raw deflection measurements, and using “untreated” as anexample, calculate the difference between nominal and with-weight. Then,take the two deflection amounts, and average them:
\[\begin{align}\delta{}C_1 & = 3.5405 in - 3.0680 in = 0.4725 in \\\delta{}C_2 & = 3.5115 in - 3.0980 in = 0.4135 in \\\delta{}C & = (0.4725 in + 0.4135 in) / 2 = 0.443 in \\\end{align}\]So, untreated, the foam deflected an average of \(0.443 in\) under a 1lb weight.
Next, bust out theSerious Engineering 101 to calculate the foam’smoment of inertia: \(\frac{width * height^3}{12}\)2
\[I = (bh^3)/12 = (3 in * (1 in)^3)/12 = 0.25 in^4\]I assumed this was constant even though it isn’t exactly. For example,the coverings aren’t zero-width.
Then use themoment of inertia to calculate themodulus of elasticity,which is the useful thing: \(\frac{force * length^3}{48 * I \delta{}C}\)3
\(I\) is themoment of inertia from above, \(\delta{}C\) thedeflectionmeasured.
\[E = \frac{FL^3}{48I\delta{}C} = \frac{1 lb * (24 in)^3}{48 * 0.25in * 0.443in} = 2600 PSI\]Repeat that mess for both one and two pound samples, and for all thecandidates. Assuming I did any of that correctly, here’s the PSI measurements.
| Sample | PSI |
|---|---|
| Untreated 1lb | 2600 |
| Untreated 2lb | 2816 |
| Kraft 1/1 1lb | 16340 |
| Kraft 1/1 2lb | 19080 |
| Kraft 2/2 1lb | 22811 |
| Kraft 2/2 2lb | 22811 |
| Fibreglass 1lb | 19692 |
| Fibreglass 2lb | 18885 |
| Kraft 1/2 1lb | 32000 |
| Kraft 1/2 2lb | 29164 |
| Kraft 2/3 1lb | 36571 |
| Kraft 2/3 2lb | 45399 |
Because the force (weight applied) should be factored out, the 1 and 2lbought to be the same. For the stiffer samples, the 1lb didn’t deflectvery much so the measurements were likely poorer. In any case, somewherebetween the 1 and 2lb PSI are about what I measured. So averaging thePSI measurements again, and sorting:
| Sample | PSI (average) | |
|---|---|---|
| Untreated | 2708 | |
| Kraft 1/1 | 17710 | |
| Fibreglass | 19288 | |
| Kraft 2/2 | 22811 | 4 |
| Kraft 1/2 | 30582 | |
| Kraft 2/3 | 40985 |
Interestingly, this puts a single layer of kraft at almost exactly thesame stiffness as a single layer of light fibreglass. With the caveatsthat I did a terrible fibreglassing job, that the fibreglass is slightlylighter than the paper, that the fibreglass I got was very lightweight,and that my measurements are crappy, this is still pretty cool. Also, 3layers on the “outside” are more than twice as stiff as a single thinfibreglass layer.
However, given that Idid do a terrible fibreglassing job whereasthe kraft goes on pretty well even when applied with no skill orpractice, I feel pretty good about ploughing onward with kraft paper. Mycurrent plan then is either one or two layers on the inside of thestructure, and three on the outside (as it’s more likely to get bashedand will be closer to water, etc.).
Speaking of water, another test I really ought to do is a more thoroughapplication of some sort of exterior paint to make sure it can bewaterproofed. But I think there’s enough options that that explorationcan be deferred until I’m actually ready to paint. Or I’ll just choosesomething cheap and go for it.
I also noticed that uneven application (i.e. more layers on one sidethan the other) seems to cause foam to warp, so “Kraft 0/3” probablywouldn’t work that well.
In what I feel is an admirable show of self-restraint, I didn’t even href any SWE’s twitter to “Twitter” here. ↩
Just because! This is Engineering and I don’t need to hear about “why are doing this?”. This number goes in the next crazy formula, so we’re darn well going to get it. ↩
Look, we’re second-string programmers pretending to be civil engineers building a bridge out of foam and paper. Just plug the damn numbers in. ↩
That 2/2 is measured as weaker than 1/2 is not a show of strength for my data. This is likely because 2/2 was the first one I did, and I didn’t wait for a full cure between layers, so it’s probably more like “1.5/1.5” or worse. ↩
Comments or corrections?Feel free tosend me an email.Back to thefront page.