Intro:
I want to keep this article as scientific as possible. I don't want my opinions in it, but rather just the facts. In wanting to keep my methods of testing pure, I will first share with you what I did.
Weighing:
I bought an OXO Good Grips food scale from Target. It has a pull out display which turned out to be a blessing. The only real way for me to get the entire sheet of foam board on the scale and not touching anything else was to center it on the scale. Which left no room to actually see the display. So I hung the pull out display from the end of a table allowing me to look under the foam board to see the reading.
I'm not sure how accurate the scale I used is. Sometimes I would get one reading, then re-measuring I would get one gram higher or lower. All of the weights I have on this articles are the ones that came up the most and that I felt like was the most accurate. I did measure all of the weights multiple times. It may still be off by a gram, but that small of a possible error isn't an issue.
Testing strength:
I cut out 10" x 20" pieces of foam board. Then I placed them on the seats of two chairs. I kept the chairs at the same distance apart and I put the foam board pieces on the chair in the same direction. I will note that I am unsure if foam board has a grain to it. (More detail on possible grain at the end of this article.)
I added bottles of water to the center of the foam board until the foam board crumpled in the middle, causing the foam board to fail. I tried to keep the weight in the center and not distributed, but it is kind of hard to properly do that when dealing with 8 or 9 bottles of water.


Results:
Adams brand
Bought at Dollar Tree
Price: $1.00 (not including tax)
Sheet size: 20" x 30" x 3/16" measurements were double checked and are true.
Total weight of sheet: 115grams
Weight per one square inch: 0.191666grams
Test 1: 10" x 20" piece weighing 38grams, broke right away when third bottle of water was added.
Test 2: 10" x 20" piece weighing 38grams, broke a few seconds after third bottle of water was added.
Each bottle of water weighs about 525 grams.
Test 1: Broke with 1575grams of weight.
Test 2: Broke with 1575grams of weight.
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Elmer's brand
Bought at Target
Price: $2.99 (not including tax)
Sheet size: 20" x 28" x 3/16" measurements were double checked and are true. note that this sheet is smaller than the other two.
Total weight of sheet: 224grams
Weight per one square inch: 0.4grams
Test 1: 10" x 20" piece weighing 80grams, broke when tenth bottle of water was added. Plenty of time was given between when bottles were added.
Test 2: 10" x 20" piece weighing 80grams, broke before tenth bottle was fully put on.
Each bottle of water weighs about 525grams.
Test 1: Broke with 5250grams.
Test 2: Broke with 5250grams.
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Flip Side brand
Bought at World of Variety (local craft shop)
Price: $3.99 (not including tax)
Sheet size: 20" x 30" x 3/16" measurements were double checked and are true.
Total weight of sheet: 249grams
Weight per one square inch: 0.415grams
Test 1: 10" x 20" piece weighing 83grams, broke a few seconds after the eighth bottle was added.
Test 2: 10" x 20" piece weighing 83grams, broke shortly after the eighth bottle was added.
Each bottle of water weights about 525grams.
Test 1: Broke with 4200grams.
Test 2: Broke with 4200grams.
Notes:
I noticed that the paper on the Adam (Dollar Tree) brand is a lot thinner and is easy to peel off. Elmer's and Flip Side are about the same and it is hard to peel off the paper. It is to the point where foam goes with the paper when you peel it off of Elmer's and Flip Side; But with Adam, you can easily remove the paper without affecting the foam.
The Adam (Dollar Tree) brand foam board is a lot easier to cut. Almost no resistance at all where as the Elmer's and Flip Side brand it can be more difficult and is common to have to cut twice to actually get the paper cut that is against the cutting surface. Elmer's and Flip Side also dull blades quicker because of this.
Conclusions:
I want to keep this up to you. There is a clear difference between Adam and the other two, but the other two really aren't that different. That doesn't mean any of them are better than the others. A lighter plane can mean that you don't crash as hard, so you don't need the strength. You may know you're going to break it regardless and you'd rather go cheap. Maybe you don't mind the extra cost or extra weight because you want the strength. It's just up to you.
The point I really wanted to get at is that there is a difference between foam boards.
Now I'm left with a pile of broken foam board.

Important Update (foam board grain):
Today I cut out a 20" x 10" piece of Adams (Dollar Tree) foam board, from a new sheet, so that any possible grain in the foam would be going the other way. This piece weighted 39 grams, instead of the 38 I got from the other two tests. This is probably from the other two pieces weighing close to 39, but this one was probably cut a little bigger. This piece handled having three water bottles on it just fine. But it broke right away once a fourth one was added. I'm not sure if this even means that the foam it's self has a grain to it. With the first tests, it could handle having three water bottles for a second, then it broke. With this test it broke right away. Clearly a fourth bottle was way too much. I think the darker streaks in the Adams foam, when you hold it up to a light, is from the glue used to hold on the paper.
Again, this second test showed that cutting the Adams foam board so any possible grain is running in another direction did improve strength. But it wasn't a significant amount. I don't think it is necessary to do the same test to the other brands because they are clearly so different from the Dollar Tree (Adams) foam board.
I don't think the foam part of foam board has any grain to it. The paper will, but that shouldn't effect the strength very much. And it may have been the paper and/or the way the paper was glued that changed the foam board's strength (a little bit). (To me it looks like long streaks of glue was applied at the factory, then the paper was added to the foam. This could cause a grain in the glue.)
I do also want to mention that with the Elmer's and Flip Side brands, the weight was spread out due to the number of water bottles used. If the same weight had been centered better, they would have broken sooner. Meaning that those two brands may not be as much stronger as they appear from my data. I think Elmer's and Flip Side are about twice the weight of Adams, and have 2-3 times the strength. Which makes sense.
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