How many cans?



Disclaimer: The experiment isn’t being conducted by me, but I have taken an interest in it because it involves:

  • a toiletry that I use regularly
  • my car
  • determining how much toiletry would be needed to fill my car

Naturally, once the experimenters got me thinking about this, I had to estimate the answer. They’re not done yet, so if you see them, ixnay on the answeray.

To begin with, they’re examining cans of Gillette Foamy with Aloe & Allantoin. I’m not incredibly picky with shaving cream. This stuff is probably the same formula marketed in a myriad of different ways. Except this shaving cream is compatible with the Trans-Warp 10 razor. (Next up: a Razor That Goes to Eleven for those special occasions when you need an extra-close shave.)

Ahem.

A can actually weighs 14.8 ounces, of which there are guaranteed 11.0 ounces of “product.”
That’s all fine and dandy, but what we need to know is the volume.

One question that lingered was how much the aeration affects the expansion. To calculate this, cans were frozen. The bottoms were hacksawed off and the contents dumped into a bucket where it could expand.

Based on Rob’s earlier work, and my personal consumption of this product, I wasn’t expecting a whole heck of a lot in each can. The expanding frozen cream (top bucket) grew to only 3″ tall. This was kind of disappointing, really.

In contrast, the room temperature can squirted into the bucket yielded 5″ worth of hot shaving action.

Conclusion: the aeration fluffs it up considerably. If we were playing an actual prank, it would also make this a lot easier than freezing and cutting the bottoms off cans.

The largest tub expanded to about 5″ from the bottom. The container is 9.5″ in diameter. This gives us an estimated volume of:

(9.5″/2)2 * pi * 5″ == 354 cubic inches of shaving cream

354 cubic inches / 1728 cubic inches per cubic foot = 0.20 cubic feet of shaving cream

Because I want to know, I measured the original can. It’s 2.5″ in diameter, 4 3/8″ in height. There’s a lens-shape at the bottom, but I estimate this “cutout” volume is less than the spout above the rim. I can also hear the shaving cream sloshing around, so let’s just simplify this and compute the volume of the cylinder:

(2.5″/2)2 * pi * 4.375 == 21 cubic inches

21 cubic inches / 1728 cubic inches per cubic foot = 0.012 cubic feet

So, based on this, the shaving cream expands just over 16 times its unaerated volume.


Finding the volume of the car proved to be tricky. The owner’s manual provided a “cargo capacity,” which I assumed meant with the rear seat down. I measured the volume of just the cargo area with the seat up, subtracted this from the bigger number, and came up with an estimate for the rear passenger compartment size. To confirm the calculations, I measured the rear compartment volume legroom plus the torso. That number was within 5% of the derived value, suggesting I could use the published front passenger numbers to compute the volume there. I came up with the following

Front passenger area: 52 cubic feet
Rear passenger area: 37 cubic feet — see, you knew it was always cramped back there.
Cargo area (in this case, referring to what’s available behind the rear seat): 27 cubic feet

Total interior room is approximately 116 cubic feet

The Bottom Line
It would be an awesome, minty-fresh, very expensive April Fools’ prank. I estimate that it would take:

116 cubic feet / 0.20 cubic feet of shaving cream per can =
580 cans of shaving cream

This is nearly four times the amount of shaving cream I’ve consumed since I was twelve. And as for cost, at $2.09 per can, even with free shipping (535 pounds!), the experimenters would be out about $1,200.

A more interesting variant would be to use biodegradable shipping peanuts, at $700, delivered anywhere in the continental U.S. (And no, they don’t pack peanuts in peanuts. I asked.)

11 thoughts on “How many cans?”

  1. Wow. This one of those things that makes me shake my head in awe (and vicarious exhaustion — not for the mathwork but for the work behind the study, plus assembling the photos and content for the post itself 🙂 ). Nice work!

  2. What is the BRF (bubble retention factor) of Gillette Foamy? Would the foam on can 1 not have dissipated by some degree by the time you got to can 580? Given the time it takes to dispense a can, times 580 cans, I’m wondering if you may actually need more.

    Just sayin’.

  3. Even though I’m tried from getting back from the weekend in Enumclaw and trying the Mutual of Enumclaw omnium races, my first thought as soon as Jim’s site loaded and this article appeared as “WTF?”. 🙂

  4. See…if they told kids that they could do this kind of stuff with math maybe they’d pay more attention in class. Kinda makes me wonder, though, how much of that shaving gel (the kind that expands only after some friction) it would take to do the same thing (sure, there’s an upper limit on the amount of expansion but before you hit that varying degrees of friction mean varying amounts of poof).

    Someone once filled my cubicle up with packing peanuts. It was awesome 🙂

  5. Woodstock: Gel would be interesting – I’m guessing it doesn’t expand as much as foam, but I could be wrong. May be worth expending one in the name of science

    John: The Bubble Retention Factor of Gillette Foamy is at least five days. I don’t know what the compressibility would be, though once you get people committed to the task of a great prank, anything is possible.

    Kiri, Claire: thanks, as always.

    Susan: just performing a public service. Of what, I don’t know.

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