Luggage shopping: Find the error

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We’ve been luggage shopping recently in honor of an upcoming sabbatical (and in recognition of the fact that pretty much every piece of luggage we own is ripped:  turns out that the combination of buying the cheapest possible suitcases and cramming them as full as possible is maybe not the best for their long-term health.)  I was looking up different kinds of suitcases, and after staring at too many numbers for too long, I suddenly noticed something weird.  The error as near as I can tell is systemmatic — it was in in the stats for every piece I looked at for this company.  Here’s an example (chosen deliberately from the newest model line, since I initially wondered if it had been fixed).

Can you find it, and tell what the (web designer?  programmer?) did wrong mathematically?

[I actually found this a couple weeks ago and send them an email to let them know, but haven’t received any reply and as of today nothing had been changed online.  I suspect it’s buried in someone’s mailbox somewhere.]

The photo in the upper left is actually of a piece of artwork called Travellers Garden by John Grimshaw at the Old Mangotsfield Station.  The photo, licensed by CC Atribuition-ShareAlike 2.0, is by Linda Bailey and can be found, of course, on Wikipedia.

9 Responses to “Luggage shopping: Find the error”

  1. Justin Wilcox Says:

    I would/could have made that mistake if I was in a rush. Its all too easy to just type “4720 in. in cm.” into google and not remember that cubic inches need a different conversion ratio to get cubic cm..

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  3. Ξ Says:

    Justin, I agree it’s an easy mistake to make. I think the reason I found it surprising was partially that it was a site-wide error, and partly because this was high-end luggage. I guess that doesn’t really make it any less likely that there would be errors, but I figured it’d be more likely that they’d be caught. [I’m assuming the error’s been around for a while, but now that I think about it, it could be relatively new if there was a recently change in the website.]

  4. Cathy Campbell Says:

    I see the error of multiplying 4720 cubic inches by 2.54 and getting 11988.8 cubic centimetres which is incorrect because the measurement is not linear. Hard to believe that this error is across the website!

    I think there is a second error. It is a basic calculation error before the conversion is even done. 25 x 18 x 11 equals 4950 so the capacity would be 4950 cubic inches, right? Or might there be some rounding happening somewhere?

  5. Ξ Says:

    Cathy — good point, and I’m not sure if it’s rounding or not. If you drop each dimension by half an inch, the product 24.5 x 17.5 x 10.5 is just over 4501, so the 4720 is within rounding leeway [I can’t think of the right way to say that — you know what I mean, I hope].

    It’s possible that it’s not an actual error, but that the capacity is less than the product of the dimensions because of thickness. There might be some padding on the front or back that shaves off a bit.

    (pausing while I play around with Wolfram Alpha)

    Actually, if you keep the longest dimensions the same, but drop the shortest by half an inch, 25x18x10.5 is 4725, which is really close. This would represent a quarter inch of padding on front and back (top and bottom? The two biggest sides.) So it might just be something like that.

    I wish I knew what, though — it looks like all their luggage has that same lower-capacity-than-expected even just in inches.

  6. Cathy Campbell Says:

    Yes, the padding & materials reduce the capacity of the suitcase. I wonder what measurements they actually use to calculate the capacity.

    I would use this problem or a similar problem in class. I would probably bring in a couple of suitcases to help students work through it. I must admit that, when I first began thinking about this problem, I forgot about the reduced capacity due to the materials.

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  9. Arjen Bax Says:

    I stumbled upon this article and didn’t see a good explanation yet why the volume of 4720 cubic inch differs so much with the product of the sides: 25*18*11=4950.
    It seems that the dimensions first have been converted to millimeters using the approximate factor 25mm/in (instead of the exact 25,4mm/in) and that the obtained volume in cubic mm has been converted back to cubic inch by dividing by the factor int(25,4**3)=16387.
    25*18*11*int(25,4)**3/int(25,4**3)=4950*0,953499725392079=4719,82364069079, which rounds to 4720 cubic inch with a relative error of about 40/10**6.

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