Last week I posted about a mistake in the translation from Imperial to Metric units on a luggage website, and Cathy Campbell pointed out in the comments another possible error: that the length times width times depth doesn’t equal the capacity. In this example:

25×18×11 equals 4950, not the 4720 cubic inches of capacity advertised. Possibly this is due to the thickness of the materials, but I’m wondering how they take that into account if that’s what it is. It seems more likely to me that they’re using a formula to get capacity than measuring it physically, but I’m not sure what formula they’re using. Anyone want to try it out? (It might be trivial or complicated; I spent more time uploading screenshots than actually working on a formula, although I did notice some oddities in the process.)

Here’s one line of luggage in this brand (the same as above), with the metric units removed because, well, they’re not all correct:

Here’s another line (same brand):

And a third line in the same brand.

Anyone want to hazard a guess as to the (possibly existing) formula(s) (now, with added parentheses!)?

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Tags: Volume formula

This entry was posted on August 10, 2010 at 7:56 pm and is filed under Problems. You can follow any responses to this entry through the RSS 2.0 feed.
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August 10, 2010 at 8:18 pm |

It’s possible — I have no idea how likely — that they actually fill the unit with some substance (beans, or some such, or sand, if they want to be more… um… granular), and then measure the volume of what fit. They’d have to have a definition of just what “full” means, and whether they count the outside pockets and whatnot, but it could work.

August 10, 2010 at 8:40 pm |

If there is a formula, it varies by product line, as there are different values for the volume of a 20x14x8.5 piece of luggage in the second and third product lines.

August 10, 2010 at 8:43 pm |

Huh; the 20x14x8.5 piece in the third product line has a volume slightly larger than the product of the linear measures.

I’m leaning toward sand or beans as a direct measure of volume.

August 10, 2010 at 9:16 pm |

I suspect we need more information about outside pockets, expansion zippers, and that sort of thing, in order to come up with a reasonable-ish formula that would explain this wacky data.

August 10, 2010 at 9:42 pm |

Joshua, that was initially why I separated it by lines, assuming that it would at least be consistent within a line (and that a formula could be determined mathematically, and might suggest reasoning if only two dimensions mattered). I also was picking similar-looking pieces of luggage [these are all wheeled pieces, for example].

I assumed it was a formula, but now I’m starting to wonder.

(For anyone who wants more data to play around with, the luggage is Briggs and Riley. The first luggage line is BRX, the second is Baseline, and the third is Transcend. If you click on a piece of luggage there’s also a link for its stats.)

August 18, 2010 at 7:26 pm |

I figure that a luggage company has a few models of luggage, and they make thousands of identical pieces of each model. They thoroughly test each model before mass-producing it, and I would certainly be inclined to think that, as part of testing it, they would measure the ACTUAL capacity of each model, by filling it with something to occupy the space, and then measuring how much of it was held by the bag.

I think you’re over-thinking it by trying to find some mathematical way to arrive at the capacity by the exterior dimensions.

August 23, 2010 at 8:44 pm |

I can believe there’s no mathematical formula, but I’m not totally convinced that there’s a logical way the volume capacity is done. There should be, I just don’t know if there is. (Maybe I need to track down a Luggage Person. Where are all the door to door salespeople these days?)

September 23, 2010 at 7:50 am |

[…] this case, the somehow-determined capacity of 4720 cubic inches is multiplied by (2.54)³, or approximately 16.387 cubic cm per cubic […]