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The maximum dimensions of airline check-in luggage are usually stated in terms of "linear inches": the sum of the item's length, width and height; most airlines seem to allow up to 62 inches total.

Why is this? Clearly, a big factor must be the dimensions of airport baggage handling systems and so on. But a conveyor has a certain width and a certain clearance above it and each of those only depends on one dimension, not the sum of all three. And if I show up with a piece of luggage with dimensions 60x1x1 inches, I'm pretty sure that'll foul up their systems, even though it's within the limit. (Actually, as I recall, some airlines also specify maximum length, width and height which would exclude my ridiculous example.)

Obviously, airlines have to deal with luggage of all kinds of different shapes and sizes and they need to express the limit in terms of some convenient number. But why are linear inches used, rather than cubic inches, which are an actual measure of volume? (And, by the way, it's not important that it's inches, rather than centimetres.)

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    Bring a 60x1x1 inches piece of luggage to play smart, the airline then will use some other hidden policy to kick you out, you can never win this war with airlines, so do not play smart ;) – Nean Der Thal May 21 '16 at 0:24
  • @HeidelBerGensis Sure. I have no intention of trying to check in such an object. I'm just asking why the policy is set in a way that might encourage a pedant to try. – David Richerby May 21 '16 at 0:34
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    I mean, the obvious answer is that the airlines are willing, to an extent, to play Tetris to fit packages of varying size into the hold, but there is still a finite amount of overall physical to work with. – LessPop_MoreFizz May 21 '16 at 1:48
  • My experience is that I've seen both quite commonly. I prefer the linear inches because more luggage can meet the requirement but sometimes I end up on an airline which specifies dimensions and some of my bags no longer fit. This is infinitely worse if my return flight gets cancelled and they book me on an airline with a different policy! It happened a few times. Not often but troublesome nonetheless. – Itai May 21 '16 at 4:25
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    It is stated in linear inches because the USA has not adopted the international system of units. – gerrit May 21 '16 at 16:22
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This is just a theory, but I suspect the airlines or airline body responsible, set a volume limit, but as Zach mentioned, this could result in people taking unwieldy sized luggage excessively long in one dimension. If you take the cubic root of this limit and multiply by 3, this results in a single measurement that simultaneously sets maximum dimensions and maximum volume.

e.g. airline wishes to set a volume limit of 8827 cubic inches. Cube root is 20.67 inches, x 3 = 62 linear inches. Assuming a granularity of 1 inch, this simultaneously sets the maximum length at 60 inches, and maximum volume at 8827 cubic inches.

Edit: I was thinking if my theory was correct, that there'd be a nice round number somewhere and I think I've found one. 5 cubic feet is 8640 cubic inches. The cube root of 8640 is 20.52 and 20.52x3 = 61.56, which rounds up to 62. The other most common limit is 45 linear inches for hand luggage which corresponds to 2 cubic feet, although ovehead bin size restrictions apply as well.

Looking further into where 5 cubic feet might have come from, it seems to be roughly the size of a tea chest, which is a common storage medium. Lots of clues but no explanation...

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    One thing I thought of, which is just complete speculation, is that enforcing a volume limit at the check-in counter would be fairly impractical, since being off by an inch on one side could result in a substantial percentage change in volume. This could easily lead to arguments and disputes, and no airline is spending that much effort to accurately measure bags. Nor does a volume limit prevent obnoxiously large, yet thin, items. A linear inch limit, as you demonstrate, nicely does the job and is fairly simple to administer. – Zach Lipton May 21 '16 at 7:48
  • Yeah. I think there's got to be a simplicity element to this to avoid arguments and such. – Berwyn May 21 '16 at 7:57
  • I suspect there's something to be said about adding together three, low two digit numbers which should be fairly easy even without a calculator vs multiplying those especially without a calculator. I had spent enough of my childhood playing with numbers that I can do 27 times 18 times 11 in my head but it is effort and takes time while adding it up is trivial and it can literally be done in the blink of an eye (especially when you don't need the exact sum just whether it's below 62). – chx May 21 '16 at 10:08
  • You don't even need to add up. Just use a tape measure starting the next measurement from where you left off on the last. – Berwyn May 22 '16 at 10:04
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    This has to be the correct answer; simply stated, linear inches is a convenient way to limit both the maximum volume and the maximum length of an item. With a 62-inch limit, the maximum volume is 5 cubic feet and the maximum length is 62 inches. FWIW, the maximum linear measurements of 62 and 45 inches may also have come from volumes of 145 liters and 55 liters, respectively. – phoog Jun 4 '16 at 21:51
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+100

Freight packed into a container (be it a plane's cargo hold or truck or something else) can be said to either "weigh out" or "cube out":

  • Weigh out - The weight of the cargo is equal to the maximum carrying capacity, even if there is more space available. Example: a truckload of gold bars
  • Cube out - The volume of the cargo is equal to the maximum carrying capacity, even if the vehicle can handle more weight. Example: a truckload of balloons

An airline's dispatcher will calculate a weight limit for a given flight based on the aircraft, the route, expected winds and weather, fuel needs, and other factors. A long-haul flight may need large amounts of fuel, reducing the weight available for cargo and making it more likely for weight restrictions to be applied, while a short-haul flight may be more likely to cube out, as the cargo space can be filled up to its volumetric capacity. If a flight happens to cube out, checking a gigantic empty suitcase may still cost the airline money, as you're occupying volume that could be used for other paying cargo.

As such, airlines are interested in both the weight and volume of cargo to maximize the amount they can carry, or at least price for it proportionally. In the cargo shipping world, this is often handled by dimensional weight: the shipper essentially pays extra to ship large, low density cargo. This is the process the industry uses to best recover their costs for shipping cargo. However, For checked bags, the less rigorous standard of linear inches is used, presumably because the average density of suitcases is fairly standard, and because enforcing such a policy would be overly difficult: passengers need something predictable and easy to understand. As such, measuring linear inches reasonably captures the major cost drivers for air cargo while providing a policy that can be reasonably implemented at check-in counters.

Speculating idly, it is also clear that measuring volume is also more difficult at the check-in counter. Suppose one has a 30" x 19" x 12" bag, giving a volume of 6,840". A measurement error of just 1" on one side could lead to a volume measurement of 7,410", an 8% increase. A rule that must be quickly enforced by airline clerks at the counter should not multiply small errors into ones that could quickly spell the difference between an allowed and a prohibited bag. And dealing with anything non-rectangular requires even more rules. In contrast, a 1" error when measuring the linear dimensions of the bag will have a small impact on the acceptability of the bag.

If a bag is unusual in size or type, it may not be able to go through the standard conveyor system (even a cardboard box is sometimes treated specially in my experience). But my understanding is that these size policies are primarily about limiting the amount of volume the bags take up in the cargo hold, not their processing through the airport's baggage system. Once it's in the cargo hold, they'll do their best to pack it in whether it's cube shaped or long and thin.

And that shouldn't be that surprising, because many airlines will take odd sized items for sports equipment like skies, sometimes at no extra charge depending on airline policy. There may be a physical limit for really long items though, such as this one (from United's policy):

Hang gliding equipment that is more than 72 inches (183 cm) in length cannot be accommodated on 737 series aircraft. Hang gliding equipment that is 108 inches (274.4 cm) in length or more cannot be accommodated on Airbus A320 or Airbus A319 aircraft.

There's a point where something is just too long to fit in the cargo hold. They're obviously not going to take something that physically can't fit, which has to include making it around the corner into the cargo hold (cargo doors are actually pretty small, especially on narrowbody and regional aircraft). The linear dimensions help prevent that case. If they measured volume, some joker would try to show up with a 600 X 1 X 0.1" box and would have to be told that's not going to fit through the door (though I'd want to know how you got it to the check-in counter in the first place).

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    All of that makes good sense but I'm not sure it answers my question. I agree that weight and volume are both significant but the point is that the sum of the linear dimensions isn't a measure of volume: the volume is the product of the linear dimensions, which is a completely different number. (I'm happy to assume that all luggage is cuboidal for the purposes of this question; the "dimensional weight" Wikipedia page describes the non-cuboidal case, too.) – David Richerby May 21 '16 at 2:59
  • @DavidRicherby That's a fair point. I edited the end a bit to try to clarify my thinking there; it is both about volume taken in the hold and something that can reasonably fit through the door, especially on bulk-loaded narrow-body aircraft. I've also checked bags that exceed the allowed dimensions without a word, so it's unclear how seriously the rules are actually taken by all airlines. – Zach Lipton May 21 '16 at 3:21
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    They're obviously not going to take something that physically can't fit. Years ago I knew a circus troupe who were flying back to Australia from Italy with their equipment. When they arrived in Australia they found that someone had taken a saw to a specialist prop ladder and cut off a couple of rungs. I assume that was in order to make it fit in the plane. – Peter M Jun 2 '16 at 15:32
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The system is set up to accommodate the infinite variety of baggage dimensions while limiting the volume to an acceptable maximum amount. However the key words in the rule are 'checked baggage'.

A cardboard box or other such packaging is not 'baggage', it is a parcel or cargo. Most airlines will accept cardboard boxes or other containers as checked baggage if they are similarly sized as baggage. But they have an out when someone tries to push the envelope say with a 60x1x1 package.

Some airlines, especially those that serve skiing destinations, will specify a maximum length as well to give them some control over folks trying to check large sports equipment carrying cases, which could be argued to be 'baggage'.

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The system has been designed so that any of the millions of different bag types can fit the measurements.

A standard use of measurement would cause trouble when you have irregular shaped boxes or fishing rods going into the hold. Containers also have a wide variety of volumes.

Here is an explanation of linear measurement

Linear inches is a term invented by the airline industry to measure baggage. The size of an item in linear inches is the sum of the length plus the width plus the height of the item. A 20-by-20-by-5-inch suitcase, a 1-by-11-by-4-inch painting and a 1-by-1-by-43-inch fishing rod are all the same size in terms of linear inches. Size restrictions are different for different classes of tickets and for different airlines, but the one constant is that airlines measure baggage in linear inches.

EDIT - Linear inches are used for uses of algebra

This has many advantages. The main one is that we can use plain algebra to find out what units to use to measure other quantities.

For example, if I measure length in inches, then what unit should I use to measure the ratio of the volume to the surface area of the object? (The ratio of volume to surface area is important because it is crucial in computing the cooling rate of physical objects.) Maths Source

  • This doesn't answer the question. Why linear inches rather than cubic inches, which are an actual measure of volume, which is the thing the airline cares about. – David Richerby Jun 2 '16 at 20:44
  • Please see my edit @DavidRicherby - does that answer it? – Nathan Shoesmith Jun 2 '16 at 20:54
  • That makes it even less clear. Essentially, your edit is explaining why the cubic inch is the correct measure of volume and the question is why the airline industry uses linear inches instead! I think we might be talking at crossed purposes -- I'm sorry if I'm not explaining myself very well. – David Richerby Jun 2 '16 at 21:17
  • I can see where you are coming from. The airline industry obviously chose this for one particular reason - how does using linear measurement for algebra make cubic inches better? I'm not saying either is better, I'm just trying to find a explanation. @DavidRicherby – Nathan Shoesmith Jun 2 '16 at 21:25

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