A Straight Dope Classic from Cecil's Storehouse of Human Knowledge

Does an airplane weigh less after the passengers have eaten their meals?

December 2, 1988

Dear Cecil:

Does an airplane have a lighter load after the passengers have consumed their rubber chicken and plastic vegetables?

Cecil replies:

Food doesn't cease to exist merely because somebody swallowed it, beanbrain. The only time a plane's mass decreases is if something gets dumped out or falls off, e.g., an engine, cabin wall, etc. Ignoring the minor reduction in weight due to the loss of moisture and carbon dioxide to the outside atmosphere during air recirculation (which would occur whether the passengers ate anything or not), the plane's load stays the same. We'll also ignore — I hate to have to throw all these qualifications in here, but I'm surrounded by nitpickers — weight loss due to jet fuel consumption during the meal.

Next time ask something a little more challenging, like whether, if a passenger tosses a baseball into the air, the plane's weight decreases by the weight of the baseball (5 to 5½ ounces, for you sticklers). Amazing answer on request.

The Teeming Millions pounce

Dear Cecil:

You recently answered "no" to the question, "does an airplane have a lighter load after the passengers have consumed their food?" Have you forgotten the second law of thermodynamics? Matter cannot be converted into energy and vice versa without some loss. When the airplane passengers eat the food, some of it is broken down in the stomach and used as energy, which is dissipated as body heat through the plane's skin into the surrounding atmosphere. The amount involved may be insignificant — perhaps as little as one billionth of a gram — but yes, the plane does lose weight in flight when the passengers eat food aboard. Looks like the real beanbrain is you, not your reader!

Cecil replies:

Oh, put a sock in it. The second law of thermodynamics, simply put, is as follows: left to themselves, things tend to go to hell in a handbasket. The truth of this assertion is irrefutable, but it has no bearing on the present discussion. What you're thinking of is Einstein's equation E = mc², which suggests that the extraction of energy from matter (e.g., during digestion) involves some loss of mass.

As you rightly note, however, in this case the amount of loss is insignificant. The average adult human requires about 2,700 kilocalories of energy per day. The potential energy of a kilogram of airline food (or of anything) is 21.5 trillion kilocalories. The loss of mass resulting from digestion is so small that it would fall within the range of error of any conceivable attempt at measurement. What we can't reliably detect we're entitled to ignore. Ergo, the plane weighs the same after mealtime as before. Go, and trouble me no more.

The applicability of E=mc² to the consumption of airline food, continued

Dear Cecil:

Regarding your recent column, in which you applied the equation E=mc² to the digestive process: not many of us have nuclear stomachs. We get our energy from chemical reactions, not nuclear reactions — that is, unless airline food is even worse than I thought. It seems you're a beanbrain, too!

PS: I really enjoy your column!

Cecil replies:

Don't bandy words with me, you slime. Despite what many of the Teeming Millions apparently believe, E=mc² applies to all reactions, not just nuclear ones. Permit me to quote from Space and Time in Special Relativity by N. David Mermin, a book I read myself to sleep with every night: "A loss of mass occurs whenever internal energy (nuclear, electrical, chemical, etc.) is converted into energy of motion. Only in the nuclear case is the amount of energy so large that [it results] in an observable change in mass, but in principle E=mc² is as descriptive of a chemical explosive, a gasoline engine, or a flying bird [or, I might add, a flying human] as it is of a nuclear explosion." Case closed.

Finally, somebody takes the bait

Dear Cecil:

Pursuant to your recent column, I now ask you something a little more challenging. If a passenger on an airplane tosses a baseball into the air, does the plane's weight decrease by the weight of the baseball? I await your amazing answer.

Cecil replies:

That's more like it. The amazing (if predictable) answer is that, although the plane experiences moment-to-moment fluctuations, on average it weighs exactly the same no matter what you do with the baseball, assuming it remains in the airplane. Bearing in mind that every action has an equal and opposite reaction, when you toss the ball upward, you simultaneously force the plane downward, increasing its weight. When the ball becomes airborne, the plane's weight decreases, then increases again when the ball lands.

Having performed various rites involving voodoo and integral calculus (one and the same, some may feel), we find that the weight of the plane during the tossing process is the same as its resting weight. This demonstrates … well, I don't know what, but surely something profound.

But our restless intellectual curiosity won't allow us to leave it at that. (Well, maybe yours will, but I'm in charge here.) Suppose we're carrying a one-pound pigeon instead of a baseball. The pigeon takes off and flies around the cabin. What does the plane weigh? Exactly the same. On average, the pigeon must exert one pound of downward force on the cabin air to keep itself aloft, and the cabin air in turn presses down on the airplane.

Now suppose somebody opens a window. Does the weight of the plane change? Well, we do have the problem that everybody in the cabin is sucked out and killed. But that's not the point I was trying to make. Antecedent to the loss of payload, the plane still weighs significantly less, if not necessarily a whole pound less, because it's no longer a closed system. Some of the downward force of the air being beat down by the pigeon's wings is dissipated to the exterior darkness. This may not seem like a big deal, and perhaps it isn't, but I've always thought an appreciation of the thermodynamic realities enhances one's quality of life.

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