Can a cloud weigh as much as a 747?
While busily working one afternoon (AKA staring at the clouds), my coworker told me that a cloud can weigh as much or more as a 747. I think she's nuts and that this is impossible. Please set her straight.
You're going to have to weasel on this one. But stick with me, chum, I've been there.
The maximum takeoff gross weight of a 747 is 875,000 pounds. Did you know this includes six million parts? Three million of which are fasteners? One and a half million of which are rivets? The people at Boeing are full of fascinating facts like this.
Anyway, let's be scientific and say a 747 weighs 400,000 kilograms. The amount of water vapor in clouds varies widely depending on temperature, pressure, etc., but five grams per cubic meter is about average. We feel confident in stating this number because it was confirmed for us by the meteorological office at the airport at the Isle of Man, off the coast of England. I'm telling you, babe, our informants are everywhere.
A good sized cumulonimbus cloud, or thunderhead, might be ten kilometers tall, with a base ten kilometers in diameter. Noodling a bit, we come up with a volume of 785 billion cubic meters per cloud (you can see this is not looking good). This gives us a mass of roughly four billion kilograms per cloud, or the equivalent of not one but 10,000 747s.
To put it another way, a modest-size cloud, one kilometer in diameter and 100 meters thick, has a mass equivalent to one 747. And they let these things just float around up there! Why, if one fell on us, it would … it would … well, it would get real foggy, that's what. Because of course weight isn't the same as mass — a cloud put on a scale wouldn't weigh anything. This fine but crucial distinction gets you off the hook in the argument you're having with your coworker.
Still, her point is that there's a lot of stuff in those clouds, and she's right. Suppose it's a dark, gray day with cloud cover one kilometer thick. Suspended above your noggin (to be precise, above the one square meter centered on your person) is the equivalent of five kilograms (11 pounds) of water! And I'm just talking about the water that's condensed into clouds — there's a lot more if you count water vapor in general. If you feel a weight hanging over you during such weather, now you know why.
The experts weigh in
In your column on the weight of a cloud versus that of a 747, you state: "Now of course, it's true that weight isn't the same as mass, and that a cloud put on a scale wouldn't weigh anything. This fine but crucial distinction gets you off the hook in the argument you're having with your coworker." Yuck! The weight of an object equals its mass times the acceleration due to gravity, 9.8 meters per second squared. Your cloud "weighs" a helluva lot!! The fact that you can't weigh something on a scale doesn't mean it has no weight. The reason that a cloud floats is that the water vapor is less dense than the surrounding air, so the surrounding air exerts an upward buoyant force (remember Archimedes?) equal to the weight of the cloud.
Nobody appreciates what I go through on this job. The biggest problem your average columnist faces is ticking off some politician. I have to fend off the freaking theoretical physicists. Dave and I had a lengthy exchange via E-mail, which I paraphrase below. Note: if you think this is complicated, be glad you didn't see the version with the equations:
Cecil: So Dave, what is the problem here? I said weight wasn't the same as mass. It's not. I said a cloud put on a scale wouldn't weigh anything. It wouldn't. My point was, "weight" could be misinterpreted. Evidence: this guy misinterpreted it. Had "mass" been used instead, there wouldn't have been an argument.
Dave: Nonsense. Weight has a precise scientific meaning.
C: Technically, yes, but as a practical matter weight is dependent on local conditions. Buoyancy makes clouds apparently weightless. Astronauts experiencing high g forces on liftoff weigh more than their normal weight. Bodies in free fall, such as astronauts in orbit, are weightless, even though they experience the pull of gravity.
D: Weightless, schmeightless. They still have weight.
C: Fine, but it's only weight by definition. In reality orbiting astronauts weigh nothing. Why, the equivalence principle, a fundamental concept of physics, tells us that a body in free fall behaves as though it's unaffected by gravity.
The Teeming Millions (bursting in): Huh?
C: Imagine a skydiver falling through a vacuum. For all the effect gravity has on him, he might as well be in deep space.
TM: Well, one difference is that in deep space you're not in danger of crashing into the Astroturf at 120 miles per hour.
C: This is a technical detail. I'm looking at the big picture.
TM: Well, what's this about astronauts in orbit being in free fall? They don't look like they're falling.
C: Trust me, gravity is pulling inexorably on them, so technically they're falling around the earth. However, because of their high orbital (well, tangential) velocity, they don't get any closer and they circle the earth indefinitely.
But let's get back to the main argument. Why am I, an astronaut in free fall, obliged to believe I have weight? I cannot determine this weight by measurement or experiment. Suppose that I had selective amnesia and forgot my earth weight and the planet I was orbiting. It would be impossible for me to determine the weight I supposedly had! You'd have to radio up and tell me! I'd have to accept it on faith! Doesn't that strike you as an essentially, you know, religious concept?
D & C (shouting as one): Wait a minute!
D: Orbital observations!
C: I was going to say that.
D: Too bad, I beat you to it. The speed and altitude of an orbiting body of known mass are a function of the mass of the body (planet) it's orbiting around. By making orbital observations you can determine the mass of the earth, and you can use that to calculate your weight. What's more, even if you never look out the window, you can prove you're in orbit rather than in deep space, and thus are not truly weightless. Get two wrenches and put them at opposites sides of the cabin of your spacecraft. Over time the wrench farther away from the earth, which is in a higher orbit and thus is traveling more slowly with respect to earth, will drift toward the back of the cabin. The nearer wrench, which is in a lower, faster orbit, will drift toward the front.
C: Shoot, you're right. Now that I think about it, even if I were falling straight toward the earth, I would be able to detect tidal variation due to the fact that the strength of gravity diminishes rapidly with distance. A wrench at the front of the spacecraft would drift forward, but one at the back would drift rearward. The equivalence principle obviously applies only to single points (center of mass). As a practical matter, in the real world of three-dimensional objects, free fall can always be distinguished from zero gravity.
But Dave, this proves my point! Even in the lofty realm of theoretical physics, we're obliged to consider practical matters! And as a practical matter clouds and orbiting astronauts are considered to be "weightless" because they behave as such. True, the letter writer's coworker was clearly talking about clouds' weight in the strict sense. I was just giving the guy a chance to weasel out of an argument in which he was, technically, wrong. You may think this unworthy. But weaseling is obviously a highly useful skill.