"You were right. Somebody blew out the hatch. They were all sucked out into space."
"Correction, sir, that's blown out."
"Thank you, Data."
"A common mistake, sir."
- William T. Riker and Data, "The Naked Now", first aired October 5, 1987
No, sorry Data, it was perfectly acceptable for Riker to say the people were sucked out into space. My guess is that the confusion here is caused, indirectly, by a common misunderstanding of what suction actually is.
We all live at the bottom of a vast ocean of air. As you probably know, air is made up of molecules, approximately 80% nitrogen and 20% oxygen with some small amounts of carbon dioxide and other gasses. These molecules are in constant random motion, striking each other, you, me, everything around us and with considerable force. This is what we call "air pressure". and it's a lot, 14.7 pounds per square inch (1.0 kilogram per square centimeter), at sea level. Molecules of air are small but there is really a lot of them and they are moving really fast.
Suction occurs when the number of molecules per volume of space on one side of an object is decreased. This is called creating a partial vacuum. When that happens, there are more molecules striking the object on the side away from the vacuum than on the side toward the vacuum. The result is that the object is pushed toward the vacuum. The key point here is that suction occurs when an object is pushed, not pulled, toward an area of low pressure.
Think about that. When you suck air into your lungs, your chest expands and your diaphram lowers, creating a partial vacuum which causes air to be pushed into your lungs by the pressure of the air around you. When you use a vacuum cleaner, a partial vacuum is created inside the machine which causes dust and dirt to be pushed into the tube by the pressure of the air in the room. It seems obvious that you couldn't breathe and that a vacuum cleaner wouldn't work without air. But it is actually the randm movement of air molecules, pushing themselves into an area where there are fewer other molecules, that makes these things work.
My guess is that this is the source of Data's confusion or, I should say, that of the show's writers. When the hull of a space ship is punctured, air pressure pushes objects toward the hole. Still, that's what suction is. It is always objects being pushed, not pulled. It's no different in space.
At this point, you might be asking, "It's just air, how strong can it be?" Well, the answer is pretty strong.
In 1654, a German scientist named Otto von Guericke build two hemispheres of copper, together they made a sphere of about 20 inches in diameter. After the air was pumped out, they couldn't be pulled apart by teams of horses. An estimate of the force required to seperate the hemispheres can be made by calculating the area of the circle made where the hemispheres came together. Now, this is another key point. You might think that since air is pressing on the hemispheres from all different directions, it would be a complicated matter to figure out how much force it would take to pull them apart. But the air pressing on the hemispheres from the sides doesn't matter, those forces are cancelling each other out. Only the component of the forces striking the hemisphere in the direction of the opposite hemisphere contributes to holding them together. This means we need only calculate the area of the circle representing the border between the two hemispheres to see how much force would be required to separate them.
So the area of the circle where the hemispheres come together is Pi times the square of the radius. Pi is approximately 3.14, the radius is 10, so the area is about 314 square inches. Assumingvon Guericke got a decent vacuum, air pressure is 14.7 pounds per square inch, so the total force would be around 4,600 pounds.
By the way, this applies to suction cups too. You can use this same method to calculate the amount of weight that can be supported by that suction cup holding the stained glass bobble on your window. Measure the diameter, devide by 2 to get the radius, use the formula PiR^2 to calculate the area, and multiply by air pressure, 14.7 pounts per square inch. Of course, that only gives you the amount of weight that can be supported assuming there is no leakage at the edges of the suction cup.
So what about our space ship crew? How much force is a person subjected to if they have normal air pressure on one side and the vacuum of space on the other? Say I'm in a space ship and a John-shaped hole is cut into the hull. I plug my body in there, normal air pressure on one side and the vacuum of space on the other. Neglecting seepage (imagine I'm wrapped in plastic wrap so i fit snugly with no leaks), how much force is there pushing me out of the ship?
We can actually calculate this fairly easily. Just as with the Magdeburg hemispheres, The force the air exerts on me depends only on the area of the hole I'm plugging with my body. So the force exerted pushing me out of the hole would be the same as if I were flat, like a cardboard cutout of myself.
Lets estimate the surface area of a cardboard cutout of myself in two parts. , my head and my body.
Not to brag, well maybe a little, but I'm pretty V-shaped from shoulders to feet.
I'm 60 inches high at the shoulders.
My shoulders are about 20 inches wide and my feet are about 6 inches wide if I stand with my legs together.
You can picture this as a 6 by 60 rectangle with a 7 by 60 inch triangle on either side.
The resulting area, lets call it A1, is:
A1 = (60 * 6) +(60 * 7 / 2 * 2)
A1 = 780 square inches
Lets approximate my head and neck as an oval, 10 inches high and 5 inches wide.
Admittedly, that's a pretty rough estimate but it should be good enough for our purposes.
The area of an elipse is Pi times major radius times minor radius.
So the area represented by my head and neck, lets call this A2, is:
A2 =3.14 * 5 * 2.5
A2 = 39.25 square inches
This gives a total area, lets call it A, of:
A = A1 + A2
A = 780 + 39.25
A ~ = 820 square inches.
Assuming normal air pressure on one side and the vacuum of space on the other, the total force would be:
F = A * P
F = 820 square inches * 14.7 pounds per square inch
F ~=12000 pounds
The force a person would experience if there was normal air pressure on one side and the vacuum of space on the other is 12,00 pounds or 6 tons. If you blow a hole in the hull of a space ship, the pressure gradient isn't going to be perfect even if you are standing right next to the hole. Still, you would experience an absolutely enormous amount of force pushing you out the hole.
So was Data correct in correcting Riker's use of "sucked out"? Well, by convention, if an object is moved by increasing air pressure on the side away from the direction of movement, that's called "blown out". Think of using a can of air to clean out a tube. If the object is moved by decreasing the pressure on the side of the object in the direction of movement, that's called "sucked out". Think of sucking an orange pit through a smoothy straw.
So which applies here? Well, it depends upon your point of reference. You could say the air pressure in the ship is an increase over that of the vacuum of space. Or you could say that by punching a hole in the hull, you introduced an area of low pressure. Neither point of reference is obviously more correct than the other.
There doesn't seem to be any convention in the engineering community to use "blown out" when talking about objects being pushed into the vacuum of space. Here is a quote from a blog entry by NASA engineer and former Space Shuttle program manager, Wayne Hale titled, Thanksgiving Memories.
"You can imagine what it would be like to be strapped down, have the suction of pure space applied to . . . . your person ."
Well, you can see whereI got the idea of calculating how much force you would experience if your body was stuck in a hole in the ship. But Mr. Hale is describing an astronaut getting stuck on a space shuttle toilet one Thanksgiving day in 2009. Note that Mr. Hale also uses the term "sucked out" to describe how odors and human waste are pushed out into space by the disposal system. Apparently, NASA makes no distinction between "blown out" or "sucked out" when it comes to the vacuum of space.
If it's good enough for NASA and Mr. Hale, it is good enough for me. And it ought to be good enough for Mr. Data.
Comments welcome: jheim@math.wisc.edu