Q: If gravity suddenly increased would airplanes fall out of the sky, or would it compress the air in such a way that airplanes could keep flying?

The original question was: “In Kurt Vonnegut’s “Slapstick” there is talk of Earth’s gravity randomly changing, causing planes to fall out of the sky. Since planes fly because of air pressure variance between the top and bottom of the wings, would an increase in gravity really make them fall? The weight of air would increase by the same relative amount as the weight of the plane.”

Most plausible-ish answer so far: If gravity suddenly increased, yes, planes would fall out of the sky. When a plane is maintaining a constant altitude, the force of gravity and the force of lift are equal. If gravity were suddenly increased, there would no longer be an equilibrium, and the plane would drop. The plane would have to pick up speed to increase the lift to match the new level of gravity. Although air pressure does affect lift (the less air pressure, the faster you have to go to get the same lift), in this case I think the increase in air pressure and the increase in the weight of the plane would cancel each other out.

Physicist: They kinda do cancel out!

So, once gravity has been turned up, and the atmosphere has had a chance to equilibrate at a higher pressure and density (and get squished shorter), planes will still be able to fly (in theory).  But if, for example, the gravity doubles, the planes will need to fly through double-density air to stay up (or fly about 41% faster).  But in so doing, they’d experience double the drag.

Unlike airplanes, dirigibles and hot air balloons would do just fine.

Lift, L, is given by \frac{1}{2} \rho v^2 A C_L, where \rho is the air density, v is the velocity, and A and CL are constants that depend on the air craft.  When a plane is flying it needs its Lift force to be greater than its weight.  You may notice that your computer (or phone, or tablet, or whatever) isn’t flying right now.  At best it’s falling.  That’s because its lift force is zero.

Drag, which affects planes, cars, sleighs, or anything else that moves through air is given by \frac{1}{2} \rho v^2 A C_D (this equation applies well to things that are faster than snails, but slower than sound).

That being said, clearly planes can fly in air of different densities.  The difference in densities between “cruising altitude” and sea level is about a factor of 4.

The problem is that, generally, the Drag and the Lift are proportional.  You may have already noticed that the equations for Lift and Drag are practically the same: L=\frac{1}{2}\rho v^2AC_L and D=\frac{1}{2}\rho v^2AC_D.  CL and CD change a bit for different scenarios, but aside from that, for any particular aircraft, the equations are proportional.

So, if the gravity doubles, then the lift needs to double (because the plane weighs twice as much).  The plane can do this by flying faster, or flying through denser air.  But whichever method is used to double the lift, will also double the drag.  The long and the short of it is: if gravity increases by some amount, then the amount of power required to keep the aircraft aloft will increase by the same amount.  For example, 5 times gravity would require 5 times the power.

So while airplanes can fly in higher gravity, it may take more power than their engines can output to keep them in the air.

This entry was posted in -- By the Physicist, Physics. Bookmark the permalink.

17 Responses to Q: If gravity suddenly increased would airplanes fall out of the sky, or would it compress the air in such a way that airplanes could keep flying?

  1. Moritz says:

    It’s even worse, since the propulsive efficency of the jet engine will probably decrease when flying at a slower speed with higher air pressures.

    And I really can’t imagine “Top Gun” at half speed.

  2. The Physicist The Physicist says:

    The volleyball scene would be even more weird and out of place.

  3. Mark says:

    Didn’t Einstein prove that there is no such force as gravity?

    If so, Why do physicists keep talking as if there is a force of gravity?

  4. The Physicist The Physicist says:

    What Einstein did proposed (and was later experimentally verified) is that the “force of gravity” is really a “pseudo-force” in the same way that the centrifugal force or coriolis force is a pseudo-force. That is, it only seems as though an object is experiencing a force from some perspectives.
    That being said, you really have to do some mental acrobatics (in a curved four dimensional Minkowski space) to keep in mind the perspective from which gravity isn’t a force. Much easier to just say “pseudo-forces are forces 90% of the time, and if there’s a problem we’ll sort it out”.
    In this case, there’s no problem with saying that gravity is a real force.

  5. Ed Matzenik says:

    I think you will find that NASA scientists have proved that planes do not fly because of air pressure variance between the top and bottom of the wings, they fly because of momentum transfer from the air that the wings deflect downward.

  6. The Physicist The Physicist says:

    You’re right. But, “momentum transfer” is just a more precise way of saying “force for some amount of time”. In this case that force takes the form of a difference of pressures over the wing’s area.

  7. I am doing a research on why do airplane do not fall when they are flying,why they do not consider a force of gravity that pulls something down the earth?

  8. what is the purpose of the black box in the airoplane

  9. Consolata says:

    and what about those satellites?

  10. The Physicist The Physicist says:

    Airplanes are affected by gravity, just like everything else, but they fight against it. A helicopter works in a much more obvious way (pushing air down), but airplanes do essentially the same thing. The black box is a very tough recording device that tells engineers what was happening right before a plane crash, so that they can avoid similar mistakes in the future.

    Satellites also experience gravity, but unlike airplanes they don’t fight gravity, they just fall continuously. In fact, there’s a post that talks about that!

  11. Jason says:

    I’m wondering: what would an increase of gravity to 1.5g do to air pressure and how would this affect terminal velocity?

  12. The Physicist The Physicist says:

    The air pressure would be increased by a factor of exactly 1.5. Air pressure is dictated by the weight of the air above you, and since the amount of mass stays the same, increasing gravity just increases the weight.
    Very weirdly, terminal velocity should stay about the same for most objects. The effect of increased weight and increased air density cancel each other out (the equation for calculating terminal velocity can be found here).

  13. Pingback: Paris | Yep.

  14. Bob says:

    What happens if a satellite is in orbit at about the altitude of the ISS and then the gravity doubles? Would it fall out of orbit from the increased gravity (assuming it remained at the same speed)?

    In orbit, there is no air resistance and no drag. In this situation, how would a satellite’s behavior differ from an airplane’s?

  15. Ajay Yadav says:

    Is there any way/method to increase gravity except the usual centrifugal force???
    Or any substance can increase gravity??
    & also can magnet attract a human like metals if there is a lot of magnet (worth earth’s core) ??
    Is MASS=Gravity?
    or gravity is something else?
    I’m pretty much certain that gravitational force a formed due to a substance is it so??

  16. Chris says:

    @ Bob: If gravity suddenly increased, a satellite would be pulled towards the earth into a tighter, faster orbit. Depending on how low it already was, and how much gravity had increased, it might be pulled into the outer atmosphere and begin to drag, at which point it would burn and fall to earth. Farther satellites might be able to maintain orbit. The ISS would have to burn in a pro grade trajectory to stabilize and trim their orbit. It’s also worth mentioning that plenty of debris would be falling towards earth, which could result in some satellites being destroyed. The moon would probably get a little closer too (technically a satellite), which means that the tides would become more intense.

    Fortunately this is an impossible scenario. @Ajav: yes, gravity is a function of mass. Even your own body has an extremely slight gravitational force. It takes a lot of mass (like the size of our planet) to generate the level of gravity we feel. The only way to increase the gravity of Earth would be to increase it’s mass.

  17. Marc Tiltman says:

    If gravity were to let’s say, suddenly double, the one very, very important reason why the plane will NEVER actually be able to take off is the strength of the materials it’s made from.
    The materials would of course all be twice as heavy, but of the same strength!
    The plane could become seriously damaged under its own weight. Add to that; fuel, luggage, freight, and of course the hundreds of passengers, all of which twice as heavy. The only place that plane will be going to is nowhere!
    If for this exercise we forget the inconvenient problem of the plane becoming a pile of junk outside departures, it could still fly, theoretically. Also the pilot and cabin crew would also have to for some reason totally ignore the fact they have all suddenly doubled in weight, all movement now very hard work and still attempt a take off.

    Drag may not be a problem, if air is twice as dense; the plane is twice as heavy.
    Weight may not be a problem, the plane is twice as heavy, but the air is twice as dense, so lift would be proportional.

    Obviously the plane will not be able to reach such great altitudes, but should still fly, and with using the same power output.
    The engines would also receive more oxygen to burn the fuel. With air twice as dense before engine compression the same engines could produce more power, provided the engines could withstand producing it.
    The engines starting system would need to be more powerful to get the engines going due to this increased internal compression.

    If gravity were to suddenly double while the planes at altitude, the sudden compression of the air would cause the twice as heavy plane to fall many thousands of feet, its momentum taking it out of control.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>