You’re technically right, of course - any body of fluid will exhibit a pressure gradient gradient in response to gravity and/or acceleration, and so any body of compressible fluid (such as air) must also exhibit a corresponding density gradient. When the aircraft is not accelerating, the air near the floor is more dense than the air near the ceiling, and when the captain firewalls the throttles, the air near the rear is more dense than the air near the front - so there must be a redistribution of air mass when the aircraft changes its acceleration. The reality, however, is that the density gradient in these circumstances is very small. At a standstill at sea level, the density of the air near your feet is 0.075067 pounds per cubic foot; the density of the air near your head is 0.075055 pounds per cubic foot. That’s under gravity of 1 g. A passenger jet accelerates during takeoff at about 0.2 forward g’s, so the gradient (per unit distance) from front to rear of the aircraft will be about 20% of what is caused by ordinary gravity. The total distance inside a 747 is about 38 times farther than your height, though, so the difference in density from front to rear during the takeoff roll will be about 7.7 times the head-to-foot difference I just mentioned:
air density at front of 747 cabin: 0.0751072 pounds per cubic foot
air density at rear of 747 cabin: 0.0750148 pounds per cubic foot
The deviation of front or rear density from mean cabin density is about 0.06 percent (yes, six hundredths of one percent). So we’re really not talking about a substantial redistribution of air in the cabin; assuming things are not going catastrophically haywire, you will not feel a rush of wind on your face when the captain throws the throttles forward, and the neutrally-buoyant balloon will exhibit any movement that would be perceptible to your unaided eye.
Thanks for all the replies. It all makes sense now. But to expand on question number 2 a bit. Someone up thread said that if a gun is fired from a moving plane that the speed of the bullet is the planes speed plus the speed of the bullet. So, it is safe to assume then that if a pilot pulled the trigger on a machine gun at Mach 2.5 (or faster than the bullet travels) that the bullets would travel faster than the plane?[/QUOTE
Yes, until friction slowed them down. But under normal circumstances they’d be far ahead of and far below the airplane by the time that became much of a factor.
You seem to have some really basic confusion about physics going on here, but just think about it. If you’re riding down the highway in your car and you hold a tennis ball up in front of your face and drop it, it falls in your lap. It doesn’t smack you in the nose at 60 miles per hour.
For amusement you may want to google the mythbusters episode where they shoot stuff off the back of a moving truck to see if they can match velocity and get it to drop straight down with respect to the ground. Pretty cool.
Imagine the airplane cabin is a perfect cylinder; the plane is sitting on the runway. Take two identical neutrally buoyant balloons that will hover 1 centimeter from the ceiling. Put 1 balloon in the cockpit and one near the tail. Now jack up the nose of the plane ~ 11 degrees (ARCTAN(.2)). Won’t both balloons end up at the same height from the ground? I am guessing the balloon in the tail will move forward toward the cockpit.
Good point. a balloon that is neutrally buoyant and of fixed density (i.e. it can’t expand or contract in response to changes in ambient pressure), placed in a compressible fluid medium (e.g. air), will be stable at a location that exhibits a particular pressure gradient (density gradient, and therefore pressure gradient, in a compressible fluid is non-linear). If you move it away from that location, it will be buoyed through through the fluid in a direction normal to the planes of constant pressure until it reaches the plane at which it is again neutrally buoyant. The planes of constant pressure are normal to the vector-sum of gravity + acceleration. When the plane is standing still, gravity points down, so the planes of constant pressure are horizontal. When the plane is accelerating forward at .2 g’s, the planes of constant pressure are reoriented: they run from the floor at the front of the aircraft to the ceiling at the rear of the aircraft, sloping upward to the rear ~11 degrees from horizontal. The balloons won’t particularly move in a front-to-rear direction, except as constrained by the walls/ceiling/floor of the fuselage; they will tend to move toward the front of the plane slightly but toward the ceiling mostly (~11 degrees from vertical), as they seek the ambient pressure gradient at which they are neutrally buoyant.
If the aircraft is filled with incompressible fluid (e.g. water), then the pressure gradient is linear, and a balloon of fixed size/density will be neutrally buoyant at any location in the fluid; there will be no redistribution of fluid mass at all when the aircraft changes acceleration, and there will be no movement of the balloon (relative to the aircraft).
In either case - compressible or incompressible fluid - if the balloon can grow/shrink in response to ambient pressure changes (as would be the case with a real balloon), then it will not be stable. There will be a single pressure at which the balloon is neutrally buoyant; if it moves above this location, the balloon expands, develops additional buoyancy and continues to rise; and if it sinks below this location, it shrinks, becomes less-than-neutrally-buoyant, and continues to sink. SCUBA divers are very familiary with this effect, as increasing depth compresses the air in their wetsuits and buoyancy compensators; maintaining a specific depth without hanging onto a fixed object (and without excessive use of the fins) can take a fair bit of attention.
Ah yes I see now. I was thinking a weight would only keep it balanced in the up/down direction. When you hold a balloon in a car, it still moves opposite the air, but you are only keeping it from going up, the balloon is still not balanced with the air.
But that leads to a puzzle. The balloon you just described acts just like a hot air balloon. You can’t feel a steady wind in a hot air balloon because the balloon moves with the air that surrounds it. But if the balloon is gaining altitude, that means it is lighter than air. Why doesn’t it go against the wind?
All objects immersed in a fluid medium that is subjected to acceleration and/or gravity are acted upon in a like manner: they experience a buoyant force in direction opposite the vector-sum of gravity and acceleration. It’s just that some objects are too dense for this buoyant force to overcome their weight. The Goodyear blimp filled with helium experiences a buoyant force equal to its total displaced volume of air; the Goodyear blimp, filled with water instead, also experiences a buoyant force equal to its total displaced volume of air. The only difference is that the blimp material, plus the helium that fills it, weighs less than that air so the net force (buoyant force minus weight) is upward; the blimp material + water weighs considerably more, so the net force on it is downward.
Likewise, all objects experiencing a relative wind are acted upon in a like manner: the flow creates a drag force that tends to accelerate the object in the direction of the flow. The wind doesn’t care what the density of the object is, it only cares what its shape is.
:dubious: I feel like I’m not explaining this one very well; maybe someone else can try?
I think I may get it: Gravity pulls the air downward. The downward force on air creates greater air pressure the lower the altitude. The pressure differential between low altitude and high altitude is what makes balloons float. The fact that air is being pushed downward creates a push upward which can overcome the weight of objects less dense than air at that altitude.
In the “helium balloon in a car” example, the only difference is that instead of air being pulled downward by gravity, it’s also being pushed backwards to the back of the car which results in the helium balloon going forward.