(Edit May 2012-- my thoughts on this matter have now changed significantly-- I'm still convinced that the earth "feels" a downward push from the wing of an aircraft in flight, equal in magnitude to the weight of the aircraft, which is also equal to the upward gravitational attraction that the aircraft exerts on the earth, but I no longer believe that this downward force need involve any specific amount of downward momentum of the air (downwash). For more, see posts 58, 61, and 72. End edit.)
Originally Posted by pmackenzie
I would say it has to be different, since the total "weight" of the box is the same if the plane is in your hand or gliding along.
It would also vary as the plane did pushovers and pullouts, just as it would if a motorcycle was doing loops on a vertical circular track. Or if you are throwing a ball up and down. Different mechanisms in each case but the principle is the same.
Consider-- plane doing loops inside a large box, with a scale under the box. The loops are positively loaded throughout, in the aircraft's reference frame-- i.e. the wing is always making some amount of positive lift in the aircraft's reference frame.
If the scale read x when the plane was at rest, I think we agree that the scale will read x during 1-G flight, and less than x during 0-G flight (doesn't occur during the loops in this example), and less still when the plane is inverted at the top of the loops but pulling positive G's (in aircraft's reference frame), and the scale will read more than x during the pullouts near the bottom of each loop. Just as if a motorcycle were doing loops around the inside of the box.
I suggest that this is due to the pressure exerted by the downwash on the various surfaces of the box as the plane flies round and round the loops. I further suggest that the pressure exerted on the walls is due to the dynamic pressure created by the downwash-- as could be measured by a pitot tube or a scale. Not due to a static pressure increase, as could be measured with an aneroid barometer. Dynamic pressure is associated with momentum.
Now, maybe at some point very close to the wall, some of the energy of the downwash is changed from dynamic pressure to static pressure as the downwash interacts with the wall. I'm not sure about this. If so, make the box sufficiently large and move the measuring instrument sufficiently far from the wall, and I suggest we'll only measure a dynamic pressure increase not a static pressure increase.
I further suggest that the momentum of the downwash is conserved indefinitely (or at least till it starts to "feel" the wall?) , and in 1-G flight exerts a force equal to the plane's weight against the ground, no matter how high the aircraft is. Yes the dynamic pressure decreases but the cross-sectional area expands, so the total force that can be exerted against a sufficiently large wall or floor-- if there is one-- stays the same.
I'm not ruling out the possibility that the momentum of the downwash can be expressed in some form other than macroscale motion of the air --consider a directed pulse of sound, etc-- but there must be momentum involved, not just a static pressure.
I may have some details wrong and would appreciate hints for fine-tuning the description but the thought experiments of the aircraft circling a point over the earth, and the aircraft doing loops inside the box, suggest that this is how it must be....
Examples of using a scale to measure dynamic pressure:
Well maybe that's a little off topic, the plate needs to sheltered from the suction of the airflow behind and also flush with the wall, if we want to measure dynamic pressure at the wall / floor-- if we want to measure dynamic pressure at some distance from the wall/ floor then we have a problem perhaps-- so instead install a streamlined pitot tube at the location of interest, pointing in the direction of interest, to sample the incoming dynamic pressure at that location....