Olin Lathrop wrote: > Gerhard Fiedler wrote: >> I understand... :) But I thought you could, too. I may be wrong... >=20 > I am not sure what that is supposed to mean. I have spent > considerable time and effort trying to explain the phenomenon of a > airplane leaving a net downdraft as it passes thru air. I'm sorry I > couldn't come up with a explanation you can believe, but I did try.=20 > I'm out of ideas how to explain it differently and have spent too > much time on it already, so I'm giving up. You never explained how the momentum is preserved, staying in a single reference system. You never even defined which reference system you're using. You rejected the Earth as reference system, but I'm pretty sure if you use Alpha Centauri as reference system things don't get easier. I'm not claiming to have the answer, and I agree that it is very likely that there is a downdraft in the air to provide the upward force on the wing that balances the force of gravity (to keep the plane at constant height), but I just don't see the conservation of momentum here -- without something else. To recap: - Reference system is the Earth. (This doesn't mean that the Earth itself is excluded; it just means that we measure all speeds relative to the Earth.) Whenever we do Newtonian physics (actually, all physics since Newton at least, excluding some theories that postulate an absolute reference) we need to define a reference system. Speed and momentum only make sense within a reference system, and are only conserved within a reference system. It is not "allowed" to change reference systems while talking about conservation of momentum. - The Earth is considered "big" relative to our experiment. Surface is flat, gravity vectors are parallel and same size. I think we already have agreed that the curvature of the Earth and its gravitational field is not relevant for our problem, and it makes things easier. - I'm looking only at the vertical component of momentum (and speed). Since momentum is a vector, each directional component has to be preserved in order for the whole to be preserved. - Air is standing still before the wing moves through. (Remember, this is "still" WRT the Earth.) No (net) movement whatsoever, also no vertical movement. Which means no vertical momentum either.=20 - Wing moves at constant speed and constant height through the air. "Height" is meant to be "distance from Earth", not something relative to wind or other odd references.=20 - Movement at constant height means there is no vertical component of the wing's speed, hence it has no vertical momentum. - The Earth, as reference frame, has no momentum whatsoever, by definition. - A downward wind, air moving downwards, does have a vertical component of its speed, and since it has a mass, there is a vertical component of the momentum. Olin suggested a "macro" view; that is, not considering that the air is made up of individual molecules that move around stochastically. We never established what exactly this means, but from what I understood Olin, he meant a simple before/after comparison of involved momentums. This is exactly what I'm trying to do here. Olin's postulate is that there is a net downdraft after the wing went through the air.=20 My doubt is:=20 - Before the wing went through a piece of air there is no vertical momentum, neither in the air nor in the wing. - If there is a net downdraft after the wing passed through a given piece of air, there must be a net downward momentum.=20 - How can this be? My postulate is that there can't be a downdraft without an updraft that balances the vertical momentum. I don't know where it is, and I don't know how this all exactly works, but conservation of momentum means that if there was no vertical momentum before, and there is a downdraft afterwards, there must be something that moves upwards to balance the downward momentum of the downdraft. (It's like if after a collision of billiard balls you see a ball move left compared to the initial movement, you know there's another one moving right, too -- even if you don't see it.) My only question is: how is the initial vertical momentum of zero preserved? And Olin, however hard he tried, wasn't able to stay within one single reference system and do a momentum balance that would result in a downdraft, parting from still air and a wing in horizontal movement. (Neither was I, but I at least acknowledged as much and introduced the idea of a balancing updraft to keep the momentum preserved.) Gerhard --=20 http://www.piclist.com PIC/SX FAQ & list archive View/change your membership options at http://mailman.mit.edu/mailman/listinfo/piclist .