Re: weight of a hovering/diving fly in a box

[John Denker <jsd@MONMOUTH.COM>]

At 11:34 AM 9/6/99 -0400, Lois Breur Krause wrote:
> the fly, when hovering, is
> not resting against the structure of the cage, nor is it supported by the
> system.

Sorry.  That's not right, for any reasonable definition of "system".

The momentum balance goes something like this:

1:      earth to fly (via gravitation)
2:      fly to air (via aerodynamics)
3:      air to air to air to air....
4:      air to box (via pressure at the surfaces)
5:      box to earth (via scale and whatever is supporting it)

All the momentum that the fly imparts to the air is eventually recaptured
by the box -- which is the whole point of having the box.

Momentum is force times time.

When the fly is in a long-term steady hover, the rate at which momentum is
recaptured (i.e. momentum per time, i.e. force on box) is equal to the rate
at which it was imparted (i.e. aerodynamic force, i.e. weight of fly).

On the second hand, there are non-hovering maneuvers that the fly could do,
during which its weight would not be supported by the box and would not be
observable on the scale.  In particular, the fly could crawl to the top of
the box and dive headlong, freely falling for a while, not supporting its
weight by lift or drag or thrust or anything else.

On the third hand, no matter what the fly does, the long-term average force
observed on the scale must equal the canonical weight of the box plus fly.
This is a consequence of conservation of momentum, and the fact that there
is no momentum going into the box+fly system other via gravitation, and no
momentum going out other than via the scale.

(Momentum conservation is upheld during the headlong dive because momentum
is accumulating in the body of the fly.  The scale is unable to detect this
type of momentum during the dive.  At the end of the dive, this momentum is
transferred to the box, in one big impulse, when the fly smacks his head
into the floor of the box.  In this situation the average force on the
scale, averaged over any interval long enough to include the dive *and* the
impact, averages out to the canonical weight of the box+fly, as advertised.)