Re: [Phys-L] Dirigible Flight Question

[John Denker <jsd@av8n.com>]

On 11/05/2012 04:11 PM, Paul Nord wrote:
> Ok, ok.  I'll give you the real question.  We've gotten bogged down
> in dirigibles and blimps.
>
> I have altitude data for a weather balloon which picks up enough ice
> at a 5 km altitude that it begins to descend.  It continues dropping
> until it reaches about 2 km where enough ice has melted to allow the
> balloon to continue its ascent.  We know the lift of the balloon.  We
> know the mass of the payload.  What is the mass at the two points
> where the velocity goes to zero?

On the timescales of interest, a weather balloon is aerodynamically
not that much different from a parachute.

I suspect that to a good-enough approximation this system is so grossly
overdamped that we can treat this using Aristotelian mechanics: an
object at rest tend to remain at rest, and an object in motion tends
to come to rest.  Inertia is (almost?) irrelevant, and the velocity goes 
to zero (almost?) as soon as the net force goes to zero.  Some of the
PER people are going to march on my castle with torches and pitchforks
for saying so, but Aristotle was not the village idiot.

I assume you know the lift as a function of altitude and temperature.
If not you can figure it out from the ideal gas law and the standard
atmosphere models.  At the points where the vertical velocity goes to 
zero, weight = lift.  Presumably you know the weight of what's /supposed/
to be on the thing.  Subtract that off and you're left with the weight
of whatever's not supposed to be there, e.g. ice, freighthopping geese,
et cetera.

It would be even smarter to include the data when the velocity is *not* 
zero.   I assume your tracking data gives you velocity.  From that you 
can figure out the *real* force-versus-velocity relationship by taking 
data in non-icing conditions.  You can then model the force-versus-velocity 
relationship for every flight.   To the extent that observed behavior 
differs from the non-icing behavior, you can infer how much ice there is.

If you want, you can cross-check the measured force-versus-velocity
profile against fluid dynamics calculations involving the shape of
the thing, the Reynolds number, et cetera ... all of which you know
... but I suspect that just measuring stuff is easier and better,
especially if you're not planning on a career as a fluid-dynamics
geek.  Aeronautical engineers have a long tradition of obtaining and
using test-flight data.

> Ok, ok.  I'll give you the real question.

I hope everybody involved can now see the advantage of asking the real
question.  For starters, from my point of view, the non-real questions 
tend to be an enormous waste of my time.  From the other party's point
of view, the real question is vastly more likely to generate a real
answer, a usable answer.

This is the sort of thing that gives ivory towers a bad name.  Often
the non-real question is both more difficult and less useful than the
real question.  When I see textbooks devoid of real-world topics and
instead full of made-up nonsense, I want to tear my hair out.