Ok, for those of you who abhor the attacks of the killer physics
nerds (sounds like a bad B movie...), you can skip this post.
- -----------------------!!! NERD ATTACK !!!----------------------------
> Terminal velocity is the speed at which the drag of falling through
> the air exactly balances the force of gravity pulling you down.
The resistance of air to the motion of bodies in free fall depends on
a lot of different stuff - for example: the size of the body, its
shape, its density, the temperature of the air, the density of the
atmosphere with respect to height, the velocity of the body through
the resisting medium...
Lots of variables...I'd worry about them only if I had the leisure to
set up the numerical analysis. Here's a useful approximation instead -
I confess, one straight out of Halliday and Resnick... ;-)
the resisting force of air is proportional to the velocity
of the falling body (and is, of course, acting in the opposite
direction of the falling body, ie upwards)
Making this approximation gets us right to an expression for terminal
velocity that's approximately correct:
k Vt = mg _or_ Vt = (mg)/k
where Vt is terminal velocity, mg is the mass of the object times
the gravitational constant, and k is some proportionality constant
>> ...but sometime back in the 50's-60's they were experimenting with
>> high altitude ejection
Now as distance from the surface of the earth ingreases, the density
of the atmosphere thins (which will decrease the value of k). But the
value of g also decreases with height. Close to the surface of the
earth (less than 10000 ft (3000 m) smells like a good approximation to
me), you could probably happily assume that both g and k were
constant, and your rule of thumb would be ok. So far, so good...
However, I believe the heights to which Scott was referring were
vastly in excess of 10000 ft - more along the lines of greater than
50000 ft. At those heights, g is less and so is k. k however is
dependent on more than just density, it's dependent on temperature,
and on the variation of density with height (which is NOT linear!
because the elemental/molecular composition of the atmosphere changes
with height also). Anyway, k will decrease faster than g, with the
result that Vt is greater at higher altitudes. Scott's very high
altitude parachutist could easily have been doing quite a klip
there...
Did the parachutist who set the record really exceed the speed of
sound? I don't know myself. Let's look at the physics real fast: the
speed of sound in a gas can be expressed as -
____________________________
v =\/(a const)(pressure)/density)
so we're looking at the ratio, really, between pressure (which will
decrease with height) and density (which will also decrease with
height). Which one decreases faster? I haven't a clue! :-( Anyone
out there with a good aero-engineering handbook? :-) A good text on
planetary science (believe it or not, that's where I learned most of
this atmosphere stuff) would have also all this stuff in there.
You know, ever since I discovered Traveller, I've been kicking myself
for having tossed my planetary science notes from grad school. :-(
There have been so many times that I've wanted to reread them since I
started playing this fool game...
- -----------------------------------------------------------------
> Possibly, GDW considers grav belts to put out a constant force,
> therefore, they would produce constant speed at max output, like
> terminal velocity.
I think it is possible, perhaps, that you have confused velocity and
force? The force that a grav belt would put out would have to be
variable. Otherwise, there would be no control on velocity! Recall
that force is (mass x acceleration). If the force is always constant,
then there would always be constant acceleration and ever increasing
speed (assuming, of course, that the grav belt force exceeds g...). I
think you must have misstated yourself :-) because to achieve a
constant velocity, you must accelerate (ie you must use a force
greater than the forces opposing you, which in this case are drag and
gravity) and then having achieved your desired velocity, the force
then must decrease to match the opposing forces such that the desired
velocity is maintained.
I myself have always ignored the limitations on grav belts - what sane
person would want to go that lethally fast anyway? ;-) (This from a
woman who's been riding motorcycles for 10 years...) If you can have
a grav belt which MUST exert a force greater than the sum of gravity
and drag, then depending on how heavy the mass in the grav belt is,
you can go as fast as you are patient enough to accelerate to... How
fast you can accelerate, however, is an entirely different matter!
;-) On the other hand, there's nothing that says there aren't either
speed limits (*gasp* no, not SPEED LIMTS!!!) or speed governers in the
grav belts themselves.
Anyway, that's enough for one evening's worth of nerd attack. Having
stuck my neck out, I'll cheerfully invite correction for any of the
REAL physicists out there... ;-)
Catie "Just Another Armchair-Physicist" Helm