# [balloon-makers] Terminal Descent

Tim Baggett tim at oasis.com
Fri Mar 8 08:43:21 CST 2002

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>Yesterday, Keith said his recent terminal descent maxed out at 1231
>feet per minute.  I figure that to be almost 14 miles per hour.
>
>While 14 mph doesn't sound so bad, I wonder from how high up I would
>have to jump to hit the ground at 14 mph.   I spent three hours(!)
>trying to calculate this with no luck.)  Just curious. 10 feet I
>could survive.  50, maybe not.

Tom! Please don't jump! We're all having fun here!

1231 ft/sec = 6.25 meters/sec

Physics derivation
Known: d = 1/2 a * t^2
d = distance moved
a = acceleration
t = time accelerated
first derivitive: v = a * t

Assume that when Tom jumps, there is no atmosphere. If there was, then
the air would cause friction and slow him down, making it take longer
for him to reach Keith's terminal descent velocity, or if the friction
is high enough he may never reach this target velocity. Good thing we
have an atmosphere however, since we ballooning would be impossible
without one.

Time needed to fall to reach 6.25 m/s (recall that acceleration of
gravity g=9.81 m/s^2 )

t = v / a = 6.25 m/s / 9.81 m/s^2 = 6.25 seconds

Tom needs to fall 6.25 seconds. How tall must the bridge be?

d = 1/2 g * t^2 = 1/2 * 9.81 m/s^2 * (6.25 s)^2 = 1.99 meters

1.99 meters comes to 6.54 feet.

This satifies my sanity check in which one of my college buddy pilots
(Dave Bair) taught me while crewing for him. He used to always ask
potential passengers if they would be willing to climb to the top of the
chase vehicle and jump off without injury  if they were forced to. If
someone said they couldn't jump off without risking injury, they didn't
fly.

Dave's reason for asking was to identify if the passenber could
withstand a worst case landing. Of course, this does not take into
account the horizontal component of a landing, which causes legs and
ankles to be bent at abnormal angles (remember, always face forward or
backwards to the direction of travel).

So, no need to be concerned about Tom's inquiry about jumping. It's only
6 1/2 feet.

>Also, the terminal velocity for a skydiver is 120 miles per hour.
>Does the streamer/parachute effect of the envelope slow things down
>that much?  Or are "terminal descent" and "terminal velocity"
>different?

There is no difference between a balloon's terminal descent and a
skydivers terminal velocity. The skydiver is in a terminal descent and,
as you calculated Tom, Keith's terminal velocity was 14 mph in his
terminal descent.

An object will stopp acceletating towards the Earth and reach it's
terminal velocity in a terminal descent once the force of the air
friction pushing the object up equals the force of gravity pulling the
object down. A skydiver, sees much less air friction than a huge balloon
envelope. Therefore, a skydiver makes a much bigger splat.

Skydiving was another hobby I kinda dabbled in for a bit. What a rush!

Tim

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