Subject:
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Re: The LEGO Didn't Break (or the HALE Mission - LEGO where it was never intended to go)
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Newsgroups:
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lugnet.robotics
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Date:
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Wed, 30 Jul 2008 18:04:43 GMT
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Viewed:
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9245 times
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In lugnet.robotics, Thomas Atkinson wrote:
> I hope ALL your data will be published.
A couple of folks have asked me about that. Trust me, anything I can will be
free for anybody who wants it, but I'll have to figure out a way to put it up.
Brickshelf is really for pictures, and I push it by posting images of data
graphs... but here, I think some folks want the actual program and actual data.
> The nerd in me really wants to know what the terminal
> velocity of a box of Styrofoam filled with Lego is...
The nerd in you is not, at all, alone :).
I know it was dropped from roughly 80,000', and made the trip to the ground in
under 23 minutes (perhaps as fast as 13 minutes). That's an average speed of
between 40 and 70 mph, but that's average - it should have been much higher in
the high, thin atmosphere, before parachute deployment. Lil' Joe was programmed
to take care of its own 'chute deployment: it timed how long it was going up,
assumed an ascent speed of at least 14' per second (data already recovered shows
it was closer to 20 ft/sec), and uses that to calculate an assumed altitude. It
then assumes a "hard deck" at 15,000', calculates a maximum drop distance, and
bases it's "free-fall" time on an average descent rate of 900 ft/sec (613 mph, a
very safe overestimate). Based on knowing all that, the free-fall time should
have been somewhere between about 40 to 70 seconds (depending on when it "turned
on"), leading to pulling 'chute at an elevation between 54,500' (likely) or as
low as 8,200' (ulp! But a drastic overestimate). during a true free-fall of 40
seconds, Lil' Joe would reach close to 870 mph, again almost certainly an
overestimate, so treat that as an upper limit.
For comparison, the main payload (coming down under a large parachute) seems to
have hit descent speeds of about 160 mph shortly after the balloon popped,
decreasing smoothly to a ground impact velocity that looks to have been around
14 mph if not less.
Where this gets interesting is in figuring out what Lil' Joe's potential impact
velocity was. The entire trip down took no more than 13 to 23 minutes, but
without any parachute the first 30,000' or more whips by in a few minutes at
*best*, even with air friction. That means the bulk of that time was spend
descending from below 54,000'. A little more math implies a ground impact
somewhere in the range of 30 to 50 mph.
Think of driving your car at slightly below highway speeds into a concrete
bridge abutment, with about an inch of stiff Styrofoam and a little bit of soft
foam as your safety system. Ouch.
And yeah, I figured all this out before the ground team had found the final
payload. This sort of thing really matters to me if I can predict things *in
advance*, rather than just casual observation after the fact. A product of my
education (physicist).
> And pictures, I'm assuming the ground recovery crew went crazy
> with pictures of the cras.. ummm landing sights.
See for yourself. I'll grab some of these for Brickshelf later on, but Eric has
started a gallery:
http://gallery.me.com/lego.professor#100014
In particular there's a picture of Lil' Joe "in situ", with the bottom blown out
(along with the tether, anchor pad, and black foam insert that should have been
inside the shell), but the NXT & SPOT not visible through the breach. From some
hasty analysis of the pictures, I think Lil' Joe actually *bounced* hard enough
that the payload shell ricocheted up while the internals were still coming down
to do that - its the only explanation I've come up with that seems to explain
the crash/landing site.
> Again, congratulations on a successful mission.
Thanks. I can't wait to see what else worked (& what didn't).
--
Brian Davis
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