The Sexy Universe

The Cameron Hoppe Project is an archive, probably forever.  Now that I've finished school, I have time to work my new blog--The Sexy Universe. Hope to see you there!

L'Histoire

It cannot be enough for a gr'up just to know facts.   Knowledge of facts isn't even close to knowing anything at all.  It is the feeling, the intuition, the experience of lives that have come before us and must unfold long after we have gone.  The sickness, struggle, victory, the birthing, and dying, the music, art, love, hatred, fear.....

These are equally our heritage and our estate.  One who would know history must not just read--but must examine, analyze and empathize.  This may be the greatest gift Guttenberg has bequeathed us.

In the words of my brother, asking German philosophers to be concise is like asking cows not to pass gas.  But sometimes someone else says it better than you ever could:

We moderns are just beginning to form the chain
of a very powerful, future sentiment,
link by link.
We hardly know what we are doing.
It almost seems to us as if it were not the question of a new sentiment,
but of the decline of all old sentiments:
the historical sense is still some thing so poor and cold,
and many are attacked by it as by a frost, made poorer and colder by it.

To others it appears as the indication of stealthily approaching age,
and our planet is regarded by them as a melancholy invalid who,
in order to forget his present condition,
writes the history of his youth.
In fact, this is one aspect of the new sentiment.

He who knows how to regard the history of man in its entirety as his own history
feels in the immense generalization all the grief
of the invalid who thinks of health,
of the old man who thinks of the dream of his youth,
of the lover who is robbed of his beloved,
of the martyr whose ideal is destroyed,
of the hero on the evening of the indecisive battle
which has brought him wounds
and the loss of a friend.

But to bear this immense sum of grief of all kinds,
to be able to bear it and yet still be the hero
who at the commencement of a second day of battle
greets the dawn and his happiness,
as one who has an horizon of centuries before and behind him,
as the heir of all nobility, of all past intellect,
and the obligatory heir (as the noblest) of all the old nobles
while at the same time the first of a new nobility
the equal of which has never been seen nor even dreamt of:

to take all this upon his soul:
the oldest,
the newest,
the losses,
hopes, conquests, and victories of man kind.

To have all this at last in one soul,
and to comprise it in one feeling:
this would necessarily furnish a happiness which man has not hitherto known,
a God’s happiness,
full of power and love,
full of tears and laughter,
a happiness which, like the sun in the evening,
continually gives of its inexhaustible riches and empties into the sea.
And like the sun, too, feels itself richest
when even the poorest fisherman rows with golden oars!
This divine feeling
might then
be called
humanity!

                          ---Nietzsche, The Joyful Wisdom 4:337                               

J'adore Halloween

                             "When ghosts and goblins by the score
                             ring your bell or pound your door
                             you better not be stingy or
                             your nightmares will come true!  Boo!"
                                                                   --Some Disney Writer

Some holidays are celebrated soberly and somberly as a matter of duty, gratitude--Veterans Day, Memorial Day, Labor Day, Easter, etc, etc.  But the only pure fun one is Halloween, my favorite.  Thanksgiving and Christmas suck, Easter blows, too much work and expectation.  Independence Day is also good, but it's a lazy good.

Halloween is perfect.  No expectations.  All the creativity and fun you can stand.  A perfect excuse to be as dumb and excited as you want.

So God Bless Halloween, and God Bless Pumpkin Pi....

Pumpkin Pi

le Saut de Baumgartner (Baumgartner's Jump)

          "And He will raise you up on eagle's wings,
          bear you on the breath of dawn,
          make you to shine like the sun,
          and hold you in the palm of His hand."
                                                 -- Josh Grobman "On Eagle's Wings"

Felix Baumgartner completed his much pre-hyped jump from 128,100 feet, achieving a top speed 1.24 times the speed of sound.  It must have been an amazing ride, with the bill footed by Red Bull and everything.  I am neon green with envy.  Sure, it could be death to try, but it would be worth it just to see the blue-glowing world one time.  Besides, the life insurance is paid.

Gravity creates constant downward acceleration.  Friction with air produces drag that runs the opposite direction in which one is moving, and is proportional to velocity squared.  So the sum of all the forces on Felix, as with any skydiver, during his fall were equal to his mass times his actual acceleration.  Since drag is proportional to the square of velocity, the drag force and the gravitational pull become equal, and acceleration reaches zero.  This is known as terminal velocity.  Not nearly as exciting as the name sounds.  I know; I was disappointed, too.  In equation form it looks like this:

The drag coefficient includes half the surface area of the guy in the suit and a proportionality constant.  Based on his reported time in freefall and an area of 4.3354 square meters I found this to be 1.15, which is actually quite reasonable.

The next issue to deal with in the problem is the air density.  Anybody who's ever been up a tall mountain or a plane ride knows air gets thinner with elevation.  As a result, drag forces are higher near the ground than at the elevation Baumgartner jumped from.  Without that included, we're only left with the beautiful sky, without any interesting math.  So we can expect that Felix's speed went way up, and then it actually decreased until he pulled his parachute at 270 seconds.  Then it really dropped.

There's a ton more I just didn't have time to do.  For example, the drag coefficient is dependent on the velocity and density of the air, the gravitational force decreases as elevation increases, etc, etc.  But I just didn't have time.  Sigh!

Enough of all that.  I drew it out on paper and coded it out in Matlab.  Let's see what it looks like.  First, his position with time:

The scale of this is in tens of thousands of feet, so you can see where he pulls the cord at 270 seconds and about 8400 feet.  At that point, his descent slows way down.  Now, the velocity of the fall:

Two important spots here.  On the right, you can see where his chute deploys.  On the left, you can see where he reached terminal velocity in the upper atmosphere about 50 seconds in.  This was his terminal velocity.  After that, the rising density of the atmosphere continually slowed him down.  Kinda like being married.

As you can see, the model is a little off; the maximum velocity should be closer to 850 feet per second, while I've got him maxing out a little over a thousand.  That is probably due to my crude modeling of gravitational and temperature gradients at high elevation.  What can I say?  There's only so many hours in a Sunday afternoon.  Oh--one last thing.  The modeling on this is highly non-linear, so I saw no way to punch out an analytical solution.  Really, I don't think there is one, but maybe someone out there knows better than I do.
The equations and code are posted here:  http://thesexyuniverse.com/2012/12/08/baumgartners-jump/


Cheers!