Working in Montréal today --Compressed Monkey Gel

Good morning folks,

I will be working in Montréal today.

Three days ago I was having lunch with David in the food court across from the Toronto office when he must have read something on the news-scroller on one of the several TVs and said, "hmmm. Iran launched a monkey into space.".

I looked up from my eggplant broccoli and blackened chicken.   "Sorry, what's that?"  You see, what entered my mind wasn't an over excited primate strapped to a backboard aboard a  Pishgam rocket with "Death to the Infidels" painted in the side, but rather some unfortunate spider monkey that inadvertently mocked Iranian president Mahmoud Ahmadinejad and was unceremoniously flung into space as some form of extremist punishment.  Scratch that, a small ceremony would be just fine.

"You mock me, you die!  Death to America and this Monkey.  How do you like my new suit, tailored nicely, yes? I could kill you all with a thought, I could kill me with a thought!". Followed by the sad tuba sound.  Mwa mwaaa.

Sorry, must have had that fun loving Ahmadinejad confused with Darth Vader.

Just to continue.... what followed in my mind was a macabre image of a teethy death grin frozen on the face of the monkey passing by confused crew members looking out windows of The International Space Station (tm).

Now then.  This got me thinking.  If this monkey were indeed flung into space without the aid of a Pishgam special, what would be needed ?

Escape velocity from our favorite planet is roughly 11.2 km/s or about 25,000 miles per hour, or about 24 times faster than the rotation of the earth at the equator.  I haven't personally verified this number, but the folks at NASA toss that number around a lot.  They sent 32 monkeys into space, even though their own experts recommended clowns, one even as late as 1985 so they should be the experts in monkey propulsion stats.

Odd though.. They lost most to "parachute deployment problems".

Yay.

There are two problems with this.  For one, when one is traveling at 33 times the speed of sound the friction of the dense air here close to us 'Surface Dwellers' is likely to cause the aforementioned grinning monkey to just burst into flames.. well not really flames but a whole step up, a superheated plasma where the monkey once was, extremely unlikely to have any ash left available for orbit let alone preserved teeth left for a grin.

Yes, a real problem.  That's why we need self propelled rockets, they travel upwards at fairly slow speeds until they reach the upper atmosphere where there is a lot less air density and then they accelerate to escape velocity.

Problem two.  How do you accelerate the monkey during the all important fling stage of its travel?  What I mean is, if you try to accelerate a monkey from a standing stop to 11.2 km/s out of a 1 metre cannon barrel, you would compress the monkey into a shallow homogenous disk of monkey gel.

Euew... Monkey gel.

Let's see if we can figure this out -- or I guess just me, I doubt I can ask the now snoring guy in 1F to spare a calculator.  A test pilot in really good physical shape can withstand 45 G acceleration on a rocket sled while wearing pressure suit and wondering why he didn't choose a career in interior decorating and wondering exactly how much urine the suit will hold.  Usual humans like us are likely to experience death or serious injury at sustained 25 G.  And just in case you are interested, protons accelerate at 190,000,000 G in the Large Hadron Collider.

So let's use 45 Gs.  We're already annoyed with the monkey enough to fling it into space but we don't want to rip off any limbs, no fun sending an armless monkey into space, hell anyone can do that.

Let's pull up some grade school physics.

1G is 9.81 m/s2 acceleration (one of those handy constants), so * 45..  we will use 441.45 m/s2 as our rate of acceleration.  I will show all math (always show your work, else ppl will doubt your answers) if so inclined you can substitute other rates of acceleration or escape velocities.

Time = (Velocity - Initial Velocity)/Acceleration
Time = (11200 m/s - 0 m/s) / 441.45 m/s2
Time = 25.37 seconds

Average Velocity = 1/2(Initial Velocity + Velocity)
Average Velocity = 1/2 (0 m/s + 11200 m/s)
Average Velocity = 5600 m/s

Distance Displacement = Average Velocity * Time
Distance Displacement = 5600 m/s * 25.37 s
Distance Displacement = 142,072 m

So we need a Rail Gun or perhaps a Trebuchet arc about 142 km long and capable of 441.45 m/s2 of acceleration of a 30 lb monkey.  I am really losing the point of this pulp, but now at least we know why it's easier to use launch vehicles to get stuff into space then just trying to throw them.

Oh yeah!  Working on Problem two, how will we accelerate the monkey to escape velocity...

Now the Trebuchet idea works well since at 142 km circumference of the half circle of acceleration, the diameter would be ..  let's see C=Pi(D) if C is 2*142 km, 284 km/3.1416 =  90 km diameter.  So the monkey would be traveling at escape velocity at an altitude of 90 km, almost the altitude of the Auroras, and just shy of the Kármán line.

Sidebar:  The Kármán line is the imaginary line where under it aeronautical lift works at velocities less than the orbital velocity, over it and and you don't need the lift because you can just travel at orbital velocities and not fall to earth.

Damn, how heavy would the Trebuchet's counter-weight need to be?  First some guides.  The optimal ratio for the Trebuchet arm is 3:1, that is the arm section in the projectile side of the fulcrum is 3 times the length of the weight side.  And then there is the sling length, not a clue.. 1/5 the arm length? and what the hell do we build this thing out of?

Ah screw it, just strap the damned monkey into a rocket.

We're out of time anyway.
This is why it takes me a while to finish my plate of food sometimes.

Have a good day, exercise your brain.