Space/Science — HabitableZone

Space/Science

Buddha's fate

I fiqured out part of the puzzle. And I believe Nick was incorrect, but haven't actually work through all the whole sequence, yet. I thought, I'll do that in this post. There are 3 major components which would slow down Buddha's pipelauncher drop from 40,000'. I've just got one part of these 3 part - the dynamic pressure part. The other other main parts would be the viscosity from pipe walls and the vacuum created in the spot the Buddha is sitting.
One factor I didn't mention was the speed of the unimaginably huge airplane which drops the pipelauncher- let's say it's 300 mph. Another thing I didn't go into was how exactly the pipelauncher left the unimaginably huge airplane [UHA]- this would quite complicated, but lets assume the meter diameter solid iron was played out the back, then the UHA climbed and let pipelauncher roll out the back, now since the UHA is imaginary let's assume it's capable of a steep climb, thereby allowing a safe exit.
The formula for dynamic pressure is very simple, but my problem was trying fiqure what the density was [slugs!]:
{which btw I've learnt about before, but for some reason they just don't stick in my mind:}
"The equation states that the static pressure (p) in the flow plus one half of the density (r) times the velocity (V) squared is equal to a constant throughout the flow, which we call the total pressure (pt) of the flow. "
pt = p + .5 * r * V^2
From:
http://wright.nasa.gov/airplane/bern.html

"While people often use pounds per cubic foot as a measure of density in the U.S., pounds are really a measure of force, not mass. Slugs are the correct measure of mass. "
http://www.2-stroke-porting.com/altiden.htm
So that^ has table for air density but also there is bigger table:
http://pdas.com/e2.htm

At 40,000' air density is .0005873 [slugs per cubic foot].
Air pressure at 40,000 is 393.1 lbs per sq ft
At 300 mph (440' per sec)- 440 squared times .5 times .0005873 equals 56.85 per sq'
20' diameter circle has 314.159 cu' so would have 17,860 lb force at ends.
Dynamic pressure inside pipe if open end is moving at 300 mph is pt= 393.1 + 56.85 or Pt= 449.95 lbs per sq'
If instead the pipelauncher was going "broadside"; it's area would be
"roughly" 20' by 400 = 8000 sq' and wind force would be 454,805 lbs of force- so it flies rather than falls at a speed of 300 mph.*Maybe* it could fly from plane launch, then stall, then proceed to go straight down- we can hope or assume:)
So I'm just going to let this thing drop for say 4000' without considering drag, just 1 gee acceleration D=1/2 Acceleration times Time squared,
so 1 gee equals 32.2' per s/s: 4000 divide by 16.1 equals 15.76 seconds, which means the speed is about 507' per sec.
Now, at this point in time our Buddha can't breath, but is able to hold his breath (breathing with a respirator is possible up to 45,000' [don't need pressure suit to inhale or hold breath]). And he is probably wondering when the "Ok, to smoke sign comes on".
Now, at 36,000' air pressure is 476.1 lbs per sq' [3.3 psi]. And temperate is a brisk 390.5 Rankine [217 Kelvin or -69.17 F]. And air density is 0.0007103 slugs per cu' So...
507 squared times .5 times .0007103 is 91.29 per sq' and times 314.159 equals: 28,680 pounds of force. With dynamic pressure of 567.39 lb/cu' (3.9 psi). [And Buddha would probably notice at this point that despite the prayer mat, his butt was starting to feel somewhat cold and that he was no longer in free fall, he knows that with gravity it's possible to light a cigarette, but he can't breathe, so it will have to wait.]
The next 10 seconds bring more joys, the pipelauncher continues to accelerate and only slightly slowed by air. Without any additional acceleration the pipelauncher would get to around 30,000'.
At 30,000' the air pressure is 629.7 Temp is 411.8 Rankine and air density is .0008907 slugs per cu'. If we plug in say 700'/sec
700 squared times .5 times .0008907 218.2 per sq' giving 68,556 lbs of force. So, lets say the average accelerate rate is 30' per s/s and over the 10 seconds the distance travelled is 6500', but speed is closer to 800'/sec [545 mph], so 800 squared times .5 times .0008907 gives 285.02 per sq' with total force of 89,543 lbs. The pressure inside the pipe is 914.7 lbs/cu' (6.35 psi).
Buddha is getting excited, he now weighs as much as if he was on Mars, and in a couple of seconds could breath, if it wasn't for the reduced pressure caused by the vacuum affect (which we aren't accounting for since we don't know how much vacuum would be actually created). He unbuttons his shirt pocket and gets out a smoke. He is so excited he doesn't even notice his butt is getting colder.
Now we going at quite a clip and still accelerating and conditions are changing rapidly, so we will look 5 seconds ahead instead of 10 seconds. At 800' /sec without any acceleration in 5 sec we go another 4000' down, so we will look at 25,000':
Air pressure: 786.3 Temp is 429.6 and air density is .0010663
If we plug in 900'/sec, we get 900 squared times .5 times .0010663
431.85 per sq' giving a force of 135670 lbs. If average acceleration is 20' per s/s than in 5 sec we only added 250' (4250' total) distance and added to our speed by 100' sec. Close enough. The pressure inside the pipe is 1218.15 lbs sq (8.46 psi) and temperature is around -30 F
Buddha now weighs about half his normal weight. After getting a smoke, he puts the pack back in his pocket, grabs the lighter, and lets out his breath.

Next 5 seconds: To 20,000':
Air pressure: 973.3 (6.76 psi) Temp 447.4 and air density is .0012673
We should be losing acceleration quickly, let's plug in 940' per sec by time we reach 20k, 940' squared times .5 times .0012673 gets 560 lbs per sq' giving total force of 175,895 lbs. [Btw, this 940' sec is 641 mph and speed of sound at 20,000 ft is 660 mph]
Air pressure inside of pipe is 1533.3 [10.6 psi]
Buddha take breath of air, it's very hard to breathe. Buddha is accustomed to breathing on mountain tops. But he feels dizzy, he see nirvana; travelling at mach 1; his butt is defintely cold; he decides now is a good time to lit a cigarette. It's been just over 35 seconds since he left the plane.
Next 2 seconds: To 18,000'
Air pressure: 1057.5 (7.3 psi) Temp: 454.5 and air density is .0013553
Plug in 950' per sec. 950 squared times .5 times .0013553 gets 611.5 lbs per sq' giving total force of 192,133 lbs. Air pressure in pipe is 1669
(11.5 psi).
Buddha lit his cigarette. Even though it's windy, Buddha is an enlighten being & can lit his cigarette, unlike the rest of us poor slobs who even in a calm day can't lit it the first time. The sun is shining, so Buddha decides he needs to stretch legs and relieve his cold butt. So, he unbuckles his seat belt.
Next 2 seconds: To 16,000'
Air pressure: 1147.5 (7.9 psi) Temp: 461.7 and air density is .0014480
Plug in 955' per sec. 955 squared times .5 times is 660 lbs per sq' giving a total force of 207441 lbs. Air pressure in pipe is 1807.5 (12.5 psi).
The Buddha picks up his prayer mat, and notices that metal of the cap is still below 0 F. This annoys him. No one mentioned getting a cold butt. He is also concerned because since he is an enlighten being, he is aware that the pipelauncher is still accelerating.
Next 2 seconds: To 14,000'
Air pressure: 1243.6 Temp: 468.8 and air density is .0015455
Plug in 957' per sec. 957 squared times .5 times is 707.7 lbs per sq' giving a total force of 222,337 lbs. Air pressure in pipe is 1951 (13.5 psi).
The Buddha notices a flying pelican, and sees that as a good sign, but also wonders why he didn't take the blue pill.
Next 2 seconds: To 12,000'
Air pressure: 1346.2 Temp: 475.9 and air density is .0016480
Plug in 958' per sec. 958 squared times .5 times is 756 lbs sq' giving total force of 237579 lbs. Air pressure in pipe is 2102 (14.6 psi)
Next second: 11,000'
Air pressure: 1400.1 Temp: 479.5 Air density: .0017011
958' per sec. 958 squared times .5 times is 780.6 Total force: 245,234 lbs. Air pressure in pipe is 2180.7
Next second: 10,000'
Air pressure: 1455.6 Temp: 483.0 Air density: .0017555
958' per sec. 958 squared times .5 times is 805.5 Total force: 253,076 lbs. Air pressure in pipe 2261 (15.7 psi)
Next second: 9000'
Air pressure: 1512.9 Temp: 486.6 Air density: .0018113
Plug in 950' per sec. 950 squared times .5 times is 817 Total force: 256,777 lbs of force. Air pressure in pipe is 2330 (16 psi).
The Buddha has noticed the deceleration, but also notices the Earth approaching him at wild pace. Notes that he was rather partial towards aluminum. And though the steel cap is slightly warmer, he has always considered steel as a cold and unforgiving substance.
Next second: 8,000'
Air pressure: 1572.1 Temp: 490.2 Air density: .0018685
Plug in 940' per sec. 940 squared times .5 times is 825.5 Total force: 259,339 lbs. Air pressure in pipe is 2397.6 (16.65 psi).
The Buddha takes out his contractual agreement and reads it very carefully.
Next second: 7,000'
Air pressure: 1633.1 Temp: 493.7 Air density: .0019270
Plug in 930' per sec. 930 squared times .5 times is 833 Total force: 261,798 lbs. Air pressure in pipe is 2466 (17 psi).
The Buddha is still going 634 mph and is 7000' above the water, but the Buddha is still reading.
Next second: 6,000'
Air pressure: 1696.0 Temp: 497.3 Air density: .0019869
Plug in 910' per sec. 910 squared times .5 times is 822.6 Total force: 258,451 lbs. Air pressure in pipe is 2518 (17.5 psi)
Next couple seconds: 5000'
Air pressure: 1760.9 Temp: 500.8 Air density: .0020482
Plug in 895' per sec. 895' squared times .5 times is 820 Total force: 257,714 lbs. Air pressure in pipe is 2581 (18 psi).
Buddha finishes reading contract, then crumples it into a very tight ball.
Next second: 4,000'
Air pressure: 1827.7 Temp: 504.4 Air density: .0021109
Plug in 880' per sec. 880' squared times .5 times is 817 Total force: 256775 lbs. Air pressure in pipe is 2645 (18 psi).
3000':
Air density: .0021752 Plug in 865' per sec. 865' squared times .5 times is 823 Total force: 258,617 lbs
2000':
Air density: .0022409 Plug in 855' per sec. 855' squared times .5 times is 819 Total force: 257,320 lbs
1000':
Air density: .0023081 Plug in 840' per sec. 840' squared times .5 times is 814 Total force: 255,819 lbs.
Perhaps, this is good time to look at the solid iron 1 meter ball, it would also have the 814 lbs per sq'. It has 2.69 sq' area and total force on it would 2190 lbs, I believe it weighed 4 tons, so at this point in time it would be pulling 3 tons on pipelauncher. Since it is hanging from 100' cable it will hit the water first.
0':
Air pressure: 2116.2 Temp: 518.7 Air density: .0023769
Plug in 830' per sec. 830' squared times .5 times is 818.7 Total force: 257,209 lbs. Air pressure in pipe is 2935 (20.38 psi).

Now, comes the fun part. What happens when this thing hits the water at 566 mph. I would have to concede that without the other factors adding to drag, it looks like Buddha is certainly going to get very wet. Unless something stops the pipelauncher, it will go another 830' in the next second, since it's only 400' long that would put Buddha 430' under water. And when you go 400' underwater, you generally get very wet.

Now, granted, it is probably a very common notion that as soon as this thing hit the water it would explode and kill the Buddha. This might be basically correct. It might be prudent for the Buddha put down his player mat and buckle up his seat belt. Or at least lie down on the cap. But believe or not the cap is still pretty cold, you would think it would be hot, but it isn't. Buddha did consider jumping into the air stream rushing by the edge of the cap, but he didn't like the idea of jumping into air moving at over 500 mph, besides the minimal impact speed would around 120 mph; he would get wet and probably die. Probably better to stay on pipelauncher.
Now the Buddha is still smoking his cigaratte, muttering about the lack of coffee on this flight. He crouches down and with pencil starting writing on the cap. First, he writes, "Buddha was here".
At this point, Buddha hears the iron ball hit the water, now he is traveling near the speed sound, so his hearing is delayed but compared to say someone 500' away in a boat, the Buddha will hear it first, not because he is an enlighten being but during the milliseconds of the sound being created, Buddha has got closer to it. What exactly the Buddha hears is hard to know- it will be a loud noise, but it's exact shape and the location it appears to be coming from, is somewhat mysterious. The pipelauncher is creating a bow wave in the air- like a boat in water. The bow wave is, of course, moving and has varying density of air, some of this air is being "stretched" over the length of the pipe. Then you have the steel itself, which can transmit sound at a higher speed than air. This not really issue I've mentioned before, but basically a pipelauncher is a huge musical instrument. What sound it makes it would be interesting. Personally, I would like it to be a roaring & ringing sound- a sound for everyone, incuding the deaf. A screaming bass from another dimension:)
Anyways, the guy in the boat, is a fisherman, he is a hindu. So far today, he has caught a few sharks. A few seconds ago he looked up when he heard a sound.

Well, that's all for the moment. It's been a long session in posting.

Log in or register to post.

The whole thread