vq
Earth
What time is it again?
Posts: 129
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Post by vq on Dec 28, 2011 1:27:44 GMT -4
Greetings! I have a few questions on the CM main parachute system that I hope someone here can answer. The command module used three parachutes, which Wikipedia says allowed the spacecraft to splash down at 22 miles per hour (9.8 m/s). What were the landing velocities for a single parachute failure (as occurred in Apollo 15) and a dual parachute failure (which as I understand was not survivable)? What was the terminal velocity of the spacecraft at sea level without main chutes deployed?
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Post by zakalwe on Dec 28, 2011 6:20:26 GMT -4
On Apollo 15, the failure of the third canopy meant that the impact speed was less than 10 metres per second (p373, How Apollo Few to the Moon), up from 8.5 metres per sec. for a 3 parachute splashdown. At 7300 metres altitude they were descending at 150 metres per second (p371, How Apollo Few to the Moon). The canopies were deployed at 3000 metres. I can't find any reference to a no-canopy freefall terminal speed.
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Post by zakalwe on Dec 28, 2011 6:23:54 GMT -4
This PDF also contains some further details on the parachute system. HTH
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Dec 28, 2011 14:54:25 GMT -4
If the capsule is falling at terminal velocity, the velocity should be proportional to the square root of 1 over the area of the parachutes. That is,
V ~ (1/A)1/2
Therefore, for 3, 2 and 1 parachutes, the velocity should be proportional to,
V ~ (1/3)1/2 = 0.5774
V ~ (1/2)1/2 = 0.7071
V ~ (1/1)1/2 = 1
Thus, if 8.5 m/s was the splashdown velocity for a normal three-parachute landing, the velocity with two parachutes should be,
V = 8.5 x 0.7071 / 0.5774 = 10.4 m/s
and for one parachute,
V = 8.5 x 1 / 0.5774 = 14.7 m/s
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Dec 28, 2011 15:09:23 GMT -4
As for the final part of your question, the formula for drag force is
FD = ρ CD A V2 / 2
where, FD = drag force ρ = air density CD = drag coefficient A = area normal to the flow V = velocity
Since the capsule is falling at terminal velocity, the drag force equals the weight of the body. The Apollo capsules had a mass of about 5,000 kg at splashdown, thus their weight was about 5000 x 9.8 = 49,000 N. Assuming the vehicle is falling heat shield down, the area is 12 m2 (3.91 m diameter). The CM drag coefficient was about 0.85 at subsonic velocity. Air density at sea level is 1.225 kg/m3. Plugging in all these number, we get
49000 = 1.225 x 0.85 x 12 x V2 / 2
V = 89 m/s (200 MPH)
EDIT #1
This assumes the the parachutes didn't deploy at all or were torn away from the CM. If the CM is falling with the uninflated parachutes dragging behind it, this would produce additional drag and slow the capsule down.
EDIT #2
Corrected the drag coefficient from 1.3 to 0.85. The 1.3 CD that I remembered was at hypersonic velocity. 0.85 is the CD at Mach 0.4.
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Post by chew on Dec 28, 2011 19:48:03 GMT -4
Adjusting the known free fall velocity at 7300 meters for sea level I get 91.6 m/s. Close enough for government work.
Hey, someone should make a poster like that. One of the famous photos of Aldrin or Irwin or Young on the Moon with the caption "Close enough for government work." We could sell it to civil servants and make a fortune.
Edit: Oops. I used the wrong scale height. It should be 91.6, not 95 m/s.
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raven
Jupiter
That ain't Earth, kiddies.
Posts: 509
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Post by raven on Dec 28, 2011 21:25:02 GMT -4
Question from the peanut gallery: Would a one parachute landing have been survivable?
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Post by chew on Dec 28, 2011 22:25:32 GMT -4
Question from the peanut gallery: Would a one parachute landing have been survivable? Splashing down with one chute would have been twice as hard as Apollo 15's splashing down with 2 chutes. Considering no one was hurt I doubt a one chute landing wouldn't be fatal. The couches were designed to protect the crew during an abort where they could possibly land on solid earth. The third chute was a back-up in case one chute failed.
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vq
Earth
What time is it again?
Posts: 129
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Post by vq on Dec 29, 2011 0:45:54 GMT -4
Thanks Bob for the equations and everyone else for the thoughts. My intuitive thought was similar, that terminal velocity under one parachute would be faster (but not all that much faster) than under two. Can anyone confirm whether or not a water landing with one fully functional and two completely failed parachutes would have been lethal? This seems like a possibility that must have been considered during mission planning.
Again, thanks!
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Dec 29, 2011 9:43:21 GMT -4
Can anyone confirm whether or not a water landing with one fully functional and two completely failed parachutes would have been lethal? Surely there were studies done on this, but I've never bothered to research it. I can't image a one-parachute landing being lethal because it's only about a 35 MPH impact. A 35 MPH automobile collision is certainly survivable, so I think a 35 MPH water landing ought to be. Many years ago I created a spreadsheet to help me estimate the peak g-force experienced during splashdown. I'll look to see if I still have it somewhere. If I can find it, I'll try to figure out the difference between 3-, 2- and 1-parachute landings.
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Post by sts60 on Dec 29, 2011 10:15:01 GMT -4
A 35 mph car wreck will easily kill you if "done right", but all capsule-landing crews are in the most survivable mode - lying flat and fully supported by an energy absorbing system, with no possibility of the violent whiplash that can damage the spinal column or collision with other hard objects. Of course, going fast enough, internal injuries will still be fatal even without these trauma modes.
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Post by chew on Dec 29, 2011 11:33:01 GMT -4
You mean the astronauts were laying flat? The capsule was suspended at an angle to cut into the water and reduce deceleration.
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Post by zakalwe on Dec 29, 2011 12:22:34 GMT -4
The couches were designed to protect the crew during an abort where they could possibly land on solid earth. The third chute was a back-up in case one chute failed. Drop tests showed that a hard landing would result in the capsule tumbling, and without retro rockets (like the Russians use) the astronauts would always be injured. The LES designed to make sure that the capsule always ended up in the sea during an abort to specifically prevent the possibility of a hard landing (using the pitch control motor).
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Post by ka9q on Dec 29, 2011 15:02:08 GMT -4
I understand the rationale for the multi-stage Apollo parachute design. But count all the parachutes! First, one pulls the apex cover away. Then two pilot chutes pull out the two drogues to slow and stabilize the CM. Then a pilot chute pulls out each of the mains, each of which unreefs twice. By my count that's *eleven* parachutes, and most of them have to work. So do all the pyrotechnics that fire the mortars and pyro cutters. I'm kinda amazed that parachutes of all kinds work as well as they do.
Suppose the Apollo CM came down on just its two drogue chutes? What would the terminal velocity be then? I realize this isn't a very realistic scenario, as you wouldn't discover that your main chutes weren't working until after you cut away the drogues.
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Post by chew on Dec 29, 2011 19:01:27 GMT -4
Suppose the Apollo CM came down on just its two drogue chutes? What would the terminal velocity be then? I realize this isn't a very realistic scenario, as you wouldn't discover that your main chutes weren't working until after you cut away the drogues. Wikipedia, without a reference, states the drogues deployed at 24,000 feet and slowed the capsule down to 125 mph. Assuming the 125 mph speed was obtained at 20,000 feet then the capsule on two drogues would have hit at 83 mph (37 m/s). I can't find any altitude - velocity figures for the drogues.
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