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Perigee
Aug 15, 2011 15:47:53 GMT -4
Post by pleasedebunkme on Aug 15, 2011 15:47:53 GMT -4
You helped me with my questions before, so I am back for more help, please. My question again centers on the re-entry corridor, with the Apollo command module entering the atmosphere. I understand that the command module came back from the moon and swung around to the far side of the Earth in an elliptical orbit. At a height of 400,000 feet, the command module was traveling at a negative 6.5 degree angle, with a velocity of 36,194 fps. As of that point in the atmosphere, the command module had not reached perigee, yet. It is my understanding that the command module would have continued to accelerate until one of two things happened: A. It reached perigee, or B. The force of the wind resistance equalled the gravitational acceleration.
I want to find out at what height the command module stopped accelerating. Also, I want to find out the final (maximum) velocity of the command module, when it did stop accelerating. How do I do this?
Thank you for your help.
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Perigee
Aug 15, 2011 17:11:31 GMT -4
Post by Bob B. on Aug 15, 2011 17:11:31 GMT -4
At a height of 400,000 feet, the command module was traveling at a negative 6.5 degree angle, with a velocity of 36,194 fps. Those were the numbers for Apollo 11 -- the other missions were a little different. The following web page gives the numbers for all the Apollo missions: history.nasa.gov/SP-4029/Apollo_18-40_Entry_Splashdown_and_Recovery.htm Technically, it never stopped accelerating. As long as the velocity’s magnitude and direction were changing, the capsule was accelerating. When slowing down it simply had a negative acceleration. According to the page referenced above, Apollo 11’s maximum entry velocity was 36,277 ft/s. As far as trying to explain how to figure it out for yourself, I believe it is too complex of a subject to try to tackle here.
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Perigee
Aug 16, 2011 1:50:26 GMT -4
Post by ka9q on Aug 16, 2011 1:50:26 GMT -4
The number I think you're looking for is called the "vacuum perigee". This is what the perigee of the entry orbit would be if the earth didn't have an atmosphere. I think it's typically around 80 nautical miles, but that's from memory. It's low enough that the spacecraft is captured by the atmosphere and slowed from its near-escape velocity to guarantee capture, then it typically rises again and enters a second and final time. The purpose of this is to spread out the heat loading over time.
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Perigee
Aug 16, 2011 7:21:03 GMT -4
Post by banjomd on Aug 16, 2011 7:21:03 GMT -4
ka9q: this is distinct from a "skip reentry", correct?
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Perigee
Aug 16, 2011 9:37:45 GMT -4
Post by Bob B. on Aug 16, 2011 9:37:45 GMT -4
The number I think you're looking for is called the "vacuum perigee". This is what the perigee of the entry orbit would be if the earth didn't have an atmosphere. If that's what he's looking for, then I can figure that out. We'll use equations 4.29, 4.30 and 4.31 from the following web page: www.braeunig.us/space/orbmech.htm#launchWe need to know GM, r, v and ϕ, from which we can calculate everything else. GM for Earth is equal to 3.986005x10 12 m 3/s 2. We know v (velocity) and ϕ (flight path angle) at Earth entry from NASA documents, which are 36,194.4 ft/s (11,032 m/s) and -6.48 degrees respectively. We also know r (radius vector), thought it may not be readily apparent. It's my understanding that the entry velocity and angle are take at an altitude of 400,000 feet, and I've been told NASA uses a value of 3443.9307 nautical miles for the radius of earth. Thus the radius vector is simply the sum of these numbers, which, when converted to meters, is 6,500,080. So we have, GM = 3.986005x10 12 m 3/s 2v = 11,032 m/s r = 6,500,080 m ϕ = -6.48 degrees From equation 4.29 we get the perigee and apogee radii: Rp = 6,416,655 m Ra = 841,873,270 m From equation 4.30 we get the eccentricity: e = 0.98487 And from equation 4.31 we get the true anomaly: v = -13.06 o, or 346.94 oTrue anomaly is the location of the spacecraft in its orbit past its perigee point. Thus, we see that Apollo 11 reached entry interface 13.06 o before perigee. The altitude at perigee is simply the perigee radius less the diameter of Earth, which is 38,495 m (20.79 n.mi.). The velocity at perigee is derived from equation 4.16, which is 11,104 m/s (36,430 ft/s). Of course, as ka9q said, this is the perigee altitude and velocity the spacecraft would achieve had it not encountered the atmosphere. According to NASA records, Apollo 11 reached a maximum entry velocity of only 36,277 ft/s because it was slowed down by the atmosphere. And it never reached perigee because it was overcome by drag and fell to Earth.
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Perigee
Aug 16, 2011 15:30:16 GMT -4
Post by lukepemberton on Aug 16, 2011 15:30:16 GMT -4
According to NASA records, Apollo 11 reached a maximum entry velocity of only 36,277 ft/s because it was slowed down by the atmosphere. And it never reached perigee because it was overcome by drag and fell to Earth. Phew, thank goodness for that Seriously though, I recall discussing this with ka9q via PM. During the Apollo 13 film, the drama of reentry was described with the CM skipping off the Earth's atmosphere if too shallow, or burning up if too steep. The latter I can understand. I have two questions: (1) ka9q explained that the CM would not actually skip of the Earth's atmosphere like a stone, but simply pass straight through the thin uppor layers and out the other side. Is this this case? I ask this question not out of disbelief, but rather to share the information imparted to me by ka9q. (I think I have quoted you correctly ka9q - sorry if I have not, and please correct me if so). (2) How did the engineers determine the reentry corridor? That is, how did they work out the balance between needing to slow the CM down and the thermal load? Was it theoretical or experimental, or a mixture of both.
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Perigee
Aug 16, 2011 16:40:28 GMT -4
Post by JayUtah on Aug 16, 2011 16:40:28 GMT -4
Isn't this just a rehash of the "antipode" hoax theory from last month? If so, then there are some open questions there regarding allegations that the CM was not structurally strong enough. Any progress on those, pleasedebunkme, or can we assume you've retracted that claim?
It sounds like what you're asking is how to determine the peak terminal velocity of the CM -- the point at which aerodynamic drag begins to slow the vehicle from its orbital velocity, which would naturally be increasing as it approached perigee.
The answer is "very carefully." Which is to say, it's not a matter of simultaneously solving the aerodynamic drag problem (in isolation) against the orbital mechanics problem (in isolation). Factors from one dynamic model actually affect the other factors.
The CM is a lifting body, which means as soon as it starts to exhibit drag, it begins to develop significant lift. That further means you can't consider the spacecraft's path solely a product of orbital mechanics. It is initially dominated by orbital mechanics as perturbed by atmospheric interaction, then later dominated by aerodynamics as perturbed by orbital mechanics. The transition between the regimes is smooth.
Seen from the other perspective, the spacecraft's drag as a function of either distance or time traveled will vary according to the flight path, and further according to meteorological atmospheric conditions and angle of attack. Some of these are not known until the entry is actually flow, but are generally second-order effects at most. Orbital velocity starts out as a first-order effect but then transitions gradually to pure ballistic flight.
There is no closed form to reconcile these two interdependent models. In practical terms, entry interface for the purpose of determining the appropriate control laws is defined as a measured atmospheric drag of 0.05 g. This is as it was for Apollo, and as we still use it. This will cause the flight control regime to transition from orbital flight to atmospheric flight. Initially in atmospheric flight the residual orbital motion is a significant perturbation, but it's modeled generally as a linear path formed by the state vector at entry interface.
So in short, the peak terminal velocity is never modeled as part of the control-law formulation. The physically accurate model is too unwieldy to work with. The physically "good enough" model (you're in an orbit until 0.05 g deceleration, then you're flying) doesn't care about it.
Good thing we can cheat on this problem. The peak velocity for Apollo 11 is a matter of record, and has been reproduced here by Bob. Because of what we know about its orbit, we can say that this peak velocity is the peak terminal velocity because it hadn't yet reached perigee. If we say that the spacecraft only slowed from that peak velocity, then we know that this slowing had to be caused by aerodynamic drag and not by anything related to orbital mechanics.
The control laws are predicated on the presumption that orbital velocity vector at entry interface and ballistic velocity vector in the aerodynamic/ballistic flight regime remain close enough for long enough to exhibit manageable error. So you can solve the spacecraft's orbit for the known peak velocity and from that obtain the corresponding true anomaly. With that you can use the orbit's geometry to determine the altitude of peak terminal velocity. That will be the easiest way to approximate the solution.
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Perigee
Aug 16, 2011 16:58:43 GMT -4
Post by JayUtah on Aug 16, 2011 16:58:43 GMT -4
(1) ka9q explained that the CM would not actually skip of the Earth's atmosphere like a stone, but simply pass straight through the thin uppor layers and out the other side. Is this this case?Yes, with a "but." An ordinary ballistic object with an unremarkable aerodynamic profile will "skip out" simply by passing through the upper layers of the atmosphere. Those upper layers have too little density to overcome the orbital velocity, so you end up with a lower-energy orbit, but the orbital mechanics regime practically dominates this scenario. Since the CM is a lifting body, it may be possible for the CM to generate enough lift in a shallow entry scenario to "skip" rather than pass through, but that would presume the CM -- for some reason -- could not be commanded to a 90-degree angle-of-attack that would essentially zero out the lift. A very remote possibility, so it's best to stick to the notion that it would simply fail to encounter enough air to reduce its velocity below some orbit. (2) How did the engineers determine the reentry corridor? That is, how did they work out the balance between needing to slow the CM down and the thermal load? Was it theoretical or experimental, or a mixture of both.Very much a mixture of both. This is evident in the vastly different entry profiles at each extreme of the corridor. In the shallow extreme the ship descends monotonically. In the deep extreme, the ship "double dips" with a climb-out in between to allow the TPS to cool. Nowadays we tend to go straight to computer models, but Apollo engineers relied more on theoretical approaches. The literature is full of theoretically derived heat-loading profiles for various angles and speeds, which were then iteratively reconciled with the CM's performance as a glider. The Apollo engineers relied heavily on empirical testing. The CM's lifting-body parameters could be determined in terrestrial wind tunnels to a great degree of certainty. There is a wind tunnel at Ames that can produce very high wind pressures that actually permit heat transfer testing. So the ablative materials can be empirically investigated there too. However the TPS design for Apollo borrowed heavily from MIRV designs in nuclear weaponeering, so there was already a wealth of empirical data on the performance of those systems. The CM did not require as much TPS testing as a clean-sheet design would have suggested.
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Perigee
Aug 16, 2011 17:34:30 GMT -4
Post by Bob B. on Aug 16, 2011 17:34:30 GMT -4
So you can solve the spacecraft's orbit for the known peak velocity and from that obtain the corresponding true anomaly. With that you can use the orbit's geometry to determine the altitude of peak terminal velocity. That will be the easiest way to approximate the solution. That much I can do. Using orbital mechanics only, Apollo 11 would reach it's maximum velocity of 36,277 ft/s at a true anomaly of -10.53 degrees and an altitude of about 304,000 feet (92.6 km).
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Perigee
Aug 16, 2011 17:34:55 GMT -4
Post by lukepemberton on Aug 16, 2011 17:34:55 GMT -4
However the TPS design for Apollo borrowed heavily from MIRV designs in nuclear weaponeering, so there was already a wealth of empirical data on the performance of those systems. The CM did not require as much TPS testing as a clean-sheet design would have suggested. Thanks for the information. That must be one impressive wind tunnel at Ames. When all is considered, Apollo is even more impressive when one places it into full perspective, and considers that the engineers of the day did not have the computing power and models of our modern era. I thought this was the case with Apollo and MIRV. My memory is telling me that ka9q discussed this with me too. I guess that provokes a different question: How much of Apollo was about researching nuclear warhead vehicles, and how much was taken from the performance of those vehicles? The reason I ask is that some HBs are not able to divorce NASA and the military. I understand there is a cross over, but that's the nature of government organisation. If I am correct, the US move into the space race exploited existing nuclear vehicles rather than the other way around. However, I guess that ICBM research and the Apollo programme were probably symbiotic to a degree, with some overlap in parts. But I would contend that Apollo was still primarily a scientific programme. It just seems such a shame that the HB community use their anger towards military enterprise to diminish a wonderful technical achievement. It is a connection that I cannot understand, and their anger seems to be quite fervent. From my experience of the HB community at YT, the hoax theorists are very anti-government and lack objectivity towards Apollo because of their anti-government stance. Take he-who-must-not-be-named and his attack on you at Yahoo forums. If I recall, he managed to drag the Iraq war into the discussion too, slandering you in the process. I'm not sure that the HBs understand that most of us are humble scientists/enigneers/enthusiasts who are not always happy with our governments either. According to the HB community, I'm a highly paid NASA/CIA shill that would do anything for my government, although I am not a US citizen, and I opposed the invasion of Iraq. A bizarre stance for a government agent. I'm still waiting to receive my pay cheque though - can you drop by the office for a word and sort it out for me
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Perigee
Aug 16, 2011 20:15:08 GMT -4
Post by JayUtah on Aug 16, 2011 20:15:08 GMT -4
Coincidence of coincidences, I stood in line at the bank just now behind my friend retired from North American, who worked on the RTCC computer programs associated with re-entry. He confirmed that the entry profiles were all formulated as a function of time, with both velocity and altitude being the typical dependent variables. Once the velocity is captured at altitude entry interface (400,000 feet MSL) it is assumed constant until transition to aerodynamic flight at approximately 250,000 ft, entry + 200 seconds. Maximum lift occurs early in the flight profile. Maximum heat loading occurs at approximately E+400 seconds for a steep entry, approximately E+700 seconds for a shallow entry. Higher peak temperature occurs in a shallow entry, but is endured for a shorter time. This should confirm that peak mission velocity can be considered suitably identical to peak terminal velocity, and occurs at around 250,000 feet MSL. However these figures are from the control-law trajectory models as used by NAA programmers. Thanks for the information. That must be one impressive wind tunnel at Ames.The large tunnel dominates the view of the Ames campus as seen from U.S. 101. "Holy [noun]" is the most common response from first-time viewers. But the high-velocity tunnel is more modest. It funnels the air down to a very small test chamber. ...the engineers of the day did not have the computing power and models of our modern era.They simply worked differently than we do. In my opinion these guys used their brains more. We can plug all kinds of problems into FE modelers and simulate many possibilities in short order. The previous generation had a more complete qualitative grasp of the physical world. Their models may seem crude and simplistic in what answers they produce, but they're very elegant in what they embody and how they were understood by those who used them. Luckily there are still enough practitioners of those old methods around to tell us when our computers get the wrong answers -- and more importantly: why. I guess that provokes a different question: How much of Apollo was about researching nuclear warhead vehicles, and how much was taken from the performance of those vehicles?I'm not sure we'll ever know. All the technology transfer I've seen in the literature is from the military toward NASA. My impression was that Apollo was considered high enough priority that it could legitimately use leading-edge military assets. The reason I ask is that some HBs are not able to divorce NASA and the military.I see that too, and I think the reasons are more psychological than factual. As you note, the hoax community on YouTube seems to be a hotbed of anti-government sentiment. If I am correct, the US move into the space race exploited existing nuclear vehicles rather than the other way around.Yes. As I said, NASA seemed to have few assets of its own in the early years and piggy-backed on the military because they were already proficient in high-performance engineering and had extensive operational facilities and experience. Regardless of your moral views on the military, from an engineering perspective they have a very good track record of handling high-risk technologies. However, I guess that ICBM research and the Apollo programme were probably symbiotic to a degree, with some overlap in parts.Yes, unavoidably so. The civilian space program occasionally served as cover for covert missions, although we know of only one such instance in Apollo (Project Chapel Bell). But rocketry is rocketry, largely regardless of its purpose. So advances in one application will naturally bleed over to others. It's no accident that after the LM team perfected chemical milling, that technique was used on the F-14 produced by the same team at the same company. Although the Saturn V was developed as a peaceful vehicle, you can bet that the contractors, who also held military development contracts, were thinking ahead of how they could apply lessons learned from the Saturn project. Contractors are generally forbidden from using secretly-developed military techniques for equivalent civilian projects. But nothing forbids the use of civilian technology for military applications. And if you're being paid to develop it, you should leverage it across as much of your business as you can. Now of course that doesn't mean you give it to your enemies. So much of the bleeding-edge technology developed for Apollo (as opposed to borrowed from the military) was also classified in order to keep it from the Soviets and to hide our overall capability from them. But on the whole, Apollo resulted in more military technology being used for civilian applications (and thereby declassified) than otherwise, such as the introduction of military-style project management techniques that have become commonplace in the world's technology industries. When the general trend is to transfer from secret projects into public projects, you get generally more disclosure. I'm not sure that the HBs understand that most of us are humble scientists/enigneers/enthusiasts who are not always happy with our governments either.For them the battle is political, so they assume our defense of NASA is just as politically motivated as their attack on it. They don't understand that their politically-minded attacks cast aspersions on legitimate achievements that are generally unrelated to the reasons for their displeasure. The rest of the world is happy to view Apollo and NASA as only tangentially connected to the military, and wholly unconnected to the CIA. The conspiracy crowd has always fantasized of the government as one huge evil empire. So much easier then to cast themselves as the avenging heroes. According to the HB community, I'm a highly paid NASA/CIA shill that would do anything for my government...That's because they're casting you in the little drama they play out for themselves in their walled garden. What does it matter that none of it -- the space science, the history, or your actual activities -- bears any resemblance to the real world. Those people are inconsequential in the real world. In their fantasy world they're the top-notch sleuths who cracked the Apollo conspiracy. The sad thing is that while they want to pose as such characters there, they cause real problems for the real people whose real-life reputations they damage with their little play-acting. I fear it's only going to be a matter of time before they style someone as a villain to the point where he takes legal action. I'm still waiting to receive my pay cheque though - can you drop by the office for a word and sort it out for me You won't get a penny from the U.S. government until you learn to spell "check" and "program." They should have covered that in the CIA orientation.
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Perigee
Aug 16, 2011 20:39:07 GMT -4
Post by Count Zero on Aug 16, 2011 20:39:07 GMT -4
The large tunnel dominates the view of the Ames campus as seen from U.S. 101. "Holy [noun]" is the most common response from first-time viewers. ...inevitably leads to: www.youtube.com/watch?v=zQVfOguNWBw ;D
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Perigee
Aug 16, 2011 21:02:39 GMT -4
Post by ka9q on Aug 16, 2011 21:02:39 GMT -4
I was going to point out what Jay has already pointed out: that the apparent "skip" in the normal Apollo entry trajectory could either be due to orbital mechanics (moving so fast that the earth's surface curves away faster than the trajectory is bent toward it by gravity) or aerodynamics (the lift produced by the Apollo CM) or a combination of both. I'd have to see the actual trajectory.
I can't remember exactly what I said last time, but I've known for some time that the CM is a lifting body so I shouldn't have said that it had to be entirely orbital mechanics during a nominal entry.
But if the entry angle was so shallow that the vacuum perigee was simply too high to effect much energy loss, then when NASA talks dramatically about the CM "skipping" back into space, never to return, it clearly would be orbital mechanics at work. Maybe that's the case we were talking about.
I don't think the CM's lift could actually be turned off or varied without shifting its c.g., which would be impractical. It was inherent in the off-center location of the c.g. It could be pointed in any direction perpendicular to the velocity vector by rolling the spacecraft to the appropriate angle, and its average value could be varied by the appropriate maneuvers. E.g., a continuous roll would zero out the average lift and the CM would follow a corkscrew path.
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Perigee
Aug 16, 2011 21:09:23 GMT -4
Post by lukepemberton on Aug 16, 2011 21:09:23 GMT -4
Thank you for a such a comprehensive reply. It is hard to reply in full at this time in the morning, since I do have to go to bed soon. I will pick up the rest tomorrow out of courtesy. It was good to hear your opinion regarding the direction of technology transfer, given your first hand experience in the industry. In my world, exploitation of research is an important aspect. The primary objective of any research is to obviously meet a specific goal or objective. However, when a research proposal is submitted as part of a program(me) of work, the research bids that meet the primary goal and have clear transferable science routes will have less problem being approved. The development of new techniques, models or applied technologies all come under the remit of transferable science. As for the political/military perspectives that the HB fraternity place on Apollo; it seems that the HBs base their agenda on hatred of government/authority. I would not be surprised if some of their backlash is due to educational experiences, and they choose to vent their aggression on those that have achieved more. I do wonder if some of it comes down to jealousy. I always look upon the Apollo program(me) as a scientific project. I was carrying out educational outreach duties about 2 months ago, and a 10 year old asked me why JFK decided to land men on the moon. Although in easier words, I replied: It was about embracing the skills of a nation to achieve something great, while creating an enduring economic, historical and academic legacy. JFK wanted to do it so America could prove to themselves as a nation that they could do it, and be proud of their achievement. I got a lot of thanks of the teachers after for highlighting the importance of the events some 40 years later. I hope that it still inspires. It is such a shame that the HBs turn it into part of their political manifesto and fail to see the longer term benefits of Apollo and the impact on their daily lives (technology transfer again). You won't get a penny from the U.S. government until you learn to spell "check" and "program." They should have covered that in the CIA orientation. Very good Actually, I think you have me handcuffed and into the back of the wagon with paycheck. Gillian can help out with this one, but I think paycheck is used by the US and British. Cheque has a very distinctive meaning in the UK. However, program is something I watch on TV, while programme is a set of coordinated events or items intended to deliver a final coherent output. I'm sure the CIA will beat it out of me eventually.
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Perigee
Aug 16, 2011 21:27:37 GMT -4
Post by echnaton on Aug 16, 2011 21:27:37 GMT -4
...then when NASA talks dramatically about the CM "skipping" back into space, never to return... Would it really have gone into orbit around the sun? I was under the impression that the maximum velocity of the capsule was under escape velocity. That the capsule would have gone into a long orbit whose return would occur long after the power ran out. Perhaps NASA implied the skipping into space to avoid planting the rather unpleasant picture in peoples minds of a dead capsule with dead astronaut crashing to earth after the loop into space.
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