How about 3 decimal places in feet, since the CM is only 60 miles up? If you're off by a hair, it turns into miles down range.
No. It's hard to imagine where to begin addressing all the fail[ure] in this statement.
First, three decimal places in feet is 0.001 foot or 0.012 inch, or about 3 sheets of cheap laser printer paper (ca. 0.004 inch per page). Do you really think rockets launched from Earth are routinely placed on the launch pad to that precision? Do you really think the
have to be? Do you honestly think through these claims before you make them?
No, it was never a requirement to fix the launch position of
any space vehicle to that precision, no matter its mission or destination. You're just pulling numbers out of your orifice because you have no clue what you're talking about and want to sound impressive. Laymen think everything in aerospace has to be established to absurd tolerances. Some things yes. It takes an engineer to know which. Laymen just apply absurd requirements across the board.
Second, guidance and propulsion dispersion accounts for far more error. Dispersion can be thought of as fastening a rifle in a vise on a sturdy anchor and then firing several shots at a very distant target. The shots still cluster and do not simply pass through the same hole exactly. This is due to the compounded error of several factors that generally cannot be controlled to sufficient precision, such as jitter in the IMU pickoffs or thrust bursts below the resolution of the accelerometers. This is practical space flight, which accounts for all such things and trims them at the end. Guidance is never just open-loop dead reckoning, although a layman might mistakenly think so.
Third, no -- errors in launch site
position do not compound, as the attached drawing illustrates. Downrange position errors at the launch site result in commensurate downrange position errors at the insertion point.
They do not compound. This is a classic layman's mistake. No one who has any experience with inertial guidance of any sort would make this sort of error. It is fundamental. It is elementary. It's like an "expert" chef not knowing the difference between cheese and an egg.
I've personally witnessed that when somebody gave me an equation with a wrong sign (+/-) that caused an error in the least significant bit of a calculation related to IMU alignment, which gets integrated (added repeatedly),
Yes, IMU alignment is important. However it has nothing to do with the launch
position.
IMU gimbal angles are picked off as a 16-bit unsigned value, typically. The physics of how it's measured preclude much higher resolution without unacceptable noise. The AGC had a 15-bit word, so the Apollo IMUs read out in 15-bit unsigned values. So 360°/(2
15) produces a metrical resolution of 0.011°. You can't measure angles any smaller than that using the IMU. Here's the part you didn't know: Theodolite alignments are precise only to about 0.05°. So you've already accumulated
five times as much measurement error as you say your coding bug caused.
Optical measurement in a stationary LM is possible to 0.02° (with astronauts demonstrating interpolation ability to near 0.01°) using the AOT. The pre-launch IMU alignment procedure uses three factors, although theoretically only two factors are required to achieve suitable alignment. These are combinations of gravity measurements and celestial sightings. Three factors are used to allow one factor to be grossly in error; only two of the factors have to work. Today's off-the-shelf automatic star trackers achieve 3-10 arcseconds (0.0008-0.0027°) of precision, now finer than most IMU resolutions.
The salient points are these.
1. Your reliance on the necessity of theodolite measurements from a carefully surveyed reference point is a red herring. In fact (and this was demonstrated in ICBM programs), celestial sighting is and has always been a better method. It is not used for initial IMU measurements at Earth launch because it is generally not available.
2. Existing guidance system performance is already demonstrably sloppier than what you claim is required, yet we manage to operate spacecraft successfully in missions that include substantial pointing constraints.
3. Dispersions resulting from guidance jitter are common and accepted.
...and they almost aborted a launch in flight...
Name the vehicle and payload, launch date and location. You won't because I know you're lying
again. No launch is ever aborted because of LSb errors in guidance. That's negligible. Strap-down gyros generate far more error than that just in normal operation, and are tolerable.
Do you honestly think these tall tales are really fooling anyone?
The
minimum IMU alignment error -- that is, the finest the IMU could be aligned by any means -- accepts a downrange error in the final insertion point, at an altitude of roughly 9 nautical miles, on the order of 3,000 feet. More than half a nautical mile! That's as accurate as any such IMU could
ever be, even in an Earth launch (which goes to much higher altitudes and compounds the IMU jitter to a much greater error). Tell me all about the bullet-with-a-bullet expectation again. Let's say the astronaut bungled the IMU celestial alignment by as much as 0.1° -- an absurdly large error, corresponding to an uncorrected IMU drift. With the error compounded through guidance integration, that's a downrange error on the order of 5 nautical miles, which is well within the sequencing maneuver's tolerance.
So what do you do about it?
Well, you simply adjust the timing of the next phasing burn. See, you're under the mistaken impression that you're trying to hit the CSM flying overhead in a single-shot maneveuver -- the "bullet with a bullet" misconception. That's not how rendezvous works. In fact you let the CSM fly overhead and go downrange a bit. Then you ascend and insert into a lower (and therefore faster) orbit. You may botch that insertion. You may be significantly up- or downrange from your desired insertion point.
Doesn't matter! The CSM is far ahead of you, and you're in a lower orbit. You have a whole set of rendezvous sequencing maneuvers ahead of you to make those orbits coincide. There never was a constraint that the inserted orbit coincide with the target orbit, hence no expectation that it should. The ascent flight plan required these maneuvers in all cases, so any ascent dispersions are simply folded into the exact parameters for those maneuvers, to be determined on the fly (literally).
Determined how? By using your radar to measure the angle, distance, and relative velocity between you and the target vehicle. If you know the orbit of one of those vehicles, you can use those measurements to derive the orbit of the other. Then the rendezvous phasing computations take hold. It doesn't matter what those orbits are. It only matters that you can
measure what they end up to be.
So you discover that because your IMU was grossly out of alignment, you ended up five nautical miles downrange from your desired insertion point. Ermagherd! How will it ever be possible to fix that! By the highly touchy procedure of ... (wait for it) ... starting the next phasing burn 5.5 seconds earlier than the baseline. Oh my golly, how can any astronaut hope to be able to do that!? Yes, we can literally be
miles off and still rendezvous.
So why bother trying to fix the launch position at all? Why bother timing the liftoff at all? Because to ascend and redezvous quickly and with the minimum expenditure of fuel is safer. We have the ability to fix the launch position to within a few miles, so do it. We have the ability to time the launch to the split-second, so do it. If done well, the result is a minimal phasing burn with minimum wait time. Earlier I said I could launch with the CSM an hour ahead of me and still be able to rendezvous. The catch is that in my lower orbit I'd have to wait several hours for those orbits to come into the proper phase, and with limited consumables on my spacecraft I don't want to. Those orbits will still coincide, but may do so only after I run out of oxygen. So I can perform a retrograde burn (velocity is a vector) and drop to an even lower, even faster orbit to speed up the rendezvous. But that's energy I'll need back later. I'll need to perform a bigger posigrade burn on my next sequencing step. And fuel is a scalar, which means I may run out of fuel if I speed up the process to fit within my oxygen consumables window.
But wait! There's another spacecraft! The CSM also has the ability to change its orbit. If I'm so far out of phase that I won't be able to get in phase before my oxygen runs out, and too low on fuel to be able to speed that process up before, I can ask the CSM to ascend to a higher, slower orbit so that I can catch up faster. Then
it can perform active-vehicle phasing burns to get me there. What a wonderfully well thought out process that was!
Now keep in mind that this had nothing to with the LM's launch
position. You are constantly and amusingly conflating those. IMU alignment and launch position are not at all related. Yes, both can produce errors that result in errors in the insertion point, to be corrected by adjusting the rendezvous sequencing timing. But you attribute the effects of one to the
kind of error produced by the other -- something no one would do if they had any knowledge or experience in this.
If I'm making an impression on you, it should be that you demonstrably have
absolutely no clue how to fly a spacecraft in space. Don't pretend you do.
In the meantime, what year are we supposed to have another manned lunar mission?
As soon as the political will supports it.
