Bob B.
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Post by Bob B. on Aug 29, 2011 10:45:48 GMT -4
It's hard to see how the LM could have gotten seriously out of plane without squandering so much delta-V that it wouldn't be able to land at all. It's not like they had a lot of fuel margin to begin with, and plane changes are notoriously expensive. That’s correct. The LM was given enough delta-v to land on the moon, not to land on the moon and make a plane change. Had the LM squandered its propellant making a plane change, there wouldn't be enough left over to land. Therefore it wasn’t possible for the LM to land at a position that was far out of plane. I would be interesting from a historical perspective to know how much work was done on this in planning for the missions and what the contingencies were. They planned for so many things that could go wrong, but was there a point in a malfunction scenario (however unlikely) in which an out of plane error was considered unrecoverable? The engineering fanboy in me always wants to know these things. The CSM typically made a plane change prior to LM ascent to bring the landing site back into the orbital plane. Over time the landing site would move out of plane, partly due to the Moon’s rotation and partly due to the CSM's orbital precession. For example, the Apollo 17 CSM performed a 366 ft/s lunar orbit plane change maneuver about 5½ hours before the LM lifted off. This is enough delta-v to make about a 4 degree plane change. We know the CSM had at least this much capacity to make a plane change. How much more it could do depends on how much unused propellant it had at the end of the mission. Each additional degree of plane change would require about 93 ft/s delta-v. On average, the CSM mass just prior to SM jettison was about 26,500 lbm. So, in rough numbers, it would take about 240 lbm propellant for each additional 93 ft/s delta-v. I don’t have the SPS propellant numbers available to me right now, but it would be pretty easy to look up how much propellant was remaining at the end of each mission. For each 240 pounds remaining, the CSM could have performed roughly one additional degree of lunar orbit plane change. Of course we have to consider that some of the remaining propellant could be unusable, i.e. it might not be possible to drain every drop from the tanks and get it into the combustion chamber. Please note that to determine how much propellant was required to provide the additional delta-v, I used the mass of the CSM at the end of the mission rather than the mass at the time the plane change was performed. At the time of the actual maneuver, the CSM would be heavier and the plane change would require more propellant. However, this unscheduled maneuver would lighten the CSM so that subsequent maneuvers, such as TEI and MCC, would require less propellant. The effect of the additional plane change on propellant usage would be as if the extra delta-v were tacked on at the end of the mission.
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Post by echnaton on Aug 29, 2011 13:00:09 GMT -4
Thanks, Bob. Excellent job as usual.
Those scenarios of pushing things to the edge make up the stuff that must have kept the mission planners up at night. Exactly how much risk do you put one man in with the hope of saving two others. Even the mission planners had a lot of fortitude. They astronaut might have died, but the planners knew they would have to live with the fact that they had made a mistake that cost a life.
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Bob B.
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Post by Bob B. on Aug 29, 2011 18:19:22 GMT -4
I just looked at the consumables summaries for the last three J-missions. Had they run the tanks dry, it appears there was enough SPS propellant to perform up to about 10 or 11 degrees of lunar orbit plane change. This assumes a few things:
1) Every pound of propellant was usable. 2) No other unplanned maneuvers would be necessary. 3) TEI could be performed from the new orbit.
I doubt any of these are true. If the LM got into some wonky orbit from which it needed to be retrieved, the CSM would have to execute maneuvers in addition to the plane change in order to rendezvous with the disabled LM. There's also a possibility further alteration of the orbit would be necessary to return to something suitable for TEI. All of these things deduct from the amount of plane change that could be performed. Nonetheless, we seem to have set the upper limit to about 10-11 degrees.
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Post by Count Zero on Aug 29, 2011 20:50:31 GMT -4
The only way they could know about it yet be unable to correct it would be if there were a failure of the RCS (attitude control system) and that would be quickly fatal anyway. Right, because in this case, aborting and dumping the descent stage would not help because the RCS jets are on the ascent stage. They'd be taking the problem with them - like when Gemini VIII got a stuck thruster and undocked from the Agena.
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Bob B.
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Post by Bob B. on Aug 30, 2011 10:34:00 GMT -4
But what if the LM went wonky and made a burn on some random heading at the worst possible time? What ever the worst possible time would be. Perhaps a failure in the descent stage that couldn't be stopped and required an emergency assent stage separation? There could be a random out of plane error with little knowledge of its extent and a limited time and fuel budget to recover. Could the abort systems have handled that? I've been thinking about this and it seems that a severe error as you describe might be correctable, provided the wonky orbit the LM ends up in is survivable for long enough that the necessary corrective action could be taken. That is, it can't be an orbit that will smack into a mountain or something like that. If the orbit is one that intersects the Moon's surface, there would be less than one hour to assess the situation and figure out how to correct it. That's not much time. However, suppose the descent engine burned to propellant depletion and placed the LM into some grossly out of plane orbit, but one with a perigee high enough to be survivable. Provided the ascent engine is operable, the LM should be able to undo most of the damage done by essentially reversing course and firing the ascent engine. The DPS had a delta-v of about 2400 m/s, while the APS had a delta-v of about 2100 m/s. That's 300 m/s short of what is needed to return to the origin orbit; however, we know the CSM had at least 300 m/s delta-v available. Therefore, it seems feasible the CSM could go after the LM and rendezvous with it once the LM has returned to an orbit that's within striking distance. Of course all of this must be accomplished within the period of time before the LM's ascent stage consumables run out.
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Post by Apollo Gnomon on Aug 30, 2011 10:59:51 GMT -4
Thanks, BobB -- these answers are exactly what I was looking for.
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Post by echnaton on Aug 30, 2011 12:17:17 GMT -4
The stuff of a FIDO's nightmares. Once stabilized, I guess the LM could have been put into a very low power mode that would extend the life of the consumables while the CSM served as the active vehicle.
I seem to be getting into a mawkish mood as the days are getting shorter.
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Bob B.
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Post by Bob B. on Aug 30, 2011 14:25:32 GMT -4
The DPS had a delta-v of about 2400 m/s, while the APS had a delta-v of about 2100 m/s. That's 300 m/s short of what is needed to return to the origin orbit; however, we know the CSM had at least 300 m/s delta-v available. Therefore, it seems feasible the CSM could go after the LM and rendezvous with it once the LM has returned to an orbit that's within striking. Oops, I just realized I made a mistake by getting confused over units. The amount of available CSM delta-v known to exist was at least 300 ft/s, not 300 m/s. (The CSM routinely performed plane changes up to about 370 ft/s.) Performing a 300 m/s burn takes up right up to the very edge of our propellant limit, perhaps leaving us a little short.
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Post by ka9q on Aug 30, 2011 16:40:23 GMT -4
I still don't see how the LM could have been placed in a wildly different plane, at least not during landing. It would have been possible to take off the wrong way, for example if the platforms had somehow been aligned 180 degrees off in azimuth on the surface, and that would certainly be unrecoverable even if they reached orbit.
Michael Collins mentions in his book another critical maneuver -- TEI -- in which the crew displayed the black humor so common to pilots and astronauts. They wanted to verify that they were properly pointed for the maneuver. Collins remarks "There's only one really bad mistake you can make here", referring to the possibility of a sign error causing them to perform TEI with the SPS pointed in the opposite direction. That would quickly result in an impact on the far side of the moon with earth never knowing why. Yet the crew gets pretty silly at this point, with Aldrin humorously working out the direction that the SPS will thrust from basic principles "Let's see... The hot gases go out that-a-way, resulting in thrust this-a-way..."
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Bob B.
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Post by Bob B. on Aug 30, 2011 17:30:38 GMT -4
I still don't see how the LM could have been placed in a wildly different plane, at least not during landing. Neither do I. We're just discussing a widely improbably "what if" scenario. It's not like I think there's any chance in hell it could actual happen.
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Post by chew on Aug 30, 2011 21:25:11 GMT -4
It shouldn't take much delta-v to correct a gross out-of-plane error during the Ascent Module launch with a little Pythagorean theory. It takes about 1853 m/s to achieve the initial orbit.
Add 1 m/s to that and you can use [18542 - 18532].5 = 61 m/s for plane change.
Or am I doing it wrong?
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Bob B.
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Post by Bob B. on Aug 30, 2011 23:01:27 GMT -4
It shouldn't take much delta-v to correct a gross out-of-plane error during the Ascent Module launch with a little Pythagorean theory. It takes about 1853 m/s to achieve the initial orbit. Add 1 m/s to that and you can use [1854 2 - 1853 2] .5 = 61 m/s for plane change. Or am I doing it wrong? You're not doing it wrong. When combined with another maneuver, a small plane change can be achieved using very little additional delta-v. However, each incremental increase in plane change requires more delta-v than the previous increment. Nonetheless, combining a plane change and an altitude change together into a single maneuver always requires less delta-v than if the maneuvers were performed separately.
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Bob B.
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Post by Bob B. on Aug 31, 2011 11:01:21 GMT -4
It shouldn't take much delta-v to correct a gross out-of-plane error during the Ascent Module launch with a little Pythagorean theory. It takes about 1853 m/s to achieve the initial orbit. Add 1 m/s to that and you can use [1854 2 - 1853 2] .5 = 61 m/s for plane change. The following is unrelated to our Apollo discussion, but it’s a good example of how the mathematics demonstrated above is put to practical use. Suppose we launch a proposed geostationary satellite into a low earth orbit (LEO) with an altitude of 200 km and an inclination of 29 degrees. From this parking orbit we need to transfer the satellite to an altitude of 35,786 km and reduce the inclination to zero. The first step is to place the satellite into a geostationary transfer orbit (GTO), which entails increasing the apogee to 35,786 km. At apogee we circularize the orbit at 35,786 km and perform the necessary plane change. The plane change is performed at apogee because the amount of delta-v required to perform the plane change is directly proportional to the satellite’s orbital velocity. Since the satellite’s velocity is much less at apogee, it is more efficient to perform the plane change then rather than at perigee. In this example, the GTO insertion burn requires 2,455 m/s delta-v. If circularization and plane change were performed as separate maneuvers, circularization would require 1,477 m/s and the plane change 1,540 m/s; however, it is never be done this way. It is far more efficient to perform a combination maneuver that completes both the altitude and plane changes with a single engine burn. In this case, geostationary orbit (GEO) insertion requires a burn of 1,848 m/s. Therefore, the entire transfer from LEO to GEO requires 4,303 m/s delta-v. However, as chew has demonstrated, a small plane change can be achieved in combination with another burn for very little additional delta-v. We can take advantage of this by performing a small part of the plane change in combination with the GTO insertion burn. Typically, American launches use GTOs with inclinations of 27 degrees, therefore a plane change of about 2 degrees is including with the GTO burn. The remaining 27-degree plane change is completed at apogee. In the case, GTO insertion with a 2-degree plane change requires 2,474 m/s, and GEO insertion with a 27-degree plane change requires 1,804 m/s. Together the total delta-v is 4,278 m/s, which is a savings of 25 m/s over the previous example. This doesn’t sound like much, but every little bit means a lot in rocketry. Of course, as the magnitude of the plane change at GTO insertion increases, the delta-v required to achieve each additional increment goes up significantly. Therefore, there’s a point at which we begin to lose our advantage. For geostationary transfer, it works out that a 2.2-degree plane change is optimum for launches from Cape Canaveral.
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Post by ka9q on Aug 31, 2011 12:23:24 GMT -4
Nonetheless, combining a plane change and an altitude change together into a single maneuver always requires less delta-v than if the maneuvers were performed separately. True, but this can be very risky. If the engine shuts down halfway through the burn, the spacecraft will very likely be on a collision course with the surface in half an orbit.
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Post by ka9q on Aug 31, 2011 12:31:37 GMT -4
Oops, scratch that. It depends on how much you're changing the altitude. If you're increasing it a lot, you're probably safe in the event of a premature shutdown. But if the maneuver is mainly a plane change, then a component of the maneuver will be counter to the initial velocity vector so the instantaneous velocity vector will first decrease, then increase. If the altitude on the other side of the orbit was low to begin with, the instantaneous periapsis could go negative.
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