Bob B.
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Post by Bob B. on Aug 31, 2011 13:48:25 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. That's going to be a problem in any plane change if you use simple vector addition. For small plane changes the effect is negligible. For large plane changes the problem can be eliminated by rotating the thrust vector during the burn so that the thrust is always at right angles to the velocity vector. ( Edit: Rather than continuously rotating the thrust vector, the same thing could be accomplished by adding one or more doglegs.) This second method changes the direction of the velocity vector without ever changing its magnitude, however more delta-v is required. In the first case, the amount of delta-v required to perform the plane change is given by the following equation: Δv = 2*Vi*sin(θ/2) where Vi is the initial velocity and θ is the angle of the plane change. In the second case it would be: Δv = Vi*θ*π/180 The equation for a combined altitude/plane change maneuver using simple vector addition is: Δv = SQRT[ Vi 2 + Vf 2 – 2*Vi*Vf*cosθ ] where Vf is the final velocity. I don't have a combined equation for the second case, but I'm sure if it were an issue, the direction of the thrust vector could be controlled during the burn to assure the velocity never drops below a critical value.
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Aug 31, 2011 17:10:31 GMT -4
Putting some number to the problem suggested by ka9q…
Consider a 60 X 60 nautical mile lunar orbit, in which the orbital velocity is 1628 m/s. Reducing this orbit to 60 X 0 nmi, i.e. setting the perigee equal to the lunar surface, the velocity would have to be reduced to 1603 m/s. Therefore, any plane change with an intermediate velocity of 1603 m/s or less runs the risk of impacting the ground should the engine fail halfway through the burn. The 1603 m/s limit is reached with a plane change of 20.1 degrees.
We know Apollo frequently used lunar orbits that dipped as low as 9 nmi, so let’s set this as our minimum safe altitude. In this case we can reduce our velocity to as low as 1607 m/s and be safe, as this would put us in a 60 X 9 nmi orbit. Using this as our limiting factor, we can safely perform plane changes up to 18.4 degrees without worry of crashing.
On the other hand, any engine failure would have me plenty worried even if crashing wasn’t one of things I had to be concerned about. In fact, crashing may be preferable to be stranded in lunar orbit waiting for my oxygen to run out.
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Post by banjomd on Sept 1, 2011 9:58:28 GMT -4
Aw, Bob B., not to worry; the CO2 buildup would probably kill you long before the O2 runs out!
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Post by chew on Sept 1, 2011 11:54:31 GMT -4
Aw, Bob B., not to worry; the CO2 buildup would probably kill you long before the O2 runs out! You have to show your work in order to get full credit for that answer. ;D
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Post by ka9q on Sept 2, 2011 3:14:29 GMT -4
No Apollo crew would ever have had to die from CO2 toxicity. If you run out of LiOH canisters, simply open up a small cabin vent and let the ECS regulators maintain the cabin pressure.
It's just like recovering from a PLSS failure during an EVA: open up the purge valve and turn on the OPS.
Of course you'd quickly deplete your O2 supply with this method, but I didn't say you wouldn't die -- only that you need not die from CO2 toxicity.
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Post by Kiwi on Sept 2, 2011 7:41:40 GMT -4
Radial Velocity ErrorThis is a subject I know nothing about, so could you guys who do, please check what our not-so-good friend Fattydash/Patrick1000 said in another wall of words at the JREF forum: I don't know why he talks about extra drift. He referred to this quote from the Mission Report, regarding Figure 5-3:
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Post by banjomd on Sept 2, 2011 7:56:33 GMT -4
No Apollo crew would ever have had to die from CO 2 toxicity. If you run out of LiOH canisters, simply open up a small cabin vent and let the ECS regulators maintain the cabin pressure. It's just like recovering from a PLSS failure during an EVA: open up the purge valve and turn on the OPS. Of course you'd quickly deplete your O 2 supply with this method, but I didn't say you wouldn't die -- only that you need not die from CO 2 toxicity. Agreed. I should've added "if nothing was done"!
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Sept 2, 2011 8:51:33 GMT -4
Kiwi,
The LM’s velocity can be described in terms of three components: radial (vertical), downrange (horizontal, or tangential, in the direction of the intended flight path), and cross-range (horizontal across the direction of intended flight path). Radial velocity is so called because it is in the direction of a radius vector emanating from the center of the moon, i.e. it is normal to the lunar surface. Fattydash/Patrick1000’s argument is spurious because he’s confusing radial velocity with cross-range velocity. He got he head up his … well, you know what.
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Post by ka9q on Sept 2, 2011 15:03:39 GMT -4
Yeah, it's pretty amusing how our friend fattydash can build so much on a simple yet fatal misconception. Like mistaking "radial error" for "crosstrack error".
The LM carried a landing radar specifically because the inertial navigation system wasn't good enough by itself. It indicated both altitude and velocity relative to the lunar surface so the guidance system and/or pilot could null all horizontal motions before landing.
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Post by drewid on Sept 3, 2011 12:23:02 GMT -4
I've been looking at that stuff as well and I've come up with a question or two.
The LM caught some extra velocity during undocking, perhaps due to residual pressure in the airlock when it was unhitched. So that mean that the CSM would have also felt that effect and slowed by some amount.
What is a the relative mass of the CSM compared to the LM, and would the retardation be enough to throw out measurements relative to the LM on the surface?
Edit, right so the CSM was 28,801kg at launch, LM was 15,065kg. but obviously the CSM lost some weight on the way.
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Post by ka9q on Sept 3, 2011 15:59:16 GMT -4
You can find the exact weights for each mission in the mission report. There's usually an appendix titled "Mass Properties" that gives the masses of each component at each point in the mission.
There's far more in there as well: center of gravities, moments and cross products of inertia, etc.
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Bob B.
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Posts: 3,072
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Post by Bob B. on Sept 3, 2011 21:16:39 GMT -4
The following should give you what you want regarding weights of various components at various times: history.nasa.gov/SP-4029/Apollo_18-37_Selected_Mission_Weights.htmAs you probably know, the CM/LM was pressurized to just 5 psi. I don't know the exact size of the docking tunnel, but it was about 30 inches diameter. This means the force pushing on the LM was about 3500 lbf, which was enough to give it an initial acceleration of about 3.3 ft/s 2. Of course, as soon as the vehicles undocked, that pressure was very quickly relieved; therefore, the duration the LM was subjected to any kind of a push was only a fraction of a second. I doubt the LM received even 1 ft/s delta-v as a result of the tunnel pressure. At the time of CSM-LM separation, the CSM's mass was only about a ton more than the LM, therefore it received just slightly less delta-v in the opposite direction.
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Post by Kiwi on Sept 4, 2011 6:29:48 GMT -4
Kiwi, The LM’s velocity can be described in terms of three components: radial (vertical), downrange (horizontal, or tangential, in the direction of the intended flight path), and cross-range (horizontal across the direction of intended flight path). Radial velocity is so called because it is in the direction of a radius vector emanating from the center of the moon, i.e. it is normal to the lunar surface. Fattydash/Patrick1000’s argument is spurious because he’s confusing radial velocity with cross-range velocity. He got he head up his … well, you know what. Thanks, Bob. Perhaps I knew a little more about it than I thought, because what he said didn't add up. I had always heard of "radial" as you describe it. So in this case, what exactly would that 20-ft/sec radial velocity residual do? Would it only cause one of the navigation modes to indicate a landing altitude below the lunar surface at touchdown, as the Mission Report says? It would be great if someone could debate Patrick1000 on this point at JREF, if he is just plain wrong. I don't know enough about it and don't believe in debating anything I know very little about because doing so can just give ABs a bad name. In fact, there's quite a bit of it in that thread, where posters have told Patrick1000 he's wrong about something but not given any evidence to prove it. He even said he doubted that some of his critics had the ability to analyse his work, and I don't blame him. I thought so too. If they can't debate a point properly they should stay out of it and leave it to those who can.
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Post by drewid on Sept 4, 2011 8:22:50 GMT -4
The other thing he's doing is taking instrumentational errors as actual real velocity. He is stating that because of the radial error of 20fps the LM is drifting south at 20fps.
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Post by drewid on Sept 4, 2011 10:14:51 GMT -4
Sorry - I moved this post as I thought it might be getting a bit OT. Started a new thread.
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