A page from the LM Timeline Book, we have a rare chance to compare the simulation 5 days prior to the actual flight, below. In short, the plot and flight trajectory offsets look quite similar.
In the direct ascent maneuver (lifting off the moon), Charlie Duke manually plotted the deltas of the flight trajectories of the LM and CM to enable a rendezvous in orbit, essential for their transfer to the orbiting spacecraft that can take them home.
and here is the Apollo 16 page, brought back from the moon, full size
It is currently available for purchase from moonpans, and here is the description of the chart by Duke himself:
The flown page is unused on the opposite side, p.43., but the simulator page covers that practice scenario as well (which did not come into play);
I can imagine there was powerful motivation to get that particular manoeuver correct.
I imagine that there would have been some complex maths involved in accurately plotting those lines.
I am going out on a limb here, but I think the computational complexity is embedded in the graph construct itself. The humans were scribes for this paper co-processor (an adjunct to the fairly limited guidance computer).
The transcript of this moment gives the sense that they spend a fair bit of time making sure the PGNS and AGS flight computers are in sync.
Liftoff (from rover cam)
And a photo of the CSM lifeboat, from the approaching LM, right before docking
thanks! As I was going to sleep last night, I read through the transcript and among the references to the LM COAS for sighting and the chart usage, I found some powerful passages, especially near the end as the pressure gave way to playfulness:
175 46 39 Mattingly: Houston, Casper is standing by.
175 46 42 Hartsfield: Roger. We’re still working on it, Ken.
175 46 49 Duke (LM onboard): He’s gone, now.
175 46 51 Young (LM onboard): Yeah, it’s sunset.
175 46 53 Duke (LM onboard): Yeah.
175 46 54 Young (LM onboard): I still got him.
175 46 55 Duke (LM onboard): You do?
175 46 56 Duke (LM onboard): You do?
175 46 57 Young (LM onboard): Yep. I can’t see him in the COAS, but I can see him outside of it.
175 47 02 Duke (LM onboard): Oh, yeah. I see him. Yeah. 411 Enter, 621 readout.
…
175 49 44 Duke (LM onboard): Well, we got a couple of marks, and I destroyed our solution. None out of plane. 81…
175 49 49 Hartsfield: Casper, the computer’s yours.
175 49 52 Duke (LM onboard):… that’s probably a pretty good number. Plus 81 plus 14.
175 49 54 Mattingly: Thank you.
175 50 02 Duke (LM onboard): Oh, marks already. Fantastic!
175 50 06 Young (LM onboard): Okay. Charlie, why don’t we get a – whatever it is you do to get a Verb 86.
…
175 51 42 Duke (LM onboard): Five marks in, John. Okay. You can – can I get a Verb 83?
175 51 52 Young (LM onboard): You can touch my computer today.
175 51 53 Duke (LM onboard): Okay.
…
175 55 14 Young (LM onboard): We in darkness?
175 55 15 Duke (LM onboard): Yeah. Think that must be him, that bright star up there.
175 55 22 Young (LM onboard): That’s him, Charlie. He’ll be at – he’ll disappear in a second when he goes into night-time.
175 55 27 Duke (LM onboard): Yeah. Okay. Coming up on 30 minutes for my chart R and R-dot.
Public Affairs Officer: This is Apollo Control Houston at 176 hours 6 minutes ground elapsed time. We show the two spacecraft at a distance of 103 nautical miles apart and a closure rate of 402 feet per second.[PAO is 11 minutes ahead of true GET].
175 55 48 Young (LM onboard): The COAS is doing pretty good, Charlie. I got it right in the middle of the COAS. Look at the needle.
175 55 52 Duke (LM onboard): Yeah. Fantastic.
175 55 54 Young (LM onboard): That’s good, isn’t it?
175 55 56 Duke (LM onboard): Super, John.
…
175 58 21 Duke (LM onboard): Man, that lift-off was something, wasn’t it?
175 5823 Young (LM onboard): That was neat.
175 58 25 Duke (LM onboard): For a while there, I did – I did – I thought we – I heard it go poop and it sort of – it sort of sat. Before it lifted off.
175 58 38 Young (LM onboard): It’s a sweet little flying machine.
175 58 39 Duke (LM onboard): Yeah.
175 58 43 Young (LM onboard): [Garble] all that stuff.
175 58 45 Duke (LM onboard): Scissors floated out. Hmm.
…
176 02 40 Duke (LM onboard): Seventy miles out, John. Get on the chart at 25 degrees. Seventy miles and 25 degrees. We’re right on the line. Golly, what is that? Want some tears ?
176 03 01 Young (LM onboard): No, thank you, Charlie.
176 03 02 Duke (LM onboard): (Laughter).
176 03 12 Duke (LM onboard): You notice our 40-g [?] bags didn’t come out with two snaps on them?
176 03 22 Young (LM onboard): Great.
176 03 35 Duke (LM onboard): What a sweet machine.
…
176 08 55 Young (LM): Hey, Houston. With 21 marks and 17 minutes, you want to just keep marking as opposed to Verb 93ing, right?
176 09 05 Irwin: Stand by.
176 09 10 Young (LM): The answer to that, Jim, is yes, I’m sure. Just want to make sure somebody thunked [sic] about it.
176 09 21 Irwin: Okay. Just continue marking, John.
176 09 25 Young (LM): Understand.
176 09 32 Irwin: Okay, you’re coming up on two minutes to LOS, and you’re looking good.
176 09 38 Young (LM): Sure am, man.
176 09 39 Irwin:… and all solutions have converged.
…
Public Affairs Officer: This is Apollo Control Houston. We’ve had Loss of Signal, now, with both spacecraft – Orion now in hot pursuit of Casper as they both pass behind the Moon. We heard at least half of the conversation as the two spacecraft were talking before we had LOS with Casper. We’re at 176 hours 24 minutes Ground Elapsed Time, and this is Apollo Control Houston.
176 11 52 Young (LM): Yeah, I could see you visually right after liftoff, when we were supposed to be like 150 miles away.
176 11 58 Mattingly: [Garble].
176 12 01 Young (LM): Charlie and I both saw you.
176 12 0X Young (LM onboard): That’s a good data point. We been asking and nobody has the answer. You can’t see it through the COAS, but you can if you look around the side.
176 12 10 Mattingly: Well, you got to be in the – … down … here; that’ll … it up.
176 12 14 Young (LM onboard): Yeah, that’s right. That’s the answer.
176 12 22 Mattingly: John, why don’t you give me a mark at 12 minutes to go or something ….
176 12 27 Young (LM): Okay.
176 12 30 Duke (LM): Man, Ken, we got a load of rocks.
176 12 33 Mattingly: Well, that’s fine. We got lots of room for them.
176 12 35 Young (LM onboard): Why? What did you do?
176 12 38 Mattingly: Man, we got the world’s two biggest trash cans you’ve ever seen.
176 12 41 Young (LM): I bet.
176 12 44 Duke (LM): Well, you ought to see the two pig pens over here. You ain’t gonna let us in!
176 12 48 Mattingly: (Laughter) … you guys really did get …
176 12 55 Young (LM): It was – it was – Geez, it’s a lot of fun, Ken.
176 13 00 Duke (LM): I never had so much fun in all my life, Ken.
…
176 15 29 Duke (LM): I don’t think we’re going to need a chart solution, but I’ll take the numbers down anyway.
176 15 31 Mattingly: Standby numbers are the same as the ground numbers.
…
176 21 46 Duke (LM onboard): How about a little shot of aqua?
176 21 49 Young (LM onboard): Man, that’s the best idea I ever heard of.
176 21 54 Mattingly: Did they tell you that they changed our schedule a little bit?
176 21 58 Young (LM): Yeah, we get to keep the Lunar Module.
176 22 04 Mattingly: Yeah, they also said we’re going home a day early.
176 22 07 Duke (LM): They didn’t tell us that.
176 22 09 Mattingly: Well, I didn’t get any answers as to why. I just got this cryptic "No [garble} P62." No – no shaping burn and come home a day early.
…
176 36 41 Young (LM onboard): Wish that cabin fan would suck all this dirt out of here.
176 36 42 Duke (LM onboard): It’s doing a pretty good job.
176 36 46 Young (LM onboard): But what happened when we lit the engine?
176 36 47 Duke (LM onboard): I know it. It came all off the floor; that’s the Velcro down.
176 36 52 Young (LM): Ken, we’re gonna need that vacuum cleaner something bad.
176 36 55 Mattingly: Oh, okay.
176 36 58 Duke (LM): You won’t even want to put on these OPSs, Ken.
176 37 01 Young (LM): That’s right.
176 37 09 Duke (LM): I only fell down six times.
176 37 12 Young (LM): Charlie – Charlie was laying down more than he was standing up.
…
176 48 56 Duke (LM): You are really bright, babe.
176 49 08 Mattingly: [Garble] against the lunar surface.
176 49 13 Duke (LM onboard): What?
176 49 14 Mattingly: You really look pretty against the lunar surface.
176 49 16 Duke (LM onboard): Oh.
176 49.18 Mattingly: You got the little split imagery in through there.
176 49 21 Young (LM onboard): You do? The red against the – the star against a red background?
176 49 22 Mattingly: Yeah.
176 49 23 Young (LM onboard): When I first saw that on Apollo 10, I thought I was in 2001. I couldn’t figure out what was happening, because the – the guys I was tracking were up above me at the time, for some reason.
…
176 59 36 Duke (LM): Orion, You are just a little tiny black dot to the unaided eye.
176 59 38 Duke (LM): Well, you look brighter than any star or planet I’ve ever seen. Against that black sky.
176 59 53 Young (LM onboard): Either that or we’re rendezvousing with Venus.
176 59 55 Duke (LM onboard): Yeah, we’re coming to Venus. (Laughter)
…
177 01 35 Young (LM onboard): We may have to not do any line-of-sight corrections.
177 01 37 Duke (LM onboard): I don’t think there’s going to be a bit. Isn’t that amazing?
177 02 06 Young (LM onboard): He is right in the middle of the COAS and he is not moving one iota.
177 02 12 Mattingly: Okay, I’ve got you at 28 foot per second.
177 02 15 Young (LM): That’s what we’ve got us at 28.3.
…
177 08 57 Duke (LM ): Boy, you are beautiful, Ken.
177 09 00 Mattingly: That’s the nicest thing anyone’s said.
177 09 01 Duke (LM onboard): Casper …
177 09 02 Young (LM onboard): What a rendezvous machine this is.
177 09 07 Duke (LM onboard): Casper is really beautiful. Okay, we’re at 800 feet at 10 feet per second, John.
…
(Houston requested to take pictures of backside of the LM before docking)
177 17 05 Young (LM onboard): These guys are crazy (laughter).
177 17 06 Duke (LM onboard): They are. Well, that’s – that’s a data point.
…
177 23 10 Young (LM): Are you there yet, Ken?
177 23 12 Mattingly: (Laughter) [Duke in tech transcript] No, no. I’ll – I’ll tell you.
177 23 15 Duke (LM): Are we there yet, daddy?
177 23 18 Mattingly: (Laughter)
177 23 27 Duke (LM onboard): I think f/8 is too bright; I think we need f/ll.
177 23 30 Young (LM onboard): Yeah, the Sun is shining on it. This is a lousy attitude for picture taking.
…
177 27 24 Young (LM): Okay, go to it. What is – Your attitude and my attitude docking-wise is compatible? It’s the same …
177 27 34 Mattingly: They had been in the simulator, and I’m sure they will be today.
177 27 38 Young (LM): I’d be surprised. The only thing nominal so far is the rendezvous. I hope the rest of it turns out that way.
…
177 29 08 Duke (LM onboard): That’s enough pictures. I’m getting tired of holding that button.
177 29 18 Young (LM onboard): What were you shooting at? One frame a second?
177 29 20 Duke (LM onboard): Well, I don’t mean holding the button, I mean holding the camera.
177 29 32 Young (LM onboard): I’m not used to this zero g.
177 29 34 Duke (LM onboard): I know it. (Laughter)
…
177 37 13 Young (LM onboard): He’s right on, about a degree off. There’s no way you can see it, Charlie.
177 37 19 Duke (LM onboard): No, I can’t see him.
177 37 21 Young (LM onboard): I want – I – I just want to be able to do something intelligent, like shut the thrusters off when we get capture.
177 37 32 Duke (LM onboard): It’s only 09:30, John; we’ve been up since – 15 hours. Not bad.
177 37 42 Young (LM onboard): Ken, you look beautiful to me.
177 37 46 Mattingly: Say again.
177 37 46 Young (LM onboard): You look right on to me. My optical sight is coming right into your docking window.
177 38 05 Young (LM onboard): Don’t hit my arm, Charlie.
177 38 07 Duke (LM onboard): I’m sorry.
177 38 08 Young (LM onboard): [Garble]
177 38 35 Young (LM onboard): How would you like to do a EVA transfer?
177 38 39 Duke (LM onboard): How would you like a kick in the behind?
177 38 42 Young (LM onboard): Hot mike to Houston. (Laughter)
177 38 48 Duke (LM onboard): No, we’re normal voice. But we got our tape recorder running. (Laughter).
…
177 38 58 Mattingly: Okay, about 5 feet.
177 40 37 Mattingly: Doesn’t look like it. I don’t have any barber poles. There we go. Took a couple of extra blurps to get you. Okay. Are you free?
177 40 52 Mattingly: Okay.
177 41 O0 Mattingly: Okay, it looks – looks pretty fair. How about if I just retract you?
177 41 25 Mattingly: I believe we’re there.
177 41 27 Mattingly: Casper’s captured Orion!
177 hl 30 CC: Very good. We were wondering what took you so long.
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