I hope you are good at Algebra, that will help.
Distance = speed * time.
In order to remain in Blackout, speed must remain higher than planned for this 1121 nmi total distance trajectory.
It starts blackout at 36Kft/sec and 320 Kft altitude, and the typical plan is to exit blackout at around 19Kft/sec at 210 Kft altitude, after 3:15 average.
A13 was calculated to come out of blackout at 3:16, but instead came out at 4:43, which is +87 seconds! In order to stay in Blackout for this extra 87 seconds, it means it didn’t slow down as fast as planned, so went faster… which means it was traveling at a higher altitude than planned – a totally different trajectory than planned, and it didn’t know it. Why not? Because before entry, they entered in all of the values to the DSKY – so if these weren’t accurate, then the entire guidance system is working off an erroneous “starting condition”… This guidance system is 100% inertial in nature – full 100% extrapolation from the starting position/angle/course, and then extrapolates where it is now…
If the CM guidance had known it’s original trajectory correctly, then it would have corrected it during this blackout, bringing it down more, to slow it down more , and achieve near the target of 3:16 blackout (+/- 20 seconds max).
Instead it misses by 87 seconds – indication that the guidance system failed to operate as intended. It went too fast for too long, at too high of an altitude.
Since this length of blackout is NOT EVEN POSSIBLE, it’s difficult to say just how much of an overshoot it would have done… but we can establish a MINIMUM overshoot estimate.
To stay in Blackout for that long, the average speed in Blackout ranges from 36Kft/sec at the start, and ends with as low as 16,000 ft/sec. (assumes an exit at around 160Kft altitude instead of the normal 210 Kft) – but here again – clearly a malfunction of the Guidance to miss the plan by so much.
If the average speed in this 283 second blackout was 22,000 ft/sec (a generous underestimate, given the speed range is 36Kft/s to 16KFt, where the mean here is 26Kft/sec.)
So if it were 20,000 Kft/sec – is 20,000 Kft * 283 = 1030 nmi.
The total target trajectory was 1121 nmi to be EXACT.
So it emerges at 16Kft/sec – and then spends another 3:19 before Drogues are deployed at 24Kft/Altitude at around 350 mph (typically).
So the average speed during this 3:29 is at least 6Kft/sec (again being generous as the mean between 16Kft and 500ft/s = 8.1KFt/sec)
So 3:29 = 209 sec * 6000 ft/sec = 205 nmi.
So this is the shortest I could devise-- being generous on estmates of speed, and we’re at 1235 nmi… which is 114 nmi overshoot.
Likely to be quite a bit more than this.
There’s a reason Kranz rejects Lovell’s explanation - because it doesn’t make sense – it doesn’t explain the whole story. Because the math doesn’t work out - because it’s fictional.
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Using more realistic values for the above, we’d get:
283 sec * 24 Kft/sec = 1130 nmi. (already passed up the ship at AOS)
209 sec * 7Kft/sec = 240 nmi
Total: 1370 nmi (250 nmi overshoot) - more reasonable.
Instead, miraculously right on target – using ONLY a blind inertial Guidance system…
The worst thing about an Inertial Guidance system is that it does NOT know how to correct it’s own malfunctions… It doesn’t get to emerge from blackout, look around and say “Hey! There’s are our ship ahead! Oh shit, better make big adjustments!” – nope, it never gets to correct for it’s own internal misjudgments.
So any signs that it “malfunctioned” is very bad news. Meaning, it didn’t know about it “being shallower than they told it” – it simply “believes what they told it, and goes from there – extrapolates from this starting point”.
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In the end, we’re talking about fiction. My point of this post is to simply show that the Apollo narrative is simply Impossible - and so we have to digest this.