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Orbital Mechanics - the FDAI - Can you eyeball space travel?


DeepSeaBase

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Taking a breather from my thought-experimenting with deep sea stuff.

A little background - in Apollo the inertial guidance system was instrumented through what's called the Flight Director Attitude Indicator (FDAI) or 8ball.

The FDAI shows your pitch, yaw and with a ring around it, your roll. But you can think of the roll as the axis on which the pitch and yaw translate.

Over time the inertial guidance system would deviate and need to be corrected using the optics.

Now it is possible to find the deviation over time by simply observing the new roll axis of the FDAI as it shifts off the poles that were at 90 deg yaw.

But I haven't been able to confirm that you can find the pitch.

The reasons this is important is because a lot of burns need to be retrograde or posigrade (prograde) and to do that you need to know you're actually in those positions. With the FDAI, I know you can find yaw 0 easy enough. Find the axis of rotation and then yaw 90deg off that and you will be at yaw 0. But I'm not sure how to find pitch 0, although intuitively it seems whatever the roll-axis pitch value is is the new 0.

So you should in theory be able to correct your FDAI without ever having to use the Guidance Computer and the optics. Useful if your Guidance Computer goes to crap AND you can't radio Huston for telemetry (which is what Apollo 13 did, basically relied on Houston for everything).

So now that I'm thinking about again after a long pause, I'm almost certain you can correct for pitch, yaw and roll based entirely from the FDAI, that's super useful and I'll need to test it in simulators.

Anyway, being able to do that gets you MOST of the way there. I'm still not sure how to find retrograde or posigrade anywhere in an elliptical transfer orbit. But I think I over-thought the problem.

The inertial guidance system should be able to tell you this if I understand its functionality correctly, because 0,0 yaw,pitch should put you at posigrade and 0,180 should put you at retrograde, anywhere in the progression of the orbit, yes?


The progression being defined as 0deg - 360deg progress through your orbit. So what I'm asking at this part of the thread is, is that how a functioning guidance system should work? Should your 0,0 always be posigrade no matter the progress in the orbit.

If yes, then determining your attitude without a guidance computer is much easier than I originally thought - provided you still have a working inertial guidance system.

But if no, then determining your pitch to posigrade/retrograde in your progression of the orbit must be known. I'm not sure yet how to determine what the pitch should be if it isn't supposed to be 0 or 180. 

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To be certain, I'm pretty sure if your roll axis was at 0 pitch and 90 yaw, and your deviated roll axis is now at 30 pitch and 70 yaw, then your corrected prograde would be 30 pitch and 340 yaw. It really should be that simple *IF* the prograde in progression of orbit is ALWAYS 0,0 without deviational error.

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