Hunchback's major (mis)understanding of Apollo TV tech.

[JayUtah]

I did read that the computer used control axes rotated 45 degrees around the X axis. But this was just to simplify the software by aligning them with the RCS thruster quads on the corners of the ascent stage. The axes were still orthogonal with each other.

That's what I was referring to.  The control axes for the LM form an orthogonal basis, but are not coincident with the spacecraft body-axis basis as is usually the case.  I went back to check, using the same drawing you saw (but which I haven't looked at for, oh, about three years).  I conflated that with the reaction-wheel technique, which can have a non-orthogonal control basis.

For those who are lost, "orthogonal" has a geometric meaning that indicates something at right angles to a reference.  It has a theoretical meaning suggesting independence of control action.  Ideally we want roll control to result only in a roll moment, and not cause unwanted pitch or yaw.  In practice, because no statically ideal RCS solution exists and no spacecraft has invariable mass properties, you can't have one control action without residual, collateral response in some other axis.  If your pitch thrusters are slightly off-center, trying to pitch up may also roll you slightly.  Hence an automatic control system will also apply compensatory roll moments with the roll thrusters to result in a "pure" pitch maneuver.

Abstractly considered then, this "messy" property actually simplifies things by requiring control laws not to assume orthogonality.  And then, for other reasons, it can be made deliberately orthogonal.  Which is to say, in thruster terms, they don't always have to be aligned with the body axes, or even at right angles to each other.  Commanded moments are then achieved by firing the combination of thrusters that produce an appropriate vector in the navigation basis.  And this is why, when you watch the actual Apollo spacecraft or the space shuttle closely, maneuvers employ a symphony of thruster firings that are more involved than just the simple, canonical moments.  Mathematically, a straightforward relationship exists between the body axes (relative to which attitude and rates are reckoned) and any control basis.

Reaction wheels on modern spacecraft are not aligned with the body axis and often are not installed at right angles to each other.  This requires any body-axis maneuver to require actuating at least two reaction wheels.  But this apparent loss is actually a win, because the wheels are arranged such that any given moment may be produced by more than one combination of wheel actuations.  And this compensates for degradation or malfunction of any one reaction wheel.

[JayUtah]

He doesn't seem to grasp the difference between the centroid of a shape and the center of mass.

That's just not something a real aerospace engineer would do.  It's like someone claiming to be an expert baker getting confused between flour and paprika.  Yes, they're both powders, but...

...all forward-firing RCS thrusters were disabled because they didn't want any impulse, however slight, reducing the net thrust.

Well, "however slight" isn't exactly the case.  Four of the Marquardt thrusters firing in the same direction is 400 lbf of thrust.  That's more than ten percent of the APS 3,500 lbf thrust -- not that they would actually be fired like that during APS-accelerated flight, but you get the idea.  Those 100-lbf Marquardt motors, which fit in shoe box, were used well into the 1990s as apogee motors on geostationary satellites.

Yes, it's amazing how well the simple processors that control traffic lights work, even though they can't do anything else.

Simple is better.  Well, more reliable anyway.  The critical functions of both the LM and CSM were not controlled by the programmable GP computer, but rather by traditional sequential and combinatorial logic implemented largely with diodes and electromechanical relays.

On a side note, he also scoffs at the notion that "little old ladies" could accurately thread the rope memory modules.

Again, more proof that he's never actually worked in an aerospace context.  Similar to your "highly-paid 'hookers'" (snicker), some of the highest-paid workers at Boeing's plant are the adhesive layup ladies who have decades of experience, a keen eye, and a steady hand.  There are many skills involved in building a spacecraft, and not all of them are cerebral.  ATK near me has an army of Kevlar threaders who wrap their SRM casings using machines many of them helped design and build.  They're coming up on retirement, and ATK is in a bit of panic to get new ones trained and experienced.

[JayUtah]

I know what deadbands are, but let me make sure I understand why they're used.

Well, take a couple steps back and enjoy the notion that everything you mentioned is, in one way or another, a valid argument for the use of deadbands in any control system -- especially an attitude-hold autopilot that uses rocket thrusters for control moments.

From the steps-back perspective, consider that you nailed the notion of discrete control variables.  Often a control system must provide inputs that are discretes (i.e., on-off values; e.g., opening the water inlet to the washing machine), or stepwise-variable (e.g., firing up the second-stage burner in an HVAC system), or continuously variable only within a narrow band (e.g., car engine speed cannot drop below about 700 RPM, and cannot exceed red-line speed).  RCS thrusters are not continuously variable.  They provide either a fixed thrust, or stepwise variable thrust in pulse mode.

And in the case of the LM ascent, the thrust is vastly oversized for the need.  Consider a home heater whose heating element (whether electrical resistance heater or combustion burner) has prodigious heat injection capacity.  If your thermometer drops only a degree below the set-point, firing up that huge beast of a heater -- even for a very short amount of time -- may rocket your temperature several degrees above the set-point.

Before we get into the mechanics of thruster ignition transience, which is correct (but a second-order consideration), let's examine the other effect you nailed head-on, because it follows directly from what we observe above and from what you noted about the mass properties of the spacecraft.  The spacecraft's center of mass changes, as you note, from fuel depletion and from other payload shifting such as fuel slosh and crew movement.  The IMU on a manned spacecraft is incredibly sensitive.  For example, the IMU on board Apollo 1 registered the motion of the entire launch vehicle due to the movement of the crew attempting to extinguish the fire and escape.  If even the slightest measurable error produced a corrective moment, there would be constant correction, overcorrection (due to non-discrete controls), and a non-stop fight between opposing controls.  Deadbands provide vital slack to prevent this.  Other techniques include more sophisticated control laws that incorporate integrated and differential process variables.  The Apollo digital autopilot implemented differential control (i.e., error rates) plus a pilot-selectable deadband.

And yes, the goal is simply "good enough" guidance, not error-free guidance.

The other concern is the classic hysteresis effect.  Between the time an error is first measured to the time the system returns to acceptable is an interval during which the system is reacting.  It may take only a few milliseconds for the error to generate a control input, but it may take considerable time -- perhaps several cycles of the control system -- for the control input to be reflected in the process variable.  When your thermostat notes that the measured temperature in the room matches the set point, it stops adding heat to the room by turning off the heating element.  But because of latency in the distribution system and latency in the thermometer, heat may continue to enter the system and cause the measured temperature to rise.  Thus, aiming instead at a deadband rather than at a precise value allows for overshoot and latency in the control loop.

Spacecraft sometimes have this constraint.  There are missions that require attitude errors to be corrected within a certain time proportional to the error magnitude.  That is, you can accept a certain magnitude of error, but you cannot accept an out-of-tolerance condition for very long.  So sometimes time-optimal control is required, not fuel-optimal control.  Different control laws, and different deadband requirements.

I presume the optimum deadband can be computed from the loss in effective thrust that comes from a particular attitude error. This varies as the cosine of the error, which for small angles is approximately 1 -- i.e., small errors are inconsequential. So the optimum deadband would be the one that equates the RCS propellant needed to maintain it with the wasted propellant by the main engine due to those cosine errors.

Am I right?

Well that's one way to formulate it, yes.  The science of spacecraft guidance is a tool kit of all such kinds of models that match various mission constraints.  Many modern missions are orbital only, and rely chiefly upon attitude control -- pointing constraints.  Planetary missions have constraints more in line with Apollo ascent guidance, and are reckoned in terms of allowable dispersion.  Dispersion on orbital approach is expressed as an allowable window in the state vector -- a literal geometric window in planet-fixed space through which the spacecraft must fly, and a conical distribution of acceptable velocity vectors.  Dispersion for landing is the landing-site ellipse.  Dispersion for rendezvous can be expressed as tolerances on the sacred 6-tuple of orbital elements.

Abstractly considered, dispersion simply accepts that no matter how adept a guidance system may be, identical starting conditions will not result in arbitrarily repeatable end conditions, due to the accumulation of low order effects that do not repeat.  Guidance dispersion is therefore simply the error analysis for guidance.  And each mission (e.g., LM ascent and rendezvous) contains an acceptable dispersion.  For most LM ascents, the acceptable dispersion was vast.  In contrast, for LM landing on Apollo 12, acceptable dispersion was considerably narrow.

So the more accurate expression of your sentiment above is how much known guidance error can I accept, integrated (and hopefully averaged) over ascent time, and still "land" in orbit with only nominal dispersion.  It's not so much the loss of thrust because the motor is slightly off-axis, but rather the naked fact that you're going the wrong direction.  So you can write the optimization problem several ways now.  You can optimize the deadband, for example, to balance between fuel for control during the ascent against fuel to correct the orbit.

In practice the Apollo deadband was simply switched between two fixed values, depending on the pointing constraint for the specific mission phase.  The deadbands were 1 degree and 0.1 degree, respectively, if I recall correctly.

[Noldi400]

Even though all this is well understood now (at least by you engineering types), a lot of it is counter-intuitive.

Remember back in the day when even intelligent, well educated aeronautical engineers were surprised by the "inertial coupling" phenomenon - also known as "the damn thing just came uncorked" - in supersonic flight which killed at least one test pilot and tried very hard to kill a few others, including Chuck Yeager.

Which seems to me just another argument that Hunchbacked has no significant engineering knowledge, whatever his claims may be.

[ka9q]

Apparently he does have a sense of shame then.

That's very hard to believe.

[ka9q]

For example, the IMU on board Apollo 1 registered the motion of the entire launch vehicle due to the movement of the crew attempting to extinguish the fire and escape.

IIRC, it sensed vehicle motion even from minor crew movements before the fire, such as somebody shifting in his couch. There's also a belief that Grissom may have been out of his couch trying to fix a balky headset connector (they were having comm problems at the time).

The other concern is the classic hysteresis effect.  Between the time an error is first measured to the time the system returns to acceptable is an interval during which the system is reacting.

Right, and here there is unavoidable lag in the control loops -- the sensors and the computers --  as well as in the actuators (the thrusters). Not only did it take time to open the propellant valves and build up chamber pressure, but the thrusters didn't stop producing thrust the instant the valve-close command was given. There was a tail-off period.

Dispersion on orbital approach is expressed as an allowable window in the state vector -- a literal geometric window in planet-fixed space through which the spacecraft must fly

I know what dispersion is, but I'm asking about something different. The issue is not accuracy but efficiency. Like most spacecraft the LM uses a closed-loop guidance system. It knew where it was (to some accuracy) and where it wanted to be, and it computed and executed what it had to do to get there. How it gets there isn't as important; many paths led to the same end point but not all of them were equally efficient.

In a random walk, your final distance from the starting point increases only as the square root of the number of steps. So it can be more efficient to let small random deviations from the path build up and fix their sum later than to spend more fuel to fly a much tighter path all the way, even though that eliminates the later correction.

Up to a point, of course. So there must have been an optimum deadband that minimized the total propellant (main engine + RCS) required to reach a given target state vector with the same given accuracy.

[ka9q]

Well, "however slight" isn't exactly the case.  Four of the Marquardt thrusters firing in the same direction is 400 lbf of thrust.  That's more than ten percent of the APS 3,500 lbf thrust -- not that they would actually be fired like that during APS-accelerated flight, but you get the idea.

With that we should be able to easily compute how far off the c.g. could be for the thrusters to still correct for it.

Let's assume the c.g. is somewhere along a diagonal line between the 3,500 lbf APS and the left front thruster. Each thruster is 100 lbf, so if the distance of the c.g. from the X axis (and APS thrust vector) was 1/(35+1) = 1/36th of the distance between the APS and the thruster, they would have produced equal and opposite torques with a 100% duty cycle on the thruster.

My best drawings of the LM don't include dimensions, but I can scale it from another drawing that gives the distance between opposite faces of the descent stage as 13 feet 10 inches (4.216 m). From that I estimate that the left front thruster is 2.33 m diagonally from the X axis. 1/36 of that is 6.5 cm. At this point, the thruster would have to fire 100% of the time to keep the LM on course. If the c.g. were even farther off center the guidance system would have to begin firing the -X (upward firing, downward thrusting) thruster on the right rear, and that would work against the thrust of the main engine.

What were the actual numbers? At ascent, the Apollo 11 LM c.g. was at (+243.5, +0.2, +2.9) inches. That's only slightly to the right of the thrust vector but actually rather significantly (7.4 cm) forward. This may explain why my same drawing appears to show the ascent engine canted slightly forward. If accurate, it indicates that the designers knew where the c.g. would be and mounted the engine accordingly. If I were them, I would have made it manually adjustable before flight.

[Peter B]

...And yes, the goal is simply "good enough" guidance, not error-free guidance.

...So the more accurate expression of your sentiment above is how much known guidance error can I accept, integrated (and hopefully averaged) over ascent time, and still "land" in orbit with only nominal dispersion.

Even though it's something I sort-of knew, it's still interesting to read here the idea that you don't have to guide a spacecraft perfectly, you merely have to guide it well enough (to get the job done). I assume therefore that the reason various mid-course corrections on Apollo missions weren't used was because the trajectory errors at the time weren't large enough to warrant correcting.

On top of this, I'm reminded of a poster called Donde at the late lamented Self Service Science Forum. Apart from his...unique...idea that pi had multiple possible values, he was convinced it would be impossible for humans to ever send spacecraft to the stars: because we wouldn't be able to aim them accurately enough. No matter how we tried to explain it, he simply wouldn't accept the idea that a hypothetical interstellar spacecraft would be able to determine how much its trajectory was deviating from the required course, and would also be able to make corresponding course corrections. In contrast he seemed to think that spacecraft were like bullets, that once fired couldn't be redirected.

[Peter B]

If I were them, I would have made it manually adjustable before flight.

Do you mind me asking why?

For one thing, any sort of adjustment mechanism would add weight on a spacecraft where gaining weight was looked on as worse than it is for Miss Universe.

And for another, what's wrong with calculating where the CoG will be beforehand, setting the aim of the APS during construction of the LM on the basis of those calculations, and leaving any fine management of the ascent trajectory to the RCS?

[ka9q]

Do you mind me asking why?

Sure. It gives you operational flexibility. Each mission carried a different crew, whose body weights varied at least a little, visited a different area of the moon and stayed for varying amounts of time, carrying different equipment and amounts of consumables down to the surface and samples back from the surface. The change was the largest between Apollos 14 and 15, the last H-mission and first J-mission.

I'm not talking about anything fancy, just an adjustable mounting bracket that would allow the engine mount to be swiveled a little before being torqued down. The bolt holes would actually lower the weight a little. 
 

[JayUtah]

Not only did it take time to open the propellant valves and build up chamber pressure, but the thrusters didn't stop producing thrust the instant the valve-close command was given. There was a tail-off period.

The Marquardt 100-lbf jets have a transient measured in a small number of milliseconds, not really something you really worry about in a 10 Hz control loop.  Does it contribute to latency?  Yes, a bit.  But ordinary process latency (e.g., moment divided by moment of inertia, integrated over time) is the cardinal limit.

Like most spacecraft the LM uses a closed-loop guidance system.

Well, yes and no on the LM ascent.  The DAP was then, and always was, closed loop at the perspective of attitude errors and error rates.  But the attitudes that the ascent guidance system fed into the DAP were static, stepwise values.  At the high level, LM ascent guidance was open-loop.

In a random walk, your final distance from the starting point increases only as the square root of the number of steps. So it can be more efficient to let small random deviations from the path build up and fix their sum later than to spend more fuel to fly a much tighter path all the way, even though that eliminates the later correction.

I see now where you wanted to go with that, and I agree.  Indeed, the overall goal of the deadband is to allow errors to accumulate to the point where it's efficient to correct them.  I never really misunderstood that or quibbled with it, but I was thinking about different ways of reckoning efficiency.  A small-tolerance ascent path leads to minimal errors in the final orbit, but necessarily consumes more fuel to keep the tolerance tight.  A large-tolerance ascent path opens the door (pun intended) to requiring a large correction after insertion, because the accumulated errors resulted in too great an error in the orbit.  And that too requires fuel.  On the LM those fuels come from the same source and can be globally optimized.  On the CSM, for example, the RCS and SPS had different fuel sources, so it might be better in that case to decide which fuel source is more important to conserve.  But the great thing about sloppy tolerances is that they're often sloppy in both directions such that they average out, and you end up adequately "bouncing between the guardrails" to get to your destination.

Up to a point, of course. So there must have been an optimum deadband that minimized the total propellant (main engine + RCS) required to reach a given target state vector with the same given accuracy.

Undoubtedly.  Any solution can be optimized, and I see what you're doing to dig away at the theory of it.  I think you're onto something.

[ka9q]

Well, yes and no on the LM ascent.  The DAP was then, and always was, closed loop at the perspective of attitude errors and error rates.  But the attitudes that the ascent guidance system fed into the DAP were static, stepwise values.  At the high level, LM ascent guidance was open-loop.

Right, my apologies for being imprecise. By "closed loop" I meant that you command the DAP to a given attitude, and it would then continuously read the gyros and fire the thrusters as needed to get there and hold that attitude, within a specified deadband.

A question on terminology: what is the specific job of a spacecraft "autopilot"? Does the autopilot only seek and maintain an externally specified attitude, or does the term include determining what that attitude needs to be, either open or closed loop?

On the LM those fuels come from the same source and can be globally optimized.  On the CSM, for example, the RCS and SPS had different fuel sources, so it might be better in that case to decide which fuel source is more important to conserve.

Right, and I've wondered why it was done that way. Was there a lot of uncertainty in how much fuel the LM RCS would need? I can see that there might be. You don't know how much the CDR will need during his manual approach and landing on an unknown terrain, and you can't always control the c.g. position on ascent as tightly as you'd like.

The Marquardt thrusters were designed to burn MMH, and they had to be requalified for Aerozine-50. It's tempting to think that they're almost the same thing as each hydrazine molecule in Aerozine-50 has, on average, one methyl group just like MMH. But chemistry doesn't always work that way...

But the great thing about sloppy tolerances is that they're often sloppy in both directions such that they average out, and you end up adequately "bouncing between the guardrails" to get to your destination.

Exactly why, in a random walk, the expected distance from the start increases as only the square root of the number of steps; some of each error cancels out some of the previous errors, so there's no point in correcting individual errors too soon. Wait to see what the vector total will be, and then correct it in one step.

Undoubtedly.  Any solution can be optimized, and I see what you're doing to dig away at the theory of it.  I think you're onto something.

Given how much analysis went into propellant optimization all over Apollo, I'm sure someone must have looked at this very closely.

[Kiwi]

On a side note, he also scoffs at the notion that "little old ladies" could accurately thread the rope memory modules.

Perhaps he should be directed to the Spacecraft Films 2-DVD set "Mission to the Moon" where he can view some early NASA documentaries in black-and-white and, in the programme about the AGC, see with his own eyes the "little old ladies" doing the threading.
http://02e5a89.netsolstores.com/missiontothemoon.aspx

The presentation of some of the programmes is quaint and amusing, but nevertheless they are very informative.  Occasionally the interviewees are stiff as a board and look a bit like possums caught in the headlights -- terrified of the camera and dearly wishing they could get back to the job they know best.

Mission to the Moon
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Man's first steps on the moon took an incredible effort by thousands of dedicated workers. In this 2-DVD set you'll see how the Apollo program took men to the moon through in-depth programs created for NASA in conjunction with M.I.T. Each of them focuses on a specific topic presenting in-depth information and hands on demonstrations of how hardware was built and operated. Most of the programs are in black and white but are some of the most informative pieces on Apollo hardware and procedures we've ever seen. Over 5 hours of material on 2 DVDs.

Contents:

THE FLIGHT OF APOLLO 4 - NASA program on the development of the Saturn V launch vehicle and the successful first flight of the vehicle in November of 1967. Color. (14:30)

FIRST SOFT STEPS- Program takes an in-depth look at the lunar pathfinders, including Ranger, the Lunar Orbiter, and Surveyor missions. These pathfinders built confidence in Apollo design and procedures prior to the first manned visits to an unknown environment. Black and White. (28:30)

FOOD FOR SPACE TRAVELERS - Development of food for space travelers, particularly during the Gemini missons and in preparation for Apollo. Filmed at the U.S. Army labs. Black and White. (28:30)

ROOM AT THE TOP - Program on the Apollo command and service modules, their development, operation and roll in the Apollo moon landings. Filmed at the North American plant at Downey, CA. Includes looks at the the internal configuration and the construction of the hardware. Black and White. (28:30)

COMPUTER FOR APOLLO - Examines the Apollo guidance computer as well as the operation of the computer in conjunction with the navigation scopes in the command module. Shows operation of the DSKY as well as the computer hardware used in Apollo. Filmed in the lab at M.I.T. Black and White. (28:30)

POWER FOR THE MOONSHIP - In-depth look at the fuel cells developed for the Apollo CSM, including a demonstration on how the fuel cell stack is built up, showing the chemical process of power generation and the waste products, including drinking water for the spacecraft. Filmed at Pratt and Whitney. Black and White. (28:30)

LANDING ON THE MOON - Tom Kelly leads a tour of the development of the Grumman lunar module, including an exterior and interior visit, and a comprehensive view of how the lunar lander is built. Filmed at Grumman at Bethpage. Black and White. (28:30)

SUITED FOR SPACE - Covers the development of the suit required to keep the astronauts alive as they explored the moon. Black and White. (28:30)

SPACE MEDICINE - Filmed at Johnson Space Center, Houston, this program deals with the physiological concerns of human space travel, especially as it relates to the lunar missions. Includes demonstration of a variety of results from previous flights as well as studies being conducted on space medicine. Black and White. (28:30)

RETURNING FROM THE MOON - Speeds returning from a lunar mission required massive protection of the command module from the heat of entering the Earth's atmosphere. Filmed at Langley and at AVCO, the contractor for the Apollo heatshield, the construction of the heatshield is demonstrated, including subjecting a sample to a hot jet, demonstration of the honeycomb bonding to the spacecraft as well as the shooting of the resin ablator into the honeycomb with a "gun." Also examined is the testing of splashdown and possible land impact. Black and White. (28:30)

[sts60]

Il est français, je pense.

His name is Xavier Pascal. He claims to have graduated from a French university and I've seen posts he's written in French.

I guess it's him, then, who has a page at the Aulis web site with a lengthy exposition claiming the AGC wouldn't work. He started off by claiming that it couldn't control the spacecraft because it would take too long to get updates from the ground computers if anything went astray - apparently spacecraft on translunar trajectories are prone to suddenly lunging off course if not constantly corrected, which would be news to controllers watching, say, Pluto-New Horizons.  (The AGC's inability to provide realtime flight control would also be news to the pilots who flew the F-8 Crusader using an AGC for the first fly-by-wire aircraft tests.)...

I mentioned the Apollo conspiracy claims to a guy I work with.  Turns out his first co-op job with NASA was working on precisely that project.