How does Hunchy, with all his claimed brilliance, miss these small basic things?
Hence why I can't accept that he's an engineer of any kind.
And in one sense these are small basic things. But in another sense they're the whole enchilada. They express a fundamentally different way of conceptualizing the spacecraft dynamic control problem than what a layman would probably envision intuitively, even a smart one.
After building a few actual spacecraft, you learn there is no optimal RCS placement. Further, other design constraints may disallow placing RCS jets where even a marginally optimal solution suggests. You quickly learn that a completely generalized vector solution (i.e., a linear algebra system) is the only way to keep from having to solve this problem minute-by-minute, spacecraft-by-spacecraft. Once you invoke this mathemagical world, you realize that you pretty much just solved every spacecraft dynamics problem, because they just become parameterized versions of the general solution. Yet the result and method are often inscrutable to the layman. The layman is still stuck on getting everything lined up perfectly to simplify the piecewise solution. Without that alignment, the piecewise solution grows into unmanageable complexity.
Most people intuitively understand inertia and momentum. That is, they know that the product of mass and velocity results in a quantity that has a real-world measurable value. An unladen shopping cart (trolley) hitting your ankles at high speed causes pain of the same approximate magnitude as a heavy-laden one hitting at slow speeds.
From this we can introduce the
moment of inertia, which is its rotational equivalent. The product of mass and velocity is still salient, but velocity in this case is how fast it's spinning. But then we realize that it depends which way we rotate. Things that are long and thin rotate more easily about one axis than the other. It complicates the reckoning of dynamic stability and control, so when playing Quidditch, the broom perhaps rolls more easily than it pitches or yaws.
The mathematically disinclined reader starts to get a headache at this point. But we again invoke linear algebra. This misnamed branch of math, among its many uses, has the practical use here summed up by: "It's a way to reason in general about several directions at once." In this world, instead of thinking about the three cardinal directions (roll, pitch, and yaw), we think about all conceivable directions simultaneously by expressing them as rotations
relative to roll, pitch, and yaw. You don't have to understand this. But what comes out of this is that moment of inertia, in real-life spacecraft control, is a
matrix, not a formula. Nine numbers, properly specified, give the moment of inertia of any body, in any axis. Or in more direct terms -- of every spacecraft that could ever be built, anywhere, by anyone.
Once you start expressing the problems and solutions in linear algebra terms, basic concepts like moment of inertia and RCS control inputs share the same visual appearance: that 3x3 matrix. And so do complex topics, like damping the effect of fuel slosh in the tanks. It's all the same stuff. Relatively advanced mathematics, but a very elegant solution.
Then when you realize that linear algebra doesn't require your reference axes and control axes to be strictly orthogonal (i.e., all at right angles to each other), you achieve another step in the generality of the solution.
And this straightforward (while admittedly math-heavy) progression from basic concepts to a fully generalized solution is what gives us the lunar module. The LM had non-orthogonal control axes, and shared a property with the CSM that it could operate with various individual RCS jets disabled. The layman, who is thinking of firing certain specific control jets to, for example, correct a roll error, shudders in horror at what he'd do if those individual jets weren't available. The engineer, with the generalized solution painstakingly achieved through analysis and theory, sits back and says smugly, "Hey, no problem." To the layman it looks like magic. It isn't; it's just math. But the ability to comprehend this kind of physics solution (or, at the limit, that such a solution is theoretically possible) is the kind of thing that separates engineers from non-engineers. Not as a value judgment, but as a qualitative difference in the mode of thought.
