Comments by "Tony Wilson" (@tonywilson4713) on "" video.
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AEROSPACE ENGINEER HERE: I am going to try and explain how this gyroscopic control sounds straight forward but its anything but straight forward. The math involved is actually the hardest math there is in all of engineering.
Sorry for the length of the explanation, but there is an interesting story at the end I promise.
FYI - I love Scotts channel its fantastic.
The only thing I don't like is he's flying and I'm not at the moment.
In my final year when we had to do 2 high level aerospace options and a few chose to do Spacecraft Dynamics which we foolishly thought would "be cool" because it sounded cool (sort of). For those unfamiliar most universities have a ranking system for classes at my college (U. of Illinois) everything was a 100, 200, 300 or 400 level class. Most undergraduate classes are 100 & 200 level while 300 & 400 are for postgraduates. However most degrees required 2 x 300 level classes. In engineering (as far as I remember) every 300 level class had a 400 level equivalent. The difference was the 400 level required a term paper that had to be presented like it would be for a conference. So when you do an engineering 300 level class you do it with the 400 level students but they have to do their term paper and present it to the class (see below).
The 2 most common classes my senior class did 2 were Finite Element Analysis and Orbital Mechanics. FEA because its reasonably straight forward and is used across many engineering fields and OM because that's what both NASA and the satellite industry want. Spacecraft Dynamics is an alternative to Orbital Mechanics and the difference is like the difference between a pilot and a navigator on an airplane. A navigator works out the path you will fly while the pilot flies it. Orbital Mechanics is analogous to navigation while Spacecraft dynamics is analogous to piloting.
Within 2 weeks of starting that class EVERY undergraduate tried to get out of it once we realised how hard the math was. Orbital Mechanics is generally regarded as one of the most math intensive classes any engineer can take because its done on spherical coordinate systems and nothing travels in a straight line. Spacecraft Dynamics is another level up on that because not only does it require solving simultaneous non-linear differential equations but doing it with coordinate transformations as well.
The Basics
To most human beings we see the world in Up-Down-Left-Right-Forward-Back. We call that a cartesian coordinate system. Think of a normal X-Y graph and then look up "smith chart" in YouTube search. In space everything is in spherical coordinates. Further every major body (like the Sun and the planets) there's its own spherical coordinate system and those systems are moving at different speeds and different orbits. That's what makes orbital mechanics the headache that it is. There's no nice simply x-y-z its all r, θ, φ. Navigating from just the earth to the Moon one you have to translated from the Earths (r, θ, φ) to the Moons (r, θ, φ) but if you want to go to Mars you have to go from the Earth (r, θ, φ) to the Mars (r, θ, φ) while dealing with the Suns (r, θ, φ). Yeah its coordinate systems within coordinate systems.
The problem with flying a spacecraft.
Why Spacecraft Dynamics gets so hard is because you have the spacecraft's own coordinate system which is in cartesian coordinates because that makes it possible to write the basic math out in the first place BUT THEN you have to translate that system into the orbital reference frame that the spacecraft is flying in and that system is a spherical coordinate system. Because the equations for gyroscopes are differential equations you start with a set of 3 dimensional simultaneous non-linear differential equations that you then have to translate into another coordinate system as well as solve it.
And why is that needed - because things like Hubble have to fly in a spherical coordinate system while orientating in a cartesian system. Gyroscopes are great because they don't need fuel but there's a things called precession.
Go look at Wikipedia for the page title Gyroscope. Down the right hand side there's 2 labelled pictures and 2 animations. Look at the 2nd animation where they show the effect of twisting a gyro about an input axis. This is the problem you can't just turn a gyro and expect an opposite rotation because precession causes a twist in the other axis. That's the effect of precession. This gets even more complex as you move from singular to multi-axis gyroscope systems because as you twist one gyro it causes the other gyro or gyros to also twist and then you get a compound precession and that math gets so horrible it still haunts me 37 years later.
I said at the start I'd give you a good story.
I did that class in 1987 during the height of Ronald Reagans Star Wars program and most (if not all) the post graduates were sponsored by DARPA and working on Star Wars stuff. I remember the term papers 2 of them presented. One was on the dynamics of rail guns but that's for another day. The other guy was doing high accuracy pointing of space based laser platforms.
He was quite possibly the smartest human I have ever met in terms of applied math to an engineering problem. He could not only solve the basic math but link it to tracking other objects on other orbits as well as ballistic trajectories but what really made his work exceptional was the anti-shake system he developed. Oh Yeah and he put this into software and could make it work in 2 dimensions. It was an amazing achievement but it then needed to be done in 3 dimensions.
The real problem with a space based laser platform is the platform wobbling or vibrating when it pans. There's nothing odd about that as every thing wobbles or vibrates when it pans. Things like robotic arms and satellite dishes all wobble when they pan. The difference is when they are attached to a large object like a planet or is in an fluid like air or water that gets damped out. In space however there's nothing but the structure of the spacecraft itself to dampen vibrations out. One way to deal with that is just pan slowly which is fine for telescopes like Hubble or a probe out at Saturn or Pluto but for a laser cannon you want to zap missiles NO, it has to pan fast, stop without any additional motions and shoot.
So even if you could solve what's arguably one of the hardest math problems ever conceived there's still the basic mechanics of a space based laser. If you just want to hit something on the ground from space we know the basics of how fast the gun will be travelling (28,000kmh) and what the range is (240km), but what does that mean.
Here's how to think of the problem.
Imagine a target 2.4km away that you have to shoot. Sounds straight forward until you check the list of longest sniper shots on Wikipedia and find only 6 times in recorded history has anyone successfully shot past 2,400m and hit the target and they were snipers in a stationary position. So just hitting something that far away is hard.
Now imagine being in a Ferrari ripping along at almost 280kmh and trying to make the same shot out the window.
Now multiply each of those numbers by 100 and that's the basic problem of shooting a stationary object from Low Earth Orbit.
which is 28,000kmh at a range of 240km.
Now take the target put it on a rocket and fire it into the sky where its going Mach 10 (or more) and its maybe 10x further away at about 2,400km and that's the basic problem of shooting an ICBM from space.
Once we realised what the basic task actually entailed we knew that part of Reagan's Star Wars could NOT work. There were other methods in the Star Wars program like the ground based interceptors that we know have. However 37 years ago we knew that shooting ICBMS with a space based laser was not practical. Even 37 years later with all the advances in computers its still NOT practical because the mechanics are still the same problem and you still have to solve the math problems before you even try and make it work. And those math problems are a nightmare because its a gyro problem.
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