The solutions they are exploring are many times less complicated and difficult than what SpaceX is doing. Saying otherwise is mischaracterising both of their achievements.
They're specifically doing smaller rockets to tackle the inverted pendulum problem first, then they will scale up. They see that as the bigger challenge, and may greatly affect the design of larger orbital rockets which have a great deal of research available to draw from for other challenges they run into. In the article they say that one of their major solutions is a gimbaling engine, which I imagine is something you would have to design a larger rocket around, rather than add in after the fact.
Control authority. That is the measure of margin a system has over a feedback mechanism's (in case of a rocket: ability to accurately apply thrust in correct vector at required frequency) ability to dampen uncontrolled perturbations.
I'd bet you that SpaceX has just as thoroughly understood and tested their working margins on their landibg system's control authority as has Blue Origin. For this reason I don't believe Blue Origin has any technical advantage over SpaceX in the manner you imply they do.
This might be hubris, but there aren't too many things us humans don't understand about rocket design at this point. The last big one was the waterhammer effect in turbo pumps supplying rocket fuel.
Understanding 1st, 2nd, and 3rd harmonic vibrations in mechanical systems is standard practice in rocket and any other airframe design (Boeing airframes, missiles/rockets, etc). It's a solved problem.
If Bezos is hanging his hat on this argument, he's reached the limit of his omnipotence.
I don't care if SpaceX or Blue Origin wind up on top, I don't own stock in either one, but I'm much more likely to trust the word of an actual certified rocket scientist than an unsourced HN comment.
Of course, its also easier to have very fast gimballing on a smaller engine, and a taller rocket bends more which makes it harder to detect exactly where it's pointed in the first place.
However, this is independent of the presence of the atmosphere. In real life, both scenarios need active control of attitude.
The yard stick has a normal force vector from the hand passing through its center of mass. It doesn't start to rotate unless an outside force is applied.
Of course in the real world it requires active control because the most minute misalignment causes a feedback that moves it further out of alignment. The rocket is exactly the same, if the thrust vector is not directly between the center of mass of the rocket, and the Earth, it starts to tip over.
If it were a stable system, misalignment would push the system back into alignment.
Outside of atmosphere and/or at low velocities, there's no instability of this kind, and "flying backwards" (=landing) makes the rocket actually auto-stable (like with a dart), even if the time constants may not necessarily be meaningful for useful control here.
So if a rocket tilts in flight, it will not tilt further and it will not fall back.
The yard stick, if tilted, will tilt further still and eventually fall, unless caught.
This is what makes your argument moot - because they do gimbal, and the gimbaling is what creates the moment/torque. In a way that is very nearly analogous to twisting your hand around slightly to balance a broomstick.
> The yardstick is unstable in inclination if it isn't vertical. The rocket is unstable in horizontal position if it isn't vertical.
The rocket is unstable in position and inclination (attitude). So you're right that there's more to it, but it's still the inverted pendulum problem for attitude, plus the rocket formulas for translation and added constraints of landing location. Are you saying Bezos is lying in this post when he explicitly says "When you do a vertical landing, you’re solving the classic inverted pendulum problem"? He would know, and I don't see a reason for him to lie about it.
Interestingly, because the CoM is so low due to the low volume of fuel by the time of landing, it's likely not as big a torque as you'd first expect (all the mass is down the base where the engines are). In that case, rocket height isn't going to have as a big an impact because it's not like it's equally dense up the entire rocket structure. I'd argue he's likely overstating the effect of rocket size on how difficult it is to achieve.
The point of the inverted pendulum problem is that the torque on a long, thin, ground-supported object (or even just any ground-supported object with a narrow base or a hinge on its bottom) is a function of its orientation. That gives you a second order differential equation for tilt. This is NOT the case with the free-flying rocket because the engine is rotating along with the rocket. You could simulate the inverted pendulum actively, by rotating the engine so that it has a fixed orientation relative to the ground (up to the gimbaling limit, which is usually <10 degrees), but you actually want to do the opposite with the landing rocket (with significant damping to boot). Basically, you want the active control system to simulate a normal pendulum, just turned upside down (but with the damping so that it doesn't actually oscillate).
> The rocket is unstable in position and inclination (attitude).
Not the latter unless you make it behave in that way. You could also check on the Apollo LM landing guidance, maybe it will become more clear if you study that.
> So you're right that there's more to it, but it's still the inverted pendulum problem for attitude
No, it's not. That's the point.
> Are you saying Bezos is lying in this post when he explicitly says "When you do a vertical landing, you’re solving the classic inverted pendulum problem"? He would know, and I don't see a reason for him to lie about it.
No, I'm saying that this phrasing makes no sense. Remember that Goddard made a similar mistake when reasoning about rockets and pendulums, so arguments to authority are demonstrably to be avoided here. A significant clarification on his part could make it more comprehensible what he actually meant, but making any kind of analogy to a ground-supported object is clearly bad when talking about a free-flying body.
For the broomstick, weight is down but "thrust" is both up and forward. So there is a moment caused by weight at the CoM and up-force at the base.
While the tall guy has more weight far from the pivot point, it also has more weight down (because more fuel to stop a heavier vehicle), more sensitivity to various winds and more physical tensions/torsions all along its body structure.
I'm not physicist/rocket scientist, so wondering if I'm missing something
They're already one step further though: actually reusing the rocket