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Comment by illys | Hacker News Reader

Like SpaceX?

"If you love rockets, you can’t help but notice that real space launch vehicles lift off the pad slowly, but model rockets zip up like darts."

That reminds me of a common issue with modeling: when you divide sizes by N, you divide surfaces/light-reflexion/air-resistance/lift by NxN and volumes/weights by NxNxN.

A 1/10th model is 1/1000th of the original weight with identical materials. All the dynamics are different and easier at smaller scales. This makes the real thing an expert work while modeling is reachable by hobbyists - very good ones in this case.

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> All the dynamics are different and easier at smaller scales.

Are you sure about this part? (not rhetoric). Non-linear scaling of surface and volume are simple to understand, but dynamics doesn't look so straight forward to me... in my short lived experience trying to fly very small model helicopters, it was clear that the smaller they are the more unstable they were. I wasn't sure how much of this was due to limitations in human reaction time and how much was inherent aerodynamic instability at smaller scales.

In these rocket models the human limitation is clearly removed, the remaining dynamics look faster at least which may or may not run up against higher frequency sensor data and processing requirements... are there other dynamics i'm missing? i guess materials don't bend much at this scale?

Different? Yes. Easier? Depends. One thing you gain with size is intertia, which grows with N³, and depending on the design, can be helpful for stability.

Yes, thanks, this is what I meant but the relationship was not clear to me before, it seems obvious in retrospect: n^3 * density = mass scales cubed, which as far as control is concerned is both good (lower impulse requirements), and bad (lower relative mass requires much finer control)... happy to be told how to express the later formally :)

I think in terms of "less mass = bad", the formal answer will be found in control theory.

The think that makes this scaling "bad" is that moment of inertia is going down faster than everything else and this means the required control frequency goes up. A Falcon-sized rocket may only need to correct its course 50 times a second while a 3-foot scale model would need to do it 10x faster. This means your sensors need to be faster, your guidance computer has to run faster, and the actuators have to be able to respond faster.

The hard things on the other side tends to be power requirements, for exactly the same reason. Mass scales up as the cube of size, including the mass of the thnigs you have to move. Although you don't have to move them as fast, the net effect is still that your power requirements become very large for large-scale vehicles.

You are certainly right on helicopters' dynamics...

I was more thinking of planes and rockets when writing on dynamics: they are shaped to break through and be tunneled by a non-moving air for stability, and their weight decreased faster than their wing surfaces, making lift easier at smaller scales.

Helicopter are a different realm: they need to survive in the middle of the wind (and turbulence) they create to lift, and they are not tunneled (their body is not aligned on the vertical flow).

Thus, as Temporal mentions it, inertia is important for helicopter stability and it is reduced with weight at smaller scales.

> I was more thinking of planes and rockets when writing on dynamics: they are shaped to break through and be tunneled by a non-moving air for stability, and their weight decreased faster than their wing surfaces, making lift easier at smaller scales.

I suppose there is also relative viscosity to take into consideration? so even if smaller scales are going to be more fidgety and "unstable" in terms of inertia (as TeMPOraL more clearly expressed)... taking aerodynamics into consideration (depending on the design) may provide more significant benefits to dynamic stability at small scales anyway.

Without being very scientific, it feels like the small scale dynamics are not merely easier, but significantly different. It's intuitive to see how insignificant aerodynamics are at take off in full scale rockets are compared to models, and how models are going to be more sensitive to aerodynamics than inertia... i suspect the proportions to the problem of dynamic stability might even be flipped.

You also have to understand that small-scale models need the time dimension to be slowed down by X too in order to get the same dynamics.

Curiously, he still has 'center core' issues even at this scale.

His rocket is '3 tubes' each with their own motor. The motors produce large thrust, so much that the energy is more than enough to break the three tubes apart if not applied in a very coordinated manner. To make 3 rockets into 1 rocket is a central issue of this design! Just like the big ones.

"All the dynamics are different and easier at smaller scales."

I suppose that's why balancing a pencil upright on your fingertip is like 10 times easier than doing the same with a broomstick, right?

I think you are being sarcastic, because I can balance a broom a lot better than a pencil on my finger, so I'm going to discuss my thoughts behind why.

Based on what you are saying and tomxor in a sibling comment. Stability seems to increase with scale. Maybe it has something to do with weight, or center of mass, or a combination of the two.

I know that the longer the object you are balancing upright on your finger (or palm for something bigger than a broom), the easier it is to compensate the shifts in center of mass as it tilts. For a pencil, technically i guess it is "easier" to balance if you are a machine able to make the fine micro adjustments required.

The equation for the period of a pendulum has sqrt(l) in it. Therefore, I would guess that to get equal dynamics at a minimum, the feedback loop speed (the time for your hand to respond in the case of the broom) has to increase by the square root of the scale factor.

And that is why I'm a web developer ;)...

I chose to avoid all math after high school, how dare you bring formulas into my civilized, philosophical discussion!

It's inertia. Among other things, the much higher inertia of the broomstick has a damping effect on changes in its motion.

A broom is much heavier.

Your arm and hand are not great at doing many precise and gentle movements per second. With the acceleration they produce they can do many small corrections for a broom position. For a pencil, much faster and gentler corrections would be needed, and the arm + hand are too slow and imprecise to tackle that.

That's the parent commenter's point.

See the sibling comment on why helicopters differ from rockets/airplanes.

I think this is an issue of inertia/mass that doesn't exist so much for craft that gain and retain stability from their surroundings.

Of course, I could also be completely wrong.

I'm actually with you on the dynamics thing- the actual oscillations are slower and smaller, but they're cubically harder to deal with. A small oscillation in a full-scale orbital rocket can shred the skin like gossamer.

However, the issue is much worse for the general problem of rockets, as the term in the rocket equation[1] is logarithmic. The difficulty takes off so quickly that rockets go from club sport difficulty (eg copenhagen suborbitals) to national research programs when the rocket is just a few times taller. It gets said semi-regularly, but if the earth was just a little bit bigger (again- gravity rises approximately with radius^3) then we would never have visited space.

[1]: https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation

It's a frustration of mine with model rollercoasters. The train zips around the track much faster than the real rides. I've been playing with ideas like magnets and DC motors to try and make the trains move more slowly.

You could add inertia by including a flywheel (or multiple) connected to the wheels of the coaster. Not sure how easy that would be at small scales though.

I think you raise a good point about scale. I don't think full sized rockets lifting off has as much to do with gimbals vs. fins as it does with sheer weight. The Saturn V had fins on it and it lifted off slow, and I'm willing to bet that it had a lot to do with the fact that a Saturn V on the launch pad weighed somewhere around 6.2 million pounds.

Scale it down a ways to something like a RIM-116 and you can see the scale come into play. This thing goes from launch to almost disappearing over the horizon in under three seconds and then hits the target.

https://www.youtube.com/watch?v=pVk9VnUkvaU

Granted, that RIM-116 does have fins. So let's take the fins away and scale up to something like a Polaris SLBM

https://www.youtube.com/watch?v=sUlXty69-Y8

Still unbelievably fast, same with the Tridents. These get popped up out of the water before they fire their main engines. It's basically free standing in the air when it fires the main and it still shoots off super fast.

https://www.youtube.com/watch?v=h5KejRbD5s0

It has nothing to do with sheer weight and everything to do with the thrust-to-weight ratio.

Saturn V was slow to liftoff because the launch configuration had a very low thrust-to-weight ratio, IIRC about 1.1

And you don't think that has anything to do with the scale of it? The size of the rocket necessitating a lower T-W ratio due to the impracticality of making a rocket engine large enough to increase it?

And yeah, sheer weight definitely has something to do with the thrust to weight ratio. It's half the equation.

Honestly, maybe partially scale, but not really. It's more a factor of what it was meant to do.

Going to the moon means extra hardware on top, which means more fuel, which means lower TWR at launch.

If you're just going to drop a 6000kg bomb on earth somewhere, you need a lot less rocket on top of that first stage, and it's going to take off a lot faster.

I think we're just going in circles now. The scale was a result of what it was meant to do. The extra hardware on top and extra fuel all add to the scale of it. It was a massive rocket because it needed to do a massive job.

Anyway, I think we've gone off track from the original point, which was that full size launch vehicles taking off slow isn't because of gimbals vs. fins, it's because they're big and heavy.

We can be pedantic and say it's specifically because of a low T-W ratio, but the T-W is low because the weight is high and it's not practical to build a massive rocket engine to increase it.

um, sure.

Yep, and it's all down to the squared/cubed law. The thrust that a rocket engine makes at a given operating pressure is proportional to the area of the bell, and so scales with the square of its linear size. The mass scales with the cube of the linear size, and so for a given shape of rocket, doubling the size will multiply the thrust/weight by a factor of 2^2 / 2^3 = 1/2.

> That reminds me of a common issue with modeling:

The scientific field that studies this is called "Dimensional Analysis", and its major is probably the Buckingham Pi-Theorem, which takes maybe 10 minutes to learn, and is one of those simple physics ideas that translate to a lot of fields (like conservation laws).

Obviously we need human ovum sized spacecraft! :P

Then maybe we can get to orbit on solar pressure alone?

Humans are not reproduced by body alone.

To produce a useful human, you need 15-20 years of upbringing by other humans, preferably in a thick layer of material culture.

Colonizing space by transporting just fertilized ova is not going to work.

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