Meithan

If the integrator is symplectic, and the velocity verlet is an example of one, then by design the energy errors should be bounded and quasi-periodic, and not add up over time -- that's the beauty of symplectic integrators. See the energy error graph I posted earlier: the energy fluctuates almost periodically (the "main" oscillation seems to have a period very similar to that of Mercury, about 1/4th of year) but the error never becomes greater than 10^-9 -- and in principle this would hold for indefinitely long periods of time. With Runge-Kutta integrators, which are not symplectic, the story is different, and the energy error will build up over time, which is why they're not preferred to study the long-term stability of gravitational systems. In practice, though, a fourth-order Runge-Kutta integrator with its gradually accumulating error should still yield better results than the second-order velocity verlet if the integrated time is not too long, simply because the error is considerably smaller in the first place (due to the method being of higher order).

Great video, thanks for posting! But I'd say that's a water splash when the trunk "lands", not sand. Edit: on fifth or so watch: yeah, could be a "sand splash", not sure now.

20 bodies is definitely doable by direct force calculation; 300 I'd say so too, depending on what system it's running on, what programming language and how small you want the timesteps to be. No, it's a Fortran code I wrote plotted with gnuplot. Keep in mind the solar system is pretty stable: the orbits are nearly circular and they're pretty far apart. Close encounters are the bane of numerical N-body simulations: they'll quickly make the numerical error really bad. If you're getting close encounters you'll probably need to make the timestep (how much each step of the calculation advances time) smaller, or even 'adaptive' (automatically adapt to be small when bodies are close and large when they are far away). But that's another story, I'd get the basic velocity verlet working first. The KSP devs ran precisely into this problem. An adaptive resolution mesh for the planets and movable coordinate origin are ingredients of the solution.

I came to this thread too late because K^2 has already provided great info. Just two things: 1) If you're simulating a small number of bodies, efficient algorithms like Barnes-Hut are unnecessary: you can just directly calculate the forces using Newton's law of gravitation. You can save somw work by avoiding doing double calculations: if you already calculated the force caused by A on B, don't compute the force by B on A, just use the previous result with a negative sign. 2) As K^2 pointed out, the Euler algorithm is a bad idea for N-body simulations. The velocity-verlet, on the other hand, is pretty good for simple simulations. I've done toy simulations of our solar system for 10,000 years using the velocity-verlet, and it's pretty stable. The first image shows the Sun, the inner planets and Jupiter. The second image shows the relative error in the total mechanical energy of the system after 1000 years. As you can see, it's tiny (no larger than 1 part in 10^9). Now, as K^2 mentioned, your simulation has three bodies, two of which are big, in close proximity, so the system might be both inherently unstable and hard to simulate accurately. Beware. Keep us posted on your results.

There's that too .

Fantastic work, arc! Thanks a lot.

I think 4-5 Gs is something astronauts can handle. 14 to 17, on the other hand, and a little swearing is more than reasonable. When they landed, the first thing the rescue crew did was give them vodka and cigarettes. That's soviet Russia.

Great write up, very clear and complete. I've sent some rep your way. As an aside for people willing to discuss the finer points of this, I'd like to add that while it's true that both the lift and drag of the fins contribute to the restoring torque in a stable rocket, I'm under the impression that it's the lift of the fins that generates the dominant contribution. I can think of several reasons for why this could be so. For small deviations from the direction of flight: (a) the lift of the fins is perpendicular to the centerline of the rocket, which favors torque production; ( the drag is nearly parallel to the centerline, which is unfavorable for torque production; © the drag area of the fins is not much larger than when the rocket is pointing in the direction of flight, so the form drag doesn't increase much; (d) for typical airfoils, lift increases faster than induced drag (for small angles of attack) So the only way for drag to be the dominant contribution would be for the drag force to be considerably larger than the lift force that can be produced. However, typical wings have lift-to-drag ratios on the order of 10, so the lift-induced torque would tend to be considerably greater for the reasons stated above. I'm no aerodynamics expert so please do correct me if I'm wrong; I bring this up to hopefully improve my understanding.

Pretty much, yeah. As long as you remain close to aligned with your velocity vector, the aerodynamic forces trying to flip you over are small and easily overcome by the TVC.

Far from it. The Soyuz LES produces much larger accelerations, as did the Apollo LES. Specifically, in the T-10a Soyuz incident, the LES produced "an acceleration of 14 to 17g (137 to 167 m/s²) for five seconds". Crew Dragon is limited to 5-6 g's.

I've been wondering about that too. I think they are the components of forces along three directions defined by your velocity vector: blue is perpendicular "up" (e.g. lift), red is parallel to velocity (e.g. drag) and yellow is perpendicular to those two, so "sideways" (e.g. your tail vertical fin counteracting yaw). I'm at work so I can't confirm ingame at the moment.

It does look like one of the SuperDraco engines shut down early, which might be the "below nominal" performance that seems to have been called out during the test. In this short video, you can see that one of the engines in the left pod on the near side of the capsule shuts down and emits a puff of smoke at around 0:04, a couple seconds before the rest of the engines shut down: https://www.youtube.com/watch?v=cyrB7kOqfdM

Yes, I just checked and 2 km from the pad is indeed pretty close to shore, I think you're right. The trunk deployment did come a bit early though (at 15 s instead of the announced 21 s).

It looks like the downrange distance was not as big as planned. It did splashdown closer to shore than I thought it would. Non-nominal burn maybe? The duration was as planned, so maybe lower thrust than expected? Or GNC problem? We'll have to wait and see. Still, a successful test in that Dragon complete all flight phases and they gathered a lot of data.

Nope, on the blurb on SpaceX's website, it's stated that

People beat me to it, but I'd say that you need the trunk and its fins to ensure aerodynamic stability of the escaping capsule. And the large thrust and gimbal capacity of the Falcon 9 first stage engines produce much more torque than the aerodynamic torque produced by the comparatively small fins during ascent, so it's not a hindrance for the whole rocket.

Congrats! I still remember my first rendezvous. Boy was that exciting, seeing another spaceship just out there, at arm's reach, both free falling at ludicrous speeds in perfect synchrony. Now you have to try docking. Rendezvous is half the work, so you're almost there. Here's what Wally Schirra, the Gemini 6 astronaut who accomplished the first successful orbital rendezvous in 1965 (although the spacecraft did not dock), had to say about rendezvous: Happy flying!

Yes, you're quite right, I hadn't thought that you can't stage it during Kerbin ascent, not even rewire fuel lines. My lander would probably go below TWR of 1 after enough of the outer asparagus stages are emptied and thus shut down and become dead weight. Doubly good thinking there, then!

Thanks for taking this on, guys. Hopefully this pushes my own entry closer to review . By the way, Kuzzter, I checked your mission report for the challenge and I have to say that it's a great design overall, and pretty aesthetic too. I specially liked your "towing boom". How is the lander mated? Docking port Jr.? Did it greatly reduce your turning rate? Also, I had a "duh" moment when I saw you just let the Eve lander get to Kerbin orbit on its own propulsion, and then refuel (if it can liftoff from Eve, it can sure as hell liftoff from Kerbin ... duh!). Good thinking there.

Indeed, the previous charts ignore TWR and it can be an important consideration since these engines don't provide a lot of thrust. I've included a minimum TWR restriction to the analysis (by asking my program to increase the number of engines in each case until the restriction is met). Edit: Charts recalculated using correct thrust values. For TWR up to 0.4 (about 4 m/s^2 of acceleration), the previous result holds: the LV-N is generally the better choice for ÃŽâ€v's larger than about 2000 m/s and payloads heavier than 5 tonnes. For TWR of 0.5-0.6, the breakeven point moves to higher ÃŽâ€v's and becomes less sensitive to payload mass (the masses of the engines are starting to become dominant). Also, a region of no solution at high ÃŽâ€v appears (to the right of the charts). This is because the LV-909 can't yield more than 7400 m/s and the solution with the LV-N would require a ridiculous amount of engines (I've limited the code 100 engines). For a TWR of 0.8 and beyond, the LV-N is too heavy to provide efficient solutions, and the LV-909 wins where a solution is possible. --- I think the bottomline is that the LV-N's efficiency makes it the better choice for TWRs up to about 0.5; beyond this it's just too heavy to satisfy the TWR restriction efficiently and the LV-909 is the only practical choice. Of course, the more sensible solution to this problem is to drop stages on the way. I've done missions to Jool with a TWR of 0.25 (with 6 LV-Ns and a total ship mass of 130 tonnes) and it's perfectly practical. It's all about whether your mission profile can work with long burns (on the order of 10 minutes). If you're curious as to why the jaggedness in some of these charts, it's because the number of engines changes suddenly to satisfy the TWR restriction. I've included the last chart to better visualize the effect: it's clear how the additional LV-N added at a ÃŽâ€v of 2200 m/s temporarily makes it a worse choice than the LV-909. Those 3 tonnes hurt! I saw that thread. The new solar power scaling is definitely making things interesting for ion drives. I've been wanting to crunch the numbers on that, but I really should get to work for now .

Wow. I know that they're trying to land a building, but putting the scale in perspective like that is just ... wow.

As people pointed out already, the comparison in the OP is a bit unfair because the fuel/total masses are different, and because the LV-N now only consumes liquid fuel so it's better to use fuel-only tanks. Waiting for someone (or the man himself) to recompute tavert's engine efficiency charts, I prepared a few of my own, which I present below. tl;dr: if you don't care about a potentially tiny TWR, a single LV-N will outperform a single LV-909 for any payload heavier than 5 tonnes and for desired ÃŽâ€v's larger than 2000 m/s; see this graph: If you prefer to avoid 30-minute burns, the LV-N is the better choice up to a TWR of 0.5; see this other post. --- Intro This is meant to give an approximate analytical perspective on the debate of LV-909 vs. LV-N as interplanetary transfer stage engines. I do this by computing the total ship mass required to yield a desired ÃŽâ€v for a specified payload mass. The "ship" is considered as one engine + fuel + fuel tanks to hold it + payload. Assumptions: Only one LV-909 or one LV-N, so no restriction on TWR. Both engines now have a thrust of 60 kN, which is not much for an interplanetary ship, so TWR considerations will be important; see my next post for an updated calculation. Single-stage ship. As we all know, dropping mass on the way yields higher ÃŽâ€v values, but I'm keeping it simple here. Propellant quantity is treated as a continuous value, so tanks are considered infinitely divisible. While this is not realistic, one could approximate this in practice by using a large numbers of small tanks (at least for LFO tanks; for LF only there are fewer options). For the LV-909 I'm assuming a fuel-to-empty tank mass ratio (my "alpha") of 8 (i.e., 8 tonnes of fuel per tonne of empy tank mass), corresponding to most LFO tanks. For the LV-N fuel-only tanks, I'm using a value of 6, the value for the Mk 2 tanks. The Mk 3 tanks have a better ratio of 8.3, even better than LFO tanks, so choosing this value would only make the case better for the LV-N. "Payload" is defined as everything that is not the engine, fuel or tanks, so it includes stuff like structural elements as well as the proper payload. Engine stats used: LV-909: Isp=345 s, mass=0.5 t; LV-N: Isp=800 s, mass=3.0 t (vacuum Isp used) --- Results With a bit of algebra, we find that for a given desired ÃŽâ€v and using the parameters of these two engines, the total ship mass for a desired payload mass is given by: where is the fuel-to-empty tank mass ratio, which states how many tonnes of fuel you get for each tonne of dry tank mass (the more, the better). Before we get to the graphs, let me take a detour to mention an important point: the fact that we're considering the mass of the fuel tanks in the calculation basically imposes a maximum achievable ÃŽâ€v for any engine, which depends on its Isp and the value of α of the tanks: For the LV-909 and assuming α=8, this turns out to be ÃŽâ€vmax = 7,444 m/s, which means that for anything close to or beyond this value, a single-stage ship using an LV-909 is impossible. For the LV-N and assuming α=6, the limiting value is ÃŽâ€vmax = 15,287 m/s. Now to the graphs. I've plotted the total ship mass vs. desired ÃŽâ€v for payload masses of 5, 10, 20 and 50 tonnes. For any desired ÃŽâ€v, the lower curve indicates the more efficient engine of the two, since it achieves that ÃŽâ€v with a smaller total ship mass (which includes its own mass and the fuel mass it needs). The vertical blue dashed line indicates the ÃŽâ€v limit for the LV-909 at ~7450 m/s. The last image shows 2D map of the regions where each engine is a better option, like tavert did. It's clear that the LV-N becomes the better choice very quickly: already at only 5 tonnes of payload it outperforms the LV-909 for any ÃŽâ€v larger than 2000 m/s. That's not a lot: it's not sufficient for a round trip to low Mun orbit unless aerobraking is heavily used for the return. From the last plot we confirm that the LV-N dominates for all but the lightest ships (< 5 tonnes) and for most useful interplanetary ÃŽâ€v figures (> 2000 m/s). But as mentioned previously, this does not consider the TWR of the resulting ship, and these solutions with a single engine might not be practical (pushing a 100 t ship with a single LV-N yields 0.6 m/s^2 of acceleration). Edit: I made some corrections since the thrust of the engines is not as high as I initially thought. Main results remain unchanged, but see my next post for the full analysis including TWR.

These are the outstanding pre-1.0 submissions (collected by Kuzzter): iLike Rovers 26 April Meithan 26 April ShadowZone 26 April HelmutK 27 April What requirements must a reviewer meet? Does it have to be someone who has completed the challenge? Because I'd be willing to review one or two in the hopes that someone will review mine .

Very clear graphical explanation, good work! Here, have some rep. I have only one minor observation. I'm not sure about this (somebody correct me if I'm wrong), but I think it's technically the increased lift from the fins (due to the higher angle of attack) what's providing the restoring torque, not the drag. Lift initially increases faster than drag as the angle of attack increases from zero. The effect also comes from the other set of fins (not shown) which are mounted at 90° from the ones you show, but I agree they are harder to depict clearly. Still, the general conclusion is correct: adding aerodynamic surfaces to the tail makes the rocket more stable. And your tips are sound.

Fantastic job, MoffKalast! The final result is really impressive. So what did you do for the LV-909s? Added a base of some sort?