Suicide burns on the fly

[sevenperforce]

Trying to get the hang of powered vertical landings.

Playing Demo.

I built a small test craft with eight pre-extended, suspension-locked landing legs and a couple of liquid-fueled engines, put RCS thrusters with plenty of propellant on the capsule up top, and stuck Jeb in it. I launch, navigate to a smooth landing area, and throttle the engines down until I start to drop, then tell Jeb to use RCS to maintain retrograde alignment.

Then I just play with the throttle to try and stick the landing.

I've gotten a couple of landings, but it's hit or miss (well, I never miss; I just hit too hard). I know how to sit down and calculate out exactly what I need for a true suicide burn, but for landings on the fly, what's the best way to eyeball my altitude and speed to pull it off smoothly?

[Nich]

Sadly I have never figured this out and use KER. I don't think I can do this in my head.

really it is just math

 

[Snark]

Not sure, does the demo include maneuver nodes?  There's a handy little trick to help with that.

1. Put yourself on a suborbital trajectory
2. Drop a maneuver node right at the spot where your projected path intersects the surface
3. Drag the retrograde handle until the projected post-maneuver path collapses to a point at the node and the grab handles on the node start flipping back and forth
4. The estimated burn time for the node is now your suicide burn duration.
5. The maneuver time is when you're due to hit the surface.

So set your SAS to "hold retrograde" (relative to surface); wait until your time-until-maneuver is around, say, 70% of the estimated burn time; then hit the gas.

[sevenperforce]

35 minutes ago, Snark said:

Not sure, does the demo include maneuver nodes?  There's a handy little trick to help with that.

1. Put yourself on a suborbital trajectory
2. Drop a maneuver node right at the spot where your projected path intersects the surface
3. Drag the retrograde handle until the projected post-maneuver path collapses to a point at the node and the grab handles on the node start flipping back and forth
4. The estimated burn time for the node is now your suicide burn duration.
5. The maneuver time is when you're due to hit the surface.

So set your SAS to "hold retrograde" (relative to surface); wait until your time-until-maneuver is around, say, 70% of the estimated burn time; then hit the gas.

Unfortunately the demo doesn't have nodes. 

I was thinking, though...it's all about energy, right? If you have a near-vertical trajectory, then you can take the mass of your craft and multiply it by g*h + 0.5*v^2 to get the sum of your potential and kinetic energy. Then, divide by the thrust of your engines at the desired throttle level. Your answer will be in units of distance and will be the altitude at which you need to begin your constant-thrust burn, since force times distance equals energy. 

Of course if your trajectory is nowhere close to vertical then you'll need to use your trajectory arc length rather than altitude, which is nonlinear. But it should be close, and you can always do a boost back to kill horizontal velocity if you need to...the difference in efficiency won't be too bad. 

This avoids the rocket equation and mass change issues altogether since the Oberth effect is worked in implicitly. 

[HebaruSan]

17 minutes ago, sevenperforce said:

Unfortunately the demo doesn't have nodes.

I think it's early career mode that doesn't have maneuver nodes. The demo has them, if you unlock them (via building upgrades) or play in sandbox.

[sevenperforce]

2 hours ago, HebaruSan said:

I think it's early career mode that doesn't have maneuver nodes. The demo has them, if you unlock them (via building upgrades) or play in sandbox.

I'm playing in sandbox. Apparently I just don't know how to use them. 

[Plusck]

7 hours ago, sevenperforce said:

Unfortunately the demo doesn't have nodes. 

I was thinking, though...it's all about energy, right? If you have a near-vertical trajectory, then you can take the mass of your craft and multiply it by g*h + 0.5*v^2 to get the sum of your potential and kinetic energy. Then, divide by the thrust of your engines at the desired throttle level. Your answer will be in units of distance and will be the altitude at which you need to begin your constant-thrust burn, since force times distance equals energy. 

Of course if your trajectory is nowhere close to vertical then you'll need to use your trajectory arc length rather than altitude, which is nonlinear. But it should be close, and you can always do a boost back to kill horizontal velocity if you need to...the difference in efficiency won't be too bad. 

This avoids the rocket equation and mass change issues altogether since the Oberth effect is worked in implicitly. 

This sounds about right.

However, as you imply, what is more important for a non-vertical burn is arc length, and that will change dramatically over the burn if you come in at a shallow angle. Rather than a boost to kill horizontal velocity, it's a boost to kill vertical that you'll need to make since your time and distance to impact will decrease as you burn. In a low TWR craft, the arc length can easily decrease faster with a retrograde burn than the craft can reduce its own velocity, making a "pure" suicide burn impossible. In that case a radial-out component becomes necessary, and with a very low TWR your suicide burn starts looking more and more like a constant-altitude burn.

The general "70% of time-to-impact" rule of thumb that Snark mentioned works well enough for reasonable TWR and reasonable approach angles. This suggests (though I haven't done the work of cancelling out the variables in the equations) that it's basically a question of dividing by the square root of two. Given that the major component in your energy-based approach is 0.5*v^2, that intuitively makes sense...

 

[sevenperforce]

2 hours ago, Plusck said:

The general "70% of time-to-impact" rule of thumb that Snark mentioned works well enough for reasonable TWR and reasonable approach angles. This suggests (though I haven't done the work of cancelling out the variables in the equations) that it's basically a question of dividing by the square root of two. Given that the major component in your energy-based approach is 0.5*v^2, that intuitively makes sense...

 

Of course, if you don't know your time-to-impact, that gets tricky. 

A really quick way of doing it (for near-vertical approaches) would be to square your velocity, divide by 20, and add that number to your altitude. Then simply divide by your vehicle's TWR to get the altitude where you need to start your burn. The first step gives you the equivalent altitude with a potential energy corresponding to your kinetic energy, and then 1/TWR is the fraction of that altitude you would need to burn for in order for the work done by your engines to match the work done by gravity.

For example, let's say you're at 640 meters, dropping at 85 m/s, and your T/W at full throttle is 3. 

85^2/20 is 361. Add to your altitude and you get 1,001 meters. Thus, you can consider your total energy to be the same as if you had dropped from 1,001 meters at a starting velocity of zero. Since your engines produce three times the force of gravity, you only need to thrust for one third of that distance, or 334 meters. 

Should be simple enough to do mid-flight.  

[Snark]

5 hours ago, Plusck said:

The general "70% of time-to-impact" rule of thumb that Snark mentioned works well enough for reasonable TWR and reasonable approach angles. This suggests (though I haven't done the work of cancelling out the variables in the equations) that it's basically a question of dividing by the square root of two.

Actually, that's not it, sqrt(2) has nothing to do with it.  The math rule I'm using is "somewhat more than 50%". 

To elaborate:

The perfect ideal case-- i.e. the shortest possible time you could wait under any circumstances-- would be 50% of time-to-impact.  That's the unattainable ideal, in the best possible conditions, assuming that:

1. you're going straight down
2. you have infinite TWR

If you're going at a shallower angle, you'll need more time.  The closer to horizontal, the bigger the effect.

If you have a lower TWR, you'll need more time.  If you have a really low TWR, you'll actually need to start burning well before the 100% mark.

The 70% number isn't any fancy math, it's basically just a reasonable compromise which I have found works well in practice.  In particular, I find that it has two properties:

• it's aggressive enough that if you follow it, you get pretty close to optimum efficiency
• it's conservative enough that you almost always end up with some safety margin and practically never crash

Rationale:

The coming-in-at-shallow-angle bit boosts the time, but not by a huge amount.  Unless you have a really low TWR craft or are landing on a world with really high orbital velocity (like Tylo), your trajectory will quickly become much more vertical as you slow down, so the shallow-angle contribution just boosts the 50% ideal by a small amount.

And as far as TWR is concerned: bear in mind that I'm talking about local TWR, i.e. your craft's thrust relative to local gravity.  Most vacuum worlds (Tylo notably excepted!) have much lower gravity than Kerbin, which means that vacuum landers usually end up having really high TWRs, like 4 or more.  So that means they can usually come reasonably close to the ideal-- TWR > 4 starts to approach "effective infinity" for the timing calculation.

So my 70% number is just a rule of thumb consisting of "start with 50% and increase that by an amount which I have found is fairly safe, given reasonable ship designs."  Personally, I tend to go a little more aggressive than that myself, down to 65% or even 60%, but when I'm giving advice to newer folks I prefer to give a suggestion that errs on the side of caution. 

The big caveat here is that if your ship has a low local TWR (e.g. something heavy and nuke-powered, for example), you'll need to allow a lot more time-- in fact, >100% if your local TWR is below 2.

[sevenperforce]

Been following this up with Grasshopper-style tests of high-thrust suicide landings, taking off vertically at random throttle and burn times, then calculating predicted apogee altitude and dividing by T/W ratio to get burn start altitude. 

Finally got it perfectly. The lump rising in my stomach as I plummeted, seemingly too fast to stop, and then the plume of fire rising under me when the speed indicator dropped to zero. Hitting X to kill the engines and seeing the dust clear. 

Really really satisfying. 

[Guest]

I believe that practice is the key. Sure, you can do the math, add mods, etc, etc, if you really want to squeeze every last drop of efficiency on the landing. But, really, it only takes about a half a dozen tries or so and you start to get a feeling for what speed at what altitude you need to be. Of course, you need to follow the same procedure each time as far as the approach is concerned. Start from the same orbit each time. Start the deceleration burn at the same point each time. Then it's all about "hitting your marks" as they say in NASCAR.

[Plusck]

5 hours ago, Snark said:

Actually, that's not it, sqrt(2) has nothing to do with it.  The math rule I'm using is "somewhat more than 50%". 

...

The big caveat here is that if your ship has a low local TWR (e.g. something heavy and nuke-powered, for example), you'll need to allow a lot more time-- in fact, >100% if your local TWR is below 2.

Yes, I've been playing around with some numbers and I've come to much the same conclusion. Though I'd still say that root two is in itself a rule of thumb which covers just about everything which moves