Duna Aerocapture Analysis

[Meithan]

I performed my first Duna aerocapture recently by following advice on the forum (and it went out well; I posted a Mission Report about it). Since I love numerical methods, I decided to try writing a program to simulate gravity and atmospheric drag, similar in scope and method to Alterbaron's fantastic Aerobraking calculator, to investigate the requirements of such a maneuver and to have a tool for my future missions.

The first application was investigating the Duna aerocapture window, inspired by the actual aerocapture I did ingame.

So I simulated a spacecraft arriving to Duna's sphere of influence on an interplanetary transfer from Kerbin, and entering the atmosphere with varying periapsis altitudes. This was the initial orbit in the simulation:

Initial orbit

Orbit type: hyperbolic (escape orbit)

Periapsis altitude: [10 to 15] km

Eccentricity: around 1.92

Excess speed: around 920 m/s

Orbit direction: retrograde

My program then solved the equations of motion and computed the trajectory the spacecraft will follow in the atmosphere, until it (a) crashed into the surface or ( climbed back to some fixed altitude outside the atmosphere. In the latter case, it then computed the final orbit the craft ended in.

Here are the results for periapsis altitudes of 10, 11, 12, 13, 14 and 15 km, the range relevant for aerocapture around Duna (coming from a Hohmann transfer from Kerbin):

Periapsis altitude: 10 km

Result: crashes into surface before exiting atmosphere

Periapsis altitude: 11 km

Result: crashes into surface before exiting atmosphere

Periapsis altitude: 12 km

Result: exits atmosphere on grazing low-eccentricity orbit (which reenters quickly)

Final apoapsis altitude: 50.83 km

Final periapsis altitude: -5.94 km

Final orbit eccentricity: 0.083

Periapsis altitude: 13 km

Result: exits atmosphere on high elliptic orbit

Final apoapsis altitude: 871.62 km

Final periapsis altitude: 11.89 km

Final orbit eccentricity: 0.564

Periapsis altitude: 14 km

Result: exits atmosphere on very high elliptic orbit

Final apoapsis altitude: 8771.25 km

Final periapsis altitude: 13.50 km

Final orbit eccentricity: 0.929

Periapsis altitude: 15 km

Result: no capture, continues past Duna on a hyperbolic escape orbit

Final eccentricity: 1.202

Final excess speed: 426.13 m/s

Conclusion: I confirm that the practical aerocapture window around Duna is in the 12-14 km range, depending on how high a final (elliptic) orbit one wants. This was calculated for an equatorial retrograde orbit (highest airpseed). For a prograde orbit, the figures should be similar, perhaps a little lower. It should be noted that the final apoapsis is very sensitive to the atmospheric periapsis used.

Edited September 16, 2013 by Meithan

[KatzOhki]

How much does your initial eccentricity and speed affect these results?

[AmpsterMan]

That is a very good rule of thumb because through the patented trial-and-error method I was able to discern that 12km-14km is a good aerocapture altitude aswell.

[musicpenguin]

Thanks for the calculator!

[MaverickSawyer]

Outstanding analysis! I am glad someone went and put the time into something like this. I can now sleep easier during my upcoming mission to Duna knowing I can use Aerocapture to save on fuel.

[Meithan]

Thanks for the calculator!

Alterbaron's calculator has been online for some time. It's much more polished than my program.

Outstanding analysis! I am glad someone went and put the time into something like this. I can now sleep easier during my upcoming mission to Duna knowing I can use Aerocapture to save on fuel.

Thanks. I can sleep easier too .

How much does your initial eccentricity and speed affect these results?

It shouldn't be tremendously sensitive to the initial orbit parameters, within reasonable limits. I expect the 12-14 km window to be valid for most Hohmann-type Kerbin-Duna transfers, since you'll be arriving to Duna with orbital parameters not all too different from those I used.

If you have any specific figures in mind I'll be happy to run those.

That is a very good rule of thumb because through the patented trial-and-error method I was able to discern that 12km-14km is a good aerocapture altitude aswell.

I guess that means my program is outputting accurate numbers then . I'll soon do the analysis for Eve, since I got a launch window coming up.

Edited September 16, 2013 by Meithan

[Meithan]

[Can an admin delete this post please? I double-posted by accident. Sorry.]

Edited September 16, 2013 by Meithan

[RoboRay]

The potential safe window is a little wider than your results, since there are many variables. I've done successful aerocaptures as low as 10.5km on Duna, arriving on a somewhat faster orbit than the usual minimum-energy Hohmann transfer. But good analysis, as I believe your results are spot-on for the more typical optimized orbits.

[AmpsterMan]

Were you able to record the gees experienced for each iteration? Might be fun/interesting to find out what they might be

[Specialist290]

Oo, I've been looking for something that can do calculations like these! (Alterbaron's works great if you have a target orbit in mind, but less so if you just want to see what happens on your current orbit with no input.) If you ever feel up to it, do you think you might release it for the rest of us to check out?

[Meithan]

The potential safe window is a little wider than your results, since there are many variables. I've done successful aerocaptures as low as 10.5km on Duna, arriving on a somewhat faster orbit than the usual minimum-energy Hohmann transfer. But good analysis, as I believe your results are spot-on for the more typical optimized orbits.

Yes, I agree the results may change a bit if the initial orbit is considerably different.

In fact, another source of error in my program is that it assumes an exactly equatorial orbit, so that airspeed is simply orbital speed plus (or minus, depending on direction) rotation speed of the planet. When the actual trajectory deviates from the equator, the airspeed calculation will be slightly off -- usually not alot, but since air resistance depends quadratically on airspeed, a small error is enough to have an impact on the characteristics of the final orbit.

While testing the program, I tried to reproduce the aerocapture I did in the game. The program predicted a final apoapsis of 534 km, while the actual final orbit ingame had an apoapsis of 518 km. Comparing my program to several quantities calculated by MechJeb, I found out that the most discrepant was my air resistance figure, and I attribute it to the effect described above.

Were you able to record the gees experienced for each iteration? Might be fun/interesting to find out what they might be

I haven't looked at the gees, but it's certainly an interesting idea. And the simulation computes acceleration at every step, of course, so it's very easy to extract that data. I'll make a plot and get back to you.

Oo, I've been looking for something that can do calculations like these! (Alterbaron's works great if you have a target orbit in mind, but less so if you just want to see what happens on your current orbit with no input.) If you ever feel up to it, do you think you might release it for the rest of us to check out?

Right now it's an ugly piece of Python code, not very user-friendly I'm afraid. If you're still interested, let me clean it up a little and I can post it.

[Specialist290]

I'm most definitely interested!

[Temstar]

Obviously G force is closely related to temperatures, but is that relationship liner? Say if you're experiencing 2G deceleration over Duna/Mars, does that mean the air around your spacecraft is heated to the same temperature as it would during Earth re-entry when deceleration is 2G?

I'm curious because in my previous experiences all the interplanetary aerocapture manoeuvres were relatively benign with deceleration under 2G, even for big ones like Jool. Eve aerocapture seems to generate the most powerful deceleration. The Apollo capsule can survive what, 9-10G of deceleration/heating? I'm interested in to know roughly how many Gs an unprotected but robustly built Kerbal spacecraft can endure when performing aerocapture.

[Meithan]

Alright, AmpsterMan, here's a plot of drag acceleration and altitude vs. time for a "typical" aerocapture around Duna (13 km periapsis in this one). The blue curve is altitude (in km, above "mean sea level"), while the red one is acceleration due to air resistance (it's given in "Duna gees", where 1 Duna g = 2.94 m/s²).

As you can see, as Temstar mentions, drag acceleration is pretty mild, peaking at around 2 Duna gees (some 6 m/s² -- not even one Kerbin gee). Kerbin launch is usually much more traumatic than this.

Edited September 17, 2013 by Meithan

[Meithan]

Obviously G force is closely related to temperatures, but is that relationship liner? Say if you're experiencing 2G deceleration over Duna/Mars, does that mean the air around your spacecraft is heated to the same temperature as it would during Earth re-entry when deceleration is 2G?

I'm curious because in my previous experiences all the interplanetary aerocapture manoeuvres were relatively benign with deceleration under 2G, even for big ones like Jool. Eve aerocapture seems to generate the most powerful deceleration. The Apollo capsule can survive what, 9-10G of deceleration/heating? I'm interested in to know roughly how many Gs an unprotected but robustly built Kerbal spacecraft can endure when performing aerocapture.

I think it'd be pretty complicated to answer that question, since you'd need a very detailed and realistic fluid simulation. Tons of things are important in aerospace applications: variation of drag coefficient with Reynolds number, supersonic effects (like wave drag), shock heating effects (no clue how to compute those), etc.

What seems to be true, though, is that aerobreaking in KSP is not very violent. How much drag deceleration does one get in Kerbin reentry with something like a command pod? I haven't looked.

[Meithan]

Let's try to see how bad it can get on Duna. Here's a failed aerocapture (initial periapsis set to 10 km):

Acceleration is given in m/s² in this one. It peaks at around 12 it seems, which isn't close to 2 (Kerbin) gees yet. Then it peaks a second time when the craft gets in the densest part of the atmosphere before crashing. I wouldn't want to be on this mission .

[tstehler1]

Since I'm restarting my save (and therefore have to redesign my interplanetary ships) when 0.22 comes out, this thread is fantastic. Thank you!

[loknar]

I don't think any scientific discussion of vanilla KSP (at this point, alpha 0.21.1) is irrelevant because the drag of a craft is just wrong.

FAR introduces drag calculation based on each parts and the craft Angle of Attack as well as stall effects.

http://forum.kerbalspaceprogram.com/showthread.php/20451-0-21-Ferram-Aerospace-Research-v0-9-6-2-Aerodynamics-Fixes-For-Planes-Rockets

The game becomes more accurate but: a discussion about aerobraking is even more difficult. When I use FAR and aerobrake, the AoA can be adjusted to increase drag, or a stall introduced to cause extreme drag. However, the added realism means that some situations you loose control or even brake apart because of uneven forces on the craft. Aerobraking has its limits.

NB: Eve is a bitch.

[Geschosskopf]

Conclusion: I confirm that the practical aerocapture window around Duna is in the 12-14 km range, depending on how high a final (elliptic) orbit one wants. This was calculated for an equatorial retrograde orbit (highest airpseed). For a prograde orbit, the figures should be similar, perhaps a little lower. It should be noted that the final apoapsis is very sensitive to the atmospheric periapsis used.

I've done quite a few aerocaptures at Duna but always prograde. For prograde, 10-12km is usually the best bet. Within the range, the specific Pe altitude is HUGELY dependent on your orbital speed relative to Duna. The faster you're going, the lower you have to go in the atmosphere to get the desired results. Of course, the desired results can differ a lot from case to case, but assuming you want to end up with the same Ap, the faster you're going, the deeper you have to go.

For example, I recently sent a flotilla of 3 ships to Duna, all launched within a couple hours of each other but with arrivals spread out over 28 days. The 1st to arrive was going like 1500m/s upon entering Duna's SOI and needed a Pe of 11km to get an Ap of over 2Mm, about 3/4 of the way out to Ike. Which was fine because this ship was going to Ike anyway. This was the only 1 of the 3 to produce fireworks. The 2nd ship arrived 10 days later going a bit slower. I wanted this one to end up in a 500km orbit. Using a Pe of 11.8km, I got an Ap of 485km or so, close enough. The 3rd ship arrived 28 days after the 1st doing about 940m/s. It's goal was a 150km Ap, and using an 11.8km Pe again gave it 146km, again close enough. So, both these ships used the same Pe but got very different Aps because of their different speeds. And the ship that went the deepest ended up with the biggest orbit, due to its much higher initial speed.

NOTE: The Pe's listed above were set when the ships were at 90km altitude. That's basically you're last chance to tweak the Pe before you enter Duna's atmosphere. The actual Pe's when the ships got there were somewhat lower due to the braking on the way to them (the 1st ship got down to 10km for example). There not being any way to really predict or control this, I use the value set at 90km as the "official" Pe value for purposes of such discussions.

Anyway, the bottom line is that aerocapture is going to be different every time you do it, even for identical ships going to the same planet. This is because the whole thing is so dependent on the ship's speed relative to Duna upon arrival and that will never be the same 2 times in a row. Your ship will always start in a slightly different orbit and you'll always do the transfer burn slightly differently, and then do some mid-course tweaks (or not) slightly differently. At Duna, a difference in speed of just 100m/s has a profound effect both on how deep you need to set your Pe to get captured at all, and the Ap you end up with afterwards.

Given this state of affairs, and the utter lack of in-game instrumentation to help, the only thing you can do is "have the boffins at Mission Control run simulations". That is, F5, set your Pe, and see what happens. If you don't like it, F9 and try a different Pe. This simulates the boffins running simulations to determine what's best for the current situation.

[Temstar]

It's of interest to me because aerocapture in KSP is a pretty standard maneuver in KSP for interplanetary travel but has never been performed anywhere in real life aside from Zond spacecraft coming back from the moon. I understand that aside from heat dissipation there are lots of technical challenges because upper atmosphere of planets tend to be pretty dynamic places compared to the static atmosphere in KSP and the thickness of upper atmosphere can vary by a great deal depending on solar activities and so on, so it's harder to figure out the PE required for aerocapture in real life.

However, I hear the actual show stopper is this - the heat dissipation is such a big deal that the heat shield required to survive an aerocapture is around as heavy as fuel required to do capture burn to insert into orbit with rockets anyway. Since there are all these other difficulties like upper atmosphere dynamics it's not worthwhile trying to go for aerocapture, instead you're better off just using rockets since the weight is going to be the same and firing rockets outside the atmosphere is an inherently controlled process unlike atmosphere passes.

It just seems that aerocapture is so gentle in KSP that you need less protection for the payload than the actual launch from Kerbin, so simple fairings (flimsier and so lighter than actual launch fairings) should be enough to survive aerocapture.

[Meithan]

For example, I recently sent a flotilla of 3 ships to Duna, all launched within a couple hours of each other but with arrivals spread out over 28 days. The 1st to arrive was going like 1500m/s upon entering Duna's SOI and needed a Pe of 11km to get an Ap of over 2Mm, about 3/4 of the way out to Ike. Which was fine because this ship was going to Ike anyway. This was the only 1 of the 3 to produce fireworks. The 2nd ship arrived 10 days later going a bit slower. I wanted this one to end up in a 500km orbit. Using a Pe of 11.8km, I got an Ap of 485km or so, close enough. The 3rd ship arrived 28 days after the 1st doing about 940m/s. It's goal was a 150km Ap, and using an 11.8km Pe again gave it 146km, again close enough. So, both these ships used the same Pe but got very different Aps because of their different speeds. And the ship that went the deepest ended up with the biggest orbit, due to its much higher initial speed.

I think my relative noobness in KSP kinda shows . Thanks for sharing this very interesting experiment. I haven't toyed with the simulator enough, I guess (and my aerobraking experience ingame is limited to one attempt).

What kind of transfers are you using, to get such large variations of speed at arrival to Duna?

NOTE: The Pe's listed above were set when the ships were at 90km altitude. That's basically you're last chance to tweak the Pe before you enter Duna's atmosphere. The actual Pe's when the ships got there were somewhat lower due to the braking on the way to them (the 1st ship got down to 10km for example). There not being any way to really predict or control this, I use the value set at 90km as the "official" Pe value for purposes of such discussions.

Yes, pre-aerobraking periapsis is the figure to quote in this kind of thing. It does decrease a little bit after the aerobraking pass (assuming you make it).

Anyway, the bottom line is that aerocapture is going to be different every time you do it, even for identical ships going to the same planet. This is because the whole thing is so dependent on the ship's speed relative to Duna upon arrival and that will never be the same 2 times in a row. Your ship will always start in a slightly different orbit and you'll always do the transfer burn slightly differently, and then do some mid-course tweaks (or not) slightly differently. At Duna, a difference in speed of just 100m/s has a profound effect both on how deep you need to set your Pe to get captured at all, and the Ap you end up with afterwards.

I see. I wasn't aware of the range of possible speeds at arrival. I had thought that, coming from an optimal Hohmann transfer, the Duna arrival orbit had to be very similar every time. Or maybe people don't use optimal Hohmann transfers all the time?

I'll do some experiments in the simulator some other day, changing the speed of the spacecraft to see how much it changes the results. I'm pretty sure it'll turn out like you're saying.

Given this state of affairs, and the utter lack of in-game instrumentation to help, the only thing you can do is "have the boffins at Mission Control run simulations". That is, F5, set your Pe, and see what happens. If you don't like it, F9 and try a different Pe. This simulates the boffins running simulations to determine what's best for the current situation.

Ha ha, yeah, that's how it actually turns out in the end. Planning and calculation goes over the board and you just F5 and pray it works. That's what I did for my first (and only) aerocapture. However, I hoped having a way to simulate things would help reduce trial-and-error a bit.

[Meithan]

However, I hear the actual show stopper is this - the heat dissipation is such a big deal that the heat shield required to survive an aerocapture is around as heavy as fuel required to do capture burn to insert into orbit with rockets anyway. Since there are all these other difficulties like upper atmosphere dynamics it's not worthwhile trying to go for aerocapture, instead you're better off just using rockets since the weight is going to be the same and firing rockets outside the atmosphere is an inherently controlled process unlike atmosphere passes.

It kinda depends on how strongly you want to aerobrake. For aerocaptures, you need to decelerate a lot and you get a single pass through the atmosphere, which is why shock heating becomes a problem and your comment makes a lot of sense. Using rockets is just easier and cheaper, I guess.

But gentler aerobraking has been used a few times in real life, with some success.

And let's not forget Curiosity. While it reentered directly instead of getting into orbit first, it did so coming from an interplanetary trajectory. I'm still impressed that they managed to predict the landing site with great accuracy. Those are amazing rocket scientists.

Not having to deal with shock heating in vanilla KSP is perhaps the biggest difference between KSP aerobraking and its real-life counterpart.

[Specialist290]

I see. I wasn't aware of the range of possible speeds at arrival. I had thought that, coming from an optimal Hohmann transfer, the Duna arrival orbit had to be very similar every time. Or maybe people don't use optimal Hohmann transfers all the time?

There are really 2 (possibly 3) factors at work here:

1. Because of the time scales, distances, and velocities involved, very small differences in initial conditions will often be magnified considerably by the time you actually travel from Kerbin to another planet's SoI.

2. It is very difficult to be consistent beyond a certain degree of precision when flying manually. The way KSP uses floating point decimals probably does not help matters. As alterbaron noted in his own experiments on precision landings on atmospheric bodies, small differences in the parameters are often magnified greatly by the time the craft reaches the ground.

3. More subjectively, there are often very good reasons why a player might choose non-optimal trajectories for their flights. With a flotilla of ships all heading to the same destination at the same time, the player might want to space out their arrivals so they have anywhere from a few hours to a few days between them so they don't have to frantically juggle all of their ships coming into the destination's SoI at the same time. Some players may also choose to operate under certain constraints, whether mod-dependent (such as life support mods) or simply for the self-imposed challenge, that dictate that they complete their missions within a certain time frame.

[FlamedSteak]

This is why I love this game, I never even thought about an aero capture.....it sounds totally plausable and utterly insane at the same time.

[AmpsterMan]

Thank you for the Gee graphs . It's interesting to note that out is not as crazy a braking as I originally thought.

One other parameter thst might affect aerocaptures is the Eccentricity of Duna's orbit because it requires marginally more fuel to reach Duna at Apohelion vs. Perihelion