Maths behind reentry

[Mmmmyum]

Part of me thinks this should be in the sciencey subforum...

Does anyone know the maths behind reentrys? Calculating heat and pinpoint landings with parachutes, as with RSS coming in from 8km/s tends to be a bit complicated.

I basically want to be able to land a 650kg probe at KSC with parachutes and without it being torn apart by the g-forces.

[MajorThomas]

Good morning from Seattle. I'm relatively new here, so please keep that in mind

I thought there was an add-on to help you pilot your way to pinpoint landings. But it sounds like you want to just calculate it? You could probably reverse-engineer the add-on, or... use trial-and-error or, as you seem to suggest, use real re-entry engineering math and just substitute in your Kerbin atmospheric model. I'm very interested in this topic, if it's not well covered in the wiki perhaps we can build up an article on it.

[tetryds]

few years ago a guy created a way to solve diferential equations involving air drag and variating gravity fields based on a spherical mass (or something like that)

he didn't know it was impossible

actually he did, but solved it anyway

the ksp maths might be what you looking for

AFAIK, mechjeb tries to determine that in a way, you should ask the creators of that mod

[Mmmmyum]

I'm using FAR, and I think you're referring to Mechjeb (which calculates stock aerodynamics). There has to be some way to do it, I know they can get the Soyuz capsules pretty close to a point, and we don't need to deal with wind or turbulence or weather, etc

[MajorThomas]

Solving complex diffy-q's usually can be done with numericals...which brings to mind a computer. And an add-on. But what I think you are after, and I too, is a relatively close, rule-of-thumb method. With a table of empirical data, one could probably get within a circle of let's hope 50km reliably. For my favorite style of navigation, eyeballing it, it would be very satisfying if I could get within 50 km of a given spot on the surface.

But to get the necessary data perhaps one must first experiment...a lot...using something like MechJeb...?

[Grover]

it is obviously possible to calculate for your KSP craft... isnt your computer calculating the descent in real time anyway? (or even up to 4x real time speed)

as for an addon, i dont know actually, i just aim for ocean if it needs to be a soft landing, the "where" doesnt matter much when you can recover a vessel from any point on Kerbin's surface for free

[Mmmmyum]

I have to land it at KSC for two reasons, I don't have proper geostationary satellites yet (don't have the tech), and because it looks cool.

I think the first way to start would be by finding an addon that shows your deceleration due to drag

[Mmmmyum]

I have to land it at KSC for two reasons, I don't have proper geostationary satellites yet (don't have the tech), and because it looks cool.

I think the first way to start would be by finding an addon that shows your deceleration due to drag

[Murph]

I'm using FAR, and I think you're referring to Mechjeb (which calculates stock aerodynamics). There has to be some way to do it, I know they can get the Soyuz capsules pretty close to a point, and we don't need to deal with wind or turbulence or weather, etc

The maths are certainly out there, NASA have been doing it since at least Apollo, using the aerodynamics of the capsule itself to adjust the descent during re-entry, and with only the minimalist on-board computing power (remember the low data rates, tiny memory, and comms blackout periods during key phases of re-entry  the re-entry data was transmitted from mission control before re-entry started). I think Gemini was a precision splashdown as well, and the Shuttle was fairly high precision as its gliding abilities were only marginally better than an aerodynamic brick. Precision being measured in nautical miles, of course, not feet, for the Gemini and Apollo capsule splashdowns. Of course, much of the precision does come from having the correct initial velocity vector before re-entry starts, which certainly can be assisted by terrestrial computing.

Mechjeb 2.1 certainly does a not bad job of de-orbit burns to drop a capsule on the grass at KSC, at least some of the time (it has an odd fail case if you ask it to land from a highly eccentric orbit). That's with stock aerodynamics, etc.

[Godot]

Dunno if this is different with FAR,

but I for my part would just go into 100km orbit and then kill all horizontal velocity when being above the target, in ordeer to get as near as possible to it (with corrective thrusts during descent, of course)

[LethalDose]

Yeah, basically what Godot said: aim to hit the atmosphere before you'd be over the center, then kill your lateral velocity when you're directly over the center. Then just chute or thrust down.

there aren't really "Maths" involved.

[Murph]

Yeah, basically what Godot said: aim to hit the atmosphere before you'd be over the center, then kill your lateral velocity when you're directly over the center. Then just chute or thrust down.

there aren't really "Maths" involved.

Congratulations, that's spectacularly inefficient, if you're talking about killing any significant amount of velocity when directly overhead. That potentially means a significantly bigger craft to start with, if you end up needing to carry another tank to fuel the burn. If you time the de-orbit burn correctly, there should be no need for anything other than relatively minor corrective burns inside the atmosphere (NASA corrected with just aerodynamics from a simple, but clever use of offset CoM, in the case of Gemini and Apollo), and possible final vertical deceleration burn for landing (if you are doing that). The very fact that the question has been asked about the maths tells me that the OP is interested in doing the efficient, "correct" method, not the brute force one.

Here's a starting point which might work. It's what I use for generic spaceplanes inbound to the KSC runway. It will likely need tuning for use with capsules, or if you need to start from a different orbit. Starting with a near perfect, 100x100km circular, equatorial / 090º orbit, I do a retro burn 180º from KSC, i.e. when I'm directly on the far side of the planet. I reduce my periapsis to 35km directly over KSC. This drops me down nicely to about 10km approaching the mountains west of KSC, for a little powered flight in. I usually hold about 10–20º nose up through re-entry, until I re-establish conventional flight.

So, adjusting for capsules with parachute final descent. Try maybe 40km or 45km periapsis directly over KSC, or do the retro burn just a little after you pass 180º from KSC. Some experimentation will be required. I have a flag permanently planted at KSC so that it's easy for me to see it on the map view, even when it's night there.

Alternatively, get MechJeb to do it and learn from what it does.

Edit: That's on stock aerodynamics, not FAR, but hopefully still gives some food for thought.

[MajorThomas]

Dunno if this is different with FAR,

but I for my part would just go into 100km orbit and then kill all horizontal velocity when being above the target, in ordeer to get as near as possible to it (with corrective thrusts during descent, of course)

Wow, I guess one could do that!

When you kill all horizontal velocity, do you mean relative to the spot directly beneath you? Because as you fall, because of angular momentum, you may start drifting "backwards" I should imagine. So I'd keep some forward motion but not a lot. Oh, for unlimited fuel and engine power...the things you can do...

[Smidge204]

This thread may be of interest to you. My only complaint about his graph is the X axis is unhelpfully labeled as "x10^5" so try to keep in mind that the initial orbit is in hundreds of thousands of meters. Should have just made in kilometers and labeled it 0, 50, 100, etc...

But whatever. I've independently discovered that returning from a 80km orbit you do indeed need to set your "contact point" about 90 degrees ahead of your target, plus or minus. This will vary quite a bit depending on your craft's drag. It's also important to note that the table is only valid for circular orbits.

Drop your Pe until your orbit intersects Kerbin ahead of the target by the specified angle and you should get fairly close. If using chutes, plan to overshoot and deploy just before you travel over the center. Landing at KSP is an art as much as a skill, really.

Protip: Send a Kerbal/probe out to sit somewhere in the center and set it as the target. This will tell you the distance to the center.

=Smidge=

[longhornchris]

The math is definitely out there, I have a textbook from grad school where the entire class was dedicated to atmospheric entry and (basic) hypersonic aerodynamics. In short, its complicated and difficult to post in a forum. Moreover, while the math is consistent, I know my textbook has Earth numbers, not Kerbin numbers and I'm too lazy to collect the data needed to properly get Kerbin numbers (although it looks like Mechjeb has them for stock KSP, not FAR).

That said, there are some basics things you can do in KSP to make it easier for precision landings. First, realize that FAR greatly changes the impact of things, and Deadly Reentry will (of course) limit your ability to simply fall. With that said, the game is consistent so the same entry angle, velocity, and craft drag should result in the same general landing spot. This will take some practice but you should be able to get an idea of where a craft will go. Best bet would be to get into a ~75km circular orbit every time and learn what it takes to and from there. consistently.

For practice, the circular crater / island is a nice target too.

Other things to remember

- The orbit path indicator in 'map' mode doesn't know about drag or parachutes - so aim long

- When coming from Mun or Minimus, remember Kerbin rotates - for prograde orbits aim long or get aerobrake into a near-circular orbit first

- Wings can help cross-range if your aerodynamics are good - I play with FAR so this does require some clever design, balance, and/or a lot of SAS torque to pull off but it can be done

- Rockets can give you lots of options on entry if you have enough fuel and are high enough

- You can cut parachutes... but if you do make sure you've got plans to stop using other methods

- If using FAR, the FAR data is useful for cross-ranging or working min/max drag profiles

[Godot]

Wow, I guess one could do that!

When you kill all horizontal velocity, do you mean relative to the spot directly beneath you? Because as you fall, because of angular momentum, you may start drifting "backwards" I should imagine. So I'd keep some forward motion but not a lot. Oh, for unlimited fuel and engine power...the things you can do...

In relation to the surface ... I usually I do it with the "Surface"-mode of the Navball (which takes into account planetary rotation) , in combination with the horizontal speed that is displayed in Kerbal Engineer Redux. On descents to Mun and together with occasional correction thrusts on the way down, I usually am able to get < 10 mm/sec in horizontal velocity

[Mmmmyum]

The math is definitely out there, I have a textbook from grad school where the entire class was dedicated to atmospheric entry and (basic) hypersonic aerodynamics. In short, its complicated and difficult to post in a forum. Moreover, while the math is consistent, I know my textbook has Earth numbers, not Kerbin numbers and I'm too lazy to collect the data needed to properly get Kerbin numbers (although it looks like Mechjeb has them for stock KSP, not FAR).

That said, there are some basics things you can do in KSP to make it easier for precision landings. First, realize that FAR greatly changes the impact of things, and Deadly Reentry will (of course) limit your ability to simply fall. With that said, the game is consistent so the same entry angle, velocity, and craft drag should result in the same general landing spot. This will take some practice but you should be able to get an idea of where a craft will go. Best bet would be to get into a ~75km circular orbit every time and learn what it takes to and from there. consistently.

For practice, the circular crater / island is a nice target too.

Other things to remember

- The orbit path indicator in 'map' mode doesn't know about drag or parachutes - so aim long

- When coming from Mun or Minimus, remember Kerbin rotates - for prograde orbits aim long or get aerobrake into a near-circular orbit first

- Wings can help cross-range if your aerodynamics are good - I play with FAR so this does require some clever design, balance, and/or a lot of SAS torque to pull off but it can be done

- Rockets can give you lots of options on entry if you have enough fuel and are high enough

- You can cut parachutes... but if you do make sure you've got plans to stop using other methods

- If using FAR, the FAR data is useful for cross-ranging or working min/max drag profiles

I'd actually like Earth's numbers, I'm using RSS so everything is Earth sized.

The lowest orbit I really use (because of remote tech) is 150km, but I'm looking at 10000km orbits as well. Orbital velocity's around 8km/s here, so just dropping down would tear my probes apart and then burn them, not to mention the delta-v needed

EDIT: Found this, basically everything I wanted http://www.faa.gov/other_visit/aviation_industry/designees_delegations/designee_types/ame/media/Section%20III.4.1.7%20Returning%20from%20Space.pdf just need to work out the drag coefficient of my probes and I should be alright

Edited December 1, 2013 by Mmmmyum