Extraorbital Atmospheric Re-Entry: Terminal Velocity?

[VNV]

Extra Orbital Atmospheric Re-Entry, or the Art of Leaping From Orbiting Starships onto Planets. Ignoring that my TITANs are donned in A.T.L.A.S. PCA and thereby protected by force-evaporating malarkey nodes, I want to know how they'd be in the middle of these jumps.

In my book, a TITAN Super Soldier leaps out of a starship orbiting outside the exosphere to join a battle on the planet below instead of getting in a drop pod or a shuttle. This is meant for shock and awe, because someone's just leapt out of a spaceship to kick your teeth in personally. In any event, a 10,000km leap would normally leave one as a pile of goop on the ground, and that's the end of that. But my TITANs, thanks to their armor, can survive this situation and go on fighting like nothing's happened.

What I want to know is simple. In each layer of the atmosphere, what would their terminal velocity be, and how hard do they hit the ground?

For reference, the average TITAN in A.T.L.A.S. PCA weighs 2,850(2,520 for the suit, 330 for the soldier) pounds, and the armor is boxy and not very aerodynamic as a result. On average, they are eight feet and four inches tall in said armor, and about three and a half feet wide at the shoulders. The planet they will be jumping onto in the scenario is Earth, since we know all of it's things.

 

[Simon Bridge]

But surely you want to know what sort of speed to expect at different altitudes?

Depends how they want to drop - head first or spread-eagle. Does the suit have anything specifically designed to increase drag? ie, the "force-evaporating malarkey nodes" would also slow the fall right?

Also - how detailed do you need? The model can get very complicated ... it involves relating the drag coefficient in air to the pressure and temperature of the air, and the shape of the falling body. However, if you only want scifi technobabble level hand-waving, then you can probably find data for that world record space-dive and get speed vs altitude or altitude-time data somewhere.

 

[VNV]

But surely you want to know what sort of speed to expect at different altitudes?

Depends how they want to drop - head first or spread-eagle. Does the suit have anything specifically designed to increase drag? ie, the "force-evaporating malarkey nodes" would also slow the fall right?

Also - how detailed do you need? The model can get very complicated ... it involves relating the drag coefficient in air to the pressure and temperature of the air, and the shape of the falling body. However, if you only want scifi technobabble level hand-waving, then you can probably find data for that world record space-dive and get speed vs altitude or altitude-time data somewhere.

I believed terminal velocity and speed of the fall were one and the same after a certain limit.

They drop head first until about 300 km and then spread eagle. The Kinetic Absorption Modules simply stop the soldier from getting knocked around by the forces. If they're falling, it won't do anything until they hit something or land, and then it becomes a 'force evaporating malarkey node'.

 

[VNV]

Also, I only need the end results. I know about all the technical algebraic formulae.

I'm trying to keep a strong base in reality here. I want the readers to look at what I present to them, see that it's realistic, perfectly detailed, and I want them to be amazed.

 

[Simon Bridge]

I believed terminal velocity and speed of the fall were one and the same after a certain limit.

Not a good assumption.

The Kinetic Absorption Modules simply stop the soldier from getting knocked around by the forces.

Ah - so they work by magic. Gotcha.

Also, I only need the end results. I know about all the technical algebraic formulae.

Since you know about all the technical algebraic formulae, you already have the end results: stick the formulae into a calculator and crunch the numbers.
The trouble with the answer here is that there are too many parameters so some fudging will be needed - you are the best person to decide where the fudge should be applied.

I want the readers to look at what I present to them, see that it's realistic, perfectly detailed, and I want them to be amazed.

(my emph) This is not possible. Even a close model will not be cheap - probably not cost effective for your purpose.

The closest you will get will be to use actual data from an actual space-jump and fudge it a bit for the suit parameters. In fact this is my recommendation. Look for data of things that have been dropped from various very high altitudes for the kinds of things you'd like to know about. This will, at least, show you what you are asking about.

The highest jump was about 40km ... "edge of space" is about 100km... so where will you start from?
Will the suit initially be in orbit? In the description, the suit starts with a small (from jumping) radial velocity as well as whatever velocity it had as part of the spacecraft . That is typically lots.

You can simplify things by using the SF properties of the suit - if it is designed to protect someone during such a jump, it probably has other designed properties relevant to the jump.

 

[VNV]

I don't know all the values of it. I can't find anything telling me how to find drag on a boxy humanoid figure.

Also, don't have a calculator. I have a simple app, and the rest I have to do by pencil and paper.

 

[Simon Bridge]

I don't know all the values of it. I can't find anything telling me how to find drag on a boxy humanoid figure.

So you don't have "all the technical algebraic formulae"?

The drag coefficient is usually something you measure - though it can be worked out by rules of thumb. There are drag calculators online for different situations - the trick is to simplify the object in question. For instance, model the suit as a box as a first approximation... then look at the specific aerodynamics with an eye to the sort of thing you want to write about. A lot of the physics will not be relevant because the occupant won't notice.

Also, don't have a calculator. I have a simple app, and the rest I have to do by pencil and paper.

There are online calculators of all kinds.

Try to work out the minimum detail you need for the story you want to tell and the expected audience. ie. you won't be presenting this as physics fact to aeronautcal and space engineers or astronaughts but you probably want somebody like Phil Plait to say, "I guess that's plausible..." Until you can narrow the problem down I don't think anyone can help you. So far the level of detail requested would require you to build a suit model, then put it in a wind tunnel.

Good luck.

 

[Filip Larsen]

Just curious here (being otherwise unfamiliar with your story), when you say "drop" do you mean a hollywood-style re-entry that goes vertical down by nulling all orbital speed well above the atmosphere or do you mean a more realistic elliptical re-entry where only a small speed reduction brings periapsis well into the atmosphere that is then used to bleed most of the orbital energy? There can be a huge difference in the deceleration profile and the amount of energy that needs to be dissipated in the two approaches.

 

[VNV]

Just curious here (being otherwise unfamiliar with your story), when you say "drop" do you mean a hollywood-style re-entry that goes vertical down by nulling all orbital speed well above the atmosphere or do you mean a more realistic elliptical re-entry where only a small speed reduction brings periapsis well into the atmosphere that is then used to bleed most of the orbital energy? There can be a huge difference in the deceleration profile and the amount of energy that needs to be dissipated in the two approaches.

I mean an elliptical jump. It's too far away for a completely vertical fall. Ten thousand kilometers(the exopause, not the edge of space but the edge of a vacuum) is a very big distance. To put it in perspective, our planet is only a few hundred km over 12,000.

 

[Filip Larsen]

I mean an elliptical jump. It's too far away for a completely vertical fall. Ten thousand kilometers(the exopause, not the edge of space but the edge of a vacuum) is a very big distance. To put it in perspective, our planet is only a few hundred km over 12,000.

I am not sure what kind of problem you envisage when you say "too far away" as the magnitude of the speed change needed for a re-entry burn starts to diminish as a function of height for high orbits. If you look at the speed changes needed for re-entry (the equation for ##\Delta v_2## on [1]), where ##r_2## represent the initial orbital radius (apoapsis) and ##r_1## represent the re-entry radius (periapsis), and then set ##r_1 = \rho r_2## and normalize relative to the circular orbital speed at periapsis then you would get a plot like in [2]. As ##\rho## goes towards zero ##r_2## goes towards infinity and you can see that when ##r_2## gets large enough (##\rho## small enough) then the needed speed change gets smaller again. In the limit where your spaceship re-enters directly from near infinity there is almost no difference in the speed change needed for an elliptical re-entry orbit compared to that of a rectilinear (vertical) re-entry orbit. But of course, the two orbits would differ hugely in their deceleration profile once in the atmosphere.

Another interesting question is whether or not your TITAN's have the ability to control direction or magnitude of their aerodynamic lift. Without any lift the re-entry will be ballistic and will in general exhibit a much larger deceleration profile than if lift is employed in a controlled manner. On Earth, this makes the difference between a cozy 3-4 G lifting re-entry and a 9+ G ballistic entry.

[1] https://en.wikipedia.org/wiki/Hohmann_transfer_orbit
[2] https://www.wolframalpha.com/input/?i=plot+sqrt(rho)(1-sqrt(2/(1+1/rho)))+for+rho+=+0+to+1

 

[GTOM]

I also think about a troop landing on hostile planet situation.
I think, the big ships should stay on GEO, and elliptical approach is more realistic than fall and decelerate above surface... while the former means, the shuttle craft has to reach the blind spot of the fleet (the other side of the planet, unless the fleet is divided) but decoys and fighters should be able protect the majority of the shuttles from surface launched missiles.
Space fighters could give some protection in the stratosphere, but in thick air, they become too clumsy, although at this point, probably the shuttles arent needed anymore, if troops can land with combat suits.

I also wonder, if a spacecraft from low orbit enters into stratosphere, could it launch effective kinetic bombardment against digged-in targets? (whether it is a viable option of high orbit launched bombardment?)

 

[Lothlorien]

Here are some bits of info I found a while ago on this subject that may help you figure out something for your story:

This is in Russian but a machine translation gives you a good idea. It is only for skydiving but the highest survivable point above the Earth they calculate to be some 460km. It includes figures, diagrams, the math and reasoning etc.
http://www.extreme-studio.com.ua/r/skydive/rekord/rekord.htm

Orbital Outfitters are working on a suit for space diving: http://orbitaloutfitters.com/what-we-do/#c1

There is also Project MOOSE, a shelved initiative by General Electric back in the 60s which would theoretically be the last hail mary chance for an astronaut to jettison an orbital platform and reenter Earth's atmosphere and potentially survive. Risk factors and the potential for a backlash by the general public if the system were to fail and perhaps many other reasons made it not get off the drawing board. The initial feasibility study is floating around somewhere and, well, it supposedly could have worked. https://en.wikipedia.org/wiki/MOOSE