Tutorial A cue-sheet based general approach to atmospheric entry

[Thorsten]

Hi to everyone.

Brief introduction - my name is Thorsten Renk, I'm a theoretical physicist by profession, and as part of my spare-time activities I'm part of the development team of the Flightgear OpenSource simulator, mainly doing weather simulation and coding OpenGL shaders. I am fascinated by all sorts of flight, which includes spaceflight, which is the reason why I'm currently looking into Orbiter as well.

Like probably others, I've been wondering about how to time de-orbit and re-entry burns correctly such as to bring a Shuttle onto the runway. On simply trying, I felt completely lost as to what exactly I had to control. I've been googling for tutorials and read some, but I feel they mostly skirt around the issues by providing a cooking recipe rather than a solid generally applicable checklist, or rely too much on 'need to practice'. At the same time, I prefer hands-on flying over an automated solution (it always seems a bit odd to me to have a simulated autopilot control a simulated plane...). I believe I've found a rather neat solution which I would like to share.

This solution applies to spacecraft with a controlled re-entry trajectory like the Shuttle or the Delta Glider - it won't work for a capsule like Vostok.

The key observation is that in such spacecraft, it is possible to control the deceleration rather precisely by controlling altitude - either with the elevator or with bank angle. Since the kinetic energy during reentry is so much more than the potential energy for a small altitude change, till the velocity drops to 1000 m/s, there's hardly any effect on velocity for going up or down in altitude, but the variation of air density with altitude allows a very precise control of the decelerating force if I can control altitude. So the only skill to master while flying re-entry is how to control altitude (which may differ from spacecraft to spacecraft) and then fly in such a way that the acceleration is stable around a given value.

The chief problem is to bring the spacecraft to a certain point with low velocity, say 20 km above Cape Canaveral with 1000 m/s. If I can control acceleration, there's a unique relation based on velocity and distance what *constant* deceleration will get me there. If my velocity for the final approach is v_end, my initial velocity is v0, the distance is d and the acceleration is a, that relation is

d = v0 * (v0-v_end)/a - (v0 - v_end)^2/(2*a)

If you're like me, you can't do this easily in your head, but a simple cue sheet with pre-tabulated values serves nicely:

v0 = 7000 - m/s

distance [km] - deceleration [m/s^2]

4500 - 5.3
4000 - 6.0
3500 - 6.8
3000 - 8.0
2500 - 9.6
2000 - 12.0
1500 - 16.0
1000 - 24.0
500 - 48.0

v0 = 5000 m/s

distance [km] - deceleration [m/s^2]

2250 - 5.3
2000 - 6.0
1750 - 6.8
1500 - 8.0
1250 - 9.6
1000 - 12.0
750 - 16.0
500 - 24.0
250 - 48.0

v0 = 3000 m/s

distance [km] - deceleration [m/s^2]

750 - 5.3
666 - 6.0
580 - 6.8
500 - 8.0
416 - 9.6
333 - 12.0
250 - 16.0
166 - 24.0
83 - 48.0

v0 = 2000 m/s

distance [km] - deceleration [m/s^2]

281 - 5.3
250 - 6.0
218 - 6.8
187 - 8.0
156 - 9.6
125 - 12.0
94 - 16.0
63 - 24.0
31 - 48.0

That's how it's used:

Fly a de-orbit and go through the messy zone when the air starts catching until you get low enough such that drag is appreciable and you velocity drops to 7000 m/s.

It is series of lookup tables based on distance to base while passing a certain value of the velocity - at the point your velocity reaches 7000 m/s, look at the distance to the base you want to reach and read off the deceleration you need to keep to get you there from the table. It doesn't matter precisely how you did your de-orbit burn, the table can accomodate a wide range of distances, the hardest limit is the structural stability of the spacecraft (I'd appreciate if someone can help me out with numbers here... I didn't find any maximal g-loads). If you're 4500 km away from the base, you just use a weak force, if you're 1000 km away you need to decelerate much harder. But the window to hit is huge - de-orbiting somewhere between 1000 and 4500 km from the base isn't a major problem I'd hope!

As you approach and the velocity drops, you make use of the follow-up tables to correct - say if you've been decelerating with 6 m/s^2 but by the time you reach 3000 m/s the distance to base reads 500 km, you know you need to ramp up acceleration to 8 m/s^2 for the next leg.

In this way, you can even accomodate curved approaches and similar corrections easily - the distance shown for a curved trajectory shown on the map will initially not be the true distance you have to fly, but you can nevertheless use the high velocity cue tables initially and you'll automatically get the relevant correction on the last leg if you keep using the distance shown in the map for the cue sheet.

Using this simple cue sheet I was able to get the Space Shuttle from ISS perfectly down to the runway on the first try with an entry trajectory that had a 90 degree angle in it, using no other instruments than the map (to know where I have to go and get distance readings) and surface MFD (to get the acceleration reading).

I believe this is how aerobraking in practice should be explained, planned and executed, because it's really simple that way and it can be done by a very general checklist which is pretty much independent of what spacecraft you're using and how precisely you control acceleration - it's just based on simple kinematic relations.

 

[MaverickSawyer]

First off, welcome aboard!

Secondly, superb rundown of this highly-understudied topic. This is likely going to be one of the few things I actually put to paper for use with Orbiter, so I don't have to pause and flip between windows. Thank you in advance!

 

[Urwumpe]

5 G is still a bit high for a gliding reentry with both DG and Shuttle - I had my best reentries flying at constant 16 m/s² as long as possible and do a small ramp up to maximal 3G for intercepting the runway. Usually I even need to reduce decelleration later to stay high on energy for the final reentry phase that way.

Just checked - even during a RTLS abort, which is the most extreme maneuver possible with the (real) Space Shuttle, you don't exceed 2.2G (during the pull up phase after ET SEP, Nz Hold with 50 ft/s²)

 

[C3PO]

In Orbiter you're free to do whatever you want, but a constant deceleration isn't very realistic. The current atmospheric model in Orbiter isn't very accurate during high altitude hypersonic flight. I've tried reentering the default Atlantis using the real STS distance/speed profile from a NASA cue-card, and the required altitude was 10-15 km lower than the real thing.

You could of course use this method to aim for 'waypoints' along the reentry profile (speed/altitude/distance). In an unpowered winged vehicle the most important part of a reentry is energy management during the final phase as you line up with the runway. You just have to make sure not to 'undershoot' the landing area. In a DG/XR craft you can just save some fuel and do a powered landing.

In the real world the main problem isn't as much slowing down, but rather to avoid overheating. Most Orbiter addons contain enough unobtainium to (almost) ignore that aspect.

 

[Thorsten]

5 G is still a bit high for a gliding reentry with both DG and Shuttle - I had my best reentries flying at constant 16 m/s² as long as possible and do a small ramp up to maximal 3G for intercepting the runway.

Well, kinematics is what it is and the tables reflect that, independent of what spacecraft you're flying or on what planet you are. If you find yourself 500 km to base with 7000 m/s velocity, I would say you've been planning poorly before, and you'd be much better off trying to divert to a different base - you should easily get ~5000+ km with that velocity at 70 km altitude. But if you for some reason absolutely need to reach that base, 5 g deceleration is what you will need to get you there.

Usually I even need to reduce decelleration later to stay high on energy for the final reentry phase that way.

The point of the exercise is to give you a precise number and checklist what deceleration you need at predictable times during the entry given your distance to base, rather than let you guess, improvise and pull a high-g late because you're overshooting. Looking at the tables, you can also infer that if you want a load of just 0.8 g, you need to be in the atmosphere ~3000 km before base, and you can plan your de-orbit accordingly In my (so far) first and only attempt, I had a constant 16 m/s^2 with peak values not exceeding 23 m/s^2 in turns. Which'd be okay for the Shuttle then.

I don't know if there's a tool, but since it's essentially ballistic flight, it's easy to work out with a pocket calculator given your orbital radius and de-orbiting delta-v at which distance to base you'll cross the 70 km altitude line. So if you do that kind of planning, you can select which g-load you would like during re-entry and select the de-orbit burn point accordingly at your convenience, and you'll never have to resort to last minute 3 g maneuvers. It becomes possible to plan, but also to adapt the plan on the fly.

The table isn't intended as a recommendation for de-orbit planning - it just tells you what deceleration is needed if you are in a certain distance with a certain velocity. Whether it makes any sense to go there (and whether it's physically even possible - I doubt the Martian atmosphere could provide 5 g deceleration) is still up to the pilot

 

[Donamy]

The longer it takes to de-orbit, the more heating.

 

[Thorsten]

In Orbiter you're free to do whatever you want, but a constant deceleration isn't very realistic. The current atmospheric model in Orbiter isn't very accurate during high altitude hypersonic flight. I've tried reentering the default Atlantis using the real STS distance/speed profile from a NASA cue-card, and the required altitude was 10-15 km lower than the real thing.

I thought this is reasonably clear, but for the record and to be on the safe side - I'm of course not kidding myself to have found a method NASA has overlooked or that a simple analytic pocket formula is all it takes to get a realistic re-entry.

I am under the impression that Orbiter aims at being educational rather than realistic. In a realistic model of the Shuttle, I would have the real instrumentation. That includes an AP capable of flying the re-entry, presumably also a Flight Director mode showing me what to do, I would have Mission Control on the line who could, even in case I forgot everything about orbital dynamics I've ever learned, tell me precisely what button to push when, I wouldn't do anything like de-orbiting in the first place without a go from Mission Control, and there would be a procedure/checklist which describes step by step how the re-entry is flown which I could simply follow (and would in fact have to) in case none of the above works.

As you tested yourself, following something like the real trajectory in fact doesn't get you there, and we also don't have the real instrumentation. So the real re-entry procedure doesn't work, that's not me proposing an unrealistic procedure where a realistic could be in place, that's Orbiter modeling simplified atmospheric flight dynamics and me coming up with an idea for a cue sheet to deal with Orbiter as it stands.

In terms of experience, I think if we had a realistic model of entry physics and fluid dynamical modeling of the Shuttle, I (or someone else) could spend some time coding the numerics of it, establishing a corridor of safe entry procedures and derive a cue sheet from that. So then any pilot could follow that cue sheet - numbers and what to look at would be different, but you'd still do it by a predictable procedure/checklist, which is what matters for immersion into the sim.

I understand that high-altitude hypersonic is tough. As I said, I come from a flightsim community, and a while ago we tried low Earth orbit in Flightgear with a Vostok model, and I had long discussions with Jon S. Berndt, the author of the JSBSim flight dynamics engine whether JSBSim would be realistic enough, and he benchmarked it against several commercial tools NASA is using for computing launches and orbits and argued that we're really close almost everywhere, but re-entry is the most challenging part - reliable tables of coefficients for airfoil and wings are hard to come by in this regime, and standard fluid dynamics has some issues there.

On a cursory glance, I had the impression that Orbiter in general has simplified atmospheric flight. In reality, supersonic wing designs usually do not have a gentle stall behaviour, for instance an SR-71 was lost during a trim test when an unstart caused a stall leading into a spin which ripped the aircraft apart, the Starfighter was notoriously accident-prone,... I don't think the high AOA behaviour of winged spacecraft in Orbiter reflects the reality. In real life, thrust vectoring is a bitch - the Harrier VTOL craft is inherently unstable in hover flight, essentially it's balancing on a column of lift and any perturbation is self-amplifying, and VTOL landings have a high accident rate. Having played around with a simulated Harrier for a while, I can appreciate why. The hover thrusters of the DG seem to reflect nothing similar.

As I said - I understand that there are limitations in the degree of realism which Orbiter simulates, my aim is not to improve the physics (that someone else can do) but to make available a procedure which allows a predictable and correctable atmospheric entry within Orbiter as it currently is, and I think the experience of that is more realistic than 'seat of your pants' flying, 'experience makes perfect' and 'I usually do that' which seems the collected wisdom of tutorials I've been looking at - I doubt NASA does it that way - but I do believe NASA has checklists and cue sheets

 

[Urwumpe]

The longer it takes to de-orbit, the more heating.

That is actually wrong - the slower you reduce your energy, the lower are the temperatures created by that.

The energy at which you start the reentry is pretty much constant, give or take a few Joules per kg.

The problemis something else with long reentries: You can only do that with capacitative heatshields. Ablative heatshields would already ablate away at lower temperatures, but take less energy with the molten heat shield particles.

With capacitative heatshields, longer reentries are actually better: As long as you still have enough lift to control your flight, you can reduce temperatures by reducing dynamic pressure. The Space Shuttle usually reenters right in the middle of the envelope between too much heating or too much dynamic pressure, and too little dynamic pressure to control flight. What you have to avoid is stalling: If you loose lift by becoming too slow, you drop first like a stone and only then slowly recover as dynamic pressure increases. Usually it increases so fast, that you will burn up or get structural damage then, before you have pulled out of the stall.

Also: The parameters of Orbiters atmosphere are accurate - the default Atlantis is not. It uses only subsonic parameters to describe its aerodynamics. But that is not Orbiters fault (at least not more than maybe 20% for its API making it hard to implement better supersonic flight models), but rather that add-on makers rarely do more than a simple lift function of "lift, drag & torque by AOA". In reality, dynamic behavior is also important in the lift functions (you can stall by changing AOA too fast), also at supersonic speeds, shifts of the center of pressure have much stronger effects - it can be really chaotic by then. The Shuttle can for example only lower its AOA from 35° to 10° around Mach 8, but not raise it again.

 

[aftercolumbia]

Thorsten, welcome to Orbiter. Your name rings a bell, but I can't figure out why.

Your formula is a basically the same as mine, which is the simplification where v_end = 0

Yours: d = v0 * (v0-v_end)/a - (v0 - v_end)^2/(2*a)
Mine: d = v0^2/(2*a)

I plug that into my Advanced DAL EL-520W handheld Orbiter/KSP auxilliary flight computer (manufactured by Sharp and available at Staples, G&T, and Office Depot for under $30) and fly... wishing I could put it on my Ravenstar HUD. I've been using it for years...

10 years ago: http://aftercolumbia.tripod.com/entrytutorial/
1 year(s) ago: https://www.youtube.com/watch?v=bIg-_xti1q4

I'm reasonably sure it would work for the Shuttle until you got into TAEM territory, at which point v0 being zero will probably drop you in the Everglades because of the Shuttle's horrendous glide ratio.

I'm pretty sure your entry profile being 10-15km lower than the real Shuttle is probably not Orbiter's fault (at least, not the atmospheric profile's fault.) I've noticed that most craft tend to have much lower lift at high alphas (angle of attack) than they should for delta-winged aircraft. It's as though the aerodynamic thinking that went into their Orbiter implementations was for straight wings, which stall. Instead of stalling, delta wings go into vortex, where the separated flow from the leading edge in the otherwise stalled condition curls around and reattaches to the wing. The drag shoots up, but the lift also shoots up instead of dropping, as in a proper stall. The result is a low L/D (about 1.6 for the Shuttle), but plenty of lift.

An interesting thing about NASA missing stuff... not saying they missed this eleventh grade equation, but I did find something that they did miss which quite surprised me: When investigating STS-107, they noticed that Columbia had a tendency to come out of her roll reversals high on energy, which the DAP (digital autopilot) immediately compensates for. They reviewed other (normal) entries and discovered that this was actually normal behaviour. One of the very first things I discovered when trying to land the Delta Glider (procedures I developed largely from first principles) is that my C-drag (my formula solved for acceleration instead of distance) shot up while doing roll reversals (unless I did them inverted, obviously.) This is simply because when reversing your roll, you point your lift vector straight up, which messes up your vertical situation and causes you to lose speed more slowly. It's the same effect, and it really, really matters when your L/D is in the 4-6 ballpark instead of Shuttle's 1.6. I was quite surprised that I beat NASA to it when they had been flying the Shuttle for 22 years and me the Delta Glider for less than 6 months! (By the way, I've read more than just the basic CAIB report; I'm pretty sure this is in one of the appendices and not in the main body of the report. The appendix material is several times as large as the main report, and I've also read the Shuttle Crew Survival Report, which was very difficult.)

For Urwumpe, you'll probably be a wee bit interested in the Youtube link... the video is titled "XR-2 Ravenstar Roll Modulated Entry in Orbiter Simulator 285C Peak Nose Temperature" ... if you have eighty-four minutes and seven seconds to spare

 

[Donamy]

I was going by what I read here.

Comparison of types of orbiter. The straight-wing design has low lift, L/D = 0.5. It achieves little crossrange, but its re-entry is brief and limits the heating rate. The delta-wing orbiter has high lift, L/D = 1.7, and achieves large crossrange. But its re-entry is prolonged and imposes both a high heating rate and a high total heat. (NASA)

 

[C3PO]

I've been looking all day for this and..... Success!!!

Reentry MFD:

It's been a while since I used it, but it works fine in 2010 P1. It's by the TransX author Duncan Sharpe. The direct link is here.

There's no documentation, but it's quite self-explanatory. Just put the file in ..\Modules\Plugin and activate it. Only one button is required to select the target base, and shows everything you need to land at the intended runway.
The most important numbers are actual and required deceleration, but there's a nice and simple graphic readout. Notice the small green circle [o] on the middle right. If it's above the center [+] you are slowing down faster than required, and vise versa. Keep it (roughly) in the center and you should arrive at TAEM in a manageable state.

But there's more. The horizontal scale of the [o] shows the delta azimuth to the target base. In this example you have to roll right to lower the azimuth.

You also get readouts for Altitude; Vertical speed; Air speed (KEAS); Ground speed; G-force; and remaining distance.

You should be able to hit the numbers using only this and Surface MFD. :thumbup:

---------- Post added at 04:04 AM ---------- Previous post was at 03:55 AM ----------

But its re-entry is prolonged and imposes both a high heating rate and a high total heat. (NASA)

But the peak heating is lower, and therefore better suited for capacitative heatshields that can radiate heat during reentry. That's why both STS and Buran had dark shielding on the bottom.

 

[Donamy]

Also higher weight from the wings and added TPS.

 

[Thorsten]

The parameters of Orbiters atmosphere are accurate - the default Atlantis is not. It uses only subsonic parameters to describe its aerodynamics. But that is not Orbiters fault (at least not more than maybe 20% for its API making it hard to implement better supersonic flight models), but rather that add-on makers rarely do more than a simple lift function of "lift, drag & torque by AOA". In reality, dynamic behavior is also important in the lift functions (you can stall by changing AOA too fast), also at supersonic speeds, shifts of the center of pressure have much stronger effects - it can be really chaotic by then.

I would be surprised if the atmosphere model is wrong - that's pretty easy to do. What's complicated is how the atmosphere interacts with objects.

I don't know how Orbiter handles flight dynamics in detail, but lift and drag for every airfoil is not a particularly simple function of AOA in the first place (actual measured curves have quite some wiggles...), and it's also not constant with airspeed. There are some cute examples where this assumption is even qualitatively wrong: In the MiG-15 for instance, transonic airflow causes the aileron action first to go to zero, and if you increase airspeed even to reverse, so you push stick left and the plane rolls right. So you need at least a 2-dim lookup table for every airfoil to get something like realistic behaviour for both subsonic and supersonic flight.

My understanding is that in hypersonic flight there's an additional complication, which is that the shockwave heat changes the atmosphere properties, so the atmosphere is no longer a fluid to be perturbed but changes dynamically. The heat can break molecule bonds for instance, changing the heat capacity and compressibility of air in the process, which in turn alters the flow field around the hypersonic disturbance. I believe that would break the correlation between IAS and the lift/drag coefficients and you'd need a 3-dim lookup table for each airfoil to model this correctly - provided you have the test data to actually fill it. I'm not overly surprised that this isn't usually done - that's a few thousand hours worth of research, modelling, benchmarking and testing to get right.

One of the very first things I discovered when trying to land the Delta Glider (procedures I developed largely from first principles) is that my C-drag (my formula solved for acceleration instead of distance) shot up while doing roll reversals (unless I did them inverted, obviously.

To be fair, it is much more pronounced in the DG, but yes, I caught that as soon as I realized that the reason I kept bouncing with the DG was that the lift/drag is so stupendously high and that I should basically never fly level unless I really want to kill vertical speed... So they really didn't know that? Sounds pretty... odd.

Your formula is a basically the same as mine, which is the simplification where v_end = 0

Indeed, it is - It'd been a miracle if I had been the first one to work that out... You also have some other constraints worked out.

So - here's my suggestion: Why don't we combine some more realistic physics constraints like limiting heat flux and structural load into improved cue sheets for a corridor of safe entry trajectories and give people some numbers to work with if they want to get the Shuttle to the runway and fly profile that is closer to reality (obviously not reality)? I mean, I came up with the whole idea in the first place because I couldn't find any good numbers, and admittedly personally I find 'use MFD XY' somewhat unsatisfactory - I usually like to understand what I'm trying to achieve and why.

 

[Donamy]

I agree, but it's also nice to have an AP for time constraints, or other aspects of the mission. Also, it looks nice from outside. :thumbup:

 

[Felix24]

NASA recently released a very well-written book called "Coming Home" which is about re-entry research and engineering, which is available for free in various formats. http://www.nasa.gov/connect/ebooks/coming_home_detail.html#.Uqs7jOJ0mVc

I found it to be extremely interesting. They discussed (among other things) the choice of whether to have a shorter, hotter re-entry profile or a longer, skipping re-entry with cooling-off periods. Early on, the skipping method was championed, but research showed that most of the re-entry heat could be safely shed in the hypersonic shock in front of a blunt-body object. Also, the radiative cooling during a skip could not dump enough heat before the next heating. Extra thermal cycles for the spacecraft were also an issue.

 

[Thorsten]

There's also an analytic solution for constant heating power. If heating power is

P = F * v

where F is the deceleration force and v the velocity, then keeping P a constant means

a = c/v

i.e. the deceleration force becomes an inverse function of the velocity - at high velocity, deceleration has be be more gentle, at lower velocity it can be a lot higher for the same thermal load.

That leads to a condition

dv = a(t) * dt = c/v(t) * dt

and inserting the boundary conditions, integrating and solving for the distance gives

d = v0/(2c) * (v0 - v_end)^2 - 1/(3*c) * (v0 - v_end)^3

That equation can be used in a similar way to determine what the acceleration for each leg should be, given current velocity and distance to base, if the heat load is to be kept a constant.

 

[Urwumpe]

Actually, the more common term for this is the "aerodynamic heatflux"

Q = q * v = 1/2 * rho * v^3

With:

Q = heatflux (Watt/m²)
q = Dynamic Pressure
rho = Air density
v = air speed

Your power would be aerodynamic heatflux multiplied by the aerodynamic cross section.

As you can already see by this single formula, the two important factors during a reentry drop by different variables:

dynamic pressure ~ v^2
heat flux ~ v^3

If you want to stay in a safe dynamic pressure range (too much can destroy a spacecraft as well) and not violate a heatflux limit, the you have to follow initially a stricter maximum limit (heatflux) until heatflux limit exceeds the dynamic pressure limit. If you just fly by maximum heat flux, you will be too fast later.

And now to the math: What is c? You never defined it. Vacuum speed of light?

 

[Thorsten]

Actually, the more common term for this is the "aerodynamic heatflux"

Fine with me - the relevant fact is that it goes like ~rho v^3, the rest combines just into an overall constant which is spacecraft-specific (and very expensive to compute).

And now to the math: What is c? You never defined it. Vacuum speed of light?

Of course not - that'd never work out dimensionally It's a constant with dimensions [m^2 / s^3] linking the acceleration with the inverse velocity - and the definition is the equation shown.

If you e.g. use c = 21.000 m^2/s^3 and have initially v = 7000 m/s, then you'd start the aerobrake with a = 21.000/7000 = 3 m/s^2 or ~0.3 g and, keeping thermal load constant during the whole aerobrake ends you at a = 21.000 / 1000 = 21 m/s^2 or ~2.1 g.

Inserting that value of c into the formula above gives you the distance covered. So all we need to compute that is a spacecraft specific number what heat flux is acceptable, then a second number what g-load is acceptable, and then the two expressions can be combined into a two-piece cue sheet which is a bit more realistic than constant acceleration.