The Myth of 25X

One item of contention that I’ve seen in the emerging space industry is about the relevance that suborbital spaceflight has for future orbital applications. With the exception of RpK, all of the current effort going into building reusable, safe, and operable launch vehicles has been focusing on suborbital vehicles first. However, while most of those companies are focusing on suborbital vehicles at first, and while most of us think we can close our business cases on suborbital, most of us fully intend to proceed on to orbital spaceflight if we can make a successful enough go at our first markets. That is one thing that MSS, XCOR, Armadillo, Blue Origin, TGV, SpaceDev, Canadian Arrow all have in common.

However the conventional wisdom in the industry is that orbital launch requires X times more energy (where X is a number that varies from 25-81 depending on who is throwing out the number) than suborbital launch, so suborbital launch really is an entirely different problem. While I will admit that suborbital spaceflight is a more benign flight regime in many ways, this particular piece of common knowledge is misleading at best, completely bogus at worst.

The origin of these numbers is the simple kinetic energy equation KE=1/2*m*v^2. Since kinetic energy is equal to the square of velocity, if you need 5 times more delta-V to get into orbit than to reach 100km, you end up needing 25 times as much energy.

The problem is that this is wrong. You don’t need 5 times as much delta-V to get into orbit as you do for a suborbital vehicle. Or to put it more correctly, people making this argument don’t seem to have a good handle on how much delta-V it really takes to make it even to 100km.

I can see where such people are probably making their mistake. If you take an extraordinarily naive first brush attempt at estimating the delta-V requirements for a 100km suborbital hop, you might just determine what cutoff velocity you would need to coast up to a 100km apogee. If you run the numbers it comes out very close to 1400m/s, which is about 1/5th of the theoretical minimum orbital velocity.

What both of those numbers (that for the suborbital delta-V requirement and for the orbital delta-V requirement) both ignore is air drag losses and “gravity losses”. If we lived on a planet without an atmosphere, and if we had engines with infinite thrust-to-weight ratios, they might have a point.

Real world orbital launch vehicles typically need to deliver 8500-10000 m/s of delta-V (compared to the orbital velocity of ~7200m/s) to reach a low earth orbit. Somewhere between 1300 and 2800 m/s of delta-V ends up getting eaten up by drag and gravity losses.

To illustrate gravity losses, imagine a vehicle just after takeoff. It has a thrust to weight ratio of say 1.2 (about what Saturn V was IIRC). That means that at that point, 1/1.2=~83% of the rocket’s thrust is just going into counteracting gravity. As an orbital vehicle gets out of the thickest part of the atmosphere, it quickly starts turning so it can start accelerating horizontally (most of reaching orbit is going fast enough sideways that you can fall without ever hitting the ground). If your engine is firing parallel to the ground, you aren’t suffering any gravity losses because your engine isn’t fighting against gravity. You are falling however, so you either need to get up to a sufficient height before you make that turn (called “lofting”), or you need to fly with your engine not quite parallel to the ground (so a tiny bit is providing some lift). But basically for orbital vehicles almost all of their drag losses occur very early on since they spend most of their flight flying horizontally. For a straight up and down suborbital flight, you might not have much higher gravity losses in nominal terms than an orbital launch vehicle, but as a percentage of the overall delta-V suborbital vehicles take a much bigger hit.

Drag also tends to impact suborbital vehicles (and reusable ones in particular) more than an orbital launch vehicle. Drag tends to scale with the frontal area of the vehicle. However, the mass tends to scale with the volume of the vehicle. If your vehicle was spherical with a radius of r, the force due to drag would scale with r^2, while the mass would scale with r^3, thus the acceleration due to drag would scale with 1/r. Basically smaller vehicles suffer much worse drag penalties than bigger vehicles. Another issue with suborbital vehicles (especially VTVL ones) is that they tend to have much squatter aspect ratios compared to orbital vehicles. Take a look at your average orbital launch vehicle, like Atlas or Delta. They are typically about 12-15x as long as they are wide (Ares I is a whopping 25:1!). Due to landing stability issues for VTVL vehicles, you’re more likely to see aspect ratios of around 3 or 4 to 1 for single stage vehicles and 6 or 8 to 1 for orbital vehicles. Squatter vehicles tend to have much higher drag losses than longer skinnier vehicles, since they have more frontal area per unit mass. Between those two issues, and the fact that suborbital vehicles spend a lot larger percentage of their flight duration inside the sensible atmosphere, and you once again end up with drag losses accounting for a much higher percentage of the delta-V required for a suborbital vehicle.

The real eye-opener for me came when I tried to toss together a quick “1DOF” trajectory model a couple of days ago. The model included drag and gravity losses, with an exponential curve fit model for the atmospheric density at various altitudes. I ignored the performance increase you get at higher altitude (due to less backpressure losses), and just picked a “mission average Isp). I assumed an average drag coefficient (for the shapes we’re interested in, the drag coefficient doesn’t change too drastically over the various Mach numbers in question). To try out the model, I put in some numbers for a vehicle that was roughly equivalent to what you would need to compete in Level 2 of the lunar lander challenge (with a huge amount of reserve propellant). I was expecting to see us get close to 100km with it, since the design had a delta-V of over 2km/s. Instead of 100km, my model showed the vehicle peaking out at only ~25km. Even doubling the propellant mass while keeping the dry mass constant wasn’t quite enough to make 100km.

The basic takeaway was that a ground launched VTVL RLV is going to take a pretty sizeable delta-V in order to actually make it even to 100km. While I didn’t keep going on trying to see what it would take (since I had to get back to work), it looks like you might need 3-3.5km/s of delta-V just to reach 100km in real life. If you’re trying to go to higher altitudes (as most of us are), you need even more delta-V.

Now, some may say that this still is only 30-40% of the delta-V needed to reach orbit, and that therefore you still need 6-9x as much energy to reach orbit, but even this is missing something important. Most orbital launch vehicles are “two-stage to orbit” vehicles, and most orbital RLVs will also be TSTO. If your first stage has 3.5km/s of delta-V with a payload equal to the fueled mass of your upper stage, and it also has 3.5km/s of delta-V, you’ve got 7km/s of delta-V overall. Which is between ~75-80% of the velocity you need to reach orbit. Which means a big VTVL “barely suborbital” vehicle with a much smaller “barely suborbital” VTVL vehicle stacked on top is going to have over 66% of the energy needed to reach orbit.

But 1.5X just doesn’t sound as impressive as 25X does it?

Now, before I wrap this up (which I need to do soon since this post has spilled over into Sunday morning), I want to add a few caveats. First off, I don’t know how the numbers pan out for ground launched HTHL vehicles. I know XCOR does, but doing a real analysis of an HTHL suborbital vehicle requires more than a simple 1DOF. My guess is that the basic conclusion, that the amount of delta-V you need to reach 100km ends up being a large fraction of the delta-V you would want out of a first stage of a TSTO orbital RLV, still holds.

Second, air launched suborbital vehicles take much smaller hits from drag losses, and can get away with much bigger expansion ratios. Which means they can get away with propulsion systems that tend to be lower performance (both from an Isp standpoint and a mass ratio standpoint) than ground launched RLVs. It also means that the delta-V required for being “barely suborbital” is lower, and hence you can build a suborbital RLV that actually is much, much lower performance than a comparable TSTO first stage. So, maybe some of the original criticism is fair–if you’re talking about air launched suborbital RLVs.

Third, there are lots of issues other than raw delta-V performance that are more challenging for orbital vehicles. TPS is one of them. Figuring out the logistics of how to recover 1st stages that land down range (or how to make them high enough performance to be able to do a Return to Launch Site landing). How to handle vehicles that are physically bigger. Etc.

But in spite of all those caveats, the conclusion you should walk away with is that suborbital vehicles really aren’t “dead ends” that have no relation to the challenges of orbital vehicles. They may deliver slightly less performance than an orbital launch vehicle stage, but the real energy difference may only be a factor of 1.5-4x, not 25x.

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Jonathan Goff

Jonathan Goff

President/CEO at Altius Space Machines
Jonathan Goff is a space technologist, inventor, and serial space entrepreneur who created the Selenian Boondocks blog. Jon was a co-founder of Masten Space Systems, and is the founder and CEO of Altius Space Machines, a space robotics startup in Broomfield, CO. His family includes his wife, Tiffany, and five boys: Jarom (deceased), Jonathan, James, Peter, and Andrew. Jon has a BS in Manufacturing Engineering (1999) and an MS in Mechanical Engineering (2007) from Brigham Young University, and served an LDS proselytizing mission in Olongapo, Philippines from 2000-2002.
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34 Responses to The Myth of 25X

  1. tonemcd says:

    Very interesting – thanks for that John, I’ve learnt quite a bit!

  2. Rand Simberg says:

    All good points, Jon. About ascent.

    Of course, the real issue is the energy that has to be dissipated to come home. I think that this will be the far greater challenges for orbital vehicle developers. Even Burt claims not to have a solution (though he may be sandbagging us). Certainly his current shuttlecock concept won’t ever scale up to an entry from orbit.

  3. Ferris Valyn says:

    John, great post as always. I may link to this post at a future date.

    Rand – I am pretty certain Rutan has said that his orbit vehicle does use his shuttlecock – of course, as you say, he may be sand-baggin us, or he may have changed his mind (the article I remember that being cited was from either late 2005 or earily 2006). Anyway, just thought I’d point this out

  4. Anonymous says:

    Thoughtful and thought-provoking, let me chew on this and ask colleagues to chew on it…

    jim O
    http://www.jamesoberg.com

  5. Robert Steinke says:

    wyAnother issue that people misunderstand is that rockets are really much more limited by conservation of momentum than conservation of energy.

    A rocket puts out the same thrust no matter how fast the vehicle is going. So going from 7km/s to 8km/s is no harder than going from 1km/s to 2km/s even though you are adding 5 times as much kinetic energy to the vehicle.

    The real figure of merit is delta-velocity, not delta-energy. Squaring the velocity change to get the “hardness” of the problem is wrong, at least for the propulsion part of the problem. Thermal protection for re-entry is a different story where you do care about the energy.

  6. Anonymous says:

    There is another issue that this post tends to overlook and that is the overhead to recover that 3.5 km/sec stage. This is one of the key problems right now with the Ares 1 vehicle as the MSFC folks are still very leery of trying to recover the 5 segment SRB due to the huge weight increase of the recovery system over that of a 4 segment booster. The reentry heat loads from that velocity are non trivial as well.

    Dennis W.

  7. Soyuz says:

    Are drag losses really that bad for VTVL’s? If i compare your numbers with the numbers in this paper: mae.ucdavis.edu/faculty/sarigul/AIAA_2003_0909_revised_Sep03.pdf You give a number of 3.5km/s to 100 km while the paper gives a delta-v of 2.1 to 2.4 km/s for vertical liftoff. So this would mean your vehicle would need up to 1 km/s delta-v more to compensate drag losses. (The paper gives a typical drag loss of 150 m/s, so six times less than your vehicle)With 1km/s delta-v drag losses a VTVL vehicle doesn’t look to appealing to me.
    Which delta-v number is Masten using for the XA1.0? And when can we expect the next Masten update?

  8. Anonymous says:

    JimO returns:

    I’m getting an amazingly rich response from my rocket scientist buddies to this essay, and may address it in an essay of my own — thanks again, John.

    In any case, on the ‘unsolved’ issue of atmospheric entry, it seems more and more clear to me that inflatable technologies will be the commercial answer here, a la the ESA/Lavochkin ‘Demonstrator’ series (IRDT program) that have been plagued with cheap booster problems.

    Seems to me, if commercial space is going to profit from a proven inflatable entry technology, then commercial space test launches ought to be offering FREE space-available flights for inflatable experiments.

    Seems only fair…

    JimO
    http://www.jamesoberg.com

  9. Mike Puckett says:

    Well said Jon. This thread ought to kill an urban myth or two.

    As to inflatibles Jim, I am still waiting to ride my moose.

    I wondered after Columbia why NASA did not simply implement an updated version of the 1960’s recommendations for project moose.

    http://www.astronautix.com/craft/moose.htm

    It seems these crude emergncy reentry vehicles could have rescued the crew provided they had a sufficient space suit as a prerequisite.

  10. Tom Cuddihy says:

    I still think the complexity that a 3 or two-stage system gets you when you have to factor in recoverability–when you get down to it, you really need to be able to take off velocity the same way you add it –with the rocket engine. Isp 950-1250sec should allow a reasonable, reliable, not grossly expensive SSTO. unfortunately, that’s an order of magnitude above what we can get from Chemical engines. Maybe that fusion thing will work out…

  11. John Carmack says:

    Drag losses aren’t nearly as bad as you calculate if you don’t fly at wide-open throttle. The optimal throttling profile is usually full throttle up to some subsonic speed, then a very reduced throttle that doesn’t cause much increase in dynamic pressure, then a throttle back up to full when most of the atmosphere is past.

    A very draggy vehicle may have an optimal burn time of 120 seconds or more.

  12. Anonymous says:

    drag loss calculations aside. I have to agree with a previous post that the big deal is the re-entry. There you do have to get rid of all the energy, wherever it may have been spent on the way up. The convective heating will go like density * V^3, so there’s a huge difference between suborbital and orbital velocities.

  13. Lee Valentine says:

    Excellent post. Suborbital, to first order, is about half of orbital.Anyone who maintains otherwise doesn’t understand the problem.

    Rockets love vacuum. After long life rocket engines, the tricky part of cheap space transportation is plowing through the atmosphere, up and down.

    To re enter the trick is to come in high, wide, and light. The opposite of every re-entry vehicle built to date.

  14. Dave says:

    Soyuz –

    We (MSS) aren’t really using dV as a design measure. As Jon and John C. point out, there are enough variables in what delta-V is necessary to get to a given sub-orbital altitude that dV is not all that useful. What I do is take a rough design, estimate the aerodynamics and run a trajectory analysis. Iterate until we are happy with the results. Go build components/sub-systems and test them. Iterate the design and trajectory analysis with real data. Repeat as necessary.

  15. meiza says:

    Yeah, what John C said. I actually happened to code a 1dof step simulator with drag too a few weeks ago. If you fly with constant throttle, with large T/W you hit constant speed really quick because of the tremendous drag forces.

    In a way, that is good too, because you can use the drag during landing to reduce terminal velocity.

    I think vertical landing performance analysis has been really little talked about, I’ll discuss it more later, I’ve done some work on it.
    In short, the sensitivity to terminal velocity is big, and actually with a few simplifications you get a really nice formula for needed landing impulse.

  16. meiza says:

    Also, I’d have to add that it’s a bit of an oxymoron to say that suborbital launches are actually good performance because they suffer from different problems than orbital launchers.
    What should matter is the problem from the second stage POV at staging: what altitude am I, and what speed, what do I have to do to thrust this payload to orbit. Compare that to ELV:s.
    (There are different ELV:s too of course, Russians use 3 stages to GEO for example. And many design and optimization targets.)

  17. Anonymous says:

    Jon Goff,

    Greetings.

    Actually, due to some recent developments, needed to get in contact with you – though this is a bad week (30April07). Attached below are some comments I sent to Jim O.

    In the course of doing flight performance though, actually get quite precise about this, evaluating the contribution of a first stage… More or less in agreement that going up is not as bad as the energy analogy suggests.

    Please drop a line.

    Wes Kelly a Desk1Triton@aol.com

    Jim,

    In this matter there are both ways to look at the problem and parts of the problem under discussion.
    So far much of the emphasis has been on ascent and velocity – which can be a component of delta v or energy, depending on what your point is. Vertical climb turns all kinetic energy to potential at 100 km.
    Lower flight paths to 100 km leave more velocity and imply more total energy involved. My analyses have preferred this condition, since it is more aligned with the orbital objective. Total orbital delta v for LEO usually come to around 30kfps. with slight variations, but most of the penalties in velocity loss are in the first stage of flight, especially gravity losses. Jon’s number low balls the losses but is a needed adjustment to the
    notion based on comparing energies of terminal velocities.

    But what else do you have to consider? How about getting back down? Do we have a good parameter for that? Maybe velocity, energy and heat flux are all good comparison points.

    WDK

  18. Kellyst says:

    A personal nit. Your fostering a myth by lumping suborbital trajectories together. I had a well know space host disregard something saying that of course ALL suborbital’s take orders of magnitude less power then orbital flight. I pointed out that a 10,000 mile suborbital ballistic requires only a couple hundred mph delta-V to get to orbit, with was why the suborbital Atlas and Titan missiles were so easy to convert to Orbital boosters with a little load lightening – or loads with fairly trivial onboard DV capacity. But the myth was to strong and he insisted that I was wrong and any orbit is several times the power demand of a suborbital.

    As to your post however – very true.
    I almost wonder if its sour grapes? Everyone who disregarded the possibility of the X-prize of being won or influencing folks, later recovered from their shock by retorting that orbital was so vastly harder that the X-prize craft still didn’t help any.

  19. Jon Goff says:

    Rand,
    I agree, that’s the point I was trying to make with my second to last paragraph. TPS is going to be far bigger of a challenge than making the jump in performance from suborbital to TSTO orbital.

    That said, if you do your suborbital vehicle right, and if you make a small orbital (or almost orbital) upper stage, you can greatly reduce the cost of experimentation for TPS development. 🙂

    ~Jon

  20. Jon Goff says:

    Dennis,
    If you start with a VTVL stage that’s capable of surviving a straight-up-and-down trajectory, it will always be able to survive a trajectory with similar delta-V that has a horizontal component. The challenge is the logistics of where you land that stage and how you get it back. RLVs I think will have an easier time with this than parachute recovered ELV stages, but it’s still a challenge–and that’s my point–all of this focus on the supposed energy difference between suborbital and orbital vehicles is misplaced. There are other issues that are much more important because that issue (the energy difference) is being overstated.

    ~Jon

  21. brian d says:

    Others have already pointed out some of the caveats for comparing suborbital to suborbital, vehicle shape, TPS, ISP, etc. With those in mind here’s another way to look at the problem using actual data. The Atlas V series 400 (no solids) delivers 12,500 kg to a 185 km circular orbit using 284,089 kg of fuel + oxidizer. Mass of fuel + oxidizer is a rough measure of energy. Now compare that mass to the mass of fuel + oxidizer of the X-15 or space ship and scale linearly by mass of the payload (12,500 kg to ? for SS1/X15). I have no clue about the specs of either of those vehicles, but maybe someone else does. I’d be curious to see how that worked out.

  22. Jon Goff says:

    Soyuz,
    There can be a lot of variability in requirements depending on what assumptions you make about vehicle size, aspect ratio, how tightly you pack things inside the vehicle, engine T/W ratios, etc. Without seeing their numbers I’d have a hard time commenting. But 150m/s sounds ridiculously low. I’m just not realistically seeing how you could get a groundlaunched VTVL vehicle to 100km for that little delta-V. I could be doing something heinously wrong, but I’m skeptical that you could get that little drag loss on something like that. Not unless you were flying a very long and skinny rocket.

    For some reason I’m having errors with opening your corrected link, or I’d try and figure out what the discrepancy is.

    ~Jon

  23. Jon Goff says:

    Tom Cuddihy,
    TSTO and 3STO is more logistically challenging than SSTO, but I think they can be made to work, without having to wait for fusion technology. Quite frankly, I think even SSTO is borderline feasible with existing technology (ie no fusion or fission or anything beyond the realm of what has been done already), it’s just tough.
    ~Jon

  24. Jon Goff says:

    John C.,

    Drag losses aren’t nearly as bad as you calculate if you don’t fly at wide-open throttle. The optimal throttling profile is usually full throttle up to some subsonic speed, then a very reduced throttle that doesn’t cause much increase in dynamic pressure, then a throttle back up to full when most of the atmosphere is past.

    Have you actually run any simulations of this, or is this just based on intuition? Because at least with the 1DOF I wrote, I wasn’t seeing any real benefit from throttling down to decrease drag losses (as you throttle down, you’re just taking worse gravity losses in exchange for lower drag). Of course that was for reasonably low-drag vehicles, maybe for something really draggy like a Pixel or one of your modular stacks it might increase performance a bit, but I think the losses may be a lot higher than you seem to be implying.

    ~Jon

  25. brian d says:

    Others have already pointed out some of the caveats for comparing suborbital to suborbital

    correction, should have been “suborbital to orbital”

    Anyone know those numbers for SS1 or X15?

  26. tankmodeler says:

    X-15 data from Astronautica:

    Crew Size: 1.

    So payload would be ~500lb including life support & suit, etc.

    Mass: 30 121 kg (66 405 lb).
    Main Engine: XLR-99.
    Main Engine Thrust: 262.445 kN (59 000 lbf).
    Main Engine Propellants: Lox/Ammonia.
    Main Engine Propellants: 20 551 kg (45 307 lb).
    Main Engine Isp: 239 sec.
    Spacecraft delta v: 2 100 m/s (6 800 ft/sec).

  27. brian d says:

    Found this on Wikipedia

    X-15 General characteristics
    Empty weight: 14,600 lb (6,620 kg)
    Loaded weight: 34,000 lb (15,420 kg)
    Max takeoff weight: 34,000 lb (15,420 kg)
    Powerplant: 1× Thiokol XLR99-RM-2 liquid-fuel rocket engine, 70,400 lbf at 30 km (313 kN)

    To orbit 12,500kg Atlas needs 284,089kg of “energy” and X-15 needs 8,800 kg (15,420kg-6,620kg) of “energy” to take 6,620kg to 100km.

    Atlas takes 32.28 times more energy to take 12,500kg to orbit. Scaling by the ratio of the payload masses (6,620/12,500) reduces the energy ratio to 17.09 to 1, orbital vs. suborbital. There’s your answer with real data.

    More scaling could be done to account for the different propellants and isps, etc, but that’s a good start.

  28. John Carmack says:

    >Have you actually run any
    >simulations of this, or is this
    >just based on intuition?

    Yes, I ran a lot of simulations in the X-Prize days. It makes a very big difference.

    John Carmack

  29. Jon Goff says:

    John,
    I’m really curious how you came to the conclusions you did then. I’m getting completely different results from the numbers I’ve run. I haven’t yet found a way using the data you’ve published to get any of your vehicles higher than 20-30km. Either the drag eats you alive, or the gravity losses.

    I may very well be doing something wrong, so I’d be curious to discuss how you did the simulations (ie what tools you used and such). I did notice that if one makes any of a number of simple mistakes on how one handles air density that it can throw your apogee number off by a factor of 2-3x.

    ~Jon

  30. brian d says:

    Jon,
    I’m curious as to what you think of the Atlas / X-15 comparison. Back-of-the-envelope calculation shows 17.1 to 1 energy ratio for orbital to suborbital and I could see further scaling arguments changing that number by a factor of 2 or so. This could possibly bolster your argument. I doubt that numbers would get as low as 4 : 1, but maybe 7 or 8 : 1. Comparing spaceship 1 to Atlas would be another data point. Do you know those specs for comparison purposes?

  31. John Carmack says:

    I wrote the code from scratch, but someone from White Sands Missile Range cross checked one of my runs a long time ago when we were discussing flights there, so I have reasonable confidence that it is close.

    The quads certainly can’t go very high with a Cd of about 1.0 and the low ballistic coefficient, but two stacked spheres with a nosecone can hit 100km from the ground with a MR of 4.

    Check your atmospheric density calculations — I used interpolation between the table values in Sutton, rather than an equation. Cross check with the V2 rocket specs, which had a mass ratio of less than 3 and a poor Isp, but could apogee at 114 MILES.

    John Carmack

  32. kert says:

    the conclusion you should walk away with is that suborbital vehicles really aren’t “dead ends” that have no relation to the challenges of orbital vehicles.
    Not to mention that this was clearly demonstrated with May 5, 1961 and followup Feb. 20, 1962 events already.

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