SSTO is a bad idea, but NTR SSTO is worse

A few months ago, I spent some time describing some calculations of payload fraction that I derived to assist in the design of rocket vehicles. My motivation for getting into this type of work came about from my work on the X-33 rocket when I was an intern at the Skunk Works. I wondered how so many people could think that SSTO (single-stage-to-orbit) was a good idea when the mathematics argued against it.
NTR-SSTO
Right after I joined NASA, in early 2000, I was in a group that was looking at some really advanced concepts, and somehow or another, we got looking at using nuclear thermal rockets for an SSTO vehicle. At first blush, the whole idea seems to make sense. Nuclear thermal rockets offer almost twice the specific impulse (Isp) of chemical rockets, and if an SSTO doesn’t have enough Isp with chemical rockets, then surely nuclear rockets must be better, right?

Wrong. Super wrong.

Nuclear-thermal SSTO turns out to be one of the worst ideas anyone has ever come up with, for two simple reasons: hydrogen and the lousy thrust-to-weight ratio of nuclear thermal rockets. Those are the same two reasons that make NTR lousy or marginal for nearly any other space application as well, but this post will focus on the issues surrounding NTR SSTO.

In the case of any earth-to-orbit vehicle, you’ve got to have the thrust to get off the ground in the first place. Let’s assume that we’re dealing with a vertically-launched NTR SSTO. It has to have a vehicle thrust-to-weight ratio greater than one, and probably a fair bit better than that in the first place, just to get off the ground. So we can take those expressions that I derived before, assuming hydrogen as a propellant and the engine thrust-to-weight ratios that have been quoted by NTR proponents like Stan Borowski to quickly try to figure a payload fraction for an NTR SSTO.

We find the propellant-mass-sensitive term (derivation here) assuming the liquid hydrogen has a density of 71 kg/m3, ullage of 3%, a mixture ratio of zero, and a tank structural mass factor of 10 kg/m3. This gives us a value of 0.1452 for this term.

(1)    \begin{eqnarray*} \notag \lambda &=& \dfrac{(MXR) \left(\dfrac{f_{OT}}{\rho_{ox}}\right) + \left(\dfrac{f_{FT}}{\rho_{fuel}}\right)}{(1 + MXR) (1 - f_{ullage})}\\ \notag &=& \frac{(0) \left(\dfrac{0 \text{kg/m}^3}{1142 \text{kg/m}^3}\right) + \left(\dfrac{10 \text{kg/m}^3}{71 \text{kg/m}^3}\right)}{(1 + 0) (1 - 0.03)}\\ \notag &=& \frac{0.141}{0.97} = 0.1452\\ \notag \end{eqnarray*}

We find the gross-mass-sensitive term (derivation here) by assuming that the engine has a vacuum thrust of 15000 lbf, a weight of 5000 lbm, and vacuum thrust-to-weight of 3 to 1. I’m not even going to “ding” the engine for sea-level performance, since as we’ll see, it won’t even matter. With a vacuum T/W of 3 and the same for the sea-level T/W and an initial vehicle thrust-to-weight ratio of 1.25, and we’ll just say that the thrust structure doesn’t weigh anything either, the gross-mass-sensitive term comes out to be 0.4167.

(2)    \begin{eqnarray*} \phi &=& \frac{T/W_{vehicle-initial} (1 + f_{TSW} (T/W_{engine-vacuum}))}{T/W_{engine-initial}}\\ &=& \frac{1.25 (1 + 0(3))}{3} = 0.4167\\ \end{eqnarray*}

We’ll also ignore any recovery hardware (wings, landing gear, TPS, etc) and say all that weighs nothing. We’ll assume that the engine has a vacuum Isp of 900 seconds and that it takes 9200 m/s of delta-V to get to orbit.

(3)    \begin{eqnarray*} {MR} &=& \exp\left(\frac{\Delta v}{v_e}\right) = \exp\left(\frac{\Delta v}{g\:I_{sp}}\right)\\ &=& \exp\left(\frac{9200 \text{m/s}}{(9.81\text{m/s}^2)\:(900\text{s})}\right)\\ &=& \exp\left(\frac{9200 \text{m/s}}{8829 \text{m/s}}\right)\\ &=& \exp(1.042) = 2.835\\ \end{eqnarray*}

Plugging those numbers in the rocket equation gives us a mass ratio of 2.835 (very good!) and a propellant mass fraction of 64.73%.

(4)    \begin{eqnarray*} {PMF} &=& \left(\frac{MR - 1}{MR}\right) = 1 - \left(\frac{1}{MR}\right)\\ &=& 1 - \left(\frac{1}{2.835}\right) = 0.6473\\ \end{eqnarray*}

Next we use the prop-mass-sensitive and gross-mass-sensitive terms, along with the propellant mass fraction to get the payload fraction (derivation here).

(5)    \begin{eqnarray*} \frac{m_{payload}}{m_{gross}} &=& 1 - {PMF} - \lambda ({PMF}) - \phi\\ &=& 1 - 0.6473 - (0.1452)(0.6473) - 0.4167\\ &=& 0.3527 - 0.0940 - 0.4167\\ &=& -0.1579\\ \end{eqnarray*}

We start out with the final mass fraction (1 – prop mass fraction) of 35.27%. It doesn’t get any better than that. Then we subtract the gross-mass-sensitive term (41.67%). Now we could stop right here, because we’re already negative (-0.064). That is to say, even before accounting for the issues with tankage, we’re already out of performance. The engines weigh too much. But we’ll keep going and subtract the product of the prop-mass-sensitive term and the propellant mass fraction (0.6473*0.1452 = 0.0940) and we end up with a payload fraction of -0.1579.

So it’s a no-go with these engines. Our payload fraction is grossly negative and we’ve got nothing. It’s clear from the magnitude of the numbers that the engine thrust-to-weight ratio is the main culprit, although the “fluffy” liquid hydrogen tanks don’t help much either.

So what kind of engine performance would you have to have to get even a zero payload fraction? Well, I ran some rough calculations based on a variety of speculative vacuum T/W ratios for some putative NTR engine, at a few different values of specific impulse and plotted the results here:
NTR-SSTO T/W ratios
The graph tells the story. To get payload fractions of zero (a launch vehicle of infinite size) you have to have a T/W at 900 sec Isp of over 10. That’s more than three times the T/W that Stan Borowski projects for his sporty 15K NTR design, which he says will have a T/W of 3. So if you think that Stan or others can design an NTR that only weighs a third of what he thinks it will weigh, then you can dream about an NTR SSTO of infinite mass.

As for me, I’ve thought for some time that NTR was a really bad idea for almost every application for which it is considered. The SSTO application is probably the worst.

About Kirk Sorensen

MS, nuclear engineering, University of Tennessee, 2014, Flibe Energy, president, 2011-present, Teledyne Brown Engineering, chief nuclear technologist, 2010-2011, NASA Marshall Space Flight Center, aerospace engineer, 2000-2010, MS, aerospace engineering, Georgia Tech, 1999
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29 Responses to SSTO is a bad idea, but NTR SSTO is worse

  1. Kirk,
    I guess another way of saying this is that unless you have an NTR approach that has dramatically better T/W ratio than previous designs, then it probably isn’t even worth analyzing it any further. That said, at least some of the DUMBO rocket proponents were claiming T/W ratios much better than 10 were feasible (I’ve heard claims as high as 50, but I don’t know if those came from the original researchers or the fanboys) with their approach. Not being a nuclear engineer, I have no way to BS-check those concepts, but it would at least seem that if people insist on investigating solid-core NTRs, they need to at least understand that if the idea doesn’t meet some minimal T/W requirement, it’s probably not worth any further analysis.

    ~Jon

  2. You got the point exactly Jon.
    This is a scoping calculation specifically designed to save time upfront by showing you where the problems are in an idea, and in this case they are primarily in the T/W ratio of the nuclear thermal rocket.

  3. mike shupp says:

    Evidently back of the envelope calculations for the DUMBO nuclear rocket proposed back in the 1950′s suggested thrust-to-weight ratios of 20 to 80. Or perhaps I’ve misread chapter 9 — doing a Google search on “Dumbo nuclear rocket” gets one to the released report.

  4. Kirk, I recommend you *dont* read James Dewar’s latest book, The Nuclear Rocket as it is terrible, but his basic argument is that using a nuclear second stage would revolutionize space, etc, etc.

    Lemme get some numbers for ya….

    Specifications Of Fourth-Generation Re-core Engine And Stage

    Engine
    800MW (40,000-pounds of thrust)
    6000-pounds engine weight
    1000-seconds of specific impulse
    100-gallons of LH2/second

    Stage
    LH2 tank weight: 20,000-pounds
    17,000-pound payload
    3000-pound cocoon (this is for recovery of the nuclear engine in the ocean)
    LH2: 90,000-gallons/45,000-pounds

    Totals:
    Engine 6000-pounds
    LH2 tank 20,000-pounds
    LH2 45,000-pounds
    Cocoon 3000-pounds
    Payload 17,000-pounds
    ——————-
    91,000-pounds

    This would be airlaunched from a cargo plane such as the C-5A from 50,000-feet. Strap-on boosters would carry the nuclear stage to 100,000-feet and then the nuclear engine would do the orbital insertion.

    I’d love to hear your opinion on his numbers…..

  5. john hare says:

    I know you weren’t asking me but…

    In the numbers you listed LH2 seems to be half a pound per gallon with engine consumption of 100 gallons per second. At 40,000 pounds of thrust that is an Isp of 800 instead of the 1,000 listed.

    An LH2 tank mass of 20,000 pounds to carry 45,000 pounds of LH2 seems excessive.

    This is a fourth generation engine sems to indicate that you must build three generations of engine before reaching the one you listed.

    I’ll definately take the advice you gave Kirk to avoid this book, and author.

  6. Ian Woollard says:

    There’s a website about this stuff here:

    http://www.projectrho.com/rocket/index.html

    I don’t think it’s *quite* as bad as you say, but NTR SSTO is pretty bad ;-)

  7. john, Dewar has only written one other book, To The End Of The Solarsystem and it is quite a good read. That’s why I read his second book.. big disappointment.

    In regards to the “fourth-generation” … yeah, he actually says at one point they he expects the 2nd and 3rd won’t be built, but a relevant test stand would be… and that’s just an example of some of the poorly named and badly explained concepts in the book.

    http://books.google.com/books?id=ATD8PQAACAAJ&source=gbs_slider_thumb

    Has my review.

  8. Charles says:

    T/W of 3 for solid-core NTR is a bit conservative.
    http://www.astronautix.com/engines/nerva.htm
    quotes Nerva 2 with a T/W of about 7.5. Still inadequate for SSTO,
    but if you combined it with a thrust-augmented high expansion nozzle, and used a variable-mixture ammonia/LH2 propellant, plus a high-performance combination for the thrust-augmentation like LOX/methylacetylene , you could wind up with a positive payload fraction.

    But yes, straight nuclear SSTO is pointless with a T/W under 20

  9. Godzilla says:

    Yes nuclear thermal SSTO is nonsense at this moment in time. With current materials technology. This is painfully obvious. Remember all those nuclear engine powered bomber concepts from the Cold War? They failed precisely for the same reasons: they were too heavy and finicky.

    I have some nits to pick here however. There are other forms of reaction mass which can be used rather than hydrogen (including ammonia) which have better density for storage, although they compromise ISP. Also later generation nuclear thermal designs, such as Project Timberwind, had T/W ratios much higher than 10 thanks to using SiC as a construction material.

    So I do not think a nuclear thermal SSTO is impossible: just beyond our technical reach at the moment. IMO it can be done, but would require a generation of effort and lots of money which we do not have. Non military uses would also be limited. If lightweight nuclear reactor technology improves this could change. But I would not bet on that. Even maintaining current reactor technology up to snuff is hard enough in the present political climate.

    I have more faith in beamed propulsion. At least the basic technologies for that are being worked on. The applications are also very interesting both for the military and civilian sector.

  10. Joe Blow says:

    @ Mr. Sorenson: Why is NTR a poor choice for other applications, especially deep space crewed missions to Mars or elsewhere (NERVA’s old goal)?

  11. roystgnr says:

    Any thoughts on LOX-Augmented NTR?

  12. Dean says:

    Besides DUMBO and Timberwind, there is LANTR. Encyclopedia Aestonautica lists an expected T/W ratio of as high as 13, though with an ISP reduced to ~ 500 isp. The tech for this is basically the same as Aerojets thrust augmentation nozzle, but with the injection of LOX rather than fuel. Borowski advocated this engine for use in a Lunar based ‘SSTO’ shuttle working between Luna and LEO and using lunar oxygen with hydrogen from earth. It would be interesting to see this idea reconsidered in light of the expected availabilty of lunar hydrogen.

  13. Paul D. says:

    Why is NTR a poor choice for other applications, especially deep space crewed missions to Mars or elsewhere (NERVA’s old goal)?

    I imagine one of the issues is acceleration being so low that the vehicle climbs significantly out of the gravity well during a burn, reducing the benefit one gets from the Oberth Effect.

    If that’s the case, nuclear thermal may make more sense for missions to small asteroids without significant gravity wells.

  14. Jonathan Goff says:

    Paul,
    I think Kirk was actually referring back to his earlier post, where he showed that for current NTR T/W ratios, and LH2 tank masses, NTRs only get a modest improvement in payload over a comparable LOX/LH2 system, but at much higher development cost.

    ~Jon

  15. Pete says:

    I should perhaps take issue with the title of this post:

    “SSTO is a bad idea, but NTR SSTO is worse”

    There are just so many assumptions, many of which are not written in stone, that go into this statement. It would perhaps be nice if it was a little more qualified.

  16. Arizona CJ says:

    Thank you for this superb article.

    Personally, I think SSTO is a great idea, PROVIDED that it is based on a breakthrough that changes the current reality of fuel fractions. IE, if a far denser, more energetic and viable fuel mix were to be discovered, SSTO might well be very viable. At today’s tech, I don’t think it is.

    As far as NTR for SSTO, I think it’s very viable, assuming one small factor; a payload with negative mass. :)

  17. GL says:

    A general question: why are SSTOs a bad idea in the author’s opinion?

    It seems to me that SSTO is the only reasonable path to low operational costs for launch vehicles. While technically challenging (I understand the technical hurdles), full re-usability in a single vehicle (that doesn’t have to have parts recovered and reintegrated) seems like the best path to low costs. I’d be interested in hearing arguments against the concept in general, other than that it’s hard.

  18. anom says:

    Kirk,

    Good post.

    The Timberwind nuclear thermal upper stage replacing the Centaur LOX/LH2 engine was supposed to have a T/W of 30; so it could work for your NTR SSTO.

    I think that the only issue with posts like this is that there are thousands of assumptions that go into a rocket making it to orbit and most of these assumption have not been tested recently.

    NTR SSTO actually becomes a good idea with a high T/W, but most people assume that a high T/W is impossible for nuclear thermal because they are not experts in what is possible for nuclear technology.

    I would love to see a post about the high T/W particle bed nuclear thermal rockets like Timberwind which were researched in the 1980′s at a T/W over 30. Are they viable today with some funding?

    I would also love to see a post on whether or not nuclear fission power in space can reach the 1 kg/kw threshold needed for 39-day voyages to Mars discussed for the VASIMR engine and also researched for Space Lasers in the 1980′s. The low-weight radiators and nuclear fission reactors for this supposedly already exist today, but most people just dismiss the entire concept of VASIMR and multi-megawatt nuclear-powered lasers because they assume that it is impossible for us to rapidly improve what has already flown in space by an order of magnitude or so (eventhough the success of the Falcon-9 has shown that you can do things different by orders of magnitude and be successful).

    I would also love to see a post discussing if SSTO is possible today using the existing 3,000-lb 1st stage of the SpaceX Falcon-1e or the 33,000-lb 1st stage of the Falcon-9. Both appear to exceed the 95% propellant mass fraction needed for SSTO with LOX/RP-1.

    How far is Jon Goff and Masten away from high T/W engines and structures for SSTO……probably very far, but that would also be a great post.

    Your post has actually done a good job of showing why NTR SSTO is a good idea……for T/W above 20.

  19. Jim Davis says:

    That said, at least some of the DUMBO rocket proponents were claiming T/W ratios much better than 10 were feasible (I’ve heard claims as high as 50, but I don’t know if those came from the original researchers or the fanboys) with their approach.

    The DUMBO fanboys seem blissfully unaware that the higher performance comes with a huge relaxation of fuel element containment criteria. Unlike the NERVA design, fission fragment/fuel element contamination of the exhaust was an integral feature of the DUMBO concept.

    Needless to say, such a feature is (and indeed should be) a complete nonstarter today.

  20. Mike Lorrey says:

    Try your numbers with NERVA 2 T/W of 7.5, and an air augmented ram ejector so you get thrust from combustion of the exhaust with atmospheric O2 (for an Isp of 3500).

  21. Roga says:

    You don’t need T/W > 1 if you do horizontal takeoff. In a chemical rocket, thrust is relatively cheap because engine mass/lb thrust is very small – so your design closes around lots of thrust and a fast burn. For an NTR, you would be much better off taking the mass hit on aerodynamic lift I suspect.

    That runs into arguments about wings on scramjets, but this is a different argument. Scramjets don’t close for two reasons that have nothing to do with the aerodynamic lift penalty – 1) They can’t start or finish the ascent, so you end up needing a separate rocket anyway; and 2) They can’t even be used to their physical limit because the Earth curves away and you lose atmosphere too quickly. An NTR does not have these problems.

  22. Mike Lorrey, I included my equations and the assumptions I used so that you can run the calculations yourself and report back on results.

  23. Mike Lorrey says:

    anom,
    “I would also love to see a post discussing if SSTO is possible today using the existing 3,000-lb 1st stage of the SpaceX Falcon-1e or the 33,000-lb 1st stage of the Falcon-9. Both appear to exceed the 95% propellant mass fraction needed for SSTO with LOX/RP-1.”

    I actually proposed that they do an experiment with an Falcon 1e first stage and install an air augmented ram ejector around the engine, akin to the GNOM missile, running the Merlin a bit more fuel rich than normal. The GNOM allegedly achieved a throw weight and range equal to a standard missile twice its mass (though other than launch of a scaled version that confirmed these numbers, it remained on paper).

    The F1e first stage should be SSTO ELV with almost no payload, but with a ram ejector installed should be able to put something useful in orbit.

  24. Zach T. says:

    Thrust to weight ratios of much better then 10:1 should be possible with modern materials technology, Tungsten Cermite in particular should allow for very high thrust to weight ratios and more importantly be very durable so the ablation of fuel elements into the working fluid stream should be near zero. In my humble opinion the reactor ablation issue is the biggest engineering challenge to make an NTR for surface launch.

    It’s unfortunate that the general public has such an irrational fear of nuclear power because I think in the long run that it’s the only way we’re ever going to do anything useful in space.

  25. Roderick Reilly says:

    Serves me right for wandering away, as I imagine this comment section is “closed” due to the late date.

    Anyway, my comment is about the SSTO concept in general:
    What really matters is not pure SSTO for its own sake, but an operational profile that amounts to the equivalent of SSTO.

    Putting a boost-phase drop tank into the design is the simplest way to reduce vehicle mass fraction for the orbiter itself. Even if you can come close to pure SSTO function in your design, it would still make sense to use a drop tank because it gives you more margin for a robust orbiter design and for more payload.

    Using an ejectable ablative nozzle insert is the simplest way to have a staged expansion ratio on the orbiter’s engines (you use an upper stage regenerative nozzle as your baseline, with the ejectable ablative nozzle inserted in it for the boost phase expansion ratio).

    You don’t have to “stage” any additional engine packages, you can recover the drop tank, and the ejectable nozzle inserts are the only things you expend.

  26. Jeff Wright says:

    I still prefere (non SSTO) NTR systems over this
    http://www.thespacereview.com/article/1690/1

  27. Jeff Wright says:

    Didn’t the folks over and Andrews have a nuclear thermal approach to the Gryphon spaceplane? It was to be going to be a two-stager with LACE at first perhaps, and then there was talk about anuclear application down the road. So much for that then…

  28. ElmarM says:

    One thing to remember about nuclear propulsion is that you can theoretically use air as your only fuel (like the “nuclear bomber” designs of the 60ies and 70ies). There are still significant challenges with that, no question about it, but it would at least purely mathematically change the equation in favor of the nuclear propulsion.

  29. Kirk,
    Your calculations are correct but I must disagree with your assumptions. Although the Center for Space Nuclear Research (CSNR) at the Idaho National Laboratory (INL) does not advocate the use of a NTR as a SSTO, we did investigate the feasibility of the idea during our CSNR Summer Fellows program in 2012. The short version of the result is that we do believe that we can build a NTR with a T/W of 12 using our tungsten cermet fuel so that the NTR could be a SSTO. While the US may not ever pursue this, other countries might as it offers the possibility of signifciantly reduced cost to orbit

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