Wednesday, February 01, 2006

Catapult Gain

The Chair Force Engineer doesn't think much of a catapult start for rockets. His point is that if your catapult gets the rocket going fast horizontally, it just makes the max Q problem and drag losses worse.

As the rocket accelerates, the dynamic pressure on the front of the craft gets larger, until it gains enough altitude and vertical velocity that the atmospheric density drops faster than the velocity component rises. The maximum pressure experienced is max Q. Max Q is a problem because that drag turns the rocket's forward velocity into heat, which the structure has to deal with somehow, usually with a thin layer of ablatives on the nose.

A study done at UC Davis, A Study of Air Launch Methods for RLVs looked at dropping the rocket from an airplane, as is done for the Pegasus and SpaceShipOne rockets. They found that the high starting altitude helped, as did releasing the rocket with some significant vertical velocity component.

The thing that air launch and (vertical) catapults have in common is they both allow the rocket to delay fighting gravity.

As I pointed out in an earlier post, a rocket coming vertically off a launch pad is losing nearly all of its delta-V to gravity losses. Later on in the flight, once a good bit of propellant has been burned off and the acceleration has improved, a much smaller portion of the delta-V is lost to gravity. Note that the total vertical impulse required is a function of the time spent getting to orbital velocity, and is insensitive to the actual flight path.

The situation is much different for a rocket firing horizontally. Delta-V expended horizontally adds to the rocket's final velocity regardless of what the current acceleration is. Unfortunately, horizontal velocity added early in the flight adds a lot of drag loss.

So to minimize gravity losses, the rocket should start out firing at least somewhat horizontally, losing vertical velocity, and only later recover that vertical velocity. There is some limit to this pattern, since too much horizontal velocity too low in the atmosphere will exacerbate drag losses, and since we don't want the rocket to smack into the ground. Starting at high altitude helps, as does starting with some vertical velocity.

This leads to a concept I'll call "catapult gain", because I haven't read about it and don't know what it's really called. If I start the rocket off with a couple hundred m/s of vertical velocity, I increase the velocity at first stage burnout by more than the initial velocity boost, for two reasons. First, the gravity losses are lower, since the rocket can postpone some of its vertical impulse to when it is more efficient. Second, the first stage rocket can start out with more gas in the tanks, burn longer, and deliver more delta-V, because it doesn't have to have positive vertical acceleration right from the start.

Catapult gain is limited to the first few hundred m/s of velocity. The first effect is limited because we're reducing gravity losses, and increasing drag losses. There is only so much gravity loss to be mined, and drag losses rachet up quickly. The second effect is limited for the same reason that upper stage minimum accelerations are limited: eventually the extra delta-V is stretched over so much time that the gravity losses start to overcome all the extra delta-V. More starting velocity is always good, of course, but the point is that it reverts to a gain of one. To give a rough idea of catapult gain, some spreadsheet calculations indicate that a 250 m/s jump reduces the upper stage delta-V requirements of a SpaceX Falcon 9 by 500 m/s, for a catapult gain of two. Lest that seem small, note that it would allow the dead weight of the upper stage to increase by around 18%, and I'd guess the payload would increase by at least twice that.

So now that I've established a motivation for a vertical catapult, let me suggest one: a steam rocket. This is a very big bottle of very hot water at very high pressure, which partially flashes to steam as it exits. It has really crappy specific impulse (about 50 seconds), but can produce really large amounts of thrust very cheaply. For a Falcon 9 stage 0, it would be an 80 tonne steel tank (HY 100, safety factor 1.5) holding 400 tonnes of water, starting at 300 degrees C and 86 bar. The thing would produce around 26 MN of thrust for about 7.5 seconds, boosting the Falcon to 280 m/s. A 25 meter pipe, inserted up the throat of the nozzle, would add another 40 m/s by acting as the piston in a cylinder, allowing the Falcon to react against the Earth instead of mere propellants.

Let me point out how simple this system is. It has no moving parts on the vehicle, no flight-operational valves, no sequencers. The nozzle is bolted down onto a seal while the water in the tank is heated (pumped through an external heat exchanger). Fire the explosive bolts and it goes. There are no gimbals, and no guidance system. The LOX-Kero first stage is started while on the pad, and fires directly onto the top of the tank, which being solid steel backed by water is unaffected. The interstage is a truss which the engines fire through. There is no recovery system: the thing sails through the air for about a minute, coasting up to 4 kilometers high, and then comes crashing down into the sea, where it eventually resurfaces, nozzle down, until it's dragged back to shore. If we wanted to be sure it doesn't sink, we could inflate a balloon inside the casing, which would passively inflate as the internal pressure dropped during boost, and would require no pyrotechnics or interface of any kind. The exhaust is hot water and steam, has mild overpressure, requires no water suppression, nor cleaning of nasty chemicals afterwards. I will guess that the tank and nozzle can be built for $500k. Fuel costs for heating it up are about $10k, so an extensive program of test-firings with dummy rockets atop would be cheap.

I recommend tilting the launch pad slightly to ensure that the thing comes down in the ocean and not back onto the pad.

The thing vents 53 tonnes of propellant per second, which is orders of magnitude more than any chemical rocket ever built, and will produce a singular launch spectacle. So long as pictures of parboiled parrots can be avoided, the PR value alone should be immense. As a side benefit it should allow the Falcon 9S9 to put more payload into orbit than a Delta IV Heavy, and maybe enough more than the Shuttle to allow it to lift Shuttle ISS cargoes with an added strongback.

EDIT NOTE: In an earlier version of this post I claimed a doubling of throw weight. Math error. That's what I get for posting after midnight.


  1. Iain,
    This is an interesting idea, but I'm not sure if the benefits are outweighed by the costs. You mention a 400 tonne steam first stage for a Falcon IX. That's about 125% bigger than the rest of the rocket. In other words, you're now over doubling the size of the rocket, most of that going into height (since you want to minimize the frontal cross sectional area to minimize drag losses). Not to mention you're now needing to heat several hundred tonnes of water. And the fact that most of the thrust from the engines during that time would be lost due to deflections of the exhaust jet when they impinge on the upper part of that tank (or at least a lot would be lost due to sine/cosine effects....

    I'm just not really sure if this idea really ends up getting you enough gain to make up for all the operational headaches.


  2. I'm almost certain I've seen something quite like this proposed as a refinement to floating sea launch -- probably Robert Truax's Sea Dragon ultra-HLLV in the 1960s.

    There's usually a glass half-empty/half-full split in how catapult ideas are received: some people run the numbers and say "every little bit helps," while others run the numbers and say "I'd rather put my effort into a little bit better rocket than take on the distractions of a whole different engineering domain."

    (Then, of course, there are those who can't run the numbers, imagine they've come up with the catapult idea for the first time, and proclaim "I've found the answer to CATS!")

  3. Interesting concept. However, the large acceleration at the end of the 0th stage burn would put very large stresses on the fully fueled 1st stage. I am not sure wether the falcon 9 can survive these stresses without reinforcements.

    And firing the 1st stage engine directly against the top of the tank of the 0th stage might not be such a good idea. Since the water temperature is below the critical point of water, an insulating steam bubble would be created in the top of the water tank. That would lead to overheating and loss of strength.

    But these are just minor nits, not showstoppers.

  4. Note that the total vertical impulse required is a function of the time spent getting to orbital velocity, and is insensitive to the actual flight path.

    I know I'm nit-picking, but this is not entirely true. Gravity does get weaker by the inverse-square law so a rocket at higher altitude loses less vertical impulse per second simply because gravity is weaker at higher altitude. Of course, the effect is relatively small and to a first order approximation the above statement is true.

  5. How about a low performance monopropellant.

    Are carbon dioxide and nitrous oxide miscible?

    I read about research surrey satellite
    limited carried out decomposing nitrous oxide using a ceramic catalyst. The only problem was that the decomposition temperature was about 1600 degC and the catalyst was melting a little.

    What if you had a mixture of 4 parts
    co2 to 1 part nitrous passing over a preheated catalyst on the way to the
    rocket nozzle, would this out perform the steam rocket.

    This set-up would also have the advantage over a steam rocket in that it could be chilled to reduce tank pressure. The attainable mass fraction would then be independent of the energy density unlike a hot water rocket.

  6. A 25 meter pipe, inserted up the throat of the nozzle, would add another 40 m/s by acting as the piston in a cylinder, allowing the Falcon to react against the Earth instead of mere propellants. Sounds like a rocket in a pipe, or is it a pipe in a rocket?. I thought you said that wouldn’t work, see for negative results.
    In that post you claimed to have looked at Bull’s work but I believe all you did was look at the story of his life as told by his critics. A look at his work would at least of shown you how guns work. In fact if you have a link to any of his work, calculations etc. I would be interested. As far as I have been able to discover he didn’t publish anything, if he had, I believe he would be alive today.
    In rocket science, the efficiency of the rocket is proportional to the temperature of the gas (velocity exiting the nozzle) and molecular weight of the gas. This is called specific impulse. In the science of internal ballistics (the sub set of ballistics concerned with the projectiles motions inside the barrel) the maximum muzzle velocity is determined, for all practical purposes, by the speed of sound in the propellant. In most cases, since the propellant is burning chemical stuff (CO2 and H2O), the speed of sound is proportional to the temperature of the burning propellant and the temperature is proportional to the cartridge or ‘cup’ pressure of the gun. (speed of sound goes up as the gas is heated, fairly independently of pressure though the calculations are complex) As the pressure goes up the initial acceleration will increase but at the limiting velocity of sound in the expanding gas the projectile will no longer be accelerated. This has always been a threshold and limited barrel lengths. An old handgun might generate ‘cup’ pressures (temperature) of 12,000 psi and be limited (regardless of barrel length) to less than 1,000 ft/sec. Magnums will generate 32,000 psi and with longer barrels can achieve 1,500 ft/sec. to 2,000 ft/sec. while rifles generating 60,000 to 70,000 psi pressures can get velocities of 3,600 ft/sec. and of course use longer barrels. There is no gun in existence today (at any payload/propellant ratio) of conventional design that will fire a projectile to an altitude of 106 miles, like Bull did in 1964 during HARP in Barbados. Pressures of 250,000 psi or greater would be required in a conventional ‘gun’ configuration to get a temperature high enough to get a muzzle velocity of the 8,000 ft/sec. required and there is no barrel in existence today that will take that stress, the mud gun included.
    Your calculations completely miss the essence of the problem. You don’t want all the propellant to burn at once, if the propellant is all going to burn at once you don’t need a barrel! Just drop your payload on top of a thermonuclear bomb and set it off. Even in this scenario the maximum velocity is the velocity of the normal shock wave of the explosion. I cannot figure out what you are talking about in your simulations except that it has nothing to do with internal ballistics. That is why I believe that 99% of engineering is just repeating what you have heard and following like sheep. There is no thinking involved, just making it up irrespective and regardless of the facts. Why does the barrel have to be straight? Have you read any of the work being proposed for electro-magnetic rail guns? Isn’t a rocket in a pipe the same as a rail gun except for the method of propulsion? (one chemical and the other electrical?) If you can do 25 meters of pipe why can’t you do 25 thousand meters?
    In the early 60’s, Babcock and Wilcox Company (today is called McDermott, incorporated in Panama, another very sad story) was granted a patent on a hydrogen gun. Their scheme was a large spherical container with a few thousand feet of pipe sticking out the top with a large steam generating boiler attached. The system used hydrogen gas under pressure as the working fluid and compressed it with the steam to expel the projectile, like squeezing a toothpaste tube. Since the speed of sound in the hydrogen is so much faster than in combustion gas (or for that matter steam) and they were heating it with the superheated steam to 1,500 F, they were able to hypothesize muzzle velocities in the 6,000 ft /sec range, never exceeding 700 psi in the barrel. Even though this is way short of orbital velocity, it was definitely in the hunt with the intercontinental ballistic missiles of the period. Of course, Bull did away with all these constraints by putting the rocket in a pipe. The rocket in a pipe allows you to control the pressure accelerating the projectile without in any way being limited by the speed of sound and not being bound by the temperature or velocity of the combustion gas. His hybrid design eliminated the huge accelerations of conventional artillery along with the terrible inefficiencies of specific impulse in rocket design. The design possibilities are endless. A high specific impulse would no longer be required, because we are pushing the projectile with a cushion of gas, a lower specific impulse would be beneficial (higher molecular weight gas). How about putting a jet engine in the pipe? Sucking and blowing at the same time. That would solve some of the hypersonic shock wave problems inside the barrel as the projectile velocity goes hypersonic. Do you think a 10-mile pipe or for that matter a hundred-mile pipe to be technically impossible for a country that welded a thousand miles of pipe in Alaska 30 years ago?
    I had always envisioned Dr. Bull building his cannon in the mountains of Guatemala or Columbia or for that matter the desert of Iraq with native laborers, carrying baskets of rubble on their heads (much like the Chinese built the Three Gorges Dam) from chicken wire and mud bricks, in that it only has to support a few hundred psi not tens of thousands and that the hypersonic shock wave produced by a million pound payload streaking skyward at 10,000+ ft/sec would make even the B&W hydrogen gun flare look like a candle. But thinking about your ‘mud gun’ I would ask, "Is it technically impossible to construct a pipe under water from Cape Canaveral east out into the Atlantic so that the discharge is 30 miles from shore?"
    Be that as it may, I am not a black helicopter guy, but to believe Bull was murdered because he was selling Saddam Hussein worthless (mathematically and scientifically indefensible) technology, as you argue, is a little hard to believe. But what isn’t hard to believe is that the United States government has actively and viscously suppressed internal ballistic science for the last 40 years to make space flight as expensive as possible for the same reason it doesn’t fund nuclear fuel processing science or allow, by law, experimentation in the field. Why are we enriching uranium 235 in exactly the same way we did for the first nuclear bombs 60 years ago? Is it because we are stupid? Do we swim in an ocean of nuclear waste instead of reprocessing because we are fools? Have we chosen to fight for oil and burn coal for the last 35 years (releasing 50 times the radioactivity into the atmosphere per KWH generated; than mining, refining, and using uranium even including the releases at Chernobyl and TMI) instead of building nuclear reactors because we are blind ignorant barbarians? Do you believe we cannot design and build efficient heavy lift vehicles because we are superstitious savages little better than monkeys? I do, absolutely and without a doubt. Three generations of rocket scientists and trillions of R&D dollars and is this the best we can do? <> I believe it is, I think we are lucky to get this far.