Saturday, May 27, 2006


Listening to NPR yesterday, I heard a guy from the New Orleans Aquarium describing the mess they found after Katrina. The equipment there had stopped working, so the interior temperature had risen into the 90s, most of the tanks had gone anoxic, the fish had died and were rotting in the heat. The tanks were a filthy, smelly, bacteria-laden mess.

The alligators, however, loved it. Somehow, perhaps because I'm the owner of two Labrador retrievers who will eat anything, my heart warms to the thought of unadulterated joy in the midst of what would turn a human stomach.

Monday, May 08, 2006

Renewables vs Nuclear

There is a great discussion over at EnergyPulse. The article suggests renewables can replace nuclear. A number of good comments that follow show the claim to be wrongheaded, but perhaps not entirely wrong.

The claim that renewables (primarily windpower) can replace nuclear is not entirely off base. We are building windpower right now faster than we are building nuclear, and the EIA predicts this will continue to be true for 30 years, even with the new subsidies. The existing U.S. nuclear plant fleet is huge, however, and renewables are not forecast to challenge the capacity of the existing nuclear base.

I think the debate between renewables and nuclear is pointless. Both are domestic supplies. I think the more interesting comparison is between domestic and foreign energy supplies, and what we can do to move to more domestic energy. Secondarily, I think there is an interesting comparison between the amounts of CO2 produced by various energy supplies.

We use oil and gas-fired turbines and hydro to follow variations in electricity demand. Our dependence on foreign oil and gas supplies is a major threat to our national security. In the U.S., hydro is all built out. I see two strategies that will help move the U.S. from foreign energy sources to domestic sources. Both could use some legislation.

  • Dynamic pricing. If the price of electricity varies minute-by- minute, many customers can time-shift their loads. This reduces variations in electrical demand and allows domestic sources (coal, nuclear, renewables) to replace foreign sources (oil, gas). Examples are ice-storing commercial cooling plants and aluminum smelters.

  • Plug-in hybrids. These gasoline and battery powered cars can charge up at night. They actually help twice: they directly shift their energy source from a foreign one (crude oil) to a domestic one (coal, nuclear, renewables). But also, the extra demand at night makes it economic to build more domestic-source generation instead of foreign-source generation.

  • As for the CO2 problem, natural gas was once sold as a cleaner, greener substitute for coal. The cost in blood and money is now clear. We should use all the windpower we can get, and conservation can help too. But I think the big answer here is hundreds of gigawatts of new nuclear generation over the next 30 years.

    I foresee the costs of coal going up in the future, from the additional costs of CO2 sequestration. I foresee the costs of nuclear coming down in the future, if many similar plants are built and regulation and operation become more standardized. So I see a second benefit to a massive nuclear buildout: a drop in the price of energy here in the U.S. I think that drop, along with a change to domestic energy supplies, could make a big difference to our balance of trade and national security.

    Tuesday, May 02, 2006

    Three Stage to Orbit

    I'm going to try to convince you [hi Jon!] that a three stage to orbit rocket might be significantly cheaper than a two stage to orbit system lifting the same size payload. My argument centers on the idea that the engines are the expensive portion of the rocket, and that tanks and structure are cheap.

    To get into a 200 km orbit, a two stage rocket generally has a first stage which burns for about 150 seconds, followed by a second stage which burns for around 500 seconds. Second stage engines deliver much more impulse per dollar, primarily because the engine burns so much longer, and also because the engine has a larger expansion ratio and so a higher specific impulse.

    The second stage burn time cannot be extended greatly beyond 500 seconds when going to low earth orbit, because the initial acceleration becomes so low that the stage falls back to earth before it achieves orbital velocity. Similarly, the first stage burn time cannot be pushed much past 150 seconds (assuming LOX/kerosene, for which the Isp is around 300 seconds) because the rocket must start with significantly more than 1 G of acceleration to get off the ground. This is easy to see: if initial acceleration is exactly 1 G, and the vehicle was all fuel and no structure, then the burn time would be exactly the Isp.

    The point of a three stage rocket is to significantly extend the first LOX/kerosene stage burn time, and improve the expansion ratio, with the use of an earlier and much cheaper stage. To yield a cost improvement, the entire new stage must cost less than the first stage engines it is replacing. Also, the development cost of the new stage must be low.

    Typically, strap-on solid rocket motors are used as cheap extra launch thrust on American or European launchers. LOX/Kerosene launchers, such as the SpaceX Falcon series and many of the Russian launchers, are so cheap that such solid rockets and their handling and cleanup are too expensive to help. I suspect that steam rockets (such as the rocket that hurled Evil Kneivel's "motorcycle" over the Snake River Canyon) may be cheap enough. Unfortunately, steam rockets have such low specific impulse (about 50 seconds) that any benefit must come from just a few hundred m/s of delta-V (realistically, around 300 m/s). The rest of this post will show that there is a very large benefit to having just a few hundred m/s of initial boost.

    One way to measure the benefit of the extra stage zero is to compare the payload of a similarly priced rockets, one with and without the extra stage. Ideally, the rockets would be seperately optimized, but that makes cost comparisons looser. Instead, we will imagine that they have the same engines and differ in smaller details like expansion ratio and tank size. The baseline rocket I have chosen is the SpaceX Falcon 1, which is promised to take 570 kg to a 200km orbit for $6.7M. My simulations show SpaceX has a significant sandbag in there, and that the rocket might deliver 670 kg at the edge of its performance envelope, and it is this larger number that I compare against when calculating the benefit of extra boost.

    The first comparison is between a series of identical Falcons, some with a stage zero delivering various burnout velocities, and one without. As shown, a 300 m/s boost allows the three-stage rocket to lift 41% more payload.

    Falcon 1 with various starting boost


    Because a three stage Falcon does not require it's LOX/kerosene engines to lift it off the ground, the engines can be configured for larger expansion and higher vacuum Isp (and thus lower sea-level Isp). Elon Musk at SpaceX has claimed that a vacuum-optimized Merlin would deliver 340 seconds Isp. In the table below, I've assumed 330 seconds, and a drop in sea-level Isp to 190. Now the three-stage 300 m/s boost lifts 61% more mass to orbit. This change carries the reliability penalty that the engines may have to be started in flight to avoid thrust instability due exit pressure being much less than sea level pressure. Note that a Falcon with no stage zero boost cannot get off the ground with higher expansion engines.

    Falcon 1 with various starting boost, Isp=330 s


    The full gain of the stage zero is realized by extending the burn time of the first LOX/kerosene stage by extending the tanks. Here I've assumed that the extra tankage and pressurant and so on weighs 4.3% of the extra propellant added. With extended tanks, the three stage 300 m/s boost lifts 138% more mass to orbit.

    Falcon 1 with various starting boost, Isp=330 s, extra propellant

    LEOextra stage 1

    You might wonder if these massive payload increases require the use of a bigger and more powerful upper stage. The answer is no, even hefting a 1595 kg payload, the existing falcon upper stage delta-V drops from 4973 to 3454 m/s. I did not look at moving propellant from the lower stage to the upper stage, which might improve the payload numbers a bit more.

    138% is a large payload increase, but we have to compare this to the cost of simply scaling up an existing rocket. Fortunately, SpaceX has done some of this work for us. Interpolating between their prices, the 138% payload boost might be sold for $1.8M more.

    Which leaves the question, can a suitable steam rocket be built to heave the Falcon 1 to 300 m/s straight up for less than $1.8M per shot, and minimal development costs?

    Here's what you'd need:
  • Mass Fraction = 80% (Shuttle SRB mass fraction is 85%, it holds 60 atmospheres pressure)
  • Mass, fuelled = 62992 kg
  • Mass, empty = 12600 kg
  • Volume = 100 m^3
  • Size = 3.6 m diameter x 10 m long

  • A 12600 kg welded stainless steel tank might cost $250,000, but can probably be recovered and reused with minimal work. I'm going to claim the expensive bit isn't the flight hardware, but rather the ground support, and I'll get to that in another post.