# [ExI] Skylon as first stage.

Keith Henson hkeithhenson at gmail.com
Wed Apr 20 14:52:39 UTC 2011

```I had two people who asked for the path into space graph and the
spread sheet to check my "rocket science" math and one who complained
in private email that the Skylon/laser/power sat posting I made
recently was incomprehensible.

So here is another shot at it:

It's been known for decades that solar power satellites *can* send
energy to the earth.  After all, communication satellites do it every
day, just not at levels useful for power.

The question is cost, and that's almost all due to the high cost of
rockets to get millions of tons of power satellite parts to GEO.

If you want to sell power on earth in serious competition with coal,
the economics indicates you need to reduce the cost of getting parts
to GEO by a factor of around 200.  That's \$20,000 per kg down to
\$100/kg.

Unfortunately, the chemical energy in rocket fuel vs. the physics
energy it takes to get to orbit just won't do it.  Round numbers, the
Falcon Heavy will put 50 tons in LEO or 25 tons in GEO for a cost of
\$100 M.  That's a reduction to \$4000/kg, a factor 5 but not enough.
Launching one every hour might get the price down to \$1000/kg which is
still too high by five times.

Skylon, the proposed rocket plane from Reaction Engines, at several
flights per hour is expected to put 10 tons in LEO and 5 tons in GEO
for a cost of \$1.5 M or \$300/kg.  *Still* too high.

A brand new concept starts with the sub orbital maximum load of 30
tons for a Skylon then uses 400 MW of laser power to get 10km/s
exhaust velocity from a second stage.  This will get 20 tons to GEO
per flight.  The estimated capital cost of the lasers (\$4 B or \$400
M/year) is under \$2/kg.  Spread over 480,000 tons per year it drives
the lift cost for parts down to \$100/kg.

If we can get the lift cost down that far, a power satellite comes in
at \$1600/kW or \$1.6 B/GW.  At that capital cost, energy from space
could sell for substantially less than energy from coal.

The development could come in as low as \$20 B, maybe less.  The profit
after this was going is up in the hundred billion a year class rapidly
growing into the trillions--enough to cope with social security and
the other cost of government.

Not that the US is likely to do it, but whoever does it will put a cap
on energy cost

Keith

On Fri, Apr 15, 2011 at 10:59 PM, Keith Henson <hkeithhenson at gmail.com> wrote:
> Skylon can boost a 30 ton payload to 157 km and 6966 m/s. see page 10 of
>
>
> That's well short of LEO and 3286 m/s short of GTO.  However, any
> acceleration over 2 m/s^2 has enough time to put the second stage
> payload in orbit.  (It falls slowly because the local g at this
> velocity is around 2 m/s^2)
>
> There are limits on how long you can accelerate with a laser because
> you have to keep the vehicle in view of the bounce mirror.
>
> GTO velocity is around 10252 m/s  To circularize the orbit at GEO
> would take 1630 .m/s more or a total delta V of 11, 682 m/s.
> Together, 4916 m/s which is about half the exhaust velocity leading to
> a mass ratio of ~1.7   Either constant acceleration or constant heater
> temperature are options.  Constant heater temperature gets the higher
> ISP. Both accelerations can't take more than 20 minutes together to
> get a transfer rate of 3 flights per hour.
>
> It turns out (from a spread sheet I ran off) that 400 MW and a flow of
> 8.33 kg/s of hydrogen results in a constant heater temperature of 3000
> deg K and an initial acceleration of 2.721 m/s^2.
>
> The vehicle enters GTO downrange 7743 km at 970 seconds with 21,900 kg
> of mass remaining.  Because thrust is constant as mass is used up
> acceleration goes up to 3.727 m/s^2.
>
> It takes until1206 seconds to reach GTO insertion, i.e., a second burn
> 5 or 15 hours later of 236 seconds.  For a first pass this is close
> enough to 20 minutes.
>
> The peak acceleration at the end of circularizing at GEO is just over
> 4 m/s^2 (all really low accelerations).  There is almost 20,000 kg
> (19937 kg) left.  I.e., 20 tons gets to GEO per Skylon flight.  The
> assumption is that everything going to GEO gets turned into power
> satellites.  (Even the sandwich wrappers for 500-1000 workers at GEO)
>
> Conventional use of Skylon will deliver about 6 tons per flight to
> GEO.  For a 3 per hour flight rate, that's 18 tons per hour.  By
> adding \$4 B of lasers (and the GEO bounce mirrors) laser boosting a
> suborbital payload will put 60 tons per hr in GEO, slightly in excess
> of 3X.
>
> Operated 90% of the time, that would be 8000h x60 t/h or 480,000 t per
> year.  That would support a substantial power satellite production, at
> 5 kg/kW, 5000 t/GW, 96 per year.  At a rock bottom price of \$1.6 B/GW
> (2 cents per kWh paid off over ten years) the revenue stream would be
> over \$150 B.
>
> ^^^^^^^^^^^^^^^^
> To put these numbers in context, for the SKYLON case where all costs
> are being recovered, the cost of launching 150,000 tonnes into orbit
> at \$200/kg is \$30,000 million per year.
>
> This compares with a cost of about \$3 trillion per year (\$3,000,000
> million) if expendable launch vehicles were to be used (although this
> flight rate is unachievable with expendable rockets).
>
> This clearly illustrates the point that a reusable spaceplane system
> is an essential, enabling part of implementing a solar power satellite
> infrastructure.
>
>
> ^^^^^^^^^^^^^^
>
>  I have assumed 5000 t per GW, the Skylon analysis assumed 3000.
>
> To put the addition of laser powered rockets in context, the same
> flight rate would allow over three times as much cargo to GEO for the
> same cost in Skylon launches.  The cost to *GEO* would come down to
> under \$100/kg, which is the magic number for two cent per kWh power,
> i.e., half the price of coal.
>
> So at least from the physics of rockets and the economics of power
> satellites, it seems to be possible to have a world with plenty of low
> cost energy.
>
> This is by no means a fully worked out proposal.  For example, I don't
> know exactly how to get the Skylons back to their launch site.
>
> But it is possible (with some more work) that the entire project to
> profitability might come in around \$20 B.  If that's the case, it's
> less than the Chunnel or Three Gorges Dam in current dollars.
>
> Keith
>
> PS.  If there is anyone besides Spike who can grok physics and spread
> sheets, be happy to send you a copy.
>

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