[ExI] Skylon as first stage.

[Keith Henson]

Skylon can boost a 30 ton payload to 157 km and 6966 m/s. see page 10 of

http://www.reactionengines.co.uk/downloads/SKYLON_User_%20Manual_rev1%5B3%5D.pdf

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.

http://www.reactionengines.co.uk/downloads/ssp_skylon_ver2.pdf

^^^^^^^^^^^^^^

 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.