# [ExI] Spacecraft (was MM)

Keith Henson hkeithhenson at gmail.com
Fri Dec 31 17:48:42 UTC 2010

```On Fri, Dec 31, 2010 at 12:32 AM,  Samantha Atkins <sjatkins at mac.com> wrote:

> On Dec 30, 2010, at 3:18 PM, Keith Henson wrote:
>>
>> And 20 years ago, that was the right conclusion.  Now we have a path,
>> even if it kind of expensive, to 9+km/sec exhaust velocity.  That
>> means mass ratio 3 rockets to LEO and even better LEO to GEO.
>
> I must have missed it.  Please give details, links, etc.  How expensive?  How large a payload? What technologies?

Context is SBSP, 200 GW of new power per year, one million tons of
parts going up per year.  That's about 125 tons per hour delivered to
GEO.

The SSTO vehicle is an evolution of the Skylon design
http://www.astronautix.com/lvs/skylon.htm swapping lox for payload and
a sapphire window between the engines with 10-20 bar hydrogen and a
deep channel heat absorber behind it.  The flow of cold hydrogen keeps
the window and the front surface of the heat absorber cool.  The
absorber is described here:
http://www.freepatentsonline.com/4033118.pdf

One part is fixed by physics and the Earth's gravity field.  The
minimum horizontal boost acceleration after getting out of the
atmosphere with substantial vertical velocity has to be slightly more
than a g to achieve orbit before running into the atmosphere.  You
want to use the minimum acceleration you can at the highest exhaust
velocity you have energy for.  This keeps down the laser power, which
is huge anyway.

This takes 15-20 minutes and only in the last third do you get up to
the full 3000 deg K and 9.8 km/sec.  The average (for this size
vehicle and 6 GW) is 8.5 km/sec, but the first 2 km/sec in air
breathing mode has an equivalent exhaust velocity of 10.5 km/sec.  So
about 1/3 of takeoff mass (300 tons) gets to orbit.  The vehicle mass
is about 50 tons leaving 50 tons for the LEO to GEO stage.

So the payload at GEO per load needs to be 1/4 to 1/3 of 125 tons.
Again using laser heated hydrogen 35 tons of a 50 ton second stage
will get there.  With some care in the design, it can all be used for
power satellite construction.

The long acceleration means the lasers must track the vehicle over a
substantial fraction of the circumference of the earth.  Based on
Jordin Kare's work, this takes a flotilla of mirrors in GEO.  Current
space technology is good enough to keep the pointing error down to .7
meters at that distance while tracking the vehicle.  The lasers don't
need to be on the equator so they can be placed where there is grid
power.  They need to be 30-40 deg to the east of the lunch point.

There are (I think) only four locations where there is an equatorial
launch site with thousands of km of water to the east.  The US has one
set, China has a better one.

The lasers are the big ticket item.  At \$10/watt, \$60 B.  The rest,
vehicles, mirrors, ground infrastructure, R&D, etc might bring it up
to \$100 B--which is a fraction of the expected profits per year from
selling that many power satellites.

I don't expect it to be done by the US.  China, maybe.

Keith

```