[AR] Re: fault tolerance (was Re: thinking big once more)
- From: Jim Davis <jimdavis2@xxxxxxxxxxxxx>
- To: arocket@xxxxxxxxxxxxx
- Date: Thu, 20 Oct 2016 19:25:41 -0500
On 10/19/2016 10:59 PM, Henry Spencer wrote:
It would be good if you'd explain why you think the *physics* doesn't
permit this.
I'll take a stab at it.
The specific energy (kinetic and potential) of a unit mass in a circular
orbit is given by:
eo = g0 * R * (1 - R / (2 * r))
where
eo - specific energy of object in circular orbit
g0 - acceleration of gravity at surface of earth
R - radius of surface of earth
r - radius of circular orbit
The minimum energy required for a unit mass to travel a distance is
given by:
ed = g0 * s / (L/D)
where
ed - minimum energy to overcome aerodynamic drag
s - distance to be traveled
L/D - lift to drag ratio
For an object in a 160 km circular orbit (LEO) the specific energy is:
eo = 32.0 MJ
For an object traveling 14,000 km (the range of the longest commercial
service) at an L/D of 15 (conservative) the specific energy is:
ed = 9.2 MJ
The ratio is
eo/ed = 3.5
That's the basic physics. When one proceeds to engineering the ratio
remains about the same, between 3 and 4, depending on the exact details.
The actual energy required is much greater in both cases, of course.
This ratio explains why it is necessary to use heroic measures (staging,
expendable hardware, thin margins, etc) to place anything in LEO or
beyond. Placing things in orbit is a much greater engineering challenge
than even the longest commercial flights.
This is why fault tolerance is more challenging in the case of a launch
vehicle when compared to aircraft.
It's a matter of physics.
Jim Davis
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