Ascender: Airship to Orbit?

Allen Meece wrote:

Here is how JPA describes their "third stage" Orbital Ascender:
The third part of the architecture is an airship/dynamic vehicle that flies
directly to orbit. In order to utilize the few
molecules of gas at extreme altitudes, this craft is big. The initial test
vehicle is 6,000 feet (over a mile) long. The
airship uses buoyancy to climb to 200,000 feet. From there it uses electric
propulsion to slowly accelerate. As it
accelerates it dynamically climbs. Over several days it reaches orbital
velocity.
Lift here is not aerodynamic lift but is rather, positive buoyancy. So it
makes the L/D ratio irrelevant. The ship is weightless at 200K feet and needs
little aerodynamic lift. As the velocity increases, so does centripetal force,
helping to "lift" the craft.


To the best of my knowledge the record altitude of
stratospheric balloon is 52 kilometers, which is only
170,603 feet. If you add solar panels and cargo,
you cannot fly much higher than 40 km.

Density of dry air equals 1.3 kg/m^3 at sea level.
At higher altitudes it drops approximately 10 times
for every 20 km of altitude gain. At 40 km
altitude the air density is about 0.01 kg/m^3.

Let us assume that the balloon is a sphere having
diameter of 100 meters, and its velocity is 100 m/s.
Aerodynamic drag of the balloon in fast, turbulent
flight equals:

F = Cd * D * V^2 * A / 2
Cd = 0.5 (coefficient of drag of a smooth sphere)
D = 0.01 kg/m^3 (air density at 40 km)
V = velocity of the balloon
A = PI * d^2 / 4 = 7854 m^2 (cross section area of
the ball shaped balloon, d = balloon diameter)

F = 0.5 * 0.01 * 100^2 * 7854 / 2 = 392700 newtons!

392700 newtons is the gravitational pull of an
object that has the mass of 40 tons. 40 tons
equals 88,358 pounds.

You can reduce the coefficient of drag several
times by making a more slender, streamlined
balloon. Let us assume that the drag equals
only 10 tons. The minimum power required to
pull the balloon at 100 m/s equals:
P = 100,000 N * 100 m/s = 10 megawatts

Solar cell weight is about 40 kg per one kilowatt
of power output. If we assume that the total
weight-to-power ratio of the propulsion (solar
cells, electric motor, and propeller) is 100 kg/kW,
the propulsion weight is 1000 tons, which is two
orders of magnitude more than the buoyancy of
the balloon. Anyone who claims that the balloon
can fly at orbital velocity (8 km/s) does not
understand aerodynamics.

__________________________________________________


You can determine the air density more precisely
using the following formula for atmospheric pressu

p = B(exp(-MgY/RT)), Whe

p = pressure at elevation Y
B = pressure at elevation zero
exp = natural exponent
M = molecular mass, or mass in kg per mol
(M = 0.0288 kg/mol for dry air)
g = acceleration due to gravity = 9.8 m/s^2
R = gas constant = 8.314 J/(mol*K)
T = absolute temperature (in Kelvins) = 273 K

Atmospheric density is proportional to its
pressure and inversely proportional to its
absolute temperature.

Andrew Nowicki wrote:

Solar cell weight is about 40 kg per one kilowatt
of power output.

Please note that there us nothing fundamental about this figure.

Direct bandgap semiconductor materials can absorb light with
a thickness of perhaps 100 nanometers (the absorption length
of ordinary crystalline silicon is much longer.)

If the density of the material is 2 g/cm^3, and the efficiency
15%, and the mass/area of the plastic, etc. onto which the PV material
is deposited is similar, then the power density in raw sunlight
is about 500 kW/kg.

This concept is already assuming the use of large, very light
inflatable structures with significant structural strength;
also assuming that those structures are thin film PV collectors
isn't much more of a stretch.

Paul