NASA SP-413 Space Settlements - Saint Ann's School

NASA SP-413 — SPACE SETTLEMENTS — A Design Study
109
Track Alignment
Three methods of track alignment might be considered.
1. Optical reticles viewed with a telescope. If the
instrument is diffraction-limited at 1-m aperture,
resolution is 10 -6 rad, or 10 -3 m at a distance of 1 km.
By elevating reticles to account for lunar surface
curvature the track may be initially aligned along the
lunar surface.
2. Accelerometry. A bucket may be instrumented with
recording accelerometers and made to traverse the track
by coasting at high velocity, for example, 10 3 m/s,
without acceleration. Track misalignments thus show
up with high resolution.
3. Zone-plate alignment. This is the system used in the
LINAC at the Stanford Linear Accelerator. Fresnel
zone plates are used to focus a laser beam to a point;
photodetectors locate the point and scan across it. The
derivative of the luminous intensity across the point is
found automatically and used to define reproducibly the
center of the point, to an accuracy of 25 m.
Launch Sequence
The launch sequence as a bucket proceeds along the track
might be described as follows:
1. Coarse acceleration — 10 km at 288 m/s 2 . The track
may be coarse-aligned since larger oscillations are
permitted than are tolerable prior to release. The
velocity is measured along the track in real time using
laser doppler; an integration time of 5 X 10 -5 s gives
velocity accurate to 2 X 10 -2 m/s. In this time the
velocity change due to acceleration is 1.5 X 10 -2 m/s so
that velocity at cutoff of the acceleration may be made
accurate to better than 3 X 10 -2 m/s.
2. Fine acceleration — 1 km at 1 m/s 2 . The track must be
fine-aligned. Laser doppler integration time is 10 -3 s;
accuracy is 10 -3 m/s; velocity change in this time is 10 -3
m/s. The velocity cutoff is accurate to approximately
this value, biased slightly above the desired velocity.
Figure 5-28 — Admissible misalignment to cause velocity error
of 10 -3 m/s.
3. Drift — 1 km with deceleration due to electromagnetic
drag, which may be below 10 -2 m/s 2 . The track is again
fine-aligned. Laser doppler integration time is 10 -2 s;
accuracy is 10 -4 m/s; velocity change in this time is
below 10 -4 m/s. A tradeoff exists between errors in
launch velocity and errors in launch location; the launch
is the event of payload release. This release occurs at a
location calculated on the basis of the tradeoff, using the
measured velocity.
4. Deceleration of bucket and return to loading zone. The
deceleration may involve regenerative braking, to
recapture (at least in part) the energy input into the
bucket.
Payload Restraint System
The payload may be of sintered lunar material, resembling a
cinder block. This block is rigidly held in place by
trapezoidal restraints fitted to the sides of the block. These
restraints are pin-secured and spring-loaded; pulling the pins
causes the restraints to spring back. A final restraint,
however, continues to press down on the block from above;
this restraint may function as a mechanical “finger.” This
holds the block down during the fine acceleration and drift
phases.
The track may be contoured to the lunar curvature, so that
the block feels an upward acceleration, at escape velocity, of
one lunar gravity (1.5 m/s 2 ). Thus, when the restraint is
rapidly pulled away, the block drifts free. There is a spring
effect due to the block having been compressed slightly by
the restraint, with strain energy being stored in the block and
converted to kinetic energy upon release. This effect leads to
velocity errors at release of less than 10 -5 m/s.
Track
The track cross section is shown in figure 5-27. This
geometry was selected purely because it is convenient for a
typical bucket; it is a conservative design in that a section of
equal mass can be given greater stiffness. The section is of
aluminum: density = 2.7 g/cm 3 , modulus of elasticity E =
7 X 10 11 dynes/cm 2 , and moment of inertia I = 40,350 t cm 4
for t = thickness in cm.
The track is laid on supports in such a manner that the sag
under its own weight, between the supports, is under 10 -2
cm. At the supports, optical measurement equipment
together with screw jacks permit accurate alignment of a
straight track. The sag is given by the formula for sag (y s ) of
a uniformly-loaded beam with ends clamped or built-in, a
condition which is met by the beam being horizontal at the
supports. This formula is
ys = WL 4 /(384 EI)
where L = distance between supports, W = weight per unit
length = (540 t g/cm) X (150 cm/s 2 ) = 0.81 N/m of length.
Then, with L= 10 3 cm = 10 m, y s = 7.5 X 10 -3 cm. This is
well within the misalignment permitted by figure 5-28.
Chapter 5 — A Tour Of The Colony