#### APPENDIX F

THE MASS DRIVER

The baseline lunar material transportation system involves a magnetically levitated vehicle, or "bucket," accelerated by a linear synchronous motor. Acceleration is at 288 m/s^2 along l0 km of track. The bucket is accelerated through use of superconducting magnets at 3T; bucket mass is under 10 kg.

The suspension and control of motion required to implement the launch with a velocity error under 10^-3 m/s are accomplished by a passive control system. The bucket and suspension are shown schematically in figure 5-27.

Figure 5-27 The suspension involves paired magnetic coils, coupled mechanically to the bucket through an attachment which provides elastic suspension and damping by an energy-attenuating block made of a rubber-like material.

Figure 5-28 Figure 5-28 shows the frequency response of this system due to excitation. At 2400 m/s the range of misalignment wavelengths of 24 to 240 m gives the most severe response. Within that wavelength range misalignments cannot exceed 0.01 cm for the induced velocity not to exceed 10^-3 rn/s. At longer and at shorter wavelengths, more severe misalignments can be tolerated; for example, up to 0.1 cm at 2400 m.

Electromagnetic "bumpiness" deserves attention. This occurs with a wavelength of approximately 1 m, that is at 2400 Hz, due to use of discrete segments of accelerating coils on the linear synchronous motor. The maximum acceleration is proportional to the maximum angle of the bucket; if the bucket pitches down by 0.01 rad, the acceleration normal to the track is 3 m/s^2. The resulting velocity normal to the track is of amplitude 1.25 X 10^-3 m/s. A tight suspension, incapable of sustaining large angular deflections in the bucket, reduces the bumpiness-induced oscillations to within desired limits. During a phase of drift, or of electromagnetic acceleration at low levels, the bumpiness may be reduced by orders of magnitude. Track misalignment and distortions, rather than electromagnetic bumpiness, are the major source of residual velocity error.

Track Alignment

Three methods of track alignment might be considered.

1. Optical reticles viewed with a telescope. If the instrument is diffraction-limited at l-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 .

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 2X 10^-2 m/s. In this time the velocity change due to acceleration is l.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.
3. Drift - 1 km with deceleration due to electromagnetic drag, which may be below 10^-2 m/s2. The track is again fine-aligned. Laser doppler integration time is l0^-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.

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 g/cm^3, modulus of elasticity E=7 X 10^1l dynes/cm^2, and momnent of inertia I = 40,350 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 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 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= 103 cm = 10 m, = 7.5 X l0^-3 cm. This is well within the misalignment permitted by figure 5-28.

The bucket has negative weight (since it is travelling at lunar escape velocity) and hence causes the beam to bend upward. The bucket has mass, say, of 30 kg; its weight is approximately 50 N. The resulting maximum static deflection is: for t = 0.5 cm. A design with t = 0.5 cm appears to offer adequate strength and rigidity.

The track mass is 27 kg/m of length. If shipped in lengths of 30m, 1671engths (5000 m) approximately fill an HLLV payload bay, > 30 m long X 8.41 m diameter, allowed mass = 135,000 kg. All allowed mass is used while efficiently filling the available volume.

The free beams oscillate with frequency near 100 Hz and amplitude under < = 3.6X10^-3 cm, so the associated transverse velocity is 3.6 X l0^-3 cm/s. But figure 5-28 shows that this input is attenuated by an order of magnitude in the bucket so that it is well within allowed limits, 0.l cm/s at the bucket.

Mass Driver Throughput

Maximum throughput for a mass driver track, given a payload mass, appears to be constrained by payload spacing and by energy dissipation. Neither of these constraints appears to prevent throughputs greatly in excess of those in the baseline system.

As a linear synchronous motor, the mass driver permits discrete, accurate control of bucket locations. Separation of buckets should be maintainable so long as each is handled by a separate driven section. At two driven sections per bucket, 2 m per driven section, 1 km/s velocity, and 10kg per bucket, maximum throughput would be 2500 kg/s. Since over 80 percent of the track operates at more than 1 km/s, special construction of the remaining 20 percent should add little cost. Possibilities include shorter driven segments to permit closer payload spacing or parallel feeder tracks interleaving payloads onto the main section.

An acceleration of 300 m/s^2 adds 300 J/kg for each meter of track. At 70 percent conversion efficiency, this deposits almost 130 J/(kg m); at the limit of 2500 kg/s this represents a heat load of 3.2 X 10^5 W for each meter of track. This, in turn, would require a radiator along the track some 300 m wide, if at the boiling point of water. Because much of this energy is lost to resistance in the bus and feeder conductors, these could be made of aluminum, thickened to reduce resistance, and made broad to serve as structural elements as well as self-cooling radiators. Such a system would reduce the need for active cooling.

 Curator: Al Globus If you find any errors on this page contact Al Globus.  