NIAC PHASE II FINAL REPORT Mach Effects for In-Space Propulsion: Interstellar Mission Date of Report: August 20, 2020 Period under review: April 2018 – August 2020 Grant (18-18NIACPro2-0003) Space Studies Institute Principal Investigator: James F. Woodward Institutional-PI: H. Fearn, Physics Department, California State University Fullerton SSI Program Manager: Gary C. Hudson Co-PIs: José Rodal, Paul March, Marshall Eubanks & Jonathan Woodland Additional scientific associations with: Daniel Kennefick, Michelle Broyles, Chip Akins and John Brandenburg FINAL REPORT – NIAC PHASE II Mach Effects for In-Space Propulsion: Interstellar Mission Table of Contents 1. Executive Summary (HF) - 2 2. Introduction (JWF) - 3 3. Calibration of balance, force and displacement - 17 4. Balance beam dynamics - 30 5. Doming of the brass and aluminum masses - 40 6. Use of glued stacks and design #1 sledge - 49 7. Design #1 sledge - 61 8. Use of glued 0.618 inch brass stack- testing vibration transmitted to Faraday cage - 69 9. Use of glued 0.618 inch brass stack with 0.18 inch aluminum L bracket and different material washers - 92 10. New sledge design #2 and use of wire springs - 111 11. Moving mass perpendicular to beam arm and re-zeroing effect on the balance - 121 12. Summary and Conclusions - 127 Addendum 13. Report from José Rodal 14. Report from Paul March 15. Report from Michelle Broyles 16. Report from Chip Akins At the beginning for the Phase 2 grant period, we employed devices made of Steiner Martins SM-111 material, (lead zirconium titanate) PZT, eight discs 2mm thick glued together with a brass mass and an aluminum mass, using rubber pads between the brass and the static L mount bracket. These devices produced on the order of 1µN of force. These early devices are discussed in the introduction, Section 2. The balance beam and its dynamics are treated in Sections 3 and 4. We found doming the brass and aluminum ballast masses prevented the PZT stacks from cracking around the edges, and determined the optimum dome height, see Section 5. We decided that to reduce high frequency vibration transmitted to the Faraday cage and hence the balance arm, a sledge arrangement might be superior to the static L bracket. See Figure 1.1. We then performed a number of tests to determine which design was better for force generation, the L bracket or new sledge, see Sections 6 & 7. Also, how much vibration was transmitted to the Faraday cage, see Section 8. We also tried different materials for the washers (instead of the rubber pad) with the static L bracket and sledge configuration, see Section 9, and different numbers of washers. At this stage we were seeing forces of order 10’s of microNewtons. Stacks glued to the masses seemed to work well and improved the force. Then came the second sledge design, see Figure 1.2, rather late – only a couple of months before the end of Phase 2. We are still in the process of testing this arrangement but have made several improvements. With this free-free motion of the device, a true in-space configuration, we are regularly seeing 100 µN or so. See Section 10. We address center of mass (CoM) shifts in Section 11. We may not yet have a space-ready device, but we are close to one. The goal of the activities funded by both NIAC phase 1 and 2 grants is captured in the title. The goal is demonstration of a propulsion system that, when scaled, is capable of supporting missions to the stars with travel times that are some reasonable fraction of a human lifetime. We have not yet produced devices that can be used as propulsors of a starship. We have, however, produced demonstration devices, suitable for deployment in space if desired, that will show the proof-of-concept beyond any doubt by perceptibly changing the motion of the vehicle carrying it. As detailed below, significant progress toward that goal has been made in the past year, and our goal of a flight ready system in a few years remains achievable. Mach Effects And How They Are Generated Mach effects are fluctuations in the rest masses of objects being “properly” accelerated while their internal energies are changing. (Proper accelerations are ones that involve changing motion with respect to local inertial frames, and consequently, the production of inertial forces. Accelerations that appear as the result of observer acceleration are not proper accelerations.) These conditions are producible in stacks of lead zirconium titanate (PZT) crystals by applying ultrasound frequency, alternating electrical voltages to electrodes embedded in the stacks. Normally, these stacks are run at an auspicious electrical resonance of the power circuit where the base frequency of the driving signal produces the expected mass fluctuations, and the second harmonic (double frequency) of the driving signal is excited and has the correct phase with respect to the base signal to “rectify” the force that the second harmonic signal produces acting on the mass fluctuations that also take place at the second harmonic frequency. Collaborations and Summary of Grant Activities Over the course of the grant, collaborative and replicatory efforts were pursued with TU Dresden, Mike McDonald at NRL, and George Hathaway of Hathaway Research. Detailed investigations were conducted to address critical questions regarding vibration artifacts, balance calibration, the impact of transformers, and the theoretical foundation of inertial induction in General Relativity. Activities of Grant Team Members and Consultants spanned five main categories: Mission Architecture (Hudson, Eubanks), Improvement of Existing Thrusters (Woodland, Fearn, Woodward, Rodal), Modeling (Rodal, Fearn, Brandenburg), Power and Electronics (March, Akins, Jenkins), and Theory (Fearn, Kennefick, Rodal, Woodward, Inan). The Fullerton force balance is a torsional pendulum calibrated using known electromagnetic forces between coil sets. Distance from the central pivot to the calibration coils is r1 = 15 cm and to the test device inside the Faraday cage is r2 = 24 cm. Because torque about the pivot must match (r1 * Fcoil = r2 * Fdevice), device force is calculated as Fdevice = (r1 / r2) * Fcoil = Fcoil / 1.6. Using Maxwell's elliptic integral formulation and calibrated optical displacement sensors (Philtec D63), the balance sensitivity was refined. Earlier measurements had used 162 mV/µN, which proved to be an overestimate by a factor of approximately 3.8 to 4 (actual conversion corresponds to ~618 mV/µN for the device). Additional optical calibration yielded a probe scaling factor of 0.75 V/µm before additional low-pass filtering and amplification. The dynamics of the balance arm supported by frictionless C-Flex flexural bearings (model E-10) are governed by the equation of a forced damped harmonic oscillator: F(t) L = I θ'' + C θ' + k θ where I is moment of inertia (~0.04824 kg·m² for the full arm assembly), C is damping constant (0.0667), k is torsional spring constant (0.0529 N·m/rad), and the characteristic natural oscillation period is approximately 6 seconds with a damping coefficient γ = 0.66. To eliminate sharp contact stress singularities and edge cracking on the PZT stacks, shallow domed profiles were machined onto the brass and aluminum end caps. Dome heights of 0.0004", 0.0005", 0.0006", and 0.0008" were evaluated using Fuji Prescale film and operational sweep runs. The optimum dome height was determined to be 0.0005 inches, providing uniform pressure distribution across the crystals without edge pinch or excessive center crowning. Experiments compared standard mechanical clamping against stacks epoxy-glued to domed ballast masses and cured at 140°F–160°F. Glued stacks using a 0.618-inch brass mass (76g) and symmetric mounting configurations produced enhanced, highly reproducible force signatures (~10 to 18 µN peak) on both forward and reverse sweep runs. A two-rail sledge mount was developed to decouple high-frequency device vibration from the Faraday cage. Systematic evaluations across various brass mass lengths (0.375" to 0.75") demonstrated that the 0.618" length (76g mass) yielded optimal resonance tuning and peak force generation. Using a Polytec OFV-2500 laser vibrometer, vibration transmission to the Faraday cage was measured. While solid L-brackets transmitted measurable vibrations in the 1–15 kHz range, the sledge mounting system effectively isolated high-frequency operating vibrations (~30–45 kHz) down to background building noise levels (~30 Hz, ~0.2 µm displacement), proving that measured forces are not vibrational artifacts. Various mounting washer materials were evaluated under vacuum: Phenolic, E-glass reinforced epoxy, Vespel (polyimide), Carbon-reinforced PEEK, and rubber inner tubing. High-temperature engineering thermoplastics like Vespel and Carbon-PEEK demonstrated superior durability, minimal viscoelastic flow/mush, low vacuum outgassing, and sustained force outputs (10–15 µN) across repeated thermal cycles. A refined 'free-free' sledge (Design #2) was engineered with 3 linear ball bushings mounted in ears at the device's center-of-mass flange, riding on precision steel guide rods. Curved gold-plated guitar wire springs (0.008" to 0.014" diameter) were used to provide soft, high-Q centering forces. This near-frictionless floating mounting allowed clear observation of ballistic movements and consistent force outputs of 50 to 100+ µN. Tests were conducted to quantify whether physical shifts of the center of mass (CoM) along the sledge slide could cause false positive beam deflections. A 0.5 mm device shift corresponded to a ~6 µN equivalent balance deflection. When high-stiffness springs restricted motion to <0.05 mm (<0.6 µN equivalent artifact), measured thrust signals remained at 50–60 µN, confirming that genuine propellantless force is produced. Over Phase II, MEGA drive force outputs improved from sub-microNewton levels to tens and hundreds of microNewtons. Crucial advancements included domed end masses, epoxy-bonded stacks, thermal-resistant PEEK/Vespel washers, and the linear ball-bearing sledge mounting. Independent replication efforts with external laboratories remain the primary next milestone. Dr. José Rodal details contributions including: analytical models of washer vibration transmissibility and finite rubber strain; calculations supporting the TU Dresden tests; image analysis of transducer Q-factors; non-linear dynamical phase portraits; publication of 'A Machian wave effect in conformal, scalar-tensor gravitational theory' in General Relativity and Gravitation (2019); correction of magnetic coil calibration equations; analytical coupled electroelasticity formulation; and mechanical design of domed interfaces and curved wire suspension springs. Paul March summarizes consulting services from May 2018 to August 2020: providing 22 years of historical Mach effect engineering data, sourcing brass and bronze electrode meshes, advising on laboratory RF amplifiers, tracking software, and circuit impedance matching. Michelle Broyles reviews contributions from June–August 2020: identifying L-bracket tuning-fork harmonic issues, proposing the floating center-of-mass linear slide mount, analyzing bearing stick-slip alleviation via acoustic vibration, introducing guitar wire centering springs, and evaluating video motion magnification. Chip Akins describes the development of the custom METDrive arbitrary waveform generator/power amplifier. The system uses FPGA logic, MCU supervisory firmware, pulse-width modulation (PWM) with a 1 MHz low-pass filter, and real-time terminal voltage/current feedback to drive reactive PZT loads up to 300 VRMS (1 A continuous) across multi-harmonic frequency sweeps.