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Photonic variable delay devices based on optical birefringence

Optical variable delay devices for providing variable true time delay to multiple optical beams simultaneously. A ladder-structured variable delay device comprises multiple basic building blocks stacked on top of each other resembling a ladder. Each basic building block has two polarization beamsplitters and a polarization rotator array arranged to form a trihedron; Controlling an array element of the polarization rotator array causes a beam passing through the array element either going up to a basic building block above it or reflect back towards a block below it. The beams going higher on the ladder experience longer optical path delay. An index-switched optical variable delay device comprises of many birefringent crystal segments connected with one another, with a polarization rotator array sandwiched between any two adjacent crystal segments. An array element in the polarization rotator array controls the polarization state of a beam passing through the element, causing the beam experience different refractive indices or path delays in the following crystal segment. By independently control each element in each polarization rotator array, variable optical path delays of each beam can be achieved. Finally, an index-switched variable delay device and a ladder-structured variable device are cascaded to form a new device which combines the advantages of the two individual devices. This programmable optic device has the properties of high packing density, low loss, easy fabrication, and virtually infinite bandwidth. The device is inherently two dimensional and has a packing density exceeding 25 lines/cm2. The delay resolution of the device is on the order of a femtosecond (one micron in space) and the total delay exceeds 10 nanosecond. In addition, the delay is reversible so that the same delay device can be used for both antenna transmitting and receiving.

Yao, X. Steve↗

Deep Space Network Antenna Logic Controller

The Antenna Logic Controller (ALC) software controls and monitors the motion control equipment of the 4,000-metric-ton structure of the Deep Space Network 70-meter antenna. This program coordinates the control of 42 hydraulic pumps, while monitoring several interlocks for personnel and equipment safety. Remote operation of the ALC runs via the Antenna Monitor & Control (AMC) computer, which orchestrates the tracking functions of the entire antenna. This software provides a graphical user interface for local control, monitoring, and identification of faults as well as, at a high level, providing for the digital control of the axis brakes so that the servo of the AMC may control the motion of the antenna. Specific functions of the ALC also include routines for startup in cold weather, controlled shutdown for both normal and fault situations, and pump switching on failure. The increased monitoring, the ability to trend key performance characteristics, the improved fault detection and recovery, the centralization of all control at a single panel, and the simplification of the user interface have all reduced the required workforce to run 70-meter antennas. The ALC also increases the antenna availability by reducing the time required to start up the antenna, to diagnose faults, and by providing additional insight into the performance of key parameters that aid in preventive maintenance to avoid key element failure. The ALC User Display (AUD) is a graphical user interface with hierarchical display structure, which provides high-level status information to the operation of the ALC, as well as detailed information for virtually all aspects of the ALC via drill-down displays. The operational status of an item, be it a function or assembly, is shown in the higher-level display. By pressing the item on the display screen, a new screen opens to show more detail of the function/assembly. Navigation tools and the map button allow immediate access to all screens.

Ahlstrom, Harlow↗

NASA Tech Briefs, October 2008

Topics covered include: Control Architecture for Robotic Agent Command and Sensing; Algorithm for Wavefront Sensing Using an Extended Scene; CO2 Sensors Based on Nanocrystalline SnO2 Doped with CuO; Improved Airborne System for Sensing Wildfires; VHF Wide-Band, Dual-Polarization Microstrip-Patch Antenna; Onboard Data Processor for Change-Detection Radar Imaging; Using LDPC Code Constraints to Aid Recovery of Symbol Timing; System for Measuring Flexing of a Large Spaceborne Structure; Integrated Formation Optical Communication and Estimation System; Making Superconducting Welds between Superconducting Wires; Method for Thermal Spraying of Coatings Using Resonant-Pulsed Combustion; Coating Reduces Ice Adhesion; Hybrid Multifoil Aerogel Thermal Insulation; SHINE Virtual Machine Model for In-flight Updates of Critical Mission Software; Mars Image Collection Mosaic Builder; Providing Internet Access to High-Resolution Mars Images; Providing Internet Access to High-Resolution Lunar Images; Expressions Module for the Satellite Orbit Analysis Program Virtual Satellite; Small-Body Extensions for the Satellite Orbit Analysis Program (SOAP); Scripting Module for the Satellite Orbit Analysis Program (SOAP); XML-Based SHINE Knowledge Base Interchange Language; Core Technical Capability Laboratory Management System; MRO SOW Daily Script; Tool for Inspecting Alignment of Twinaxial Connectors; An ATP System for Deep-Space Optical Communication; Polar Traverse Rover Instrument; Expert System Control of Plant Growth in an Enclosed Space; Detecting Phycocyanin-Pigmented Microbes in Reflected Light; DMAC and NMP as Electrolyte Additives for Li-Ion Cells; Mass Spectrometer Containing Multiple Fixed Collectors; Waveguide Harmonic Generator for the SIM; Whispering Gallery Mode Resonator with Orthogonally Reconfigurable Filter Function; Stable Calibration of Raman Lidar Water-Vapor Measurements; Bimaterial Thermal Compensators for WGM Resonators; Root Source Analysis/ValuStream[Trade Mark] - A Methodology for Identifying and Managing Risks; Ensemble: an Architecture for Mission-Operations Software; Object Recognition Using Feature-and Color-Based Methods; On-Orbit Multi-Field Wavefront Control with a Kalman Filter; and The Interplanetary Overlay Networking Protocol Accelerator.

Source record↗

Radar Wind Profiler (RWP) and Radio Acoustic Sounding System (RASS) Instrument Handbook

The radar wind profiler (RWP) is an active remote-sensing instrument that can routinely, and virtually unattended, observe wind and turbulence in the troposphere through scattering from clear-air irregularities of the atmospheric refractive index (Gage and Balsley 1978). The principle of Doppler radars in general is based on sending electromagnetic pulses in the vertical and several tilted directions (vertical and oblique beams) and measuring the signal that is scattered back by atmospheric turbulence at all heights and received at the antenna. The RWPs provides measurements of backscattered signal strength and wind profiles nominally between 0.1 km and 6 km. The RWP operation assumes that the wind field is homogeneous over the spatial separation of the antenna beams, which is a safe assumption under stable atmospheric conditions. However, the wind may be different between the beams due to significant changes in the wind field, resulting in erroneous wind calculations. Therefore, the radial measurements are averaged over a sufficient time period to validate the assumption of homogeneity.

54 ENVIRONMENTAL SCIENCES↗

Rendezvous radar for the orbital maneuvering vehicle

This paper describes the development of the Rendezvous Radar Set (RRS) for the Orbital Maneuvering Vehicle (OMV) for the National Aeronautics and Space Administration (NASA). The RRS was to be used to locate, and then provide vectoring information to, target satellites (or Shuttle or Space Station) to aid the OMV in making a minimum-fuel-consumption approach and rendezvous. The RRS design is that of an X-Band, all solid-state, monopulse tracking, frequency hopping, pulse-Doppler radar system. The development of the radar was terminated when the OMV prime contract to TRW was terminated by NASA. At the time of the termination, the development was in the circuit design stage. The system design was virtually completed, the PDR had been held. The RRS design was based on Motorola's experiences, both in the design and production of radar systems for the US Army and in the design and production of hi-rel communications systems for NASA space programs. Experience in these fields was combined with the latest digital signal processor and micro-processor technology to design a light-weight, low-power, spaceborne radar. The antenna and antenna positioner (gimbals) technology developed for the RRS is now being used in the satellite-to-satellite communication link design for Motorola's Iridium telecommunications system.

Locke, John W.↗

Autonomous Ocean World Exploration: Advancement of a Virtual Testbed

The search for life (extinct or extant) and potentially habitable bodies in our solar system and beyond is one of the 12 priority science questions outlined in the National Acadamies’ 2022 decadal survey [5]. Extraterrestrial destinations containing liquid water present an opportunity to search for life as we know it, and in recent years an increasing number of such locations have been discovered within our solar system. Several Jovian moons—Europa, Ganymede, and Callisto [10]—and the Saturnian moons Enceladus [8] and Titan [9] are known or suspected to harbor massive subsurface oceans. Of these "ocean worlds", Europa is the focus of at least one planned NASA orbiter mission, Europa Clipper [4], and an early lander mission concept, the Europa Lander [2, 3]. Whereas most robotic missions to the Moon and Mars (e.g. orbiters, rovers, landers) to date have had ground controllers on Earth tightly involved in mission operations, missions to more distant worlds will require a high degree of onboard autonomy due to long communication lags and blackouts, harsh environments (radiation, cold), and more limited battery and hardware life. The past decade has seen great advances in both AI technologies and computing scalability and performance that offer promising solutions for spacecraft autonomy and motivate the software system and research programs described in this paper. The Ocean Worlds Autonomy Testbed for Exploration, Research, and Simulation (OceanWATERS) [1], which has been in development at the NASA Ames Research Center since 2018, is a virtual environment for testing lander autonomy solutions. It is built on the Robot Operating System (ROS), runs on consumer-grade Linux workstations, and was released as open source in 2020. OceanWATERS provides a physical and visual simulation of a prototypical lander in a Europa-like environment (Figure 1). The lander was modeled after requirements and specifications made in JPL’s Europa Lander Study of 2016 [3]. Simulated lander systems include stereo cameras and spotlights mounted on an antenna mast that pans and tilts, a 6 degrees of freedom (DoF) robotic arm with a force-torque sensor and two interchangeable end effectors, and a battery pack power system. The environment consists of multiple terrain models including a highly detailed model sourced from the FROST dataset [11], simulation of surrounding planetary bodies based on an ephemeris model, and lighting from the sun with associated surface illumination, reflectance, and shadows. Operations supported by OceanWATERS include panoramic and directed imaging of the environment and lander workspace, Cartesian and joint-level arm commanding, grinding of the terrain surface (e.g. digging a trench), and scooping of ground material (Figure 2) which can be discarded or collected as science samples in a receptacle that can be emptied (science operations themselves are not simulated). These operations are realized as ROS Actions and are complimented by a wide selection of telemetry that is continually produced by each lander subsystem. The power system model is driven by the open-source Generic Software Architecture for Prognostics (GSAP) [11] that predicts the battery’s remaining useful life and other characteristics. As a testbed for high-level autonomy, OceanWATERS provides an execution framework based on PLEXIL [12], an open-source plan specification language and execution engine developed largely at Ames. NASA's initial development of OceanWATERS, as well the Ocean Worlds Lander Autonomy Testbed (OWLAT) [6], a complimentary physical testbed developed at JPL, was the first step in a plan for realizing candidate onboard autonomy solutions for such planetary landers. In 2020 NASA solicited applications for its Autonomous Robotics Research for Ocean Worlds (ARROW) program, and in 2021 the similar Concepts for Ocean worlds Life Detection Technology (COLDTech) program. Collectively six research teams, based in universities and companies across the United States, were awarded grants to develop and demonstrate autonomy solutions on OceanWATERS and OWLAT. These 1–2-year projects have now finished or are nearing completion, and a wide variety of autonomy challenges in ocean world surface missions were addressed. Prototyped and demonstrated solutions have included autonomous discovery, response and adaptation to system faults and unexpected environmental events, world model synthesis through perception, plan synthesis using learned models, methods to optimize sample target selection and prioritize science data transmission, extension of PLEXIL for stochastic decision-making, and an integration of a model of JPL’s mission-ready COLDArm [7]. Technologies used in these projects include many forms of machine learning, causal reasoning, automated planning, Markov decision processes, formal methods, and other advanced techniques. A more detailed summary of the ARROW and COLDTech projects is given herein. OceanWATERS has had significant enhancements since its open-source release in 2020. Many of its new features were driven or shaped by feedback from the ARROW and COLDTech teams and requirements of their projects. In support of enabling autonomous adaptation to spacecraft faults (a specific capability solicited by both programs), a fault injection and detection framework was developed that supports a wide and growing range of fault types such as locked joints, image loss, and battery failures. The power system model was completed and integrated into the simulator, starting as a single-cell battery model and later upgraded to a multi-cell model with associated faults such as cell disconnection. Arm/terrain interaction was improved by adding a force-torque sensor and associated faults, and an analytic dig force model based on the Balovnev bucket force equations. Environment fidelity was increased by modeling terrain deformation resulting from digging and scooping; visual improvements were made in textures, lighting, and shadows. To facilitate interoperation with OWLAT, a unified command and telemetry interface between the testbeds was developed at the ROS level, along with a PLEXIL interface. The number of lander operations was greatly expanded (e.g. with Cartesian-based arm and antenna movement), and a framework was designed for users to build their own lander actions. A GUI for PLEXIL plan selection was created (Figure 3), and an expansive set of plans were added, such as those that illustrate patterns for fault handling. This paper provides a self-contained high-level description of OceanWATERS, focusing on more detailed coverage of the aforementioned enhancements. It provides a high-level summary of the projects undertaken by participants in the ARROW and COLDTech programs and how these efforts have helped shape OceanWATERS. Finally, potential future work and directions for the testbed are listed, as likely informed by the recent planetary science decadal survey [5].

K Michael Dalal↗

A real-time signal combining system for Ka-band feed arrays using maximum-likelihood weight estimates

A real-time digital signal combining system for use with Ka-band feed arrays is proposed. The combining system attempts to compensate for signal-to-noise ratio (SNR) loss resulting from antenna deformations induced by gravitational and atmospheric effects. The combining weights are obtained directly from the observed samples by using a sliding-window implementation of a vector maximum-likelihood parameter estimator. It is shown that with averaging times of about 0.1 second, combining loss for a seven-element array can be limited to about 0.1 dB in a realistic operational environment. This result suggests that the real-time combining system proposed here is capable of recovering virtually all of the signal power captured by the feed array, even in the presence of severe wind gusts and similar disturbances.

Vilnrotter, V. A.↗

Real-time combining of residual carrier array signals using ML weight estimates

A real-time digital signal combining system for use with array feeds is proposed. The combining system attempts to compensate for signal-to-noise ratio (SNR) loss resulting from antenna deformations induced by gravitational and atmospheric effects. The combining weights are obtained directly from the observed residual carrier samples in each channel using a 'sliding-window' implementation of a maximum-likelihood (ML) parameter estimator. It is shown that with averaging times of about 0.1 s, combining loss for a seven-element array can be limited to about 0.1 dB in a realistic operational environment. This result suggests that the real-time combining system proposed here is capable of recovering virtually all of the signal power captured by the array feed, even in the presence of severe wind gusts and similar disturbances.

Vilnrotter, Victor A.↗

Strategy for reflector pattern calculation: Let the computer do the work

Using high frequency approximations, the secondary pattern of a reflector antenna can be calculated by numerically evaluating a radiation integral I(u,v). In recent years, tremendous effort has been expended to reducing I(u,v) to Fourier integrals. These reduction schemes are invariably reflector geometry dependent. Hence, different analyses/computer software development must be carried out for different reflector shapes/boundaries. it is pointed out, that, as the computer power improves, these reduction schemes are no longer necessary. Comparable accuracy and computation time can be achieved by evaluating I(u,v) by a brute force FFT described in this note. Furthermore, there is virtually no restriction on the reflector geometry by using the brute force FFT.

Lam, P. T.↗

Strategy for reflector pattern calculation - Let the computer do the work

Using high frequency approximations, the secondary pattern of a reflector antenna can be calculated by numerically evaluating a radiation integral I(u,v). In recent years, tremendous effort has been expended to reducing I(u,v) to Fourier integrals. These reduction schemes are invariably reflector geometry dependent. Hence, different analyses/computer software development must be carried out for different reflector shapes/boundaries. It is pointed out, that, as the computer power improves, these reduction schemes are no longer necessary. Comparable accuracy and computation time can be achieved by evaluating I(u,v) by a brute force FFT described in this note. Furthermore, there is virtually no restriction on the reflector geometry by using the brute force FFT.

Lam, P. T.↗

New antenna feed revitalizes Space Shuttle tracker at NASA Edwards

An account is given of the upgrading of a 12-ft-diameter single-channel monopulse tracking system, which had been relegated to slaved backup status at NASA Edwards, to support research flights for Ames Dryden Research Center and for tracking orbital passes of the Space Shuttle and Shuttle landings both at Edwards and at White Sands. The improved system is now a stand-alone telemetry tracking system. A new conical scanning feed (known as Radscan) replaces the single channel monopulse feed in the upgraded system. Where previously the system would not autotrack at elevation angles below 5 degrees, it now automatically acquires the Space Shuttle when it appears on the horizon and autotracks from approximately 2 degrees in elevation to touchdown, and does so virtually unattended.

Wrin, J. W.↗

PSA: A program to streamline orbit determination for launch support operations

An interactive, menu driven computer program was written to streamline the orbit determination process during the critical launch support phase of a mission. Residing on a virtual memory minicomputer, this program retains the quantities in-core needed to obtain a least squares estimate of the spacecraft trajectory with interactive displays to assist in rapid radio metric data evaluation. Menu-driven displays allow real time filter and data strategy development. Graphical and tabular displays can be sent to a laser printer for analysis without exiting the program. Products generated by this program feed back to the main orbit determination program in order to further refine the estimate of the trajectory. The final estimate provides a spacecraft ephemeris which is transmitted to the mission control center and used for antenna pointing and frequency predict generation by the Deep Space Network. The development and implementation process of this program differs from that used for most other navigation software by allowing the users to check important operating features during development and have changes made as needed.

Legerton, V. N.↗

Wide scanning spherical antenna

A novel method for calculating the surface shapes for subreflectors in a suboptic assembly of a tri-reflector spherical antenna system is introduced, modeled from a generalization of Galindo-Israel's method of solving partial differential equations to correct for spherical aberration and provide uniform feed to aperture mapping. In a first embodiment, the suboptic assembly moves as a single unit to achieve scan while the main reflector remains stationary. A feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan thereby eliminating the need to oversize the main spherical reflector. In an alternate embodiment, both the main spherical reflector and the suboptic assembly are fixed. A flat mirror is used to create a virtual image of the suboptic assembly. Scan is achieved by rotating the mirror about the spherical center of the main reflector. The feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan.

Shen, Bing↗

Considerations for high accuracy radiation efficiency measurements for the Solar Power Satellite (SPS) subarrays

The relatively large apertures to be used in SPS, small half-power beamwidths, and the desire to accurately quantify antenna performance dictate the requirement for specialized measurements techniques. Objectives include the following: (1) For 10-meter square subarray panels, quantify considerations for measuring power in the transmit beam and radiation efficiency to + or - 1 percent (+ or - 0.04 dB) accuracy. (2) Evaluate measurement performance potential of far-field elevated and ground reflection ranges and near-field techniques. (3) Identify the state-of-the-art of critical components and/or unique facilities required. (4) Perform relative cost, complexity and performance tradeoffs for techniques capable of achieving accuracy objectives. the precision required by the techniques discussed below are not obtained by current methods which are capable of + or - 10 percent (+ or - dB) performance. In virtually every area associated with these planned measurements, advances in state-of-the-art are required.

Kozakoff, D. J.↗

Differential InP HEMT MMIC Amplifiers Embedded in Waveguides

Monolithic microwave integrated-circuit (MMIC) amplifiers of a type now being developed for operation at frequencies of hundreds of gigahertz contain InP high-electron-mobility transistors (HEMTs) in a differential configuration. The differential configuration makes it possible to obtain gains greater than those of amplifiers having the single-ended configuration. To reduce losses associated with packaging, the MMIC chips are designed integrally with, and embedded in, waveguide packages, with the additional benefit that the packages are compact enough to fit into phased transmitting and/or receiving antenna arrays. Differential configurations (which are inherently balanced) have been used to extend the upper limits of operating frequencies of complementary metal oxide/semiconductor (CMOS) amplifiers to the microwave range but, until now, have not been applied in millimeter- wave amplifier circuits. Baluns have traditionally been used to transform from single-ended to balanced configurations, but baluns tend to be lossy. Instead of baluns, finlines are used to effect this transformation in the present line of development. Finlines have been used extensively to drive millimeter- wave mixers in balanced configurations. In the present extension of the finline balancing concept, finline transitions are integrated onto the affected MMICs (see figure). The differential configuration creates a virtual ground within each pair of InP HEMT gate fingers, eliminating the need for inductive vias to ground. Elimination of these vias greatly reduces parasitic components of current and the associated losses within an amplifier, thereby enabling more nearly complete utilization of the full performance of each transistor. The differential configuration offers the additional benefit of multiplying (relative to the single-ended configuration) the input and output impedances of each transistor by a factor of four, so that it is possible to use large transistors that would otherwise have prohibitively low impedances. Yet another advantage afforded by the virtual ground of the differential configuration is elimination of the need for a ground plane and, hence, elimination of the need for back-side metallization of the MMIC chip. In turn, elimination of the back-side metallization simplifies fabrication, reduces parasitic capacitances, and enables mounting of the MMIC in the electric-field plane ("E-plane") of a waveguide. E-plane mounting is consistent with (and essential for the utility of) the finline configuration, in which transmission lines lie on a dielectric sheet in the middle of a broad side of the waveguide. E-plane mounting offers a combination of low loss and ease of assembly because no millimeter-wave wire bonds or transition substrates are required. Moreover, because there is no ground plane behind the MMIC, the impedance for the detrimental even (single-ended) mode is high, suppressing coupling to that mode. Still another advantage of E-plane mounting is that the fundamental waveguide mode is inherently differential, eliminating the need for a balun to excite the differential mode.

Kangaslahti, Pekka↗

Modal Field Reconstruction in Resonant Cavities in the Fundamental and Undermoded Frequency Regimes

Theory, simulations, and experiments are presented that demonstrate reconstruction of electromagnetic fields in a cavity from sparse probe measurements. Such techniques are often referred to as virtual sensing, allowing fields at unobserved locations to be predicted. These methods are appropriate for the fundamental and undermoded regimes, providing the ability to estimate fields (and shielding effectiveness) throughout an arbitrarily shaped cavity from a few judiciously spaced probes. A modal simulation method is implemented that allows the response of arbitrarily shaped cavities to be rapidly computed with respect to varying probe locations and slot parameters, enabling statistical analysis of probe placement on reconstruction performance. A cylindrical vessel with numerous probe holes is developed for experiments, referred to as Perforated Vessel 2 (PV2). Experiments are performed on the vessel with and without a steel box inside, where transmit power is delivered into the vessel either through probes (probe injection) or through slots using an external antenna (slot excitation). Simulations and experiments illustrate that when the number of probes is minimal (equal to the number of mode coefficients to be estimated at each frequency), probe placement is critical to avoid missed peaks and to have acceptable reconstruction error. Probe placement becomes less important as the number of probes is increased, but care is still required to avoid probe locations giving poor performance.

42 ENGINEERING↗

NASA 60 GHz intersatellite communication link definition study. Baseline document

The overall system and component concepts for a 60 GHz intersatellite communications link system (ICLS) are described. The ICLS was designed to augment the capabilities of the current Tracking and Data Relay Satellite System (TDRSS), providing a data rate capacity large enough to accommodate the expected rates for user satellites (USAT's) in the post-1995 timeframe. The use of 60 GHz for the anticipated successor to TDRSS, the Tracking and Data Acquisition System (TDAS), was selected because of current technology development that will enable multigigibit data rates. Additionally, the attenuation of the earth's atmosphere at 60 GHz means that there is virtually no possibility of terrestrially generated interference (intentional or accidental) or terrestrially based intercept. The ICLS includes the following functional areas: (1) the ICLS payload package on the GEO TDAS satellite that communicates simultaneously with up to five LEO USAT's; (2) the payload package on the USAT that communicates with the TDAS satellite; and (3) the crosslink payload package on the TDAS satellite that communicates with another TDAS satellite. Two methods of data relay on-board the TDAS spacecraft were addressed. One is a complete baseband system (demod and remod) with a bi-directional 2 Gbps data stream; the other is a channelized system wherein some of the channels are baseband and others are merely frequency translated before re-transmission. Descriptions of the TDAS antenna, transmitter, receiver, and mechanical designs are presented.

Source record↗

A Flight Evaluation and Analysis of the Effect of Icing Conditions on the ZPG-2 Airship

A series of test flights was conducted by the U. S. Navy over a 3- year period to evaluate the effects of icing on the operation of the ZPG-2 airship. In supercooled. clouds, ice formed only on the forward edges of small protuberances and wires and presented no serious hazard to operation. Ice accretions of the glaze type which occurred in conditions described as freezing drizzle adversely affected various components to a somewhat greater extent. The results indicated, a need for protection of certain components such as antennas, propellers, and certain parts of the control system. The tests showed that icing of the large surface of the envelope occurred only in freezing rain or drizzle. Because of the infrequent occurrence of these conditions, the potential maximum severity could not be estimated from the test results. The increases in heaviness caused by icing in freezing rain and drizzle were substantial, but well within the operational capabilities of the airship. In order to estimate the potential operational significance of icing in freezing rain, theoretical calculations were used to estimate: (1) the rate of icing as a function of temperature and rainfall intensity, (2) the climatological probability of occurrence of various combinations of these variables, and (3) the significance of the warming influence of the ocean in alleviating freezing-rain conditions. The results of these calculations suggest that, although very heavy icing rates are possible in combinations of low temperature and high rainfall rate, the occurrence of such conditions is very infrequent in coastal areas and virtually impossible 200 or 300 miles offshore.

Lewis, Willilam↗