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NASA NTRS2003

Control of Thermo-Acoustics Instabilities: The Multi-Scale Extended Kalman Approach

"Multi-Scale Extended Kalman" (MSEK) is a novel model-based control approach recently found to be effective for suppressing combustion instabilities in gas turbines. A control law formulated in this approach for fuel modulation demonstrated steady suppression of a high-frequency combustion instability (less than 500Hz) in a liquid-fuel combustion test rig under engine-realistic conditions. To make-up for severe transport-delays on control effect, the MSEK controller combines a wavelet -like Multi-Scale analysis and an Extended Kalman Observer to predict the thermo-acoustic states of combustion pressure perturbations. The commanded fuel modulation is composed of a damper action based on the predicted states, and a tones suppression action based on the Multi-Scale estimation of thermal excitations and other transient disturbances. The controller performs automatic adjustments of the gain and phase of these actions to minimize the Time-Scale Averaged Variances of the pressures inside the combustion zone and upstream of the injector. The successful demonstration of Active Combustion Control with this MSEK controller completed an important NASA milestone for the current research in advanced combustion technologies.

Dzu K Le↗

NASA NTRS2026

Experimental Study of Aeropropulsive Interactions for Electric Ducted Fans on a Wing

The Adaptable Distributed Electric Propulsion Testbed (ADEPT)Wing was tested in the NASA Langley 12-Foot Low-Speed Tunnel to investigate electric propulsion technologies for commercial transport aircraft. The purpose of the test was to study the aeropropulsive effects across angle of attack and fan speed variations for several propulsor placements and array sizes, and to investigate how distributed electric propulsion (DEP) can be leveraged for augmented lift and vehicle control. Six electric ducted fan (EDF) array placements were tested by positioning the fans along the leading and trailing edges on the top and bottom surfaces, as well as centered on the chord line in front of and behind the wing. Each fan placement configuration was tested with an array of one, three, and five EDFs to characterize an aeropropulsive extrapolation effect, and the bare wing was tested separately to provide baseline aerodynamic measurements. The results compare the longitudinal forces and moments for each configuration by analyzing the combined aeropropulsive interaction effects, and offer valuable insight into considerations for fan placement along a wing to enable the benefits of DEP integration.

Rose Weinstein↗

NASA NTRS2002

The Design and Use of Calorimeters For Characterization of High-Enthalpy Flows in Arc-Heated Test Facilities

High-enthalpy, arc-heated flows used for aerothermal testing present a challenging environment for flow characterization. This paper describes the design and use of cooled dwell probes used for heat-transfer and pressure characterization of the NASA and United States Department of Defense (DoD) arc facilities located at Moffett Field, CA, and Arnold Air Force Base, TN. Dwell calorimeters designed, fabricated, and tested by Thermal Technologies, Inc. (TTI) in the NASA IHF and the USAF H1 and H2 arc test facilities provide heat flux and pressure data with excellent repeatability. These calorimeters use standard Gardon calorimeter gages and pressure ports with unique cooling systems enabling them to withstand the severe arc-heated environments for durations sufficient for acquisition of steady-state data. The TTI probes have proven very robust in the extreme aerothermal environments of these facilities. This paper provides an overview of calorimeter instruments typically used in arc facilities, discusses design features of the TTI dwell probes, presents selected data acquired by the TTI calorimeters, and provides comparisons with data acquired from using measurement techniques.

D Mark Smith↗

NASA NTRS2026

Improvement of Odor Control for the UWMS Hard-Sided Fecal Canister and the Alternate Fecal Canister

On longer range exploration missions, the mass and volume of critical hardware and consumables required to support crew will pose a big stowage challenge. This includes the hardware for the collection and storage of human metabolic solid waste. The amount of stowage needed for this hardware both before (empty) and after (full) use will be a significant burden on the overall spacecraft habitable volume, layout, and design. To help with this challenge, the National Aeronautics and Space Administration (NASA) Mars Campaign Office (MCO) Logistics Reduction (LR) Portfolio has developed a collapsible canister for the collection and containment of fecal deposits. The Alternate Fecal Canister (AFC) is a collapsible alternative to the exploration toilet Hard-sided Fecal Canister (HFC). The AFC in its empty state has a volumetric benefit to smaller vehicles on longer missions. The current designs for HFC and AFC were tested with human fecal material for odor containment at White Sands Test Facility (WSTF) where the tests on both were unsuccessful. The source of the lack of containment was isolated to a gasket used on both HFC and AFC. The gasket used was found to be open cell in design. This paper provides a summary of the materials selection and testing process to identify a replacement gasket material with the intention to replace the gaskets on both existing units as well as incorporate it into the designs going forward for future builds for exploration. Details will be provided on the design of the canisters interface with the odor bacteria lid which led to the selection of the thickness of the desired replacement. Finally, the paper will provide an update on the testing in advance of a return to WSTF for final testing and detail plans to complete testing and perform a demonstration on ISS with UWMS.

ECLSS↗

NASA NTRSDate not supplied

The Aeolus-Earth DWTS Heliophysics Mission

The Aeolus-Earth Mission (DWTS-Helio) is a recently selected NASA Heliophysics investigation that will apply the innovative Doppler Wind Temperature Sounder (DWTS) technique to the Space Atmosphere Interaction Region (SAIR) at ~105-180 km. The technique, invented by Gordley & Marshall (2011), applies the Doppler Scanning with Gas Filter (DSGF) technique using a cryo-cooled MWIR radiometer to view the limb of the atmosphere from LEO (orbital velocity creates the Doppler shifts required by the technique). For this implementation of DWTS, a Nitric Oxide (NO) low pressure gas cell is used. The limb of the atmosphere is observed from a spacecraft at orbital velocity, and as an observed air volume passes through the field of view, this velocity creates a set of Doppler-shifted images. These images are used to create Doppler Integrated Pass (DIP) signals, from which atmospheric temperature and wind profiles are extracted (it may be considered a converse of the successful in-flight calibration of gas cells used for the HALOE instrument). The technique is relative, removing the need for absolute radiances, and the signal-to-noise ratio for this technique is high, resulting in good measurement precision. Different gas cells can be used to create different altitude coverage and may be combined to measure a more continuous altitude range. For example, using a NO cell captures the lower atmosphere from 30-50km as well as the SAIR, while using the 13 isotopologue of CO2 would capture 50-120km. Due to the desired data volume as well as power and thermal considerations, this initial Aeolus-Earth flight will be more suited for a ‘hosted’ payload on an Orbital Maneuvering Vehicle platform instead of the ‘free-flyer’ option originally investigated. Lastly, the technique is sufficiently powerful that a two-channel system could produce full Mars atmosphere data not currently possible.

DWTS↗

NASA NTRS2026

Computational Materials for Qualification and Certification (CM4QC) Strategy Document: Maturation of Computational Materials Methods for Aviation-Focused Qualification and Certification of Metal Additive Manufacturing (as an Example of Process-Intensive Materials)

Although considerable scientific and technological advances have been made in recent years in additive manufacturing (AM) processes, these advances have not translated into significant market penetration of AM parts within the aviation industry. It is broadly acknowledged that using traditional qualification and certification (Q&C) approaches for AM components is one of the most significant barriers to broader adoption of AM, resulting in high costs, long product development and certification timelines, and complex design iterations during the product development cycle. A new approach is urgently needed. This document lays out a vision for a new Q&C paradigm with increased use of computational materials (CM) methods aimed at decreasing the time and cost of Q&C of process-intensive material (PIM) approaches in the aviation industry, with AM as the immediate use case. This vision was developed with substantial input from industry, regulatory agencies, government research organizations, and academia.

Edward H Glaessgen↗

NASA NTRS1997

NiH2 Battery Reconditioning for LEO Applications

This paper summarizes reasons for and benefits of reconditioning nickel-hydrogen (NiH2) batteries used for Low Earth Orbit (LEO) applications. NiH2 battery cells do not have the classic discharge voltage problems more commonly associated with nickel-cadmium (NiCd) cells. This is due, in part, to use of hydrogen electrodes in place of cadmium electrodes. The nickel electrode, however, does have a similar discharge voltage signature for both cell designs. This can have an impact on LEO applications where peak loads at higher relative depths of discharge can impact operations. Periodic reconditioning provides information which can be used for analyzing long term performance trends to predict usable capacity to a specified voltage level. The reconditioning process described herein involves discharging NiH2 batteries at C/20 rates or less, to an average cell voltage of 1.0 volts or less. Recharge is performed at nominal C/5 rates to specified voltage/temperature (V/T) charge levels selected to restore required capacity with minimal overcharge. Reconditioning is a process of restoring reserve capacity lost on cycling, which is commonly called the memory effect in NiCd cells. This effect is characterized by decreases in the discharge voltage curve with operational life and cycling. The end effect of reconditioning NiH2 cells may be hidden in the versatility, of that design over the NiCd cell design and its associated negative electrode fading problem. The process of deep discharge at lower rates by way of reconditioning tends to redistribute electrolyte and water in the NiH2 cell electrode stack, while improving utilization and charge efficiency. NiH2 battery reconditioning effects on life are considered beneficial and may, in fact. extend life based on NiCd experience. In any case, usable capacity data obtained from reconditioning is required for performance evaluation and trend analysis. Characterization and life tests have provided the historical data base used to determine the need for reconditioning in most battery applications. The following sections briefly describe the background of NiH2 battery reconditioning and testing at Lockheed Martin Missiles & Space (LMMS) and other aerospace companies.

Armantrout, J. D.↗

NASA NTRSDate not supplied

Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft

Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.

power↗

NASA NTRS2026

Global Model Estimates of Atmospheric Al, Ca, Fe, Si, and Ti from Dust and Non-Dust Aerosols Informed by EMIT Surface Mineralogy and Evaluated Against Observations

Atmospheric deposition of micro-nutrients like Fe has been shown to be important for ocean biogeochemistry. The largest source of atmospheric Fe and other elements (e.g., Ca, Al, Si, and Ti) is desert dust, although there are significant non-dust sources in some regions. However, past estimates of these elements have been substantially uncertain due to limited information about the composition of the desert source regions. Here we use elemental distributions estimated from new Earth Surface Mineral Dust Source Investigation (EMIT) observations, which provide mineralogical composition at the surface of the Earth based on imaging spectroscopy measurements from the International Space Station. We add in other sources of these elements (anthropogenic and natural) and compare to a compilation of available surface concentration data from stations over land and from shipborne observations. Our results suggest that the modeled distribution is similar to available observations, but discrepancies still exist in both natural desert dust regions as well as regions dominated by anthropogenic sources. Global budgets for the elements Ca, Al, Fe, Si, and Ti suggest that desert dust remains the dominant source for these elements but anthropogenic or volcanic sources are also important for these elements. Changes in elemental distributions since preindustrial times were also estimated.

aerosols↗

NASA NTRS2026

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

A thermochemically-closed sonic-flow inversion framework (TSIF) is developed to infer bulk enthalpy and total temperature upstream of a choked nozzle in arc-jet flows. The formulation recasts a pressure-rise total enthalpy quantification technique as an inverse problem in characteristic-velocity c * space using measured mass flow rate, upstream total pressure, gas composition, and nozzle throat geometry as inputs. Unlike calorimetric energy-balance approaches or optical diagnostics, the method relies primarily on routinely measured facility quantities combined with explicit thermochemical closure. Thermochemical states are obtained using NASA’s open-source Chemical Equilibrium with Applications (CEA) code, enabling construction of a chemistry-consistent relation between characteristic velocity, total enthalpy, and total temperature under equilibrium or frozen assumptions. A discharge coefficient is self-calibrated using cold-flow (arc-off) operation data and applied to hot-flow (arc-on) measurements, enabling upstream losses to be accounted for without empirical correlations. The framework is applied to air, N 2 , and CO 2 –N 2 arc-jet flows and demonstrates expected trends for the inferred thermochemical states as function of arc power, specific energy input, mass-flow, heater configuration, and test gas. In the air limit, under equilibrium assumptions, the method recovers the classical high-enthalpy asymptotic correlation of Winovich with a mean residual of 4.4%, demonstrating compatibility with established sonic-flow scaling, while extending applicability to arbitrary multi-species mixtures and non-equilibrium chemistry. The framework provides a mixture-flexible methodology for determining bulk thermochemical states in modern arc-jet environments using routine facility pressure, mass-flow, gas-composition, and nozzle-geometry information together with a cold-flow calibration.

stagnation heat flux↗

NASA NTRS2026

Thermochemically-Closed Sonic-Flow Inversion for Enthalpy and Temperature in Multispecies Arc-Jet Flows

inviscid theory↗

NASA NTRS1985

Summary of recent NASA propeller research

Advanced high speed propellers offer large performance improvements for aircraft that cruise in the Mach 0.7 to 0.8 speed regime. At these speeds, studies indicate that there is a 15 to near 40 percent block fuel savings and associated operating cost benefits for advanced turboprops compared to equivalent technology turbofan powered aircraft. Recent wind tunnel results for five eight to ten blade advanced models are compared with analytical predictions. Test results show that blade sweep was important in achieving net efficiencies near 80 percent at Mach 0.8 and reducing nearfield cruise noise about 6 dB. Lifting line and lifting surface aerodynamic analysis codes are under development and some results are compared with propeller force and probe data. Also, analytical predictions are compared with some initial laser velocimeter measurements of the flow field velocities of an eight bladed 45 swept propeller. Experimental aeroelastic results indicate that cascade effects and blade sweep strongly affect propeller aeroelastic characteristics. Comparisons of propeller nearfield noise data with linear acoustic theory indicate that the theory adequately predicts nearfield noise for subsonic tip speeds, but overpredicts the noise for supersonic tip speeds.

Daniel C Mikkelson↗

NASA NTRSDate not supplied

Lessons Learned From A Cryogenic Motor Configuration Study for Aircraft Propulsion

Cryogenic electric machines are a promising technology for multi megawatt electric aircraft drivetrains. Superconducting stators that make use of low AC loss superconducting wires are considered to be a key component for these cryogenic machines. NASA has undertaken 6-year technical challenge to address this need by designing a 5 MW superconducting motor and cryogenic drive and developing multi-MW prototypes. This poster shares the lessons learned from a completed design study that evaluated several configurations of a 5 MW cryogenic motor for this application. The lessons are drawn from a qualitative study of 16 configurations and a quantitative study of 8 down selected configurations. The quantitative study involved using a motor design code based on analytical calculations (electromagnetic, thermofluid, mechanical, and motor sizing) to determine each configuration’s Pareto front of total efficiency and total specific power. This poster builds upon preliminary results that were previously presented by (1) reporting final results based on a revised design code for each configuration, including a considerable increase in fidelity for a novel radial flux motor and (2) making a down selection of the configuration for future detailed design and demonstration and documenting the rationale for the selection.

Superconductors↗

NASA NTRS1994

Bipolar Ag-Zn battery

The silver-zinc (AgZn) battery system has been unique in its ability to safely satisfy high power demand applications with low mass and volume. However, a new generation of defense, aerospace, and commercial applications will impose even higher power demands. These new power demands can be satisfied by the development of a bipolar battery design. In this configuration the power consuming, interelectrode current conductors are eliminated while the current is then conducted via the large cross-section electrode substrate. Negative and positive active materials are applied to opposite sides of a solid silver foil substrate. In addition to reducing the weight and volume required for a specified power level, the output voltage performance is also improved as follows. Reduced weight through: elimination of the plastic cell container; elimination of plate leads and intercell connector; and elimination of internal plate current collector. Increased voltage through: elimination of resistance of current collector; elimination of resistance of plate lead; and elimination of resistance of intercell connector. EPI worked previously on development of a secondary bipolar silver zinc battery. This development demonstrated the electrical capability of the system and manufacturing techniques. One difficulty with this development was mechanical problems with the seals. However, recent improvements in plastics and adhesives should eliminate the major problem of maintaining a seal around the periphery of the bipolar module. The seal problem is not as significant for a primary battery application or for a requirement for only a few discharge cycles. A second difficulty encountered was with activation (introducing electrolyte into the cell) and with venting gas from the cell without loss of electrolyte. During previous work, the following projections for energy density were made from test data for a high power system which demonstrated in excess of 50 discharge/charge cycles. Projected system power = 100 kilowatts; discharge time = 30 seconds; discharge current density = 1.75 amps/sq in.; system weight = 86 lbs (9.7 WH/lb); and system volume = 1071 cu. in. (.78 WH/cu. in.). EPI is currently working on a development program to produce a bipolar silver-zinc battery design for NASA. The potential application would be to power electromechanical actuators for space launch vehicles.

Giltner, L. John↗

NASA NTRS2026

Satellite Optical Remote Sensing of Clouds and Aerosols: From Particle Single-Scattering and Gaseous Absorption Through Radiative Transfer to Retrieval Products

Clouds and aerosols are fundamental regulators of Earth’s radiation budget and climate system, influencing both solar and terrestrial radiation through scattering, absorption, and emission processes. Accurate characterization of their physical and radiative properties from space requires a rigorous understanding of particle single-scattering, gaseous absorption, and radiative transfer in the atmosphere, as well as reliable inversion methods. This review synthesizes the physical foundations and algorithmic implementations of satellite-based passive optical remote sensing of clouds and aerosols, spanning the ultraviolet to thermal infrared spectral range. Beginning with electromagnetic scattering theory and state-of-the-art methods for computing single-scattering by nonspherical particles and computationally efficient methods for accounting for atmospheric absorption, we discuss the radiative transfer framework underpinning cloud and aerosol retrievals. The connection between single-scattering and multiple-scattering is rigorously formulated. We then summarize operational and research-grade retrieval techniques, including cloud masking and thermodynamic phase determination, CO₂ slicing for cloud-top pressure, the Nakajima-King shortwave bi-spectral, and infrared split-window approaches for cloud optical thickness and effective particle size, inversion algorithms for determining aerosol properties from multi-spectral and/or multi-angle radiometric and polarimetric measurements, and active-passive sensing synergy. Examples of the global cloud and aerosol climatologies are illustrated using observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Multi-angle Imaging SpectroRadiometer (MISR). Furthermore, the unique strengths of active remote sensing techniques based on spaceborne lidar observations are briefly elaborated in the context of studying ice clouds composed of randomly and horizontally oriented ice crystals, which is a significant challenge for conventional passive remote sensing techniques. By connecting physical theory to practical retrievals, this review highlights both the maturity of current methodologies and the remaining challenges in reducing uncertainties in particle morphology, vertical structure, absorption, and aerosol-cloud interactions. Furthermore, the impact of artificial intelligence (AI) on atmospheric remote sensing is briefly addressed.

Aerosols↗

NASA NTRSDate not supplied

Automatic Dependent Surveillance-Broadcast (ADS-B) In-Trail Procedures (ITP)

Aircraft in oceanic and remote non-radar airspace frequently fly for extended periods of time in the same direction, at the same time, along similar flight paths as other aircraft. Since there is no radar surveillance, controllers use procedural separation to ensure that aircraft remain separated. Procedural separation distances are typically larger than radar separation distances and as a result aircraft operating in oceanic airspace are sometimes held at non-optimal flight levels due to conflicting traffic at intervening flight levels. Automatic Dependent Surveillance-Broadcast (ADS-B) In-Trail Procedures (ITP) were developed to enable flight level change maneuvers that would otherwise not be possible with current procedural separation standards. Aircraft operators choosing to equip with an ADS-B transceiver and an appropriate onboard decision support system would be able to take advantage of these procedures when operating in proximity to aircraft equipped with a suitable ADS-B transmitter (“ADS-B Out”). The ability to perform in-trail maneuvers to achieve more time at optimum altitudes could result in more efficient and predictable flight profiles thereby saving fuel and in some cases allowing operators to make beneficial operational decisions. NASA first began developing ADS-B ITP in 2003 as a result of a desire to develop methodologies, concepts, and procedures to reduce separation requirements for future air transportation systems using airborne ADS-B. The objectives were to provide insight into the details necessary to reduce separation requirements for the future and to develop applications that could provide incentives for operators to voluntarily equip with transformational technologies. From 2003 to 2008, NASA conducted research that supported the development of ITP including batch simulations, human-in-the-loop experiments and avionics and separation standards development. This research showed enough maturity and benefit that in 2008, the FAA Surveillance and Broadcast Services (SBS) program adopted ADS-B ITP as one of their three key, near-term applications to make use of ADS-B-In. The FAA developed an agreement with NASA to transition the technology and established an FAA project for the purpose of performing an operational trial of ADS-B ITP in revenue service in the summer of 2011. The objectives of the project are to a) validate the operational performance and economic benefits of ITP; and b) develop and validate ADS-B ITP Minimum Operational Performance Specifications (MOPS) material. As a part of this project, the FAA established agreements with United Airlines and Honeywell. The agreements include the work necessary for the development, certification and installation of onboard systems for twelve United Airlines 747-400s. ITP system development is nearly complete and certification activities are underway. The FAA project has also been working with Oakland Oceanic Control Center (ZOA) and the FAA’s Oceanic and Offshore Operations Office to develop controller procedures and safety analyses that are required to support the flight trial. The FAA has also been working on the development of an ITP Operational Specification that should be approved this April. The presentation will cover some of the key aspects of the development, challenges, and integration required to successfully transition ADS-B ITP from a concept in 2003 to flight trials in revenue service in 2011.

Kenneth M Jones↗

NASA NTRSDate not supplied

Thermomechanical Modeling of Woven Materials With Particle-Based, Explicit-Fiber Simulations

Fiber-based materials are extensively used to protect spacecraft during entry. Insulative fibers, often in a fiber network or woven, provide rigidity, strength, and control of material anisotropy and density. Woven thermal protection materials, such as ADEPT (Adaptable, Deployable Entry and Placement Technology), 3D-MAT (3-Dimensional Multifunctional Ablative Thermal Protection), and 3MDCP (3D Woven Mid-Density Carbon Phenolic), enable missions with stronger and denser materials for entry profiles with high shear and heat flux. Vulnerabilities to woven thermal protection materials include manufacturing-induced material property variation, and impact from micrometeoroids. Simulating woven materials under these conditions require models that can resolve hierarchal structures, thermomechanical behavior, and failure. To address this, we simulate weave thermal conduction and mechanical deformation. We simulate the full weave with a coarse-grained yarn model is presented. The model combines a validated, high-resolution single 3MDCP yarn model and phenolic resin model. Instead of modeling every fiber, each yarn ply with order 10, instead of order 1000, fibers. The discrete element bonded particle model (DEM-BPM) of fibers captures the thermal and mechanical behavior within and between fibers. We study the proportion of heat transfer and stress via the contact network, fiber bonds, and overall weave geometry.

bonded particle↗

NASA NTRS2005

Chapter 19A – Radar Cross Section

The material in this Section will provide the novice Flight Test Engineer (FTE) with a brief overview of the radar cross section (RCS) concept. Brief details of radar range descriptions, operations, target calibrations, and data reduction are included. It is noted that these range operations concentrate on the "static" test range rather than the much more sophisticated "dynamic" test range. The dynamic test range is what the FTE will probably work with. Radar reflectivity measurement has developed over the last two decades from a relatively simple endeavor involving the measurement of target RCS amplitude statistics to involving wide band, coherent systems that can measure high resolution images of targets as well as, in many cases, the polarization and phasing properties. This rapid growth in RCS technology has occurred because of the increased use of radar in today's commercial and military systems. In general, the goal for commercial systems is to enhance radar reflectivity, whereas the military goal is to reduce radar reflectivity. Also, classification and identification are important for military purposes because in adverse weather radar may be the only system that may be capable of separating enemy targets from friendly ones. This Section will discuss the fundamentals of RCS. Since the flight test techniques associated with RCS measurements are very similar to those of antenna pattern measurements, both will be presented at the same time in Section 19B Antenna Radiation Pattern Measurements.

Robert W Borek↗