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Realtime Three-Dimensional Simulation

Real-time three-dimensional simulations are dependent of three areas: databases and models (3D geometric polygon structure, multiple levels of detail, sound sample waveforms, optimized for interactive, real time use); software applications (software program that controls input devices, visual channels, scene objects, interaction, collision detection, special effects, time of day, weather, I/O, and communication); and hardware (computer, sound processor, monitors control sticks, position trackers, head-mounted displays, amplifiers, speakers, and communications.

Ramsdell, Craig↗

Existing and Required Modeling Capabilities for Evaluating ATM Systems and Concepts

ATM systems throughout the world are entering a period of major transition and change. The combination of important technological developments and of the globalization of the air transportation industry has necessitated a reexamination of some of the fundamental premises of existing Air Traffic Management (ATM) concepts. New ATM concepts have to be examined, concepts that may place more emphasis on: strategic traffic management; planning and control; partial decentralization of decision-making; and added reliance on the aircraft to carry out strategic ATM plans, with ground controllers confined primarily to a monitoring and supervisory role. 'Free Flight' is a case in point. In order to study, evaluate and validate such new concepts, the ATM community will have to rely heavily on models and computer-based tools/utilities, covering a wide range of issues and metrics related to safety, capacity and efficiency. The state of the art in such modeling support is adequate in some respects, but clearly deficient in others. It is the objective of this study to assist in: (1) assessing the strengths and weaknesses of existing fast-time models and tools for the study of ATM systems and concepts and (2) identifying and prioritizing the requirements for the development of additional modeling capabilities in the near future. A three-stage process has been followed to this purpose: 1. Through the analysis of two case studies involving future ATM system scenarios, as well as through expert assessment, modeling capabilities and supporting tools needed for testing and validating future ATM systems and concepts were identified and described. 2. Existing fast-time ATM models and support tools were reviewed and assessed with regard to the degree to which they offer the capabilities identified under Step 1. 3 . The findings of 1 and 2 were combined to draw conclusions about (1) the best capabilities currently existing, (2) the types of concept testing and validation that can be carried out reliably with such existing capabilities and (3) the currently unavailable modeling capabilities that should receive high priority for near-term research and development. It should be emphasized that the study is concerned only with the class of 'fast time' analytical and simulation models. 'Real time' models, that typically involve humans-in-the-loop, comprise another extensive class which is not addressed in this report. However, the relationship between some of the fast-time models reviewed and a few well-known real-time models is identified in several parts of this report and the potential benefits from the combined use of these two classes of models-a very important subject-are discussed in chapters 4 and 7.

Odoni, Amedeo R.↗

Flight Testing and Real-Time System Identification Analysis of a UH-60A Black Hawk Helicopter with an Instrumented External Sling Load

Helicopter external air transportation plays an important role in today's world. For both military and civilian helicopters, external sling load operations offer an efficient and expedient method of handling heavy, oversized cargo. With the ability to reach areas otherwise inaccessible by ground transportation, helicopter external load operations are conducted in industries such as logging, construction, and fire fighting, as well as in support of military tactical transport missions. Historically, helicopter and load combinations have been qualified through flight testing, requiring considerable time and cost. With advancements in simulation and flight test techniques there is potential to substantially reduce costs and increase the safety of helicopter sling load certification. Validated simulation tools make possible accurate prediction of operational flight characteristics before initial flight tests. Real time analysis of test data improves the safety and efficiency of the testing programs. To advance these concepts, the U.S. Army and NASA, in cooperation with the Israeli Air Force and Technion, under a Memorandum of Agreement, seek to develop and validate a numerical model of the UH-60 with sling load and demonstrate a method of near real time flight test analysis. This thesis presents results from flight tests of a U.S. Army Black Hawk helicopter with various external loads. Tests were conducted as the U.S. first phase of this MOA task. The primary load was a container express box (CONEX) which contained a compact instrumentation package. The flights covered the airspeed range from hover to 70 knots. Primary maneuvers were pitch and roll frequency sweeps, steps, and doublets. Results of the test determined the effect of the suspended load on both the aircraft's handling qualities and its control system's stability margins. Included were calculations of the stability characteristics of the load's pendular motion. Utilizing CIFER(R) software, a method for near-real time system identification was also demonstrated during the flight test program.

McCoy, Allen H.↗

Modeling, Monitoring and Fault Diagnosis of Spacecraft Air Contaminants

Control of air contaminants is a crucial factor in the safety considerations of crewed space flight. Indoor air quality needs to be closely monitored during long range missions such as a Mars mission, and also on large complex space structures such as the International Space Station. This work mainly pertains to the detection and simulation of air contaminants in the space station, though much of the work is easily extended to buildings, and issues of ventilation systems. Here we propose a method with which to track the presence of contaminants using an accurate physical model, and also develop a robust procedure that would raise alarms when certain tolerance levels are exceeded. A part of this research concerns the modeling of air flow inside a spacecraft, and the consequent dispersal pattern of contaminants. Our objective is to also monitor the contaminants on-line, so we develop a state estimation procedure that makes use of the measurements from a sensor system and determines an optimal estimate of the contamination in the system as a function of time and space. The real-time optimal estimates in turn are used to detect faults in the system and also offer diagnoses as to their sources. This work is concerned with the monitoring of air contaminants aboard future generation spacecraft and seeks to satisfy NASA's requirements as outlined in their Strategic Plan document (Technology Development Requirements, 1996).

Ramirez, W. Fred↗

Real-Time Optical Fuel-to-Air Ratio Sensor for Gas Turbine Combustors

The measurement of the temporal distribution of fuel in gas turbine combustors is important in considering pollution, combustion efficiency and combustor dynamics and acoustics. Much of the previous work in measuring fuel distributions in gas turbine combustors has focused on the spatial aspect of the distribution. The temporal aspect however, has often been overlooked, even though it is just as important. In part, this is due to the challenges of applying real-time diagnostic techniques in a high pressure and high temperature environment. A simple and low-cost instrument that non-intrusively measures the real-time fuel-to-air ratio (FAR) in a gas turbine combustor has been developed. The device uses a dual wavelength laser absorption technique to measure the concentration of most hydrocarbon fuels such as jet fuel, methane, propane, etc. The device can be configured to use fiber optics to measure the local FAR inside a high pressure test rig without the need for windows. Alternatively, the device can readily be used in test rigs that have existing windows without modifications. An initial application of this instrument was to obtain time-resolved measurements of the FAR in the premixer of a lean premixed prevaporized (LPP) combustor at inlet air pressures and temperatures as high as 17 atm at 800 K, with liquid JP-8 as the fuel. Results will be presented that quantitatively show the transient nature of the local FAR inside a LPP gas turbine combustor at actual operating conditions. The high speed (kHz) time resolution of this device, combined with a rugged fiber optic delivery system, should enable the realization of a flight capable active-feedback and control system for the abatement of noise and pollutant emissions in the future. Other applications that require an in-situ and time-resolved measurement of fuel vapor concentrations should also find this device to be of use.

Nguyen, Quang-Viet↗

X-33 Integrated Test facility, Extended Range Simulation

In support of the X-33 Single Stage To Orbit program, NASA Dryden Flight Research Center was selected to provide continuous communications coverage of the X-33 vehicle from launch, through landing at Malmstrom Air Force Base, Montana and Michaels Army Air Field, Utah. An extensive real-time range simulation capability is being developed to ensure successful communications with the autonomous X-33 vehicle. This paper will provide an overview of the various levels of simulation being developed to support the X-33 extended range subsystems. These subsystems include the Flight Termination System, L-Band command uplink subsystem and the S-Band telemetry downlink subsystem. In addition, the radar model developed provides continuous azimuth, elevation and range information based on the flight trajectory. The Dynamic Ground Station Analysis model developed by NASA Goddard Space Flight Center, calculate the received signal strength at each ground station. This model takes into consideration Radio Frequency (RF) link parameters such as frequency, antenna gain, space loss, plasma effects and the vehicle's position and attitude at any point in time during the flight path. All three RF links are then attenuated based on this calculated level and the RF signals are sent into telemetry receivers to emulate remote sites, or the power incident on the vehicle from uplinked signals. The best source received telemetry data is then passed back to the Launch and Mission Control Monitoring System (LMCMS) resident in the Operations Control Center. The LMCMS also provides the range simulation system the uplink command combined with differential GPS corrections. Later stages will require the progressive integration of actual range hardware with this simulation effort, leading to communication between telemetry, uplink and FTS antennas at NASA Dryden Flight Research Center, with vehicle antennas mounted on the Walter C. Williams Research Aircraft Integration Facility (RAIF). Decommutated Pulse Code Modulated (PCM) data is displayed on one of the four monitors that comprise the Range Safety Officer's (RSO) station. Also displayed are instantaneous impact prediction models, and Federal Aviation Administration (FAA) data for notification of other traffic in the area. Aside from initiating the flight termination command and validating communication links, the RSO station with the range simulation will be used to provide both range control and range safety officers training. The training is necessary to perform their respective functions with greater levels of confidence prior to first flight.

Sharma, Ashley↗

Principal Investigator-in-a-Box

Human performance in orbit is currently limited by several factors beyond the intrinsic awkwardness of motor control in weightlessness. Cognitive functioning can be affected by such factors as cumulative sleep loss, stress and the psychological effects of long-duration small-group isolation. When an astronaut operates a scientific experiment, the performance decrement associated with such factors can lead to lost or poor quality data and even the total loss of a scientific objective, at great cost to the sponsors and to the dismay of the Principal Investigator. In long-duration flights, as anticipated on the International Space Station and on any planetary exploration, the experimental model is further complicated by long delays between training and experiment, and the large number of experiments each crew member must perform. Although no documented studies have been published on the subject, astronauts report that an unusually large number of simple errors are made in space. Whether a result of the effects of microgravity, accumulated fatigue, stress or other factors, this pattern of increased error supports the need for a computerized decision-making aid for astronauts performing experiments. Artificial intelligence and expert systems might serve as powerful tools for assisting experiments in space. Those conducting space experiments typically need assistance exactly when the planned checklist does not apply. Expert systems, which use bits of human knowledge and human methods to respond appropriately to unusual situations, have a flexibility that is highly desirable in circumstances where an invariably predictable course of action/response does not exist. Frequently the human expert on the ground is unavailable, lacking the latest information, or not consulted by the astronaut conducting the experiment. In response to these issues, we have developed "Principal Investigator-in-a-Box," or [PI], to capture the reasoning process of the real expert, the Principal Investigator, and combine that with real-time data available in space in order to advise the astronaut about how to proceed in real time. [PI] advises the astronaut during the progress of an experiment in much the same way a real Principal Investigator might do while looking over the astronaut's shoulder. In its original application, [PI] mimicked several of the tasks of the Principal Investigator, including data quality monitoring, troubleshooting, prescheduling, protocol management and "interesting data" detection. The proposed research focuses on the efficacy of this technique as applied to the data quality monitoring and troubleshooting aspects of [PI].

Young, Laurence R.↗

The Mathematics of Navigating the Solar System

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

Hintz, Gerald↗

On-Line, Self-Learning, Predictive Tool for Determining Payload Thermal Response

This paper will present the results of a joint ManTech / Goddard R&D effort, currently under way, to develop and test a computer based, on-line, predictive simulation model for use by facility operators to predict the thermal response of a payload during thermal vacuum testing. Thermal response was identified as an area that could benefit from the algorithms developed by Dr. Jeri for complex computer simulations. Most thermal vacuum test setups are unique since no two payloads have the same thermal properties. This requires that the operators depend on their past experiences to conduct the test which requires time for them to learn how the payload responds while at the same time limiting any risk of exceeding hot or cold temperature limits. The predictive tool being developed is intended to be used with the new Thermal Vacuum Data System (TVDS) developed at Goddard for the Thermal Vacuum Test Operations group. This model can learn the thermal response of the payload by reading a few data points from the TVDS, accepting the payload's current temperature as the initial condition for prediction. The model can then be used as a predictive tool to estimate the future payload temperatures according to a predetermined shroud temperature profile. If the error of prediction is too big, the model can be asked to re-learn the new situation on-line in real-time and give a new prediction. Based on some preliminary tests, we feel this predictive model can forecast the payload temperature of the entire test cycle within 5 degrees Celsius after it has learned 3 times during the beginning of the test. The tool will allow the operator to play "what-if' experiments to decide what is his best shroud temperature set-point control strategy. This tool will save money by minimizing guess work and optimizing transitions as well as making the testing process safer and easier to conduct.

Jen, Chian-Li↗

Acceptance Testing of a Satellite SCADA Photovoltaic-Diesel Hybrid System

Satellite Supervisory Control and Data Acquisition (SCADA) of a Photovoltaic (PV)/diesel hybrid system was tested using NASA's Advanced Communication Technology Satellite (ACTS) and Ultra Small Aperture Terminal (USAT) ground stations. The setup consisted of a custom-designed PV/diesel hybrid system, located at the Florida Solar Energy Center (FSEC), which was controlled and monitored at a "remote" hub via Ka-band satellite link connecting two 1/4 Watt USATs in a SCADA arrangement. The robustness of the communications link was tested for remote monitoring of the health and performance of a PV/diesel hybrid system, and for investigating load control and battery charging strategies to maximize battery capacity and lifetime, and minimize loss of critical load probability. Baseline hardware performance test results demonstrated that continuous two-second data transfers can be accomplished under clear sky conditions with an error rate of less than 1%. The delay introduced by the satellite (1/4 sec) was transparent to synchronization of satellite modem as well as to the PV/diesel-hybrid computer. End-to-end communications link recovery times were less than 36 seconds for loss of power and less than one second for loss of link. The system recovered by resuming operation without any manual intervention, which is important since the 4 dB margin is not sufficient to prevent loss of the satellite link during moderate to heavy rain. Hybrid operations during loss of communications link continued seamlessly but real-time monitoring was interrupted. For this sub-tropical region, the estimated amount of time that the signal fade will exceed the 4 dB margin is about 10%. These results suggest that data rates of 4800 bps and a link margin of 4 dB with a 1/4 Watt transmitter are sufficient for end-to-end operation in this SCADA application.

Kalu, A.↗

Results From The First Interactive Scientific Expert System In Space

We describe recent work on automation and support of science experiments on the Space Shuttle. PI-in-a-Box, the first interactive expert system for scientific support, was flown onboard STS-58 in October 1993. It was designed to help astronauts perform better science in space by providing expert-level advice in real-time. The system provides help with 'technician' tasks such as data acquisition, data quality monitoring, and diagnostic, troubleshooting and repair. The system also performs 'expert' reasoning on the scientific model and experiment steps scheduling. It can make scheduling recommendations based on hardware status, time available, and agreement between predictions and flight data. The system was successfully deployed and used throughout the mission. Most of the 'technician' skills of the system were used with success. The scientific model study performed correctly, but we believe the results were not exploited by the astronauts because of Spacelab operational pressures. Also, portions of the system were designed around rigid schedule constraints that were essentially relaxed during the mission. This version was tailored to a specific vestibular experiment known as the 'rotating dome'. We are currently expanding our effort in various scientific (other life and microgravity sciences experiments) and technological directions (integrated telescience, astronaut science advisor, and autonomous control).

Groleau, Nicolas↗

Results from the First Interactive Scientific Expert System in Space

We describe recent work on automation and support of science experiments on the Space Shuttle. PI-in-a-Box, the first interactive expert system for scientific support, was flown onboard STS-58 in October 1993. It was designed to help astronauts perform better science in space by providing expert-level advice in real-time. The system provides help with "technician" tasks such as data acquisition, data quality monitoring, and diagnostic, troubleshooting and repair. The system also performs "expert" reasoning on the scientific model and experiment steps scheduling. It can make scheduling recommendations based on hardware status, time available, and agreement between predictions and flight data. The system was successfully deployed and used throughout the mission. Most of the "technician" skills of the system were used with success. The scientific model study performed correctly, but we believe the results were not exploited by the astronauts because of Spacelab operational pressures. Also, portions of the system were designed around rigid schedule constraints that were essentially relaxed during the mission. This version was tailored to a specific vestibular experiment known as the "rotating dome". We are currently expanding our effort in various scientific (other life and microgravity sciences experiments) and technological directions (integrated telescience, astronaut science advisor, and autonomous control).

Groleau, Nicolas↗

Exploring Gigabyte Datasets in Real Time: Architectures, Interfaces and Time-Critical Design

Architectures and Interfaces: The implications of real-time interaction on software architecture design: decoupling of interaction/graphics and computation into asynchronous processes. The performance requirements of graphics and computation for interaction. Time management in such an architecture. Examples of how visualization algorithms must be modified for high performance. Brief survey of interaction techniques and design, including direct manipulation and manipulation via widgets. talk discusses how human factors considerations drove the design and implementation of the virtual wind tunnel. Time-Critical Design: A survey of time-critical techniques for both computation and rendering. Emphasis on the assignment of a time budget to both the overall visualization environment and to each individual visualization technique in the environment. The estimation of the benefit and cost of an individual technique. Examples of the modification of visualization algorithms to allow time-critical control.

Bryson, Steve↗

Real-Time Simulation

Coryphaeus Software, founded in 1989 by former NASA electronic engineer Steve Lakowske, creates real-time 3D software. Designer's Workbench, the company flagship product, is a modeling and simulation tool for the development of both static and dynamic 3D databases. Other products soon followed. Activation, specifically designed for game developers, allows developers to play and test the 3D games before they commit to a target platform. Game publishers can shorten development time and prove the "playability" of the title, maximizing their chances of introducing a smash hit. Another product, EasyT, lets users create massive, realistic representation of Earth terrains that can be viewed and traversed in real time. Finally, EasyScene software control the actions among interactive objects within a virtual world. Coryphaeus products are used on Silican Graphics workstation and supercomputers to simulate real-world performance in synthetic environments. Customers include aerospace, aviation, architectural and engineering firms, game developers, and the entertainment industry.

Source record↗

An Architecture for Real-Time Interpretation and Visualization of Structural Sensor Data in a Laboratory Environment

A visualization system is being developed out of the need to monitor, interpret, and make decisions based on the information from several thousand sensors during experimental testing to facilitate development and validation of structural health monitoring algorithms. As an added benefit the system will enable complete real-time sensor assessment of complex test specimens. Complex structural specimens are routinely tested that have hundreds or thousands of sensors. During a test, it is impossible for a single researcher to effectively monitor all the sensors and subsequently interesting phenomena occur that are not recognized until post-test analysis. The ability to detect and alert the researcher to these unexpected phenomena as the test progresses will significantly enhance the understanding and utilization of complex test articles. Utilization is increased by the ability to halt a test when the health monitoring algorithm response is not satisfactory or when an unexpected phenomenon occurs, enabling focused investigation potentially through the installation of additional sensors. Often if the test continues, structural changes make it impossible to reproduce the conditions that exhibited the phenomena. The prohibitive time and costs associated with fabrication, sensoring, and subsequent testing of additional test articles generally makes it impossible to further investigate the phenomena. A scalable architecture is described to address the complex computational demands of structural health monitoring algorithm development and laboratory experimental test monitoring. The researcher monitors the test using a photographic quality 3D graphical model with actual sensor locations identified. In addition, researchers can quickly activate plots displaying time or load versus selected sensor response along with the expected values and predefined limits. The architecture has several key features. First, distributed dissimilar computers may be seamlessly integrated into the information flow. Second, virtual sensors may be defined that are complex functions of existing sensors or other virtual sensors. Virtual sensors represent a calculated value not directly measured by particular physical instrument. They can be used, for example, to represent the maximum difference in a range of sensors or the calculated buckling load based on the current strains. Third, the architecture enables autonomous response to preconceived events, where by the system can be configured to suspend or abort a test if a failure is detected in the load introduction system. Fourth, the architecture is designed to allow cooperative monitoring and control of the test progression from multiple stations both remote and local to the test system. To illustrate the architecture, a preliminary implementation is described monitoring the Stitched Composite Wing recently tested at LaRC.

Doggett, William↗

Satellite ATM Networks: Architectures and Guidelines Developed

An important element of satellite-supported asynchronous transfer mode (ATM) networking will involve support for the routing and rerouting of active connections. Work published under the auspices of the Telecommunications Industry Association (http://www.tiaonline.org), describes basic architectures and routing protocol issues for satellite ATM (SATATM) networks. The architectures and issues identified will serve as a basis for further development of technical specifications for these SATATM networks. Three ATM network architectures for bent pipe satellites and three ATM network architectures for satellites with onboard ATM switches were developed. The architectures differ from one another in terms of required level of mobility, supported data rates, supported terrestrial interfaces, and onboard processing and switching requirements. The documentation addresses low-, middle-, and geosynchronous-Earth-orbit satellite configurations. The satellite environment may require real-time routing to support the mobility of end devices and nodes of the ATM network itself. This requires the network to be able to reroute active circuits in real time. In addition to supporting mobility, rerouting can also be used to (1) optimize network routing, (2) respond to changing quality-of-service requirements, and (3) provide a fault tolerance mechanism. Traffic management and control functions are necessary in ATM to ensure that the quality-of-service requirements associated with each connection are not violated and also to provide flow and congestion control functions. Functions related to traffic management were identified and described. Most of these traffic management functions will be supported by on-ground ATM switches, but in a hybrid terrestrial-satellite ATM network, some of the traffic management functions may have to be supported by the onboard satellite ATM switch. Future work is planned to examine the tradeoffs of placing traffic management functions onboard a satellite as opposed to implementing those functions at the Earth station components.

vonDeak, Thomas C.↗

Edge smoothing for real-time simulation of a polygon face object system as viewed by a moving observer

The visual system within an aircraft flight simulation system receives flight data and terrain data which is formated into a buffer memory. The image data is forwarded to an image processor which translates the image data into face vertex vectors Vf, defining the position relationship between the vertices of each terrain object and the aircraft. The image processor then rotates, clips, and projects the image data into two-dimensional display vectors (Vd). A display generator receives the Vd faces, and other image data to provide analog inputs to CRT devices which provide the window displays for the simulated aircraft. The video signal to the CRT devices passes through an edge smoothing device which prolongs the rise time (and fall time) of the video data inversely as the slope of the edge being smoothed. An operational amplifier within the edge smoothing device has a plurality of independently selectable feedback capacitors each having a different value. The values of the capacitors form a series which doubles as a power of two. Each feedback capacitor has a fast switch responsive to the corresponding bit of a digital binary control word for selecting (1) or not selecting (0) that capacitor. The control word is determined by the slope of each edge. The resulting actual feedback capacitance for each edge is the sum of all the selected capacitors and is directly proportional to the value of the binary control word. The output rise time (or fall time) is a function of the feedback capacitance, and is controlled by the slope through the binary control word.

Lotz, Robert W.↗

High sensitivity real-time NVR monitor

A real time non-volatile residue (NVR) monitor, which utilizes surface acoustic wave (SAW) resonators to detect molecular contamination in a given environment. The SAW resonators operate at a resonant frequency of approximately 200 MHz-2,000 MHz which enables the NVR monitor to detect molecular contamination on the order of 10.sup.-11 g-cm.sup.-2 to 10.sup.-13 g-cm.sup.2. The NVR monitor utilizes active temperature control of (SAW) resonators to achieve a stable resonant frequency. The temperature control system of the NVR monitor is able to directly heat and cool the SAW resonators utilizing a thermoelectric element to maintain the resonators at a present temperature independent of the environmental conditions. In order to enable the direct heating and cooling of the SAW resonators, the SAW resonators are operatively mounted to a heat sink. In one embodiment, the heat sink is located in between the SAW resonators and an electronic circuit board which contains at least a portion of the SAW control electronics. The electrical leads of the SAW resonators are connected through the heat sink to the circuit board via an electronic path which prevents inaccurate frequency measurement.

Bowers, William D.↗