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Articles 61 - 90 of 97
Full-Text Articles in Aerospace Engineering
Multimission Aircraft Design Study: Electromagnetic Compatibility, Jenna M. Davis
Multimission Aircraft Design Study: Electromagnetic Compatibility, Jenna M. Davis
Theses and Dissertations
The multi-mission aircraft (MMA) technical feasibility study looked at the replacement of the aging fleet of C-135 and C-130 theater based command & control (C2) and intelligence, surveillance and reconnaissance (ISR) fleet. It is proposed that the MMA be out-fitted to combine some or all the functions of existing AWACS, JSTARS, RIVET JOINT, COMPASS CALL, and ABC CC platforms. It would also have links to other manned or unmanned ISR aircraft, as well as satellites. The objective of the proposed design study is to examine the technical risks involved in combining multiple functions onto one aircraft that currently reside on …
Cargo Aircraft Bombing System (Cabs), Gurler Ari
Cargo Aircraft Bombing System (Cabs), Gurler Ari
Theses and Dissertations
From the early days of aviation, bombs typically have been carried by either fighter or bomber aircraft in the inventory. On the other hand, more and more long-range, precision-guided missiles are being produced with ranges that vary from tens to hundreds of miles. With such missiles, targets can be destroyed without placing personnel and equipment into close proximity to the targets. The mass delivery of standoff weapons could be especially advantageous during the early phases of an air campaign. This study considers the use of cargo aircraft for carrying and launching bombs and missiles. It discusses many aspects of a …
Analysis Of Cooperative Behavior For Autonomous Wide Area Search Munitions, Orhan Gozaydin
Analysis Of Cooperative Behavior For Autonomous Wide Area Search Munitions, Orhan Gozaydin
Theses and Dissertations
This research investigates the effectiveness of autonomous wide area search munitions using cooperative and non-cooperative behavior algorithms under various scenarios. The scenarios involve multiple autonomous munitions searching for an unknown number of targets with different priorities at unknown locations. For the cooperative cases, communications are allowed between the munitions to help locate, identify, and decide to pursue an attack on a target or to continue searching the rest of the battlefield. For non cooperative cases, munitions independently search, detect, identify and decide to attack an identified target or continue to search. Performance of the cooperative munitions depends on numerous parameters …
Computational Fluid Dynamics Investigation Of Vortex Breakdown For A Delta Wing At High Angle Of Attack, Jacob A. Freeman
Computational Fluid Dynamics Investigation Of Vortex Breakdown For A Delta Wing At High Angle Of Attack, Jacob A. Freeman
Theses and Dissertations
Using the commercially available FLUENT 3-D flow field solver, this research effort investigated vortex breakdown over a delta wing at high angle of attack (α) in preparation for investigation of active control of vortex breakdown using steady, along- core blowing. A flat delta-shaped half-wing with sharp leading edge and sweep angle of 60° was modeled at α=18° in a wind tunnel at Mach 0.04 and Reynolds number of 3.4 x 105. A hybrid (combination of structured and unstructured) numerical mesh was generated to accommodate blowing ports on the wing surface. Results for cases without and with along-core blowing …
Development Of An Experimental Test Section For Forcing Unsteady Flow In A Linear Compressor Cascade Using Circular Rods, Patrick C. Wade
Development Of An Experimental Test Section For Forcing Unsteady Flow In A Linear Compressor Cascade Using Circular Rods, Patrick C. Wade
Theses and Dissertations
Upstream propagating waves impinging on a cascade of compressor blades were examined in an effort to better understand the influence of downstream components on high cycle fatigue in turbine engines. An array of cylinders was used to simulate the unsteady field generated by a rotor downstream of a set of stators. The unsteady flow upstream of a single cylinder and an array of cylinders, with and without an upstream cascade, was examined experimentally and computationally. Computational results indicate that the cylinders would only shed coherently when placed downstream of a set of blades. Coherent shedding is created when each of …
Development And Simulation Of A Pseudolite-Based Flight Reference System, Terry J. Bouska
Development And Simulation Of A Pseudolite-Based Flight Reference System, Terry J. Bouska
Theses and Dissertations
Current flight reference systems are vulnerable to GPS jamming and also lack the accuracy required to test new systems. Pseudolites can augment flight reference systems by improving accuracy, especially in the presence of GPS jamming. This thesis evaluates a pseudolite-based flight reference system which applies and adapts carrier-phase differential GPS techniques. The algorithm developed in this thesis utilizes an extended Kalman filter along with carrier-phase ambiguity resolution techniques. A simulation of the pseudolite-based positioning system realistically models measurement noise, multipath, pseudolite position errors, and tropospheric delay. A comparative evaluation of the algorithms performance for single and widelane frequency measurements is …
Ins Aiding Using Passive, Bearings-Only Measurements Of An Unknown Stationary Ground Object, Alec E. Porter
Ins Aiding Using Passive, Bearings-Only Measurements Of An Unknown Stationary Ground Object, Alec E. Porter
Theses and Dissertations
The theory for Inertial Navigation System (INS) aiding using passive, bearings only measurements of an unknown stationary ground object, in the vein of optical flow measurement, is developed. Stand-alone bearings-only measurements over time of an unknown, but stationary, ground object are shown to yield estimates of the aircraft’s aerodynamic angles, viz., the angle of attack and sideslip angle. Two new equations containing the aircraft’s angular navigation variables ψ, θ, φ, γ, H, and the aerodynamic angles are derived. This allows an update of the aircraft’s attitude, thus making INS aiding using passive, bearings-only measurements possible. Moreover, the use of stadiametry, …
Cubesat 2002: Current Design Overview, Robert J. Twiggs
Cubesat 2002: Current Design Overview, Robert J. Twiggs
Robert "Bob" Twiggs STEM Education Collection
A PowerPoint Presentation created by Professor Bob Twiggs titled "Cubesat 2002: Current Design Overview" from February 5, 2003.
Computational Simulation And Piv Measurements Of The Laminar Vortical Flowfield For A Delta Wing At High Angle Of Attack, Russell M. Cummings, Scott A. Morton, Stefan G. Siegel
Computational Simulation And Piv Measurements Of The Laminar Vortical Flowfield For A Delta Wing At High Angle Of Attack, Russell M. Cummings, Scott A. Morton, Stefan G. Siegel
Aerospace Engineering
The low-speed, laminar flowfield for a 70°-sweep delta wing is investigated. Solutions to the unsteady, three-dimensional, compressible Navier-Stokes equations were obtained on an unstructured grid to match results from an experiment performed in a water tunnel. The experiment was conducted with the delta wing at an angle of attack of 35° and the freestream flow at a root-chord Reynolds number of 40,700. The computational results are analyzed and compared with the experimental results in order to show how computations and experiments can be conducted in a synergistic fashion. Details about the primary vortex location, vortex burst, secondary vortex, and shear …
Des Grid Resolution Issues For Vortical Flows On A Delta Wing And An F-18c, Scott A. Morton, Mathew B. Steenman, Russell M. Cummings, James R. Forsythe
Des Grid Resolution Issues For Vortical Flows On A Delta Wing And An F-18c, Scott A. Morton, Mathew B. Steenman, Russell M. Cummings, James R. Forsythe
Aerospace Engineering
An assessment of unstructured grids for use in Detached-Eddy Simulations (DES) of vortical flowfields over two configurations, a 70 degree delta wing and an F-18C are presented. The role of the grid in detached eddy simulations of vortical flowfields, including complex features such as vortex breakdown, is assessed on a delta wing with comparison to wind tunnel data. Adaptive mesh refinement is applied to the delta wing grid to improve the focus region aft of the vortex breakdown where massively separated flow exists and unsteady pressures are generated that could impact the loads on vertical tails of more complex configurations. …
A Multifaceted Approach To The Aiaa Foundation Undergraduate Team Aircraft Design Competition, Russell M. Cummings, Aaron R. Byerley
A Multifaceted Approach To The Aiaa Foundation Undergraduate Team Aircraft Design Competition, Russell M. Cummings, Aaron R. Byerley
Aerospace Engineering
A multifaceted, novel approach was used to help students create entries for the AIAA Foundation Undergraduate Team Aircraft Design Competition. Each entry involved the design, analysis, construction, and testing of the aircraft. Three groups were involved for each airplane: the first group was responsible for the airframe, the second group was responsible for the engine, and the third group was responsible for the construction and flight testing of a radio-controlled flying model. There was an overall Chief Executive Officer who insured that engine-airframe integration issues were addressed. Students from a variety of majors, both technical and non-technical, participated in various …
From Learning To Talk To Learning Engineering; Drawing Connections Across The Disciplines, Nikos J. Mourtos
From Learning To Talk To Learning Engineering; Drawing Connections Across The Disciplines, Nikos J. Mourtos
Faculty Publications
This paper introduces eight so-called conditions of learning (immersion, demonstration, engagement, expectations, responsibility, approximation, employment and response), which have been previously established for the learning of literacy. It is stipulated that these conditions are universal in nature; in other words, they must be present for any learning to occur. When these conditions are met, students learn more efficiently and are able to enjoy and appreciate their subject matter. The article discusses briefly how these conditions were established and their relevance in the study of engineering. More importantly, the article also presents examples of how these conditions can be satisfied in …
Cool Flames In Propane-Oxygen Premixtures At Low And Intermediate Temperatures At Reduced-Gravity, Howard Pearlman, Michael R. Foster, Devrez Karabacak
Cool Flames In Propane-Oxygen Premixtures At Low And Intermediate Temperatures At Reduced-Gravity, Howard Pearlman, Michael R. Foster, Devrez Karabacak
Faculty Publications - Biomedical, Mechanical, and Civil Engineering
No abstract provided.
Aspects Of Control For A Parafoil And Payload System, Nathan Slegers, Mark Costello
Aspects Of Control For A Parafoil And Payload System, Nathan Slegers, Mark Costello
Faculty Publications - Biomedical, Mechanical, and Civil Engineering
A parafoil controlled by parafoil brake deflection offers a lightweight and space-efficient control mechanism for autonomous placement of air-dropped payloads to specified ground coordinates. The work reported here investigates control issues for a parafoil and payload system with left and right parafoil brakes used as the control mechanism. It is shown that parafoil and payload systems can exhibit two basic modes of lateral control, namely,roll and skid steering. These two modes of lateral steering generate lateral response in opposite directions. For example, a roll steer configuration turns left when the right parafoil brake is activated, whereas a skid steer configuration …
Comparison Of Measured And Simulated Motion Of A Controllable Parafoil And Payload System, Nathan Slegers, Mark Costello
Comparison Of Measured And Simulated Motion Of A Controllable Parafoil And Payload System, Nathan Slegers, Mark Costello
Faculty Publications - Biomedical, Mechanical, and Civil Engineering
For parafoil and payload aircraft, control is affected by changing the length of several rigging lines connected to the outboard side and rear of the parafoil leading to complex changes in the shape and orientation of the lifting surface. Flight mechanics of parafoil and payload aircraft most often employ a 6 or 9 DOF representation with the canopy modeled as a rigid body during flight. The effect of control inputs is idealized by the deflection of parafoil brakes on the left and right side of the parafoil. Using a small parafoil and payload aircraft, glide rates and turn performance were …
Simultaneous Observations Of Mesospheric Gravity Waves And Sprites Generated By A Midwestern Thunderstorm, D. D. Sentman, E. M. Wescott, R. H. Picard, J. R. Winick, H. C. Stenbaek-Nielsen, E. M. Dewan, D. R. Moudry, F. T. São Sabbas, M. J. Heavner, J. Morrill
Simultaneous Observations Of Mesospheric Gravity Waves And Sprites Generated By A Midwestern Thunderstorm, D. D. Sentman, E. M. Wescott, R. H. Picard, J. R. Winick, H. C. Stenbaek-Nielsen, E. M. Dewan, D. R. Moudry, F. T. São Sabbas, M. J. Heavner, J. Morrill
United States Air Force: Publications
The present report investigates using simultaneous observations of coincident gravity waves and sprites to establish an upper limit on sprite-associated thermal energy deposition in the mesosphere. The University of Alaska operated a variety of optical imagers and photometers at two ground sites in support of the NASA Sprites99 balloon campaign. One site was atop a US Forest Service lookout tower on Bear Mt. in the Black Hills, in western South Dakota. On the night of 18 August 1999 we obtained from this site simultaneous images of sprites and OH airglow modulated by gravity waves emanating from a very active sprite …
On The Use Of Rigging Angle And Canopy Tilt For Control Of A Parafoil And Payload System, Nathan Slegers, Mark Costello
On The Use Of Rigging Angle And Canopy Tilt For Control Of A Parafoil And Payload System, Nathan Slegers, Mark Costello
Faculty Publications - Biomedical, Mechanical, and Civil Engineering
Controllable parafoil and payload aircraft are controlled with downward deflection of left and right parafoil brakes. Lateral control is obtained by differential deflection while longitudinal control is created by collective deflection of the left and right side parafoil brakes. The work reported considers an alternative method to control parafoil and payload air vehicles by tilting the parafoil canopy for lateral control and changing rigging angle for longitudinal control. Using a nonlinear 9 degree of freedom simulation model, it is shown that canopy tilt provides a powerful lateral control mechanism and rigging angle provides a viable longitudinal control mechanism.
A Single-Element Tuning Fork Piezoelectric Linear Actuator, J. Satonobu, K. Nakamura, S. Ueha, Daniel S. Stutts, James R. Friend
A Single-Element Tuning Fork Piezoelectric Linear Actuator, J. Satonobu, K. Nakamura, S. Ueha, Daniel S. Stutts, James R. Friend
Mechanical and Aerospace Engineering Faculty Research & Creative Works
This paper describes the design of a piezoelectric tuning-fork, dual-mode motor. The motor uses a single multilayer piezoelectric element in combination with tuning fork and shearing motion to form an actuator using a single drive signal. Finite-element analysis was used in the design of the motor, and the process is described along with the selection of the device's materials and its performance. Swaging was used to mount the multilayer piezoelectric element within the stator. Prototypes of the 25-mm long bidirectional actuator achieved a maximum linear no-load speed of 16.5 cm/s, a maximum linear force of 1.86 N, and maximum efficiency …
A Product Architecture-Based Conceptual Dfa Technique, Robert B. Stone, Daniel A. Mcadams, Varghese J. Kayyalethekkel
A Product Architecture-Based Conceptual Dfa Technique, Robert B. Stone, Daniel A. Mcadams, Varghese J. Kayyalethekkel
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A conceptual design for assembly (DFA) method is introduced in this paper. The method incorporates DFA analysis into the conceptual design phase. Current DFA methods, essentially all of which are post-design DFA analyses, are reviewed with emphasis on the popular Boothroyd and Dewhurst method. The product architecture-based conceptual DFA method developed and presented in this article uses two relatively new concepts: the functional basis and the method of module heuristics. The functional basis is used to derive a functional model of a product in a standard language and the module heuristics are applied to the functional model to identify a …
Stochastic Game Approach To Air Operations, Ben G. Fitzpatrick, William M. Mceneaney, Istvan G. Lauko
Stochastic Game Approach To Air Operations, Ben G. Fitzpatrick, William M. Mceneaney, Istvan G. Lauko
Mathematics, Statistics and Data Science Faculty Works
A Command and Control (C2) problem for Military Air Operations is addressed. Specifically, we consider C2 problems for air vehicles against ground based targets and defensive systems. The problem is viewed as a stochastic game. In this paper, we restrict our attention to the C2 level where the problem may consist of a few UCAVs or aircraft (or possibly teams of vehicles); less than say, a half-dozen enemy SAMs; a few enemy assets (viewed as targets from our standpoint); and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are …
Experimental Studies Assessing The Repeatability Of A Functional Modeling Derivation Method, Mark A. Kurfman, Michael E. Stock, Robert B. Stone, Jagan Rajan, Kristin L. Wood
Experimental Studies Assessing The Repeatability Of A Functional Modeling Derivation Method, Mark A. Kurfman, Michael E. Stock, Robert B. Stone, Jagan Rajan, Kristin L. Wood
Mechanical and Aerospace Engineering Faculty Research & Creative Works
This paper presents the results of research attempts to substantiate repeatability and uniqueness claims of a functional model derivation method following a hypothesis generation and testing procedure outlined in design research literature. Three experiments are constructed and carried out with a participant pool that possesses a range of engineering design skill levels. the experiments test the utility of a functional model derivation method to produce repeatable functional models for a given product among different designers. in addition to this, uniqueness of the functional models produced by the participants is examined. Results indicate the method enhances repeatability and leads designers toward …
Mapping Function To Failure Mode During Component Development, Irem Y. Tumer, Robert B. Stone
Mapping Function To Failure Mode During Component Development, Irem Y. Tumer, Robert B. Stone
Mechanical and Aerospace Engineering Faculty Research & Creative Works
When designing aerospace systems, it is essential to provide crucial failure information for failure prevention. Failure modes and effect types of analyses and prior engineering knowledge and experience are commonly used to determine the potential modes of failures a product might encounter during its lifetime. When new products are being considered and designed, this knowledge and information is expanded upon to help designers extrapolate based on their similarity with existing products and the potential design tradeoffs. in this work, we aim to enhance this process by providing design-aid tools which derive similarities between functionality and failure modes. Specifically, this paper …
Modeling Fracture In Laminated Automotive Glazing Impacted By Spherical Featureless Headform, Lokeswarappa R. Dharani, S. R. Mettu, S. Zhao, S. D. Barbat, L. Chai
Modeling Fracture In Laminated Automotive Glazing Impacted By Spherical Featureless Headform, Lokeswarappa R. Dharani, S. R. Mettu, S. Zhao, S. D. Barbat, L. Chai
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Laminated glass consisting of two soda lime glass plies adhered by a polyvinyl butyral interlayer (PVB) is used for automotive glazing. This paper describes the application of a dynamic, nonlinear finite element method to investigate the failure modes of a laminated glass subjected to low-velocity impact with a spherical head form. Crack type, crack location and crack initiation time are evaluated using the maximum principal stress and J-integral criterion. Failure occurred due to flexural stresses and not bearing stresses. the first crack always initiated at the center of the outer impacted ply and PVB interface, and later on the exterior …
Comparison Of 3-, 5-, And 6-Phase Machines For Automotive Charging Applications, B. Zhang, Hua Bai, Walter Eversman, Ronald J. Krefta, Duane J. Buening, Steven Pekarek, Gregory R. Holbrook
Comparison Of 3-, 5-, And 6-Phase Machines For Automotive Charging Applications, B. Zhang, Hua Bai, Walter Eversman, Ronald J. Krefta, Duane J. Buening, Steven Pekarek, Gregory R. Holbrook
Mechanical and Aerospace Engineering Faculty Research & Creative Works
In this paper, the performance of a 5-phase claw-pole machine/converter system is compared with those of 3-phase and 6-phase systems of the same volume. It is shown that the acoustic output of the 5-phase machine compares favorably with that of the 6-phase machine and is much lower than that of the 3-phase machine over a majority of the operating range. In addition, the output current produced by the 5-phase machine Is, in general, 6-8% higher than those of the 3-phase and 6-phase machines. These results suggest that for maximizing power density while minimizing cost and acoustic noise, 5-phase machines provide …
Missile Longitudinal Autopilot Design Using A New Suboptimal Nonlinear Control Method, Ming Xin, S. N. Balakrishnan
Missile Longitudinal Autopilot Design Using A New Suboptimal Nonlinear Control Method, Ming Xin, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
A missile longitudinal autopilot is designed using a new nonlinear control synthesis technique called the θ-D approximation. The particular θ-D methodology used is referred to as the θ-D H2 design. The technique can achieve suboptimal closed-form solutions to a class of nonlinear optimal control problems in the sense that it solves the Hamilton-Jacobi-Bellman equation approximately by adding perturbations to the cost function. An interesting feature of this method is that the expansion terms in the expression for suboptimal control are nothing but solutions to the state-dependent Riccati equations associated with this class of problems. The θ-D H2 design has the …
Proper Orthogonal Decomposition Based Modeling And Experimental Implementation Of A Neurocontroller For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look, Radhakant Padhi
Proper Orthogonal Decomposition Based Modeling And Experimental Implementation Of A Neurocontroller For A Heat Diffusion System, Prashant Prabhat, S. N. Balakrishnan, Dwight C. Look, Radhakant Padhi
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Experimental implementation of a dual neural network based optimal controller for a heat diffusion system is presented. Using the technique of proper orthogonal decomposition (POD), a set of problem-oriented basis functions are designed taking the experimental data as snap shot solutions. Using these basis functions in Galerkin projection, a reduced-order analogous lumped parameter model of the distributed parameter system is developed. This model is then used in an analogous lumped parameter problem. A dual neural network structure called adaptive critics is used to obtain optimal neurocontrollers for this system. In this structure, one set of neural networks captures the relationship …
Approximate Dynamic Programming Based Optimal Neurocontrol Synthesis Of A Chemical Reactor Process Using Proper Orthogonal Decomposition, Radhakant Padhi, S. N. Balakrishnan
Approximate Dynamic Programming Based Optimal Neurocontrol Synthesis Of A Chemical Reactor Process Using Proper Orthogonal Decomposition, Radhakant Padhi, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
The concept of approximate dynamic programming and adaptive critic neural network based optimal controller is extended in this study to include systems governed by partial differential equations. An optimal controller is synthesized for a dispersion type tubular chemical reactor, which is governed by two coupled nonlinear partial differential equations. It consists of three steps: First, empirical basis functions are designed using the "Proper Orthogonal Decomposition" technique and a low-order lumped parameter system to represent the infinite-dimensional system is obtained by carrying out a Galerkin projection. Second, approximate dynamic programming technique is applied in a discrete time framework, followed by the …
Hierarchical Optimal Control Of A Turning Process - Linearization Approach, Anand Dasgupta, B. Pandurangan, Robert G. Landers, S. N. Balakrishnan
Hierarchical Optimal Control Of A Turning Process - Linearization Approach, Anand Dasgupta, B. Pandurangan, Robert G. Landers, S. N. Balakrishnan
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Machining process control technologies are currently not well integrated into machine tool controllers and, thus, servomechanism dynamics are often ignored when designing and implementing process controllers. In this paper, a hierarchical controller is developed that simultaneously regulates the servomechanism positions and cutting forces in a lathing operation. The force process and servomechanism system are separated into high and low levels, respectively, in the hierarchy. The high level goal is to maintain a constant cutting force to maximize productivity while not violating a spindle power constraint. This goal is systematically propagated to the lower level and combined with the low level …
Output Feedback Force Control For A Parallel Turning Operation, Raghusimha Sudhakara, Robert G. Landers
Output Feedback Force Control For A Parallel Turning Operation, Raghusimha Sudhakara, Robert G. Landers
Mechanical and Aerospace Engineering Faculty Research & Creative Works
Parallel machine tools (i.e., machine tools capable of cutting a part with multiple tools simultaneously but independently) are being utilized more and more to increase operation productivity, decrease setups, and reduce floor space. Process control is the utilization of real-time process sensor information to automatically adjust process parameters (e.g., feed, spindle speed) to increase operation productivity and quality. To date, however, these two technologies have not been combined. This paper describes the design of an output feedback controller for a parallel turning operation that accounts for the inherent nonlinearities in the force process. An analysis of the process equilibriums explains …
Intelligent Strain Sensing On A Smart Composite Wing Using Extrinsic Fabry-Perot Interferometric Sensors And Neural Networks, Kakkattukuzhy M. Isaac, Donald C. Wunsch, Steve Eugene Watkins, Rohit Dua, V. M. Eller
Intelligent Strain Sensing On A Smart Composite Wing Using Extrinsic Fabry-Perot Interferometric Sensors And Neural Networks, Kakkattukuzhy M. Isaac, Donald C. Wunsch, Steve Eugene Watkins, Rohit Dua, V. M. Eller
Electrical and Computer Engineering Faculty Research & Creative Works
Strain prediction at various locations on a smart composite wing can provide useful information on its aerodynamic condition. The smart wing consisted of a glass/epoxy composite beam with three extrinsic Fabry-Perot interferometric (EFPI) sensors mounted at three different locations near the wing root. Strain acting on the three sensors at different air speeds and angles-of-attack were experimentally obtained in a closed circuit wind tunnel under normal conditions of operation. A function mapping the angle of attack and air speed to the strains on the three sensors was simulated using feedforward neural networks trained using a backpropagation training algorithm. This mapping …