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Results for “Snell's Law”

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NASA NTRS1993

A survey of propfan noise propagation at cruise

Acoustic measurements collected during the Propfan Test Assessment (PTA) program in 1989 had demonstrated that cruising Propfans have undesirably high far-field noise level. This study attempts to investigate the source of these noise disturbances generated by a single-rotating propeller with supersonic tip speed. Various atmospheric and propagation effects responsible for shaping the far-field acoustics will be examined. A methodology for analyzing Propfan propagation noise is proposed based on the theory of geometrical acoustics. This approach allows acoustic rays to be traced into the far-field via Snell's law. Amplitude variation along the rays are evaluated by applying the Blokhintzev energy invariant principle. Additional terms are appended to the energy invariant principle to account for propagation and atmospheric effects. A FORTRAN program is written to analyze the rays emitted from a helicoidal source path traced by supersonic helical speed blade tip. Earlier papers by Myers and Farassat have demonstrated the presence of Mach envelopes that lead to formation of caustics. Linear geometric acoustics is used to ascertain the existence of these nonlinear caustics in the far-field. The importance of caustics to Propfan noise generation is then studied.

Sim, Ben WEL-C.↗

NASA NTRS1995

Radiative transfer in a semiinfinite medium with a specularly reflecting boundary

A consistent solution of the radiative transfer equation characterizing photon transport in a semi-infinite medium of refractive index greater than or equal to one is obtained following the method of Sobolev. Fresnel specular reflection, Snell's law and isotropic scattering are assumed. An algorithm is developed and its accuracy is demonstrated. A numerical Laplace transform inversion leads to an efficient evaluation for the interior flux and source function distributions.

Ganapol, B. D.↗

NASA NTRS2002

Panoramic Refracting Optic

An optical device having a semi-spherical or hemispherical field-of-view is provided. A conically-shaped piece of optical material has an annular surface satisfying Snell's Law for total internal reflection with respect to light passing through the piece and incident on the annular surface from within the piece.

Lindner, Jeffrey L.↗

NASA NTRS2003

Panoramic Refracting Conical Optic

Lindner, Jeffrey L.↗

NASA NTRS2004

Modeling of a Variable Focal Length Flat Lens Using Left Handed Metamaterials

Left Handed Metamaterials (LHM) were originally purposed by Victor Veselago in1968. These substances would allow a flat structure to focus electromagnetic (EM) waves because they have a negative index of refraction. A similar structure made from conventional materials, those with a positive index of refraction, would disperse the waves. But until recently, these structures have been purely theoretical because substances with both a negative permittivity and negative permeability, material properties necessary for a negative index of refraction, do not naturally exist, Recent developments have produced a structure composed of an array of thin wires and split ring resonators that shows a negative index of refraction. area smaller than a square wavelength. How small the area is can be determined by how perfectly the lens is polished and how pure the substance is that composes the lens. These lenses must also be curved for focusing to occur. The focal length is determined by the curvature of the lens and the material. On the other hand, a flat structure made from LHM would focus light because of the effect of a negative index of refraction in Snell s law. The focal length could also be varied by simply adjusting the distance of the lens from the source of radiation. This could create many devices that are adjustable to different situations in fields such as biomedical imaging and communication. the software package XFDTD which solves Maxwell s equations in the frequency domain as well as the time domain. The program used Drude models of materials to simulate the effect of negative permittivity and negative permeability. Because of this, a LHM can be simulated as a solid block of material instead of an array of wires and split ring resonators. After a flat lens is formed, I am to examine the focusing effect of the lens and determine if a higher resolution flat lens can be developed. Traditional lenses made from conventional materials cannot focus an EM wave onto an My goal was to model LHMs and create a flat lens from them. This was to be done using

Reinert, Jason↗

NASA NTRS2011

Monolithic, High-Speed Fiber-Optic Switching Array for Lidar

Current fiber switch technologies use mechanical means to redirect light beams, resulting in slow switch time, as well as poor reliability due to moving parts wearing out quickly at high speeds. A non-mechanical ability to switch laser output into one of multiple fibers within a fiber array can provide significant power, weight, and costs savings to an all-fiber system. This invention uses an array of crystals that act as miniature prisms to redirect light as an electric voltage changes the prism s properties. At the heart of the electro-optic fiber-optic switch is an electro- optic crystal patterned with tiny prisms that can deflect the beam from the input fiber into any one of the receiving fibers arranged in a linear array when a voltage is applied across the crystal. Prism boundaries are defined by a net dipole moment in the crystal lattice that has been poled opposite to the surrounding lattice fabricated using patterned, removable microelectrodes. When a voltage is applied across the crystal, the resulting electric field changes the index of refraction within the prism boundaries relative to the surrounding substrate, causing light to deflect slightly according to Snell s Law. There are several materials that can host the necessary monolithic poled pattern (including, but not limited to, SLT, KTP, LiNbO3, and Mg:LiNbO3). Be cause this is a solid-state system without moving parts, it is very fast, and does not wear down easily. This invention is applicable to all fiber networks, as well as industries that use such networks. The unit comes in a compact package, can handle both low and high voltages, and has a high reliability (100,000 hours without maintenance).

Suckow, Will↗

NASA NTRS2004

Measurement of an Evaporating Drop on a Reflective Substrate

A figure depicts an apparatus that simultaneously records magnified ordinary top-view video images and laser shadowgraph video images of a sessile drop on a flat, horizontal substrate that can be opaque or translucent and is at least partially specularly reflective. The diameter, contact angle, and rate of evaporation of the drop as functions of time can be calculated from the apparent diameters of the drop in sequences of the images acquired at known time intervals, and the shadowgrams that contain flow patterns indicative of thermocapillary convection (if any) within the drop. These time-dependent parameters and flow patterns are important for understanding the physical processes involved in the spreading and evaporation of drops. The apparatus includes a source of white light and a laser (both omitted from the figure), which are used to form the ordinary image and the shadowgram, respectively. Charge-coupled-device (CCD) camera 1 (with zoom) acquires the ordinary video images, while CCD camera 2 acquires the shadowgrams. With respect to the portion of laser light specularly reflected from the substrate, the drop acts as a plano-convex lens, focusing the laser beam to a shadowgram on the projection screen in front of CCD camera 2. The equations for calculating the diameter, contact angle, and rate of evaporation of the drop are readily derived on the basis of Snell s law of refraction and the geometry of the optics.

Chao, David F.↗

NASA NTRS1987

A ray tracing model for leaf bidirectional scattering studies

A leaf is modeled as a deterministic two-dimensional structure consisting of a network of circular arcs designed to represent the internal morphology of major species. The path of an individual ray through the leaf is computed using geometric optics. At each intersection of the ray with an arc, the specular reflected and transmitted rays are calculated according to the Snell and Fresnel equations. Diffuse scattering is treated according to Lambert's law. Absorption is also permitted but requires a detailed knowledge of the spectral attenuation coefficients. An ensemble of initial rays are chosen for each incident direction with the initial intersection points on the leaf surface selected randomly. The final equilibrium state after all interactions then yields the leaf bidirectional reflectance and transmittance distributions. The model also yields the internal two dimensional light gradient profile of the leaf.

Brakke, T. W.↗

NASA NTRS1990

Nonlinear inversion flight control for a supermaneuverable aircraft

This paper describes the use of nonlinear dynamic inversion for the design of a flight control system for a supermaneuverable aircraft. First, the dynamics to be controlled were separated into fast and slow variables. The fast variables were the angular rates and the slow variables were the attitude angles. Then a nonlinear inversion controller was designed for the fast variables. This stabilized the longitudinal short-period and improved the lateral-directional responses over a wide range of angle of attack by making use of a combination for aerodynamic surfaces and thrust vectoring control. Outer loops were then closed to allow the pilot to control the slow dynamics, the angle of attack, side-slip angle and the velocity bank angle. Nonlinear inversion was also used to design of the outer loop control laws. The dynamic inversion control laws were compared with more conventional, gain-scheduled control laws and were shown to yield much better performance.

Snell, S. Antony↗

NASA NTRS1992

Nonlinear feedback control of highly manoeuvrable aircraft

This paper describes the application of nonlinear quadratic regulator (NLQR) theory to the design of control laws for a typical high-performance aircraft. The NLQR controller design is performed using truncated solutions of the Hamilton-Jacobi-Bellman equation of optimal control theory. The performance of the NLQR controller is compared with the performance of a conventional P + I gain scheduled controller designed by applying standard frequency response techniques to the equations of motion of the aircraft linearized at various angles of attack. Both techniques result in control laws which are very similar in structure to one another and which yield similar performance. The results of applying both control laws to a high-g vertical turn are illustrated by nonlinear simulation.

Garrard, William L.↗

NASA NTRS1993

Cancellation control law for lateral-directional dynamics of a supermaneuverable aircraft

Cancellation control laws are designed which reduce the high levels of lateral acceleration encountered during aggressive rolling maneuvers executed at high angle of attack. Two independent problem are examined. One is to reduce lateral acceleration at the mass center, while the other focuses on lateral acceleration at the pilot's station, located 7.0 m forward of the mass center. Both of these problems are challenging and somewhat different in their limitations. In each case the design is based on a linearization of the lateral-directional dynamics about a high angle of attack condition. The controllers incorporate dynamic inversion inner loops to provide control of stability-axis roll- and yaw-rates and then employ cancellation filters in both feed-forward and feed-back signal paths. The relative simplicity of the control laws should allow nonlinear generalizations to be devised. Although it is shown that lateral acceleration can be reduced substantially by such control laws, this is at the cost of slowed roll response, poor dutch-roll damping or a combination of the two.

Snell, Antony↗

NASA NTRS1992

Preliminary assessment of the robustness of dynamic inversion based flight control laws

Dynamic-inversion-based flight control laws present an attractive alternative to conventional gain-scheduled designs for high angle-of-attack maneuvering, where nonlinearities dominate the dynamics. Dynamic inversion is easily applied to the aircraft dynamics requiring a knowledge of the nonlinear equations of motion alone, rather than an extensive set of linearizations. However, the robustness properties of the dynamic inversion are questionable especially when considering the uncertainties involved with the aerodynamic database during post-stall flight. This paper presents a simple analysis and some preliminary results of simulations with a perturbed database. It is shown that incorporating integrators into the control loops helps to improve the performance in the presence of these perturbations.

Snell, S. A.↗

NASA NTRS1991

Optimization of lateral-directional dynamics for an aircraft operating at high angle of attack

In this paper, the control laws for the lateral-directional dynamics of a supermaneuverable aircraft is analyzed with a view to reducing the levels of lateral acceleration and sideslip, which are encountered during aggressive rolling maneuvers at high angles of attack. The analysis uses a linearized model of the lateral-directional dynamics and thus H-free-flow techniques can be applied. It is shown that trade-offs exist between simultaneously minimizing lateral acceleration measured at the pilot's station, ny(p), minimizing sideslip and minimizing tracking errors between the roll-rate about the velocity vector and its command. The paper concludes that a significant reduction in ny(p) is only attainable by compromising the roll-rate performance.

Snell, S. A.↗