Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “root”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47

Theoretical parametric study of the relative advantages of winglets and wing-tip extensions

It was found that for identical increases in bending moment, a winglet provides a greater gain in induced efficiency than a tip extension. Winglet toe-in angle allows design trades between efficiency and root moment. A winglet showed the greatest benefit when the wing loads were heavy near the tip. Washout diminished the benefit of either tip modification, and the gain in induced efficiency became a function of lift coefficient; heavy wing loadings obtained the greatest benefit from a winglet, and low speed performance was enhanced even more than cruise performance. Both induced efficiency and bending moment increased with winglet length and outward cant. The benefit of a winglet relative to a tip extension was greatest for a nearly vertical winglet. Root bending moment was proportional to the minimum weight of bending material required in the wing; it is a valid index of the impact of tip modifications on a new wing design.

Heyson, H. H.↗

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UDU/T/, where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and colored process noise parameters increases mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

Free vibration analysis of spinning flexible space structures

Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.

Gupta, K. K.↗

A technique for measurement of material damping in metals

The paper outlines the theory, design, and application of an apparatus based on the single beam resonant dwell technique to determine the damping capacity of metallic materials by measuring the response of a structural element to excitation at a modal frequency. In this apparatus, a cantilever beam specimen of a test material is clamped to a bar which is connected at one end to an electromagnetic shaker and at the other to a heavy base. The thickness of the bar at the base end is reduced by two saw cuts to provide a pivot around which the remainder of the bar can rotate when excited by the shaker which is connected to the bar by a rod passing through a hole in the base. The response of the supporting system to shaker excitation is measured with an accelerometer mounted on the bar at the root of the specimen. Specimen response is measured optically with a low-power microscope with a reticle. Specimen loss factor is determined in terms of acceleration at the beam root, beam tip displacement, and the beam natural frequency.

Heine, J. C.↗

State-space formulations for flutter analysis

Two state-space methods for true-damping flutter analysis are presented here. The aerodynamic matrix is assumed to be function of the complex reduced frequency p (off-the-imaginary axis aerodynamics) as the ones provided for instance by the computer code SOUSSA (Steady, Oscillatory and Unsteady, Subsonic and Supersonic Aerodynamics). This matrix is approximated by a third order polynomial or by a Pade's matrix approximant. Then the equations are cast into a suitable state space format including the Laplace transform of the space vector, a frequency-independent matrix, and the flight speed. The solution is then obtained by standard root-locus methods. Results are in good agreement with existing ones in a suitable range of the flutter reduced frequency. A discussion on spurious roots is also included.

Weiss, S. J.↗

Gram-Schmidt algorithms for covariance propagation

This paper addresses the time propagation of triangular covariance factors. Attention is focused on the square-root free factorization, P = UD(transpose of U), where U is unit upper triangular and D is diagonal. An efficient and reliable algorithm for U-D propagation is derived which employs Gram-Schmidt orthogonalization. Partitioning the state vector to distinguish bias and coloured process noise parameters increase mapping efficiency. Cost comparisons of the U-D, Schmidt square-root covariance and conventional covariance propagation methods are made using weighted arithmetic operation counts. The U-D time update is shown to be less costly than the Schmidt method; and, except in unusual circumstances, it is within 20% of the cost of conventional propagation.

Thornton, C. L.↗

Aeroelastic stability of coupled flap-lag-torsional motion of helicopter rotor blades in forward flight

A set of coupled periodic nonlinear differential flap-lag-torsional equations of blade motion is described which can simulate a blade having a precone, twist, distributed torsion, root torsion, torque offset, blade-root offsets, and offsets among the elastic axis, the aerodynamic center, and the blade cross-sectional center of mass. It is noted that the aerodynamic loads derived for these equations are applicable to cases of both hover and forward flight. The aeroelastic stability of a hingeless helicopter blade is investigated by linearizing the nonlinear differential equations of motion about a time-dependent equilibrium position of the helicopter in forward flight, using propulsion and moment trim procedures. A comparison of the results with those obtained previously for coupled flap-lag-torsional boundaries in hover indicates that aeroelastic-stability margins are degraded due to forward flight.

Friedmann, P.↗

Transequatorial loops interconnecting McMath regions 12472 and 12474

The paper reviews the life history of one transequatorial loop in a system observed in soft X-rays for at least 1.5 days and which interconnected a newly born active region with an old region. The birth of the selected loop is discussed along with properties of the interconnected active regions, sharpening and brightening of the loop, decay of the loop system, and physical relations between the interconnected regions. It is concluded that: (1) the loop was most probably born via reconnection of magnetic-field lines extending from the two active regions toward the equator, which occurred later than 33 hr after the younger region was born; (2) the fully developed interconnection was composed of several loops, all of which appeared to be rooted in a spotless magnetic hill of preceding northern polarity but were spread over two separate spotty regions of southern polarity in the magnetically complex new region; (3) the loop electron temperature increased from 2.1 million to 3.1 million K in one to three hours when the loop system brightened; and (4) the loops became twisted during the brightening, possibly due to their rise in the corona while remaining rooted in moving magnetic features in the younger region.

Svestka, Z.↗

Dynamic wind-tunnel tests of an aeromechanical gust-alleviation system using several different combinations of control surfaces

Some experimental results are presented from wind tunnel studies of a dynamic model equipped with an aeromechanical gust alleviation system for reducing the normal acceleration response of light airplanes. The gust alleviation system consists of two auxiliary aerodynamic surfaces that deflect the wing flaps through mechanical linkages when a gust is encountered to maintain nearly constant airplane lift. The gust alleviation system was implemented on a 1/6-scale, rod mounted, free flying model that is geometrically and dynamically representative of small, four place, high wing, single engine, light airplanes. The effects of flaps with different spans, two size of auxiliary aerodynamic surfaces, plain and double hinged flaps, and a flap elevator interconnection were studied. The model test results are presented in terms of predicted root mean square response of the full scale airplane to atmospheric turbulence. The results show that the gust alleviation system reduces the root mean square normal acceleration response by 30 percent in comparison with the response in the flaps locked condition. Small reductions in pitch-rate response were also obtained. It is believed that substantially larger reductions in normal acceleration can be achieved by reducing the rather high levels of mechanical friction which were extant in the alleviation system of the present model.

Stewart, E. C.↗

Plans for wind energy system simulation

A digital computer code and a special purpose hybrid computer, were introduced. The digital computer program, the Root Perturbation Method or RPM, is an implementation of the classic floquet procedure which circumvents numerical problems associated with the extraction of Floquet roots. The hybrid computer, the Wind Energy System Time domain simulator (WEST), yields real time loads and deformation information essential to design and system stability investigations.

Dreier, M. E.↗

Impact behavior of filament wound graphite/epoxy fan blades

The fabrication and impact tests of graphite/epoxy filament wound fan blades are discussed. Blades which were spin tested at tip speeds up to 305 meters per second retained their structural integrity. Two blades were each impacted with a 454 gram slice of a 908 gram simulated bird at a tip speed of 263 meters per second and impact angles of 22 and 32 deg. The impact tests were recorded with high-speed movie film. The blade which was impacted at 22 deg sustained some root delamination but remained intact. The 32 deg impact separated the blade from the root. No local damage other than leading edge debonding was observed for either blade. Results of a failure mode analysis are also discussed.

Bowles, K. J.↗

Flat growth of 7075, 7475, 7050 and 7049 aluminum alloy plate in stress corrosion environments: 2-year marine atmosphere results

Marine atmospheric exposure of smooth and precracked specimens from 7075, 7475, 7050 and 7049 plates support the conclusion that for a given strength level, the short transverse stress corrosion resistance of 7050-T7X and 7049-T7X is superior to that of 7075-T7X. The threshold stress intensity (K sub Iscc) for these alloys is about 25 MPa square root m at a yield strength of about 460 MPa; the corresponding yield strength level for 7075-T7X at this SCR level is about 425 MPa. Additional tests on two lots of high-toughness 7475 plate indicate that this alloy is capable of achieving K sub Iscc values of about 35 MPa square root m at yield strengths of 400-450 MPa. Precracked specimens from all these 7XXX-series alloys are subject to self loading from corrosion product wedging. This effect causes stress corrosion cracks to continue growing at very low apparent stress intensities, and should therefore be considered a potential driving force for stress corrosion in design and materials selection.

Dorward, R. C.↗

TNT equivalency of M10 propellant

Peak, side-on blast overpressure and scaled, positive impulse have been measured for M10 single-perforated propellant, web size 0.018 inches, using configurations that simulate the handling of bulk material during processing and shipment. Quantities of 11.34, 22.7, 45.4, and 65.8 kg were tested in orthorhombic shipping containers and fiberboard boxes. High explosive equivalency values for each test series were obtained as a function of scaled distance by comparison to known pressure, arrival time and impulse characteristics for hemispherical TNT surface bursts. The equivalencies were found to depend significantly on scaled distance, with higher values of 150-100 percent (pressure) and 350-125 percent (positive impulse) for the extremes within the range from 1.19 to 3.57 m/cube root of kg. Equivalencies as low as 60-140 percent (pressure) and 30-75 percent (positive impulse) were obtained in the range of 7.14 to 15.8 m/cube root of kg. Within experimental error, both peak pressure and positive impulse scaled as a function of charge weight for all quantities tested in the orthorhombic configuration.

Mcintyre, F. L.↗

Red and photographic infrared linear combinations for monitoring vegetation

In situ collected spectrometer data were used to evaluate and quantify the relationships between various linear combinations of red and photographic infrared radiances and experimental plot biomass, leaf water content, and chlorophyll content. The radiance variables evaluated included the red and photographic infrared (IR) radiance and the linear combinations of the IR/red ratio, the square root of th IR/red difference, the vegetation index, and the transformed vegetation index. In addition, the corresponding green and red linear combinations were evaluated for comparative purposes. Three data sets were used from June, September, and October sampling periods. Regression analysis showed the increase utility of the IR and red linear combinations vis-a-vis the same green and red linear combinations. The red and IR linear combinations had 7% and 14% greater regression significance than the green and red linear combinations for the June and September sampling periods, respectively. The VI, TVI, and square root of the IR/red ration were the most significant followed closely by the IR/red ratio. Less than 6% difference separated the highest and lowest of these four IR and red linear combinations. The use of these linear combinations was shown to be sensitive primarily to the green leaf area or green leaf biomass.

Tucker, C. J.↗

A triangular covariance factorization for sequential filtering algorithms

A method for propagating the square-root of the state error covariance matrix in lower triangular UDU form is described. This update method can be combined with the UDU transformation used by Bierman to obtain the equations of a square-root free triangular estimation algorithm. The method is compared with the state transition matrix time update algorithm on the basis of integration accuracy, computational efficiency and storage requirements.

Tapley, B. D.↗

Theory of the control of structures by low authority controllers

The novel idea presented is based on the observation that if a structure is controlled by distributed systems of sensors and actuators with limited authority, i.e., if the controller is allowed to modify only moderately the natural modes and frequencies of the structure, then it should be possible to apply root perturbation techniques to predict analytically the behavior of the total system. Attention is given to the root perturbation formula first derived by Jacobi for infinitesimal perturbations which neglect the induced eigenvector perturbation, a more general form of Jacobi's formula, first-order structural equations and modal state vectors, state-space equations for damper-augmented structures, and modal damping prediction formulas.

Aubrun, J. N.↗

Flap-lag-torsion flutter analysis of a constant life rotor

The constant lift rotor (CLR) employs a control input of pitch moment to several airfoil sections which are free to pivot on a continuous spar, allowing them to change their pitch to obtain the desired lift. A flap-lag-torsion flutter analysis of a constant lift rotor blade in hover was developed. The blade model assumes rigid body flap and lead-lag motions at the root hinge and each strip undergoes an independent torsional motion. The results are presented in terms of root locus plots of complex eigenvalues as a function of thrust. The effects of several parameters (including structural damping, center of gravity and elastic axis offset from aerodynamic center, compressibility pitch-lag and pitch-flap coupling) on the blade dynamics are examined. With a suitable combination of lag damper and pitch-flap coupling, it is possible to design a constant lift rotor blade free from flutter instability.

Chopra, I.↗

Impact behavior of filament-wound graphite/epoxy fan blades

The fabrication and impact tests of graphite/epoxy filament wound fan blades are discussed. Blades which were spin tested at tip speeds up to 305 m/sec retained their structural integrity. Two blades were each impacted with a 454-g slice of a 908-g simulated bird at a tip speed of 263 deg and impact angles of 22 deg and 32 deg. The impact tests were recorded with high-speed movie film. The blade which was impacted at 22 deg sustained some root delamination but remained intact. The 32 deg impact separated the blade from the root. No local damage other than leading-edge debonding was observed for either blade. The results of a failure mode analysis are also discussed.

Bowles, K. J.↗