Analytical study of effects of product of inertia on airplane spin entries, developed spins, and spin recoveries
Inertia product and inertia moment variation effect on spin entry, developed spin, and spin recovery of airplanes
AIRCRAFT↗
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A theoretical analysis of the effect of aileron inertia and hinge moment on the maximum rolling acceleration of airplanes in abrupt aileron rolls
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AILERONS - DEFLECTION↗
The forces and moments acting on parts of the XN2Y-1 airplane during spins
The magnitudes of the yawing moments produced by various parts of an airplane during spins have previously been found to be of major importance in determining the nature of the spin. Discrepancies in resultant yawing moments determined from model and full-scale tests, however, have indicated the probable importance of scale effect on the model. In order to obtain data for a more detailed comparison between full-scale and model results, flight tests were made to determine the yawing moments contributed by various parts of an airplane in spins. The inertia moment was determined by the usual measurement of the spinning motion, and the aerodynamic yawing moments on the fuselage, fin, and rudder were determined by pressure-distribution measurements over these parts of the airplane. The wing yawing moment was determined by taking the difference between the gyroscopic moment and the fuselage, fin, and rudder moments. The numerical values of the wing yawing moments were found to be of the same order of magnitude as those measured in wind tunnels.
Scudder, N F↗
Venusian atmospheric and Magellan properties from attitude control data
Results are presented of the study of the Venusian atmosphere, Magellan aerodynamic moment coefficients, moments of inertia, and solar moment coefficients. This investigation is based upon the use of attitude control data in the form of reaction wheel speeds from the Magellan spacecraft. As the spacecraft enters the upper atmosphere of Venus, measurable torques are experienced due to aerodynamic effects. Solar and gravity gradient effects also cause additional torques throughout the orbit. In order to maintain an inertially fixed attitude, the control system counteracts these torques by changing the angular rates of three reaction wheels. Model reaction wheel speeds are compared to observed Magellan reaction wheel speeds through a differential correction procedure. This method determines aerodynamic, atmospheric, solar pressure, and mass moment of inertia parameters. Atmospheric measurements include both base densities and scale heights. Atmospheric base density results confirm natural variability as measured by the standard orbital decay method. Potential inconsistencies in free molecular aerodynamic moment coefficients are identified. Moments of inertia are determined with a precision better than 1 percent of the largest principal moment of inertia.
Croom, Christopher A.↗
Geometrical and inertial properties of a class of thin shells of a general type
IBM 7094 Fortran program for evaluating surface area, centroids of surface volume or masses, and moments of inertia for thin walled shells
IBM 7094 COMPUTER↗
Convection in the moon and the existence of a lunar core.
Lunar core and convection in analysis of lunar principal moments of inertia and surface ellipticity
INERTIA MOMENT↗
Determination of parameters related to the interior of Mercury.
Discussion of the determination possibilities and requirements for certain crucial inertia-moment and radial-mass-distribution parameters of Mercury. It is shown that the high precision of 1 min of arc, which reasonable bounds on some of these parameters demand, cannot be obtained by either earth-based observations or the television imagery of the Mariner 73 flyby. Some methods are proposed for both landers and orbiters that could determine unambiguously most of these parameters.
Peale, S. J.↗
A Study of Feature Extraction Using Divergence Analysis of Texture Features
An empirical study of texture analysis for feature extraction and classification of high spatial resolution remotely sensed imagery (10 meters) is presented in terms of specific land cover types. The principal method examined is the use of spatial gray tone dependence (SGTD). The SGTD method reduces the gray levels within a moving window into a two-dimensional spatial gray tone dependence matrix which can be interpreted as a probability matrix of gray tone pairs. Haralick et al (1973) used a number of information theory measures to extract texture features from these matrices, including angular second moment (inertia), correlation, entropy, homogeneity, and energy. The derivation of the SGTD matrix is a function of: (1) the number of gray tones in an image; (2) the angle along which the frequency of SGTD is calculated; (3) the size of the moving window; and (4) the distance between gray tone pairs. The first three parameters were varied and tested on a 10 meter resolution panchromatic image of Maryville, Tennessee using the five SGTD measures. A transformed divergence measure was used to determine the statistical separability between four land cover categories forest, new residential, old residential, and industrial for each variation in texture parameters.
Hallada, W. A.↗
Dynamics and control of a tumbling satellite retrieval device
The problem of capturing a satellite in an uncontrolled three-axis tumble is addressed. The proposed solution is a truss which opens and engulfs the satellite, resulting in coincident centers of mass. Torques are then applied to the truss so that it matches the tumble rates of the satellite and remains motionless in the satellite's reference frame. Equations are derived which show how to vary the mass distribution to match any set of inertia moment ratios. The physical system is shown to be controllable. An optimal control algorithm for tumble matching is then derived and a computer simulation is developed.
Neff, J. M.↗
A study of curvilinear flight
When an airplane describes a curve it takes a certain time for it to turn from level to inclined position and then back to level again. In the following, we express the motion about the horizontal axis as "roll" or "bank" and the motion perpendicular to the vertical axis, i.e., the actual curve, as "turn." Equations and tables provide results on various aspects of turns, control settings, acceleration, inertia moments, and angular velocity.
Kruse, Helmuth↗
Determining the Products of Inertia for Small Scale UAVs
Moments of inertia and products of inertia often need to be determined for aircraft. As complex bodies, their mass properties need to be determined experimentally for best accuracy. While several moment of inertia experimental techniques have been developed, there are few to determine the products of inertia. Products of inertia can be easily determined mathematically if the angle between the aircraft x body axis and principal x axis is known. This method finds the principal inclination angle by mathematically correlating the measured moments of inertia about a range of axes of the aircraft. This correlation uses a least squares error minimization of a mathematical model that describes the ellipse of inertia in the aircraft's x-z axes plane. Results from a test conducted on a small scale UAV (Unmanned Aerial Vehicle) at NASA Armstrong Flight Research Center is also presented, which is an example of the intended application of this technique.
mass properties↗
Static aeroelasticity and the flying wing, revisited
The roll dynamic behavior of some wing configurations is examined. Analysis shows that the static divergence instability which occurs for symmetrical or clamped sweptforward wings is modified by roll freedom. The instability found in the present highly idealized analysis is still of an aperiodic nature, but at a speed above the conventional divergence speed. The magnitude of this difference is seen to be a function of the ratio of the wing roll mass moment of inertia to the mass moment of inertia of the wing about the roll axis, and this difference may be quite significant.
Weisshaar, T. A.↗
Gyroscopic Motion of an Unsymmetrical Satellite Under No External Forces
This report gives the results of an investigation on the transition from spin about the axis of minimum moment of inertia to spin about the axis of maximum moment of inertia by dissipation of internal mechanical energy. A mathematical discussion, together with charts and diagrams, shows that angular velocities and nutation angle are dependent on the energy and symmetry factors. The low stability of rotation about the axis of maximum moment of inertia, when this inertia is only slightly greater than the mean moment of inertia, is shown.
Kuebler, Manfred E.↗
Thermally driven mass flows in the convection zone of the sun
A formulation of the fluid dynamics of convective regions is developed which leads to an analytical description of the solar rotation, the Evershed flow, and the supergranulation. The starting point of the present formulation is the mixing length picture of convective equilibrium, but the earlier point mass model for convective molecules is replaced here by a model with both inertia and intrinsic moment of inertia. This extension introduces three rotational degrees of freedom into the dynamics of individual convective molecules, which enter into the dynamical equations for a mixing length fluid in the form of a separate vector field which we term the spin field. It is shown that for convective molecules having a spherically symmetric mass distribution, the spin field is proportional to the local vorticity.
Dijkhuis, G. C.↗
Pluto and Triton: Interactions Between Volatiles and Dynamics
Volatiles moving across the surfaces of Pluto and Triton can give rise to interesting dynamical consequences. Conversely, measurement of dynamical states can help constrain the movement of volatiles and interior structure of both bodies. Polar wander may theoretically occur on both Triton and Pluto. Triton's obliquity is low, so that the equatorial regions receive more insolation than the poles. Hence there is a tendency for nitrogen ice to sublime at the equator and condense at the poles, creating polar caps. If the nitrogen supply is large enough, then these caps could move in approximately 10(exp 5) years the global equivalent of 200 m of ice to the poles. At this point the equatorial moment of inertia becomes larger than the moment of inertia measured about the rotation axis, so that Triton overbalances and becomes dynamically unstable. The satellite then undergoes polar wander, restoring stability when the new equator contains the excess matter. Hence the pole may be continually wandering. Neptune raises a permanent tidal bulge on Triton, so that the satellite's surface is elongated like a football, with the long axis pointing at Neptune. This is expected to be the axis about which the pole wanders. Volatile migration would resurface the satellite to some depth and wandering would disturb leading side/trailing side crater statistics. Additional information is contained in the original extended abstract.
Rubincam, D. P.↗
A low-order global gravity field of Venus and dynamical implications
An estimate of sixth-degree and sixth-order harmonic coefficients of the global gravity field of Venus is obtained by processing the long periodic variations of the mean orbital elements of the Pioneer Venus orbiter. Approximately 220 days of data are included in this reduction, which provides almost complete longitudinal coverage. Oblateness is estimated to be -5.97 + or - 3.2 x 10 to the -6. It is noted that the amplitudes of other coefficients are similar to the predicted coefficients using Kaula's rule under equal stress assumption. Atmospheric density values as a function of altitude are obtained to help model drag perturbation. A radial acceleration map at 100 km above the Venus surface is generated, and correlation between gravity anomalies and major topographic features is observed. Spectral analysis of the harmonic model suggests that the interior density anomalies are like those on earth. The orientation angles of the principal axes of the moments of inertia are computed, and deviation of the maximum moment of inertia axis from the spin axis is observed to be small (less than 5 deg). It is found that the minimum moment of inertia axis passes through the Aphrodite and Beta regions.
Ananda, M. P.↗
Algorithms for Determining Physical Responses of Structures Under Load
Ultra-efficient real-time structural monitoring algorithms have been developed to provide extensive information about the physical response of structures under load. These algorithms are driven by actual strain data to measure accurately local strains at multiple locations on the surface of a structure. Through a single point load calibration test, these structural strains are then used to calculate key physical properties of the structure at each measurement location. Such properties include the structure s flexural rigidity (the product of the structure's modulus of elasticity, and its moment of inertia) and the section modulus (the moment of inertia divided by the structure s half-depth). The resulting structural properties at each location can be used to determine the structure s bending moment, shear, and structural loads in real time while the structure is in service. The amount of structural information can be maximized through the use of highly multiplexed fiber Bragg grating technology using optical time domain reflectometry and optical frequency domain reflectometry, which can provide a local strain measurement every 10 mm on a single hair-sized optical fiber. Since local strain is used as input to the algorithms, this system serves multiple purposes of measuring strains and displacements, as well as determining structural bending moment, shear, and loads for assessing real-time structural health. The first step is to install a series of strain sensors on the structure s surface in such a way as to measure bending strains at desired locations. The next step is to perform a simple ground test calibration. For a beam of length l (see example), discretized into n sections and subjected to a tip load of P that places the beam in bending, the flexural rigidity of the beam can be experimentally determined at each measurement location x. The bending moment at each station can then be determined for any general set of loads applied during operation.
Richards, W. Lance↗
Centroid and moments of an area using a digitizer
The centroid and moments of an area program provides the centroid, moments of inertia, product of inertia, radii of gyration, and area of any closed planar geometric figure. The figure must be available in graphic form and is digitized once with chart digitizer (graphic tablet). The digitizer origin may be set anywhere on the digitizer table. After digitizing, fifteen quantities are calculated and displayed: (1) area (2) moment of inertia of area with respect to digitizer x-axis, (3) moment of inertia of area with respect to digitizer y-axis, (4) product of inertia of area with respect to digitizer axes, (5) first moment of x for digitizer axes, (6) first moment of y for digitizer axes, (7) x coordinate of centroid, (8) y coordinate of centroid, (9) moment of area inertia of with respect to x axis through centroid, (10) moment of inertia of area with respect to y axis through centroid, (11) product inertia of area with respect to x and y axes through centroid, (12) polar moment of inertia of area around centroid, (13) radius of gyration about digitizer x axis, (14) radius of gyration about digitizer y-axis; and (15) variance in the x-direction.
Patch, R. W.↗