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NASA NTRS1943

The Effect of Mass Distribution on the Lateral Stability and Control Characteristics of an Airplane as Determined by Tests of a Model in the Free-Flight Tunnel

The effects of mass distribution on lateral stability and control characteristics of an airplane have been determined by flight tests of a model in the NACA free-flight tunnel. In the investigation, the rolling and yawing movements of inertia were increased from normal values to values up to five times normal. For each moment-of-inertia condition, combinations of dihedral and vertical-tail area representing a variety of airplane configurations were tested. The results of the flight tests of the model were correlated with calculated stability and control characteristics and, in general, good agreement was obtained. The tests showed the following effects of increased rolling and yawing moments of inertia: no appreciable change in spiral stability; reductions in oscillatory stability that were serious at high values of dihedral; a reduction in the sensitivity of the model to gust disturbances; and a reduction in rolling acceleration provided by the ailerons, which caused a marked increase in time to reach a given angle of bank. The general flight behavior of the model became worse with increasing moments of inertia but, with combinations of small effective dihedral and large vertical-tail area, satisfactory flight characteristics were obtained at all moment-of-inertia conditions.

STABILITY & CONTROL, LATERAL↗

NASA NTRS1981

Tidal variations of earth rotation

The periodic variations of the earths' rotation resulting from the tidal deformation of the earth by the sun and moon were rederived including terms with amplitudes of 0.002 millisec and greater. The series applies to the mantle, crust, and oceans which rotate together for characteristic tidal periods; the scaling parameter is the ratio of the fraction of the Love number producing tidal variations in the moment of inertia of the coupled mantle and oceans (k) to the dimensionless polar moment of inertia of the coupled moments (C). The lunar laser ranging data shows that k/C at monthly and fortnightly frequencies equals 0.99 + or - 0.15 and 0.99 + or - 0.20 as compared to the theoretical value of 0.94 + or - 0.04.

Yoder, C. F.↗

NASA NTRS1976

Flutter of asymmetrically swept wings

Two formulations of the oblique wing flutter problem are presented; one formulation allows only simple wing bending deformations and rigid body roll as degrees of freedom, while the second formulation includes a more complex bending-torsional deformation together with the roll freedom. Flutter is found to occur in two basic modes. The first mode is associated with wing bending-aircraft roll coupling and occurs at low values of reduced frequency. The second instability mode closely resembles a classical bending-torsion wing flutter event. This latter mode occurs at much higher reduced frequencies than the first. The occurrence of the bending-roll coupling mode is shown to lead to lower flutter speeds while the bending-torsion mode is associated with higher flutter speeds. The ratio of the wing mass moment of inertia in roll to the fuselage roll moment of inertia is found to be a major factor in the determination of which of the two instabilities is critical.

Weisshaar, T. A.↗

NASA NTRS1971

Angular momentum desaturation for Skylab using gravity gradient torques

An angular momentum desaturation method for momentum exchange devices of orbiting spacecraft is described. The specific application of the method is to the Skylab which contains three double-gimbaled control moment gyros for precise attitude control and maneuvering. It is assumed that the attitude reference is inertially fixed and that two of the vehicle principal moments of inertia are much larger than the third. Gravity gradient torques and resultant angular momentum accumulation are developed for small deviations from the reference. The assumed moment-of-inertia distribution allows desaturation about all axes with only two attitude angles each for the two axes with large moments of inertia. The necessary desaturation maneuvers can be decoupled for a special set of orbital coordinates. All maneuvers are made during the night portion of the orbit, and the percentage utilized for desaturation is selectable. Expressions for the attitude angle commands are developed assuming infinite vehicle rates. The effect of finite rates introduces an efficiency into the desaturation. Expressions for this efficiency are developed and means for compensation are treated. Arbitrary misalignments between geometric vehicle axes and principal moment-of-inertia axes are permissible. An angle bias about the sun line minimizes the angular momentum accumulation about the sun line projection into the orbital plane. Adaptive desaturation maneuver limiting consistent with the available maneuver momentum is included.

Kennel, H. F.↗

NASA NTRS1974

Experimental determination of airplane mass and inertial characteristics

Current practices are evaluated for experimentally determining airplane center of gravity, moments of inertia, and products of inertia. The techniques discussed are applicable to bodies other than airplanes. In pitching- and rolling-moment-of-inertia investigations with the airplane mounted on and pivoted about knife edges, the nonlinear spring moments that occur at large amplitudes of oscillation can be eliminated by using the proper spring configuration. The single-point suspension double-pendulum technique for obtaining yawing moments of inertia, products of inertia, and the inclination of the principal axis provides accurate results from yaw-mode oscillation data, provided that the sway-mode effects are minimized by proper suspension rig design. Rocking-mode effects in the data can be isolated.

Wolowicz, C. H.↗

NASA NTRS2015

Fuel Distribution Estimate via Spin Period to Precession Period Ratio for the Advanced Composition Explorer

The spin period to precession period ratio of a non-axisymmetric spin-stabilized spacecraft, the Advanced Composition Explorer (ACE), was used to estimate the remaining mass and distribution of fuel within its propulsion system. This analysis was undertaken once telemetry suggested that two of the four fuel tanks had no propellant remaining, contrary to pre-launch expectations of the propulsion system performance. Numerical integration of possible fuel distributions was used to calculate moments of inertia for the spinning spacecraft. A Fast Fourier Transform (FFT) of output from a dynamics simulation was employed to relate calculated moments of inertia to spin and precession periods. The resulting modeled ratios were compared to the actual spin period to precession period ratio derived from the effect of post-maneuver nutation angle on sun sensor measurements. A Monte Carlo search was performed to tune free parameters using the observed spin period to precession period ratio over the life of the mission. This novel analysis of spin and precession periods indicates that at the time of launch, propellant was distributed unevenly between the two pairs of fuel tanks, with one pair having approximately 20% more propellant than the other pair. Furthermore, it indicates the pair of the tanks with less fuel expelled all of its propellant by 2014 and that approximately 46 kg of propellant remains in the other two tanks, an amount that closely matches the operational fuel accounting estimate. Keywords: Fuel Distribution, Moments of Inertia, Precession, Spin, Nutation

Moment of Inertia↗

NASA NTRS1976

Does Mercury have a molten core

A feasible nonseismic observational experiment is proposed for determining the existence and extent of a conducting molten core within Mercury. This experiment would utilize the effects of a liquid core on the dynamics of Mercury's rotation; two necessary conditions for performing it are that the core must not follow the mantle's forced librations in longitude but must follow the mantle on the timescale of the 250,000-yr precession. A method is developed by assuming these conditions to be satisfied, and bounds are established on the core viscosity for which they are satisfied. It is shown that the value of the ratio of the moment of inertia of the mantle to the largest principal moment of inertia of the entire planet would indicate whether the core is most probably solid, partially fluid, or entirely fluid. Techniques are suggested for determining the unknowns required to compute the necessary ratio.

Peale, S. J.↗

NASA NTRS2012

Precision Mass Property Measurements Using a Five-Wire Torsion Pendulum

A method for measuring the moment of inertia of an object using a five-wire torsion pendulum design is described here. Typical moment of inertia measurement devices are capable of 1 part in 10(exp 3) accuracy and current state of the art techniques have capabilities of about one part in 10(exp 4). The five-wire apparatus design shows the prospect of improving on current state of the art. Current measurements using a laboratory prototype indicate a moment of inertia measurement precision better than a part in 10(exp 4). In addition, the apparatus is shown to be capable of measuring the mass center offset from the geometric center. Typical mass center measurement devices exhibit a measurement precision up to approximately 1 micrometer. Although the five-wire pendulum was not originally designed for mass center measurements, preliminary results indicate an apparatus with a similar design may have the potential of achieving state of the art precision.

Swank, Aaron J.↗

NASA NTRS2013

Lunar Science from Lunar Laser Ranging

Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/solid-mantle boundary, tidal Love number k2, and moment of inertia differences. There is weaker sensitivity to flattening of the core/mantle boundary (CMB) and fluid core moment of inertia. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to variations in lunar rotation, orientation and tidal displacements. Past solutions using the LLR data have given results for Love numbers plus dissipation due to solid-body tides and fluid core. Detection of the fluid core polar minus equatorial moment of inertia difference due to CMB flattening is weakly significant. This strengthens the case for a fluid lunar core. Future approaches are considered to detect a solid inner core.

Love numbers↗

NASA NTRS1995

Determination of Eros Physical Parameters for Near Earth Asteroid Rendezvous Orbit Phase Navigation

Navigation of the orbit phase of the Near Earth steroid Rendezvous (NEAR) mission will re,quire determination of certain physical parameters describing the size, shape, gravity field, attitude and inertial properties of Eros. Prior to launch, little was known about Eros except for its orbit which could be determined with high precision from ground based telescope observations. Radar bounce and light curve data provided a rough estimate of Eros shape and a fairly good estimate of the pole, prime meridian and spin rate. However, the determination of the NEAR spacecraft orbit requires a high precision model of Eros's physical parameters and the ground based data provides only marginal a priori information. Eros is the principal source of perturbations of the spacecraft's trajectory and the principal source of data for determining the orbit. The initial orbit determination strategy is therefore concerned with developing a precise model of Eros. The original plan for Eros orbital operations was to execute a series of rendezvous burns beginning on December 20,1998 and insert into a close Eros orbit in January 1999. As a result of an unplanned termination of the rendezvous burn on December 20, 1998, the NEAR spacecraft continued on its high velocity approach trajectory and passed within 3900 km of Eros on December 23, 1998. The planned rendezvous burn was delayed until January 3, 1999 which resulted in the spacecraft being placed on a trajectory that slowly returns to Eros with a subsequent delay of close Eros orbital operations until February 2001. The flyby of Eros provided a brief glimpse and allowed for a crude estimate of the pole, prime meridian and mass of Eros. More importantly for navigation, orbit determination software was executed in the landmark tracking mode to determine the spacecraft orbit and a preliminary shape and landmark data base has been obtained. The flyby also provided an opportunity to test orbit determination operational procedures that will be used in February of 2001. The initial attitude and spin rate of Eros, as well as estimates of reference landmark locations, are obtained from images of the asteroid. These initial estimates are used as a priori values for a more precise refinement of these parameters by the orbit determination software which combines optical measurements with Doppler tracking data to obtain solutions for the required parameters. As the spacecraft is maneuvered; closer to the asteroid, estimates of spacecraft state, asteroid attitude, solar pressure, landmark locations and Eros physical parameters including mass, moments of inertia and gravity harmonics are determined with increasing precision. The determination of the elements of the inertia tensor of the asteroid is critical to spacecraft orbit determination and prediction of the asteroid attitude. The moments of inertia about the principal axes are also of scientific interest since they provide some insight into the internal mass distribution. Determination of the principal axes moments of inertia will depend on observing free precession in the asteroid's attitude dynamics. Gravity harmonics are in themselves of interest to science. When compared with the asteroid shape, some insight may be obtained into Eros' internal structure. The location of the center of mass derived from the first degree harmonic coefficients give a direct indication of overall mass distribution. The second degree harmonic coefficients relate to the radial distribution of mass. Higher degree harmonics may be compared with surface features to gain additional insight into mass distribution. In this paper, estimates of Eros physical parameters obtained from the December 23,1998 flyby will be presented. This new knowledge will be applied to simplification of Eros orbital operations in February of 2001. The resulting revision to the orbit determination strategy will also be discussed.

Miller, J. K.↗

NASA NTRS1959

Investigation of the Stability of Very Flat Spins and Analysis of Effects of Applying various Moments Utilizing the Three Moment Equations of Motion

Based on linearized equations of motion utilizing only the three moment equations and assuming only flat-spin conditions, it appears that contemporary designs (with the moment of inertia about the wing axis I(sub Y) considerably greater than the moment of inertia about the fuselage axis I(sub X) having positive values of C(sub l, sub p) (rolling-moment coefficient due to rolling) or positive values of C(sub l, sub beta) (rolling-moment coefficient due to sideslip) will probably not have a stable spin in the flat-spin region near an angle of attack of 90 deg. If the damping in pitch in flat-spin attitudes is zero, stable flat-spin conditions may not be possible on an airplane having the mass primarily distributed along the wings. The effect of moving ailerons with the spin or the effect of applying a positive pitching moment producing recovery for contemporary fighter designs will be greatest for large negative values of C(sub n, sub beta) (yawing-moment coefficient due to sideslip). In addition, for a certain critical value of positive C(sub n, sub beta), the rolling moment applied by moving ailerons with the spin or the application of a positive pitching moment will have no effect on reducing the spin rate.

Klinar, Walter J.↗

NASA NTRS1973

Skylab attitude control and angular momentum desaturation with one double-gimbaled control moment gyro

In case two control moment gyros fail, attitude control of Skylab can be maintained with the thruster attitude control system. This results, however, in a severely increased fuel consumption, depleting the fuel in a few days. Therefore, an alternate concept was developed which does not have large fuel consumption under any circumstances. In this concept the attitude reference is commanded to oscillate in the orbital plane with twice the orbital frequency and the remaining control moment gyro controls about orbital north and about the minimum moment-of-inertia axis, while the thruster attitude control system controls rate only about the remaining axis. This rate control in conjunction with the restoring torque due to the gravity gradient will keep bounded the excursion of the minimum moment-of-inertia axis out of the orbital plane. This alternate concept has the additional advantage that it needs no information on the principal moment-of-inertia axes misalignment and is completely insensitive to star tracker failure. Proper phasing of the attitude reference oscillation even allows angular momentum desaturation, which is responsible for the insensitivity of the thruster fuel consumption to unknown disturbances, like vent torques and magnetic torques.

Kennel, H. F.↗

NASA NTRS1943

Determination of the Mass Moments and Radii of Inertia of the Sections of a Tapered Wing and the Center-of-Gravity Line along the Wing Span

For computing the critical flutter velocity of a wing among the data required are the position of the line of centers of gravity of the wing sections along the span and the mass moments and radii of inertia of any section of the wing about the axis passing through the center of gravity of the section. A sufficiently detailed computation of these magnitudes even if the weights of all the wing elements are known, requires a great deal of time expenditure. Thus a rapid competent worker would require from 70 to 100 hours for the preceding computations for one wing only, while hundreds of hours would be required if all the weights were included. With the aid of the formulas derived in the present paper, the preceding work can be performed with a degree of accuracy sufficient for practical purposes in from one to two hours, the only required data being the geometric dimensions of the outer wing (tapered part), the position of its longerons, the total weight of the outer wing, and the approximate weight of the longerons, The entire material presented in this paper is applicable mainly to wings of longeron construction of the CAHI type and investigations are therefore being conducted by CAHI for the derivation of formulas for the determination of the preceding data for wings of other types.

Savelyev, V. V.↗

NASA NTRS1991

Adaptation of Diaphyseal Structure With Aging and Increased Mechanical Usage in the Adult Rat: A Histomorphometrical and Biomechanical Study

The experimental increase in mechanical usage or overloading of the left hindlimb was produced by immobilization of the contralateral hindlimb. The right hindlimb was placed in a flexed position against the body and was immobilized using an elastic bandage. Some control animals were sacrificed initially at time zero and increased mechanical usage and age-matched control animals were sacrificed after 2, 10, 18, and 26 weeks of treatment. All animals received double bone fluorochrome labeling prior to sacrifice. Cortical bone histomorphometry and cross-sectional moments of inertia were determined. Marrow cavity enlargement and total cross-sectional area expansion represented the age-related cortical bone changes. Increased mechanical usage enhanced periosteal bone modeling in the formation mode and dampened endocortical bone remodeling and bone modeling in the resorption mode (resorption drift) to create a slight positive bone balance. These observations are in general agreement with Frost's postulate for mechanical effects on bone modeling and remodeling. The maximum moment of inertia did not change significantly in either control or overloaded tibial shafts. The minimum and polar moment of inertias in overloaded bones increases over those of controls at 18 and 26 weeks of the experiment.

Jee, Webster S. S.↗

NASA NTRS1991

Adaptation of Diaphyseal Structure with Aging and Increased Mechanical Usage in the Adult Rat: A Histomorphometrical and Biomechanical Study

Jee, Webster S. S.↗

NASA NTRS1959

Analysis of Flow-System Starting Dynamics of Turbopump-Fed Liquid-Propellant Rocket

Two rocket configurations with turbopump drive were investigated analytically. In one configuration the inlet pressure to the turbine was fixed at the design value. The second configuration employed a "bootstrap" technique for supplying energy to the turbine. An injector was the chief resistance between the pump and the rocket combustion chamber. From the analysis two parameters were developed from which the speed response time of the turbopump, the flow response time, and the maximum dynamic line loss could be evaluated. These parameters were functions of turbopump moment of inertia, design performance of the turbine, and flow-system geometry. The moment of inertia of the turbopump and the ratio of turbine torque at zero speed to design torque had the most influence on the starting dynamics of the flow system. These parameters were also applicable to the bootstrap configuration as long as the inlet pressure to the turbine exceeded half the design value.

Krebs, Richard P.↗

NASA NTRS1992

Cold dissipationless collapse of spherical systems - Sensitivity to the initial density law

The collapse of cold, initially spherical systems with varying degrees of central condensation is investigated. The way in which the final shape of a collapsing system depends on the initial density law is examined. For an initial stellar number density rho varies as r exp -n, where n is in the range 0-2.5, the final, nearly prolate shape is given by a/c is approximately equal to 1.28(1 + 0.16 n), where a/c is the ratio of long to short axes of the inertia ellipsoid computed from the moment of inertia tensor of the most tightly bound 80 percent of the mass. The properties associated with the final states in the present computations are also studied. The collapsing systems develop an anisotropic halo dominated by radial orbits surrounding an isotropic core as predicted by Burkert (1990).

Cannizzo, John K.↗

NASA NTRS1972

NERVA mass properties computer methodology

The computer codes are presented that were used for the weight, center of gravity, and mass moment of inertia calculations and documentation for the NERVA. The two programs, E15301 and 12001B, are the basic tools used for weights work on the NERVA program. Used in conjunction with one another, they allow for rapid weights estimates for new concepts or changes while allowing for orderly documentation, which is a necessity in any effective weights effort. Program E15301 requires that each component be resolved into a collection of standard shapes. Separate subroutines then process geometric and material density data for each entry. The master program the performs all calculations necessary to combine these results into a total weight, center of gravity, and moment of inertia for the component. Program 12001B accepts previously calculated weight and center of gravity data for individual components. The program sums weights and calculates center of gravities and moments of inertia for systems of up to four levels of assemblies. The output identifies the engine parts in a format usable directly in a formal report.

Hall, I. K.↗