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NASA NTRS1962

The Restricted Three-Body-Problem as a Perturbation of Euler's Problem of Two Fixed Centers and Its Application to Lunar Trajectories

The restricted Three-Body-Problem considers the motion of an infinitesimal mass under the gravitational attraction of two finite masses, which revolve about their common center of gravity in coplanar circles. It is well known that Euler's problem of two fixed centers, consisting of the motion of an infinitesimal mass under the gravitational attraction of two finite masses fixed in space, can be solved by elliptic functions. The idea presented here is to take the solution of Euler's problem as the solution of the restricted Three-Body-Problem by allowing the initial values to be functions of time now. Differential equations for the perturbed initial values are established. These equations can be given in closed form by using the fact that the transformation to the perturbed initial values of Euler's problem is canonical. Thus, an approximation can be obtained for the solution of the restricted Three-Body-Problem. The method can also be used to represent classes of neighboring trajectories for guidance purposes.

Euler equation↗

NASA NTRS1971

Aerodynamic characteristics of an all-body hypersonic aircraft configuration at Mach numbers from 0.65 to 10.6

Aerodynamic characteristics of a model designed to represent an all body, hypersonic cruise aircraft are presented for Mach numbers from 0.65 to 10.6. The configuration had a delta planform with an elliptic cone forebody and an afterbody of elliptic cross section. Detailed effects of varying angle of attack (-2 to +15 deg), angle of sideslip (-2 to +8 deg), Mach number, and configuration buildup were considered. In addition, the effectiveness of horizontal tail, vertical tail, and canard stabilizing and control surfaces was investigated. The results indicate that all configurations were longitudinally stable near maximum lift drag ratio. The configurations with vertical tails were directionally stable at all angles of attack. Trim penalties were small at hypersonic speeds for a center of gravity location representative of the airplane, but because of the large rearward travel of the aerodynamic center, trim penalties were severe at transonic Mach numbers.

Nelms, W. P., Jr.↗

NASA NTRS1994

The Aluminum Falcon: a Low Cost Modern Commercial Transport

The American Institute of Aeronautics and Astronautics (AIAA) released a Request For Proposal (RFP) in the form of an undergraduate design competition for a 153 passenger jet transport with a range of 3,000 nautical miles. The primary requirement for this aircraft was low cost, both in acquisition and operation, with a technology availability date of the year 2000. This report presents the Non-Solo Design Group's response to the RFP, the Aluminum Falcon (AF-1). Non-Solo's approach to development was to take the best elements of seven individual preliminary designs, then combine and refine them. The resulting aircraft meets or exceeds all requirements of both the RFP and the Federal Aviation Administration (FAA). Highlights include a revolutionary wing planform, known as an M-wing, which offers many advantages over a conventional aft swept wing. For example, the M-wing lessens the travel in the aircraft center of gravity caused by fuel being stored in the wing. It also reduces the amount of torque imposed on the center wing box because more of the lifting load acts near the fuselage joint, rather than behind it. In essence, the M-wing offers the best of both worlds: using a forward swept wing root places the aerodynamic center of the wing further forward and allows the landing gear to be placed without the use of a yahudi. At the same time, with the outboard section swept backward the tip retains an amount of aeroelastic dampening that is lost on a completely forward swept wing. The result is a wing which has many advantages of a straight, unswept wings without the severe compressibility effects at high Mach numbers. Other highlights include judicious use of composites, giving recognition to the importance of weight and its effect on aircraft cost and performance, and an advanced passenger entertainment system which can be used as a source of revenue for the airlines. This aircraft meets the low-cost doctrine with an acquisition cost of $29 million and a direct operating cost of 3.5 cents per seat mile. The AF-1 incorporates new ideas with existing technology to result in an aircraft that will retain market viability well into the next century.

Bryant, Mark↗

NASA NTRS1982

Gravity receptors in a microcrustacean water flea - Sensitivity of antennal-socket setae in Daphnia magna

Gravity receptors of Dephnia magna were discovered on the basal segment of the swimming antennae and were shown to respond to upward water currents that pass the animal as it sinks between swimming strokes. Sensitivity of the gravity perceiving mechanism was tested by subjecting daphnids to a series of five decreasingly dense aqueous solutions (neutral density to water) in darkness (to avoid visual cues). Three-dimensional, video analysis of body position (pitch, yaw and roll) and swimming path (hop and sink, vertical and horizontal patterns) revealed a gradual threshold that occurred near a density difference between the animal and its environment of less than 0.25%. Because daphnids do not sink but continue to slide after stroking in the increased density solutions, gravity perception appears to occur during a vertical swing of the longitudinal body axis to the vertical plane, about their center of gravity, and, thereby, implies a multidirectional sensitivity for the antennal-socket setae.

Meyers, D. G.↗

NASA NTRS1989

Transonic aerodynamic characteristics of a proposed Assured Crew Return Capability (ACRC) lifting-body configuration

The investigation was conducted in the Calspan 8-Ft Transonic wind tunnel at Mach numbers from 0.6 to 1.2. The 0.07-scale model had a low aspect ratio body with a flat undersurface. A center fin and two tip fins were mounted on the aft upper body. The tip fins were rolled outboard 40 deg from the vertical. Elevon surfaces made up the trailing edges of the outboard fins and body flaps were located on the upper and lower aft fuselage. Results of the investigation indicated that the model was longitudinally and laterally stable about a center-of-gravity position of 0.54 body length. The maximum trimmed lift-drag ratio was about 3.1 at M = 0.6. The small center fin contributed only a small positive increment to lateral stability but was effective as a yaw control device. Protuberances on the forebody had little effect on the aerodynamic characteristics of the configuration. The model with pitch controls undeflected had desirable longitudinal trim characteristics.

Ware, George M.↗

NASA NTRS1984

L-1011 testing with relaxed static stability

Wind tunnel and flight tests indicate that fuel savings of 2 percent can be achieved by center of gravity (C.G.) management for an L-1011 with the current wing configuration. The normal c.b. location is at 25 percent mean aerodynamic center (MAC). The maximum fuel saving occurs for a C.G. location of 35 percent MAC. However, flight at 35 percent requires that the C.G. range be extended aft of the 35-percent point. Flight at C.G. locations aft or 35 percent requires a pitch active control system (PACS) so that handling qualities are not significantly degraded. The development of this PACS is discussed.

Rising, J. J.↗

NASA NTRS1988

Experimental investigation of hypersonic aerodynamics

An extensive series of ballistic range tests were conducted at the Ames Research Center to determine precisely the aerodynamic characteristics of the Galileo entry probe vehicle. Figures and tables are presented which summarize the results of these ballistic range tests. Drag data were obtained for both a nonablated and a hypothesized ablated Galileo configuration at Mach numbers from about 0.7 to 14 and at Reynolds numbers from 1000 to 4 million. The tests were conducted in air and the experimental results were compared with available Pioneer Venus data since these two configurations are similar in geometry. The nonablated Galileo configuration was also tested with two different center-of-gravity positions to obtain values of pitching-moment-curve slope which could be used in determining values of lift and center-of-pressure location for this configuration. The results indicate that the drag characteristics of the Galileo probe are qualitatively similar to that of Pioneer Venus, however, the drag of the nonablated Galileo is about 3 percent lower at the higher Mach numbers and as much as 5 percent greater at transonic Mach numbers of about 1.0 to 1.5. Also, the drag of the hypothesized ablated configuration is about 3 percent lower than that of the nonablated configuration at the higher Mach numbers but about the same at the lower Mach numbers. Additional tests are required at Reynolds numbers of 1000, 500, and 250 to determine if the dramatic rise in drag coefficient measured for Pioneer Venus at these low Reynolds numbers also occurs for Galileo, as might be expected.

Intrieri, Peter F.↗

NASA NTRS2008

Aerodynamics for the Mars Phoenix Entry Capsule

Pre-flight aerodynamics data for the Mars Phoenix entry capsule are presented. The aerodynamic coefficients were generated as a function of total angle-of-attack and either Knudsen number, velocity, or Mach number, depending on the flight regime. The database was constructed using continuum flowfield computations and data from the Mars Exploration Rover and Viking programs. Hypersonic and supersonic static coefficients were derived from Navier-Stokes solutions on a pre-flight design trajectory. High-altitude data (free-molecular and transitional regimes) and dynamic pitch damping characteristics were taken from Mars Exploration Rover analysis and testing. Transonic static coefficients from Viking wind tunnel tests were used for capsule aerodynamics under the parachute. Static instabilities were predicted at two points along the reference trajectory and were verified by reconstructed flight data. During the hypersonic instability, the capsule was predicted to trim at angles as high as 2.5 deg with an on-axis center-of-gravity. Trim angles were predicted for off-nominal pitching moment (4.2 deg peak) and a 5 mm off-axis center-ofgravity (4.8 deg peak). Finally, hypersonic static coefficient sensitivities to atmospheric density were predicted to be within uncertainty bounds.

Edquist, Karl T.↗

NASA NTRS1985

Oblique wing ready for research aircraft

Performance features and possible design configurations for oblique wings which would lower the supersonic drag characteristics of fighter aircraft are described. The oblique shape reduces wave drag in proportion to the wing length, and can achieve reductions by factors of 4-16. Variable sweep would be accompanied by fuel pumping to maintain an acceptable center of gravity and tail loading. The lift forces remain balanced and thus remove fuselage loads considerations. Extra tail loading to handle longitudinal moments of center-of-lift shifts with variable sweep aircraft are also eliminated. However, oblique wings couple the roll, pitch and yaw axes and require digital controls to provide balancing forces. NASA has initiated a four phase design, construction and flight test program to examine the flight envelope of oblique wings on the F-8 aircraft.

Gregory, T.↗

NASA NTRS1986

Hybrid deployable/erectable solar dynamic box truss system

The design of a hybrid deployable/erectable solar dynamic box truss power generation system for the initial operation capability (IOC) of the Space Shuttle is examined. An organic Rankine cycle heat engine for IOC solar power generation is studied. The design configuration is a simple parabolic concentration where the receiver is located in the focal plane with its aperture at the focal point. The relationship between concentrator size and collection efficiency is analyzed. The geometry of the deployable graphite/epoxy box truss ring and the reflective panels of the system are described. Mass properties and dynamic analyses are performed to evaluate the center of gravity location and moments of inertia characteristics of the energy conversion subsystem (ECS). The deployable/erectable truss is applicable for large IR space telescopes and center and offset fed ECSs.

Coyner, J. V., Jr.↗

NASA NTRS2007

Interface for Physics Simulation Engines

DSS-Prototyper is an open-source, realtime 3D virtual environment software that supports design simulation for the new Vision for Space Exploration (VSE). This is a simulation of NASA's proposed Robotic Lunar Exploration Program, second mission (RLEP2). It simulates the Lunar Surface Access Module (LSAM), which is designed to carry up to four astronauts to the lunar surface for durations of a week or longer. This simulation shows the virtual vehicle making approaches and landings on a variety of lunar terrains. The physics of the descent engine thrust vector, production of dust, and the dynamics of the suspension are all modeled in this set of simulations. The RLEP2 simulations are drivable (by keyboard or joystick) virtual rovers with controls for speed and motor torque, and can be articulated into higher or lower centers of gravity (depending on driving hazards) to enable drill placement. Gravity also can be set to lunar, terrestrial, or zero-g. This software has been used to support NASA's Marshall Space Flight Center in simulations of proposed vehicles for robotically exploring the lunar surface for water ice, and could be used to model all other aspects of the VSE from the Ares launch vehicles and Crew Exploration Vehicle (CEV) to the International Space Station (ISS). This simulator may be installed and operated on any Windows PC with an installed 3D graphics card.

Damer, Bruce↗

NASA NTRS1954

Wind-tunnel Tests of a Model of a Wingless Fin-controlled Missile to Obtain Static Stability and Control Characteristics Through a Range of Mach Numbers from 0.5 to 0.88

An investigation at medium to high subsonic speeds has been conducted in the Langley low-turbulence pressure tunnel to determine the static stability and control characteristics and to measure the fin normal forces and moments for a model of a wingless fin-controlled missile. The data were obtained at Reynolds number of 2.1 x 10(6) based on the missile maximum diameter or 17.7 x 10(6) based on missile length; this Reynolds number was found to be large enough to avoid any large scale effects between the test and the expected flight Reynolds number. With the horizontal-fin deflection limited to a maximum of 6 degrees, longitudinally stable and trimmed flight could not be maintained beyond an angle of attack of 17 degrees for a Mach number of 0.88 and beyond 20 degrees for a Mach number of 0.50 for any center-of-gravity location without the use of some auxiliary stability or control device such as jet vanes. Mach number had no appreciable effect on the center-of-pressure positions and only a slight effect on neutral-point position. There was a shift in neutral-point position of about 1 caliber as the angle of attack was varied through the range for which the neutral point could be determined. Yawing the model to angles of sideslip up to 7 degrees had little effect on the longitudinal stability at angles of attack up to 15 degrees; however, above 15 degrees, the effect of sideslip was destabilizing. With the vertical fins at a plus-or-minus 6 degree roll deflection, the rolling moment caused by yawing the model at high angles of attack could be trimmed out up to angles of sideslip of 6.5 degrees and an angle of attack of 26 degrees for a Mach number of 0.50; this range of sideslip angles was reduced to 3 degrees at a Mach number of 0.88. The data indicated that, at lower angles of attack, the trim range extended to higher angles of sideslip. The total normal-force and hinge-moment coefficients for both horizontal fins were slightly nonlinear with both angle-of-attack and fin deflection. The effect of Mach number was to reduce the slopes of the hinge-moment coefficient with angle of attack and deflection angle. In general, the effort of increasing the sideslip angle was to reduce the values of the fin normal-force and hinge-moment coefficients.

Burrows, Dale L↗

NASA NTRS2004

Effects of Gravity on Bubble Formation in an Annular Jet

The effects of gravity on the bubble formation in an annular jet were studied. The experiments were conducted in the 2.2-second drop tower at the NASA Glenn Research Center. Terrestrial gravity experiments were conducted at the Fluid Dynamics Research Laboratory at the University of Oklahoma. Stainless steel tubing with inner diameters of 1/8" (gas inner annulus) and 5/16" (liquid outer annulus) served as the injector. A rectangular test section, 6" x 6" x 14" tall, made out of half-inch thick Lexan was used. Images of the annular jet were acquired using a high-speed camera. The effects of gravity and varying liquid and gas flow rates on bubble size, wavelength, and breakup length were documented. In general, the bubble diameter was found to be larger in terrestrial gravity than in microgravity for varying Weber numbers (0.05 - 0.16 and 5 - 11) and liquid flow rates (1.5 ft/s - 3.0 ft/s). The wavelength was found to be larger in terrestrial gravity than in microgravity, but remained constant for varying Weber numbers. For low Weber numbers (0.05 - 0.16), the breakup length in microgravity was significantly higher than in terrestrial gravity. Comparison with linear stability analysis showed estimated bubble sizes within 9% of experimental bubble sizes. Bubble size compared to other terrestrial gravity experiments with same flow conditions showed distinct differences in bubble size, which displayed the importance of injector geometry on bubble formation.

Koepp, R. A.↗

NASA NTRS1999

Silicon bulk micromachined, symmetric, degenerate vibratorygyroscope, accelerometer and sensor and method for using the same

When embodied in a microgyroscope, the invention is comprised of a silicon, four-leaf clover structure with a post attached to the center. The whole structure is suspended by four silicon cantilevers or springs. The device is electrostatically actuated and capacitively detects Coriolis induced motions of the leaves of the leaf clover structure. In the case where the post is not symmetric with the plane of the clover leaves, the device can is usable as an accelerometer. If the post is provided in the shape of a dumb bell or an asymmetric post, the center of gravity is moved out of the plane of clover leaf structure and a hybrid device is provided. When the clover leaf structure is used without a center mass, it performs as a high Q resonator usable as a sensor of any physical phenomena which can be coupled to the resonant performance.

Tang, Tony K.↗

NASA NTRS2024

Development of Weighout Process and Evaluations for Underwater Partial Gravity EVA Simulations

For the upcoming Artemis lunar missions, astronauts will needto train in a spacesuit where partial gravity can be simulated such as NASA Neutral Buoyancy Lab (NBL). At the NBL, dive weights and foam can be added around the spacesuit to attaina satisfactory center of buoyancy (CB) and center of gravity (CG) location to simulate the lunar gravity (1/6thG) effects. If CG and CB are not co-located properly, incorrect righting moments can be introduced, and both simulation quality and EVA task performance can be impaired. Based on the findings from the initial testingusing xEMU spacesuits, it was observed that the weigh-out method (i.e., determination of the weights and foam quantities and position) needed further development to improve the simulation quality, especially for the subjects who experienced excessive instability. This paper aims to present the on-going effort to improve the weigh-out process for enabling NBL lunar EVA simulations. For this effort, a human-suit model was created to use suit CAD and 3D human body scansto estimate both CB and CG location for each suited subject. NBL weigh-out testing was performed to characterize the effects of CG and CB positioning, in which the 3D human-suit model was used to determine optimal weigh-out combinations of weights and foam. Postural, balance, and subjective feedback were gathered for each weigh-out configuration. The results indicated that, as the CB was shifted higher and the CB and CG located closer to each other, the subject tended to be more stable and their EVA performance improved. A high CB location was then prioritized across 4 additional subjects in both small and large size spacesuits. When compared to the initial xEMU test series, improved performance was observed across all subjects as the CB moved higher and aligned closer to the system CG.

Seyed Pouyan Sabahi↗

NASA NTRS1959

Stability Investigation of a Blunted Cone and a Blunted Ogive with a Flared Cylinder Afterbody at Mach Numbers from 0.30 to 2.85

A cone with a blunt nose tip and a 10.7 deg cone half angle and an ogive with a blunt nose tip and a 20 deg flared cylinder afterbody have been tested in free flight over a Mach number range of 0.30 to 2.85 and a Reynolds number range of 1 x 10(exp 6) to 23 x 10(exp 6). Time histories, cross plots of force and moment coefficients, and plots of the longitudinal force,coefficient, rolling velocity, aerodynamic center, normal- force-curve slope, and dynamic stability are presented. With the center-of-gravity location at about 50 percent of the model length, the models were both statically and dynamically stable throughout the Mach number range. For the cone, the average aerodynamic center moved slightly forward with decreasing speeds and the normal-force-curve slope was fairly constant throughout the speed range. For the ogive, the average aerodynamic center remained practically constant and the normal-force-curve slope remained practically constant to a Mach number of approximately 1.6 where a rising trend is noted. Maximum drag coefficient for the cone, with reference to the base area, was approximately 0.6, and for the ogive, with reference to the area of the cylindrical portion, was approximately 2.1.

Coltrane, Lucille C.↗

NASA NTRS2024

Development of Weigh-out Process and Evaluations for Underwater Partial Gravity Simulations

For the upcoming Artemis lunar missions, astronauts will need to train in a spacesuit where partial gravity can be simulated such as the NASA Neutral Buoyancy Lab (NBL). At the NBL, dive weights and foam can be added around the spacesuit to attain a satisfactory center of buoyancy (CB) and center of gravity (CG) location to simulate the lunar gravity (1/6thG) effects. If CG and CB are not co-located properly, incorrect righting moments can be introduced, and both simulation quality and EVA task performance can be impaired. Based on the findings from the initial testing using xEMU spacesuits, it was observed that the weigh-out method (i.e., determination of the weights and foam quantities and position) needed further development to improve the simulation quality, especially for the subjects who experienced excessive instability. This paper aims to present the on-going effort to improve the weigh-out process for enabling NBL lunar EVA simulations. For this effort, a human-suit model was created to use suit CAD and 3D human body scans to estimate both CB and CG location for each suited subject. NBL weigh-out testing was performed to characterize the effects of CG and CB positioning, in which the 3D human-suit model was used to determine optimal weigh-out combinations of weights and foam. Postural, balance, and subjective feedback were gathered for each weigh-out configuration. The results indicated that, as the CB was shifted higher and the CB and CG located closer to each other, the subject tended to be more stable and their EVA performance improved. A high CB location was then prioritized across 4 additional subjects in both small and large size spacesuits. When compared to the initial xEMU test series, improved performance was observed across all subjects as the CB moved higher and aligned closer to the system CG.

Pouyan Sabahi↗

NASA NTRS2024

Development of Weigh-out Process and Evaluations for Underwater Partial Gravity Simulations

Pouyan Sabahi↗