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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Spiral Lamber's Problem with Generalized Logarithmic Spirals

Lambert’s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert’s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.\

Roa, Javier↗
NASA NTRS2012

Discovery of Small-Scale Spiral Structures in the Disk of SAO 206462 (HD 135344B)(exp 1): Implications for the Physical State of the Disk from Spiral Density Wave Theory

We present high-resolution, H-band, imaging observations, collected with Subaru /HiCIAO, of the scattered light from the transitional disk around SAO 206462 (HD 1353448). Although previous sub-mm imagery suggested the existence of the dust-depleted cavity at r <= 46 AU, our observations reveal the presence of scattered light components as close as O".2 (approx 28 AU) from the star. Moreover , we have discovered two small-scale spiral structures lying within 0".5 (approx 70 AU). We present models for the spiral structures using the spiral density wave theory, and derive a disk aspect ratio of h approx. 0.1, which is consistent with previous sub-mm observations. This model can potentially give estimates of the temperature and rotation profiles of the disk based on dynamical processes. independently from sub-nun observations. It also predicts the evolution of the spiral structures, which can be observable on timescales of 10-20 years, providing conclusive tests of the model. While we cannot uniquely identify the origin of these spirals, planets embedded in the disk may be capable of exciting the observed morphology. Assuming that this is the case, we can make predictions on the locations and, possibly, the masses of the unseen planets. Such planets may be detected by future multi-wavelengths observations,

Muto, T.↗
NASA NTRS2012

Discovery of Small-Scale Spiral Structures in the Disk of SAO 206462 (HD 135344B): Implications for the Physical State of the Disk from Spiral Density Wave Theory

We present high-resolution, H-band, imaging observations, collected with Subaru/HiCIAO, of the scattered light from the transitional disk around SAO 206462 (HD 135344B). Although previous sub-mm imagery suggested the existence of the dust-depleted cavity at r approximates 46 AU, our observations reveal the presence of scattered light components as close as 0".2 (approx 28 AU) from the star. Moreover, we have discovered two small-scale spiral structures lying within 0".5 (approx 70 AU). We present models for the spiral structures using the spiral density wave theory, and derive a disk aspect ratio of h approx 0.1, which is consistent with previous sub-mm observations. This model can potentially give estimates of the temperature and rotation profiles of the disk based on dynamical processes, independently from sub-mm observations. It also predicts the evolution of the spiral structures, which can be observable on timescales of 10-20 years, providing conclusive tests of the model. While we cannot uniquely identify the origin of these spirals, planets embedded in the disk may be capable of exciting the observed morphology. Assuming that this is the case, we can make predictions on the locations and, possibly, the masses of the unseen planets. Such planets may be detected by future multi-wavelengths observations.

Grady, C. A.↗
NASA NTRS1990

Spiral structure of M51: Streaming motions across the spiral arms

The atomic hydrogen (HI) and the H alpha emission line in the grand-design spiral galaxy M51 have been observed with the Westerbork Synthesis Radio Telescope and the Taurus Fabry-Perot imaging spectrometer, respectively. Across the inner spiral arms significant tangential and radial velocity gradients are detected in the H alpha emission after subtraction of the axi-symmetric component of the velocity field. The shift is positive on the inside and negative on the outside of the northern arm. Across the southern arm this situation is reversed. The direction of the shifts is such that the material is moving inward and faster compared to circular rotation in both arms, consistent with the velocity perturbations predicted by spiral density wave models for gas downstream of a spiral shock. The observed shifts amount to 20 to 30 km (s-1), corresponding to streaming motions of 60 to 90 km (s-1) in the plane of the disk (inclination angle 20 degrees). Comparable velocity gradients have also been observed by Vogel et al. in the CO emission from the inner northern arm of M51. The streaming motions in M51 are about 2 to 3 times as large as the ones found in HI by Rots in M81, and successfully modelled by Visser with a self-consistent density wave model. Researchers have not been able to detect conclusively streaming motions in the HI emission from the arms, perhaps due to the relatively poor angular resolution (approx. 15 seconds) of the HI observations.

Tilanus, R. P. J.↗
NASA NTRS1981

Surface photometry of spiral galaxies. I - Theoretical color variation and surface brightness across spiral arms

A method for the construction of color variations and surface brightness across a galactic spiral arm, using the concepts and results of the density-wave theory, is developed. The color variation measured by the index Q varies with the ratio of the light of young stars to that of the old stars, the initial mass function, and the pattern speed. The fact that the variation of brightness and color across a spiral arm is relatively smooth and symmetrical and not sharp as in the galactic shock picture is due to the smearing-out effects of star formation inside a cloud in the regions behind the galactic shock, and the tendency of new stars to fall back to small galactocentric distances after their formation because of their lower angular velocity at birth. Both effects arise naturally in the context of the density-wave theory.

Yuan, C.↗
NASA NTRS1979

Gravitational collapse in dust lanes and the appearance of spiral structure in galaxies

The possibility is considered that there are two types of spiral for each spiral galaxy: an underlying spiral of relatively old stars seen in red and IR photographs and a spiral outlined by H II regions and young bright blue stars. The origin of the first spiral is attributed to large-scale spiral density waves, and the second spiral is identified as a stochastic spiral. It is suggested that there is a physical or causal connection between the two spirals and that dust lanes play the role of intermediary. An analysis is performed which shows that such a model can account for the formation and destruction of giant molecular cloud complexes and for observed spiral structure in one simple unified theory.

Elmegreen, B. G.↗
NASA NTRS1993

High chemical abundances in stripped Virgo spiral galaxies

Based on a comparison of the oxygen abundances in H 2 regions in field and Virgo cluster late type spiral galaxies, Shields, Skillman, & Kennicutt (1991) suggested that the highly stripped spiral galaxies in the Virgo cluster have systematically higher abundances than comparable field galaxies. In April 1991 and May 1992 we used the blue channel spectrograph on the MMT to obtain new observations of 30 H 2 regions in Virgo spiral galaxies. These spectra cover the wavelength range from (O II) lambda 3727 to (S II) lambda 6731. We now have observed at least 4 H II regions in 9 spiral galaxies in the Virgo cluster. Combining (O II) and (O III) line strengths, we calculate the H II region oxygen abundances based on the empirical calibration of Edmunds & Pagel (1984). These observations show: (1) The stripped, low luminosity Virgo spirals (N4689, N4571) truly have abundances characteristic of much more luminous field spirals; (2) Virgo spirals which show no evidence of stripping (N4651, N4713) have abundances comparable to field galaxies; and (3) Evidence for transition galaxies (e.g., N4254, N4321), with marginally stripped disks and marginal abundance enhancements. The new observations presented here confirm the validity of the oxygen over-abundances in the stripped Virgo spirals. Shields et al. (1991) discussed two different mechanisms for producing the higher abundances in the disks of stripped galaxies in Virgo. The first is the supression of infall of near-primordial material, the second is the suppression of radial inflow of metal-poor gas. Distinguishing between the two cases will require more observations of the Virgo cluster spirals and a better understanding of which parameters determine the variation of abundance with radius in field spirals (cf., Garnett & Shields 1987).

Skillman, E. D.↗
NASA NTRS2010

Model for Simulating a Spiral Software-Development Process

A discrete-event simulation model, and a computer program that implements the model, have been developed as means of analyzing a spiral software-development process. This model can be tailored to specific development environments for use by software project managers in making quantitative cases for deciding among different software-development processes, courses of action, and cost estimates. A spiral process can be contrasted with a waterfall process, which is a traditional process that consists of a sequence of activities that include analysis of requirements, design, coding, testing, and support. A spiral process is an iterative process that can be regarded as a repeating modified waterfall process. Each iteration includes assessment of risk, analysis of requirements, design, coding, testing, delivery, and evaluation. A key difference between a spiral and a waterfall process is that a spiral process can accommodate changes in requirements at each iteration, whereas in a waterfall process, requirements are considered to be fixed from the beginning and, therefore, a waterfall process is not flexible enough for some projects, especially those in which requirements are not known at the beginning or may change during development. For a given project, a spiral process may cost more and take more time than does a waterfall process, but may better satisfy a customer's expectations and needs. Models for simulating various waterfall processes have been developed previously, but until now, there have been no models for simulating spiral processes. The present spiral-process-simulating model and the software that implements it were developed by extending a discrete-event simulation process model of the IEEE 12207 Software Development Process, which was built using commercially available software known as the Process Analysis Tradeoff Tool (PATT). Typical inputs to PATT models include industry-average values of product size (expressed as number of lines of code), productivity (number of lines of code per hour), and number of defects per source line of code. The user provides the number of resources, the overall percent of effort that should be allocated to each process step, and the number of desired staff members for each step. The output of PATT includes the size of the product, a measure of effort, a measure of rework effort, the duration of the entire process, and the numbers of injected, detected, and corrected defects as well as a number of other interesting features. In the development of the present model, steps were added to the IEEE 12207 waterfall process, and this model and its implementing software were made to run repeatedly through the sequence of steps, each repetition representing an iteration in a spiral process. Because the IEEE 12207 model is founded on a waterfall paradigm, it enables direct comparison of spiral and waterfall processes. The model can be used throughout a software-development project to analyze the project as more information becomes available. For instance, data from early iterations can be used as inputs to the model, and the model can be used to estimate the time and cost of carrying the project to completion.

Mizell, Carolyn↗
NASA NTRS1990

The molecular spiral arms of NGC 6946

From CO-12(J=1 to 0) observations at 45 seconds resolution Tacconi and Young (1989) have found evidence for enhancements in both the CO emissivity and the massive star formation efficiency (MSFE) on optical spiral arms of the bright spiral galaxy NGC 6946. In the optically luminous and well-defined spiral arm in the NE quadrant, there are enhancements in both the H2 surface density and MSFE relative to the interarm regions. In contrast, a poorly defined arm in the SW shows no arm-interarm contrast in the MSFE. To further investigate the molecular gas content of these two spiral arms, researchers have made CO-12 J=2 to 1 and 3 to 2 observations with the James Clerk Maxwell Telescope. In the J=2 to 1 line, they made observations of the NE and SW spiral arm and interarm regions in 4 x 9 10 seconds spaced grids (36 points per grid). Because of decreased sensitivity in the J=3 to 2 line, they were limited to mapping the two arm regions in 2 x 3 10 seconds spaced grids (6 points per grid). The centers of each of the grids lie 2.4 minutes to the NE and 2.3 minutes to the SW of the nucleus of NGC 6946. With the CO J=2 to 1 data researchers are able to fully resolve the two observed spiral arms in NGC 6946. In both cases the CO emission is largely confined to the optical spiral arm regions with the peak observed T asterisk sub A being up to 4 times higher on the spiral arms than in the interarm regions. Researchers are currently estimating massive star formation efficiencies on and off the spiral arms through direct comparison of the CO maps with an H alpha image. They are also comparing the CO J=2 to 1 data with an HI map made at similar resolution. Thus, they will be able to determine structure in all components of the IS on scales of less than 20 inches.

Tacconi, L. J.↗
NASA NTRS1993

Can cluster environment modify the dynamical evolution of spiral galaxies?

Over the past decade many effects of the cluster environment on member galaxies have been established. These effects are manifest in the amount and distribution of gas in cluster spirals, the luminosity and light distributions within galaxies, and the segregation of morphological types. All these effects could indicate a specific dynamical evolution for galaxies in clusters. Nevertheless, a more direct evidence, such as a different mass distribution for spiral galaxies in clusters and in the field, is not yet clearly established. Indeed, Rubin, Whitmore, and Ford (1988) and Whitmore, Forbes, and Rubin (1988) (referred to as RWF) presented evidence that inner cluster spirals have falling rotation curves, unlike those of outer cluster spirals or the great majority of field spirals. If falling rotation curves exist in centers of clusters, as argued by RWF, it would suggest that dark matter halos were absent from cluster spirals, either because the halos had become stripped by interactions with other galaxies or with an intracluster medium, or because the halos had never formed in the first place. Even if they didn't disagree with RWF, other researchers pointed out that the behaviour of the slope of the rotation curves of spiral galaxies (in Virgo) is not so clear. Amram, using a different sample of spiral galaxies in clusters, found only 10% of declining rotation curves (2 declining vs 17 flat or rising) in opposition to RWF who find about 40% of declining rotation curves in their sample (6 declining vs 10 flat or rising), we will hereafter briefly discuss the Amram data paper and compare it to the results of RWF. We have measured the rotation curves for a sample of 21 spiral galaxies in 5 nearby clusters. These rotation curves have been constructed from detailed two-dimensional maps of each galaxy's velocity field as traced by emission from the Ha line. This complete mapping, combined with the sensitivity of our CFHT 3.60 m. + Perot-Fabry + CCD observations, allows the construction of high-quality rotation curves. Details concerning the acquisition and reduction procedures of the data are given in Amram. We present and discuss our preliminary analysis and compare them with RWF's results.

Amram, P.↗
NASA NTRS2002

Comparison Made of Operating Characteristics of Spiral Bevel Gears Manufactured Using Different Methods

Spiral bevel gears are important components on all current rotorcraft drive systems. These components are required to operate at high speeds, high loads, and for an extremely large number of load cycles. In this application, spiral bevel gears are used to redirect the shaft from the horizontal gas turbine engine to the vertical rotor. Because of the high expense of manufacturing these gears, methods that can achieve the same level of performance at reduced cost are highly desirable to aerospace gear manufacturers. Gears manufactured for aerospace applications use high-quality materials and are manufactured to tight tolerances. Special manufacturing machine tools and computer numerically controlled coordinate measurement systems have enabled rotorcraft drive system manufacturers to produce extremely high-quality gears during their normal production. Because of low production rates for rotorcraft, these gears are manufactured in small batches, and thus are unable to benefit from the economics of high production numbers as in other industries. In this investigation, two different manufacturing methods, face-milled and face-hobbed, were used to fabricate spiral bevel gears. For face-milled spiral bevel gears, grinding of the contacting surfaces is the final manufacturing step. At least two different specialty machines are needed to generate the teeth for face-milled spiral bevel gears. For face-hobbed gears, hard cutting is the final manufacturing process. The same machine is used to rough cut and finish cut the gears. This study compared the operational behavior of face-milled spiral bevel gears with that of face-hobbed spiral bevel gears. Test hardware was manufactured to fit within NASA Glenn Research Center's Spiral Bevel Test Facility and to aerospace quality standards. Tests were conducted for stress, vibration, and noise. A comparison of the results attained indicated that the face-hobbed gears had a lower alternating stress level with a more even distribution of loading across the teeth, and slightly reduced levels of vibration and noise. Results of this study show that the face-hobbed method is a viable and lower-cost alternative for producing aerospace-quality spiral-bevel gears.

Handschuh, Robert F.↗
NASA NTRS1985

Star formation in grand design and flocculent spiral galaxies

An examination is conducted of the colors and neutral hydrogen contents of spiral galaxies which have been classified in the Elmegreen and Elmegreen arm morphology system. Using these data, possible differences between the star formation activity in spiral galaxies with and without classic spiral arms are delineated. At the same revised Hubble type, spiral galaxies with regular global arm patterns (the grand design spirals) are bluer than spiral galaxies lacking such patterns (the flocculent spirals) by a small, but statistically significant amount (approximately 0.05 in B-V and approximately 0.15 in U-V). The neutral hydrogen contents of the two groups are roughly similar, implying the star formation rate averaged over a Hubble time has been approximately the same in grand design and flocculent systems. The color differences can be explained either by using an initial mass function in the flocculent spiral galaxies which is deficient in massive stars by a factor of 2 compared with the grand design systems, or by a decrease of 30 percent in the ratio of recent to past star formation rates in flocculent galaxies. The possibility is discussed that systematic Hubble type misclassifications significantly affect these conclusions.

Romanishin, W.↗
NASA NTRS1995

Design considerations for an archimedean slot spiral antenna

The design goal is to develop a 118-157 MHz, vertically polarized, low-profile (or conformal) antenna as a replacement for VHF AM blade antennas on aircraft. This design is to be arrived at by scaling the dimensions of an antenna designed for a center frequency of 1.1 GHz. The design prior to scaling may have the following maximum dimensions: diameter less than 3.70 in. and thickness less than 0.50 in. Although a four-arm spiral design was originally suggested, a two-arm spiral may also be used, as both mode-1 and mode-2 (sum and difference) radiation patterns aren't required. While a four-arm spiral can easily be designed should both sum and difference patterns be required, the two-arm design will provide the required sum pattern and simplify the design problem somewhat: only one feed is required, and the feed area geometry is more straightforward. Polarization requirements dictate that a slot spiral be used, as opposed to a wire spiral. Two similar radiating structures were considered. The first is the standard archimedean spiral antenna. The second is a hollow archimedean spiral antenna, essentially a standard archimedean spiral with the inner portion removed.

Nurnberger, Michael W.↗
NASA NTRS2014

Investigation of Spiral Bevel Gear Condition Indicator Validation via AC-29-2C Using Fielded Rotorcraft HUMS Data

This report presents the analysis of gear condition indicator data collected on a helicopter when damage occurred in spiral bevel gears. The purpose of the data analysis was to use existing in-service helicopter HUMS flight data from faulted spiral bevel gears as a Case Study, to better understand the differences between HUMS data response in a helicopter and a component test rig, the NASA Glenn Spiral Bevel Gear Fatigue Rig. The reason spiral bevel gear sets were chosen to demonstrate differences in response between both systems was the availability of the helicopter data and the availability of a test rig that was capable of testing spiral bevel gear sets to failure. The objective of the analysis presented in this paper was to re-process helicopter HUMS data with the same analysis techniques applied to the spiral bevel rig test data. The damage modes experienced in the field were mapped to the failure modes created in the test rig. A total of forty helicopters were evaluated. Twenty helicopters, or tails, experienced damage to the spiral bevel gears in the nose gearbox. Vibration based gear condition indicators data was available before and after replacement. The other twenty tails had no known anomalies in the nose gearbox within the time frame of the datasets. These twenty tails were considered the baseline dataset. The HUMS gear condition indicators evaluated included gear condition indicators (CI) Figure of Merit 4 (FM4), Root Mean Square (RMS) or Diagnostic Algorithm 1 (DA1) and +/- 3 Sideband Index (SI3). Three additional condition indicators, not currently calculated on-board, were calculated from the archived data. These three indicators were +/- 1 Sideband Index (SI1), the DA1 of the difference signal (DiffDA1) and the peak-to-peak of the difference signal (DP2P). Results found the CI DP2P, not currently available in the on-board HUMS, performed the best, responding to varying levels of damage on thirteen of the fourteen helicopters evaluated. Two additional CIs also not in the on-board system, DiffDA1and SI1, also performed well responding to twelve and ten of the fourteen helicopters evaluated respectively. Of the three CIs currently available in the MSPU, DA1, FM4 and SI3, SI3, responded to eight, DA1 responded to six and FM4 responded to four of the fourteen helicopters evaluated. FM4, the poorest performing CI, was not as responsive to damage as the other five CIs. Conversely, when compared to the other two, it was the only CI that responded to damage on two helicopters. CI response could not be correlated to specific failure modes due to limited pictures and subjective descriptions found within the TDA. Flight regime did affect CI response to some gear faults. Due to the range of operating conditions for each regime, more studies are required to determine their sensitivity to regimes.

rotorcraft↗
NASA NTRS1990

Molecular gas and star formation in the centers of Virgo spirals

The CO and H alpha flux distributions for a sample of Virgo spirals were mapped out in an attempt to understand the coupling between gas dynamics and star formation in spiral galaxies. A broad range of morphological types were observed (types Sab through Scd) under the hypothesis that the gas dynamics is most influential in determining the overall appearance of a spiral galaxy. Only non-barred spirals were considered so that the well-studied but complicated properties of bars and their role in inducing star formation would not be a factor. All galaxies were chosen from the Virgo cluster to eliminate uncertainties due to distance errors. Since the dynamical seat of a spiral is at its center, it was expected that the dynamics of the central region would influence global properties of the rest of the disk. This could happen through the existence or absence of an inner Lindblad resonance (according to the degree of central concentration of mass) to modulate swing amplification of spiral waves, or the persistence of an oval distortion to initiate an instability which leads to spiral structure.

Canzian, Blaise↗