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NASA NTRS1984

Finding maximum on an array processor with a global bus

The problem of finding the maximum of a set of values stored one/processor on an n x n array of processors is analyzed. The array has a time-shared global bus in addition to conventional processor-processor links. A two-phase algorithm for finding the maximum is presented that uses conventional links during the first phase and the global bus during the second. This algorithm is faster than algorithms that use either only the global bus or only the conventional links. Two types of interconnection patterns (the eighth nearest neighbor and the fourth nearest neighbor) are analyzed. In both cases it is shown that the time required to find the maximum using the two-phase algorithm is 0(n to the 2/3-power) assuming the propagation speed of the global bus to be a constant independent of the size of the array. In the case where the propagation speed is logarithmic in the number of processors, the time to find the maximum is 0(/n-squared log n/1/3), for both types of arrays. Extensions to q-dimensional arrays show that the two-phase algorithm is superior for any fixed value of q.

Bokhari, S. H.↗

NASA NTRS1985

Effect of maximum lift to drag ratio on optimal aeroassisted plane change

The influence of the maximum lift-to-drag ratio on the turning performance of an Orbital Transfer Vehicle is analyzed. Chapman's variables are used to formulate the equations of motion which are valid for both atmospheric flight and flight in a vacuum in a Newtonian gravitational field. Of the six adjoint variables involved in the variational formulation, four exact integrals and two approximate relations are obtained. This leads to an approximate but explicit control law for the lift and bank control. The control law is tested numerically for a whole range of entry speeds, from parabolic entry to near-circular entry with several values of maximum lift-to-drag ratio. The extensive numerical results, which are very accurate as compared to the exact optimal values, show that the maximum plane change for any speed ratio V(entry)/V(final) is simply proportional to the maximum lift-to-drag ratio, and depends solely on this parameter.

Johannesen, J. R.↗

NASA NTRS1986

The effect of the heliospheric current sheet on cosmic ray intensities at solar maximum - Two alternative hypotheses

The capabilities of two alternative models for accounting for the reversal of the solar magnetic field polarity at the point of solar maximum and for the associated modulation of cosmic ray intensities at 1 AU are assessed. One model posits a continuous increase in the inclination of the heliospheric current sheet to a point of verticality at maximum, when it overturns and the reversal occurs. The alternative view is that the sun sheds the magnetic field of the previous cycle and generates a new field of opposite polarity. Some data do exist for a tilted current sheet which increases its tilt with proximity to the solar maximum. However, coronal data also support the presence of isolated regions of anomalous polarity which spread over the surface of the sun as maximum approaches, a condition commensurate with flux shedding. Both models predict heliospheric current sheet configurations which would produce some cosmic ray modulations observed over the course of the solar cycle.

Thomas, B. T.↗

NASA NTRS1988

A prediction for the maximum phase and duration of sunspot cycle 22

A projected value of the maximum amplitude of sunspot cycle 22 is used to predict the ascent, maximum phase, and length of the cycle. It is suggested that cycle 22 will have a lower maximum amplitude than cycle 21. This would make cycle 22 a 'negative-valued' maximum amplitude first-difference cycle with an ascent with a median value of 4 years. Cycle 22 is predicted to be a long-period cycle with a length in the range of 138 + or - 8 months. It is concluded that cycle 22 will probably peak sometime in the latter half of 1990 or the first half of 1991 and that it will not end until early to mid 1998.

Wilson, Robert M.↗

NASA NTRS1989

Estimates of the maximum time required to originate life

Fossils of the oldest microorganisms exist in 3.5 billion year old rocks and there is indirect evidence that life may have existed 3.8 billion years ago (3.8 Ga). Impacts able to destroy life or interrupt prebiotic chemistry may have occurred after 3.5 Ga. If large impactors vaporized the oceans, sterilized the planets, and interfered with the origination of life, life must have originated in the time interval between these impacts which increased with geologic time. Therefore, the maximum time required for the origination of life is the time that occurred between sterilizing impacts just before 3.8 Ga or 3.5 Ga, depending upon when life first appeared on earth. If life first originated 3.5 Ga, and impacts with kinetic energies between 2 x 10 the the 34th and 2 x 10 to the 35th were able to vaporize the oceans, using the most probable impact flux, it is found that the maximum time required to originate life would have been 67 to 133 million years (My). If life originated 3.8 Ga, the maximum time to originate life was 2.5 to 11 My. Using a more conservative estimate for the flux of impacting objects before 3.8 Ga, a maximum time of 25 My was found for the same range of impactor kinetic energies. The impact model suggests that it is possible that life may have originated more than once.

Oberbeck, Verne R.↗

NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗

NASA NTRS1993

The use of polar-orbiting satellite sounding data to estimate rural maximum and minimum temperatures

Atmospheric sounding products from NOAA's polar-orbiting satellites were used to derive and test predictive equations of rural shelter-level maximum and minimum temperatures. Sounding data from both winter and summer months were combined with surface data from over 5300 cooperative weather stations in the continental United States to develop multiple linear regression equations. Separate equations were developed for both maximum and minimum temperature, using the three types of sounding retrievals (clear, partly cloudy, and cloudy). Clear retrieval models outperformed others, and maximum temperatures were more accurately predicted than minimums. Average standard deviations of observed rural shelter temperatures within sounding search areas were of similar magnitude to root-mean-square errors from satellite estimates for most clear and partly cloudy cases, but were significantly less for cloudy retrieval cases. Model validation for surrogate polar and tropical climatic regions showed success in application of the four clear retrieval models (maximum and minimum temperature, for both winter and summer). This indicates the potential adaptability of these models to estimates of rural shelter temperature in areas outside of the United States.

Johnson, Gregory L.↗

NASA NTRS1946

Effect of Mach and Reynolds Numbers on Maximum Lift Coefficient

A knowledge of the effects of Mach and Reynolds numbers on the maximum lift coefficient is becoming of greater importance as the speeds and altitudes attainable by modern airplanes continually increase. Since most maximum-lift tests conducted to date have been either at full-scale Reynolds numbers and low Mach numbers or at high Mach numbers and small Reynolds numbers, very little is known about the inter-related effects of these two parameters on the maximum lift coefficient. In order to obtain quantitative information on these effects, flight tests were conducted at Ames Aeronautical Laboratory on six airplanes, three having NACA conventional airfoil sections, two having NACA low-drag sections, and the sixth having a North American Aviation - NACA compromise low-drag section. The results of these tests which cover a range of Mach numbers from 0.15 to 0.72 and of Reynolds numbers from 4,400,000 to 19,500,000 are assembled, together with a considerable quantity of pertinent wind-tunnel data, and analyzed in the present report. From this analysis, general conclusions have been reached indicating the manner in which the maximum lift coefficient is influenced by variations of Mach and Reynolds numbers.

AIRPLANES - BELL P-63A (AMER ) FLIGHT TESTS↗

NASA NTRS1951

Two-dimensional Cascade Investigation of the Maximum Exit Tangential Velocity Component and Other Flow Conditions at the Exit of Several Turbine Blade Designs at Supercritical Pressure Ratios

The nature of the flow at the exit of a row of turbine blades for the range of conditions represented by four different blade configurations was evaluated by the conservation-of-momentum principle using static-pressure surveys and by analysis of Schlieren photographs of the flow. It was found that for blades of the type investigated, the maximum exit tangential-velocity component is a function of the blade geometry only and can be accurately predicted by the method of characteristics. A maximum value of exit velocity coefficient is obtained at a pressure ratio immediately below that required for maximum blade loading followed by a sharp drop after maximum blade loading occurs.

TURBINES - AXIAL FLOW↗

NASA NTRS1945

Summary of Measurements in Langley Full-Scale Tunnel of Maximum Lift Coefficients and Stalling Characteristics of Airplanes

The results of measurements in the Langley full-scale tunnel of the maximum lift coefficients and stalling characteristics of airplanes have been collected. The data have been analyzed to show the nature of the effects on maximum lift and stall of wing geometry, fuselages and nacelles, propeller slipstream, surface roughness, and wing leading-edge appendages such as ducts, armaments, tip slats, and airspeed heads. Comparisons of full-scale-tunnel and flight measurements of maximum lift and stall are included in some cases, and the effects of the different testing techniques on the maximum-lift measurements are also given.

Sweberg, Harold H↗

NASA NTRS1994

Spacecraft maximum allowable concentrations for selected airborne contaminants, volume 1

As part of its efforts to promote safe conditions aboard spacecraft, NASA requested the National Research Council (NRC) to develop guidelines for establishing spacecraft maximum allowable concentrations (SMAC's) for contaminants, and to review SMAC's for various spacecraft contaminants to determine whether NASA's recommended exposure limits are consistent with the guidelines recommended by the subcommittee. In response to NASA's request, the NRC organized the Subcommittee on Guidelines for Developing Spacecraft Maximum Allowable Concentrations for Space Station Contaminants within the Committee on Toxicology (COT). In the first phase of its work, the subcommittee developed the criteria and methods for preparing SMAC's for spacecraft contaminants. The subcommittee's report, entitled Guidelines for Developing Spacecraft Maximum Allowable Concentrations for Space Station Contaminants, was published in 1992. The executive summary of that report is reprinted as Appendix A of this volume. In the second phase of the study, the Subcommittee on Spacecraft Maximum Allowable Concentrations reviewed reports prepared by NASA scientists and contractors recommending SMAC's for 35 spacecraft contaminants. The subcommittee sought to determine whether the SMAC reports were consistent with the 1992 guidelines. Appendix B of this volume contains the first 11 SMAC reports that have been reviewed for their application of the guidelines developed in the first phase of this activity and approved by the subcommittee.

National Research Council↗

NASA NTRS1996

Spacecraft Maximum Allowable Concentrations for Selected Airborne Contaminants

National Research Council↗

NASA NTRS1996

Spacecraft Maximum Allowable Concentrations for Selected Airborne Contaminants

As part of its efforts to promote safe conditions aboard spacecraft, NASA requested the National Research Council (NRC) to develop guidelines for establishing spacecraft maximum allowable concentrations (SMACs) for contaminants, and to review SMACs for various spacecraft contaminants to determine whether NASA's recommended exposure limits are consistent with the guidelines recommended by the subcommittee. In response to NASA's request, the NRC organized the Subcommittee on Guidelines for Developing Spacecraft Maximum Allowable Concentrations for Space Station Contaminants within the Committee on Toxicology (COT). In the first phase of its work, the subcommittee developed the criteria and methods for preparing SMACs for spacecraft contaminants. The subcommittee's report, entitled Guidelines for Developing Spacecraft Maximum Allowable Concentrations for Space Station Contaminants , was published in 1992. The executive summary of that report is reprinted as Appendix A of this volume. In the second phase of the study, the Subcommittee on Spacecraft Maximum Allowable Concentrations reviewed reports prepared by NASA scientists and contractors recommending SMACs for approximately 35 spacecraft contaminants. The subcommittee sought to determine whether the SMAC reports were consistent with the 1992 guidelines. Appendix B of this volume contains the SMAC reports for 12 chemical contaminants that have been reviewed for their application of the guidelines developed in the first phase of this activity and approved by the subcommittee. This report is the second volume in the series Spacecraft McLrimum Allowable Concentrations for Space Station Contaminants . The first volume was published in 1994.

National Research Council↗

NASA NTRS1996

Monitoring of Time-Dependent System Profiles by Multiplex Gas Chromatography with Maximum Entropy Demodulation

The maximum entropy technique was successfully applied to the deconvolution of overlapped chromatographic peaks. An algorithm was written in which the chromatogram was represented as a vector of sample concentrations multiplied by a peak shape matrix. Simulation results demonstrated that there is a trade off between the detector noise and peak resolution in the sense that an increase of the noise level reduced the peak separation that could be recovered by the maximum entropy method. Real data originated from a sample storage column was also deconvoluted using maximum entropy. Deconvolution is useful in this type of system because the conservation of time dependent profiles depends on the band spreading processes in the chromatographic column, which might smooth out the finer details in the concentration profile. The method was also applied to the deconvolution of previously interpretted Pioneer Venus chromatograms. It was found in this case that the correct choice of peak shape function was critical to the sensitivity of maximum entropy in the reconstruction of these chromatograms.

Becker, Joseph F.↗

NASA NTRS1959

Maximum Mean Lift Coefficient Characteristics at Low Tip Mach Numbers of a Hovering Helicopter Rotor Having an NACA 64(1)A012 Airfoil Section

An investigation has been conducted on the Langley helicopter test tower to determine experimentally the maximum mean lift-coefficient characteristics at low tip Mach number and a limited amount of drag- divergence data at high tip Mach number of a helicopter rotor having an NACA 64(1)AO12 airfoil section and 8 deg of linear washout. Data are presented for blade tip Mach numbers M(t) of 0.29 to 0.74 with corresponding values 6 6 of tip Reynolds number of 2.59 x 10(exp 6) and 6.58 x 10(exp 6). Comparisons are made between the data from the present rotor with results previously obtained from two other rotors: one having NACA 0012 airfoil sections and the other having an NACA 0009 airfoil tip section. At low tip Mach numbers, the maximum mean lift coefficient for the blade having the NACA 64(1)AO12 section was about 0.08 less than that obtained with the blade having the NACA 0009 tip section and 0.21 less than the value obtained with the blade having the NACA 0012 tip section. Blade maximum mean lift coefficient values were not obtained for Mach number values greater than 0.47 because of a blade failure encountered during the tests. The effective mean lift-curve slope required for predicting rotor thrust varied from 5.8 for the tip Mach nuniber range of 0.29 to 0.55 to a value of 6.65 for a tip Mach number of 0.71. The blade pitching-moment coefficients were small and relatively unaffected by changes in thrust coefficient and Mach number. In the instances in which stall was reached, the break in the blade pitching-moment curve was in a stable direction. The efficiency of the rotor decreased with an increase in tip speed. Expressed as figure of merit, at a tip Mach number of 0.29 the maximum value was about 0.74. Similar measurements made on another rotor having an NACA 0012 airfoil and with a rotor having an NACA 0009 tip section, showed a value of 0.75. Synthesized section lift and profile-drag characteristics for the rotor-blade airfoil section are presented as an aid in predicting the high-tip-speed performance of rotors having similar airfoils.

Powell, Robert D., Jr.↗

NASA NTRS1960

Measurement of the Maximum Speed Attained by the X-15 Airplane Powered with Interim Rocket Engines

On August 4, 1960, a flight was made with the X-15 airplane to the maximum speed expected with the interim rocket engines. Fully corrected airspeed measurements showed that the maximum Mach number of 3.1 +/- 0.04 and maximum true airspeed of 2,196 mph +/- 35 were attained at an altitude of 69,600 feet. At Mach numbers greater than 2.0 the pitot-static tube exhibited a negative static-pressure error which resulted in a Mach number correction of -0.18 at the maximum speed.

Stillwell, Wendell H.↗

NASA NTRS1949

Flight Investigations at High-Subsonic, Transonic, and Supersonic Speeds to Determine Zero-Lift Drag of Fin-Stabilized Bodies of Revolution having Fineness Ratios of 12.5, 8.91, and 6.04 and Varying Positions of Maximum Diameter

Rocket-powered models were flown at high-subsonic, transonic, and supersonic speeds to determine the zero-lift drag of fin-stabilized parabolic bodies of revolution differing in fineness ratio and in position of maximum diameter. The present paper presents the results for fineness ratio 12.5, 8.91 and 6.04 bodies having maximum diameters located at stations of 20, 40, 60, and 80 percent of body length. All configurations had cut-off sterns and all had equal base, frontal, and exposed fin areas. For most of the supersonic-speed range models having their maximum diameters at the 60-percent station gave the lowest values of drag coefficient. At supersonic speeds, increasing the fineness ratio generally reduced the drag coefficient for a given position of maximum diameter.

Hart, Roger G.↗

NASA NTRS1946

Knock-Limited Performance of Triptane and Xylidines Blended with 28-R Aviation Fuel at High Compression Ratios and Maximum-Economy Spark Setting

An investigation was conducted to evaluate the possibilities of utilizing the high-performance characteristics of triptane and xylidines blended with 28-R fuel in order to increase fuel economy by the use of high compression ratios and maximum-economy spark setting. Full-scale single-cylinder knock tests were run with 20 deg B.T.C. and maximum-economy spark settings at compression ratios of 6.9, 8.0, and 10.0, and with two inlet-air temperatures. The fuels tested consisted of triptane, four triptane and one xylidines blend with 28-R, and 28-R fuel alone. Indicated specific fuel consumption at lean mixtures was decreased approximately 17 percent at a compression ratio of 10.0 and maximum-economy spark setting, as compared to that obtained with a compression ratio of 6.9 and normal spark setting. When compression ratio was increased from 6.9 to 10.0 at an inlet-air temperature of 150 F, normal spark setting, and a fuel-air ratio of 0.065, 55-percent triptane was required with 28-R fuel to maintain the knock-limited brake power level obtained with 28-R fuel at a compression ratio of 6.9. Brake specific fuel consumption was decreased 17.5 percent at a compression ratio of 10.0 relative to that obtained at a compression ratio of 6.9. Approximately similar results were noted at an inlet-air temperature of 250 F. For concentrations up through at least 20 percent, triptane can be more efficiently used at normal than at maximum-economy spark setting to maintain a constant knock-limited power output over the range of compression ratios tested.

Held, Louis F.↗