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A method of calculating the horizontal tail area for an airplane equipped with flaps is presented.. The general problem of tail design, the effects of flaps on the factors involved, and the manner in which the flaps change the requirements upon which the minimum horizontal tail area is based are discussed.
Results are presented from an investigation of the variation with Reynolds number and Mach number of the total, base, and skin-friction drag of seven boattail bodies of revolution designed for minimum wave drag according to the theory of NACA-TN-2550. The tests covered a Reynolds number range from approximately 1.0 x 10(6) to 10.0 x 10(6) at Mach numbers of 1.62, 1.93, and 2.41 respectively.
The proof of the theorem that the elliptical distribution of lift over the span is that which will give rise to the minimum induced drag has been given in a variety of ways, generally speaking too difficult to be readily followed by the graduate of the average good technical school of the present day. In the form of proof this report makes an effort to bring the matter more readily within the grasp of this class of readers.
An analysis has been made of the drag losses in airplane flight of cross-flow plate and tubular intercoolers to determine the cooling-air weight flow and pressure drop that give a minimum drag loss for any given cooling effectiveness and, thus, a maximum power-plant net gain due to charge-air cooling. The drag losses considered in this analysis are those due to (1) the extra drag imposed on the airplane by the weight of the intercooler, its duct, and its supports and (2) the drag sustained by the cooling air in flowing through the intercooler and its duct. The investigation covers a range of conditions of altitude, airspeed, lift-drag ratio, supercharger-pressure ratio, and supercharger adiabatic efficiency. The optimum values of cooling air pressure drop and weight flow ratio are tabulated. Curves are presented to illustrate the results of the analysis.
Tests were made to fill partly the need for information on the effect of afterbody dimensions on the hydrodynamic stability of a flying boat in smooth water. The dimensions investigated were depth of step, angle of afterbody keel, and length of afterbody. An analysis of the data showed that as either the afterbody length or keel angle was increased an accompanying increase in depth of step was required in order to maintain adequate landing stability. The landing-tests results have been reduced to an empirical formula giving the minimum depth of step in terms of afterbody length and keel angle. This formula is compared with results from other tank tests, and the correlation is fairly good. The formula thus becomes of use in preliminary design.
The linearized drag integral for bodies of revolution at supersonic speeds is presented in a double-integral form which is not based on slender-body approximations but which reduces to the equal slender-body expression in the proper limit. With the aid of a suitably chosen auxiliary condition, the minimum-external-wave-drag problem is solved for a transition section connecting two semi-infinite cylinders. The projectile tip is a special case and is compared with the Von Karman projectile tip. Calculations are presented which indicate that the method of analysis gives good first-order results in the moderate supersonic range.
Several variational problems involving optimum wing and body combinations having minimum wave drag for different kinds of geometrical restraints are analyzed. Particular attention is paid to the effect on the wave drag of shortening the fuselage and, for slender axially symmetric bodies, the effect of fixing the fuselage diameter at several points or even of fixing whole portions of its shape.
An investigation has been conducted in the Langley 9-inch supersonic tunnel to determine the effect of the variation with Reynolds number and Mach number of the total, base, and skin-friction drag at zero lift of seven boattail bodies of revolution designed for minimum wave drag according to NACA TN 2550. The tests covered a Reynolds number range from approximately 1.0 x 10(6) to 10.0 x 10(6) at Mach numbers of 1.62, 1.93, and 2.41, respectively. The results show that base drag and, in general, the total drag increase with increasing values of the ratio of base area to maximum area B/S(sub max), although the results reported in NACA TN 3054 showed that the wave drag decreased with increasing values of B/S(sub max). The laminar skin-friction drag is in agreement with the theoretical predictions used, and, within the Mach number range of these tests, the simple Blasius incompressible theory gives a satisfactory prediction. Except for values of B/S (sub max) near 1, the Reynolds number of transition increases with increasing Mach number and as this ratio approaches 1 this variation is seen to reverse. These variations in Reynolds number of transition with Mach number appear to be associated with the changes in pressure gradient over the rear of the bodies.
The completeness properties of the Schrodinger minimum uncertainty states (SMUS) and of some of their subsets are considered. The invariant measures and the resolution unity measures for the set of SMUS are constructed and the representation of squeezing and correlating operators and SMUS as superpositions of Glauber coherent states on the real line is elucidated.
Recently, dense gases have been investigated for many engineering applications such as for turbomachinery and wind tunnels. Supersonic nozzle design for these gases is complicated by their nonclassical behavior in the transonic flow regime. In this paper a method of characteristics (MOC) is developed for two-dimensional (planar) and, primarily, axisymmetric flow of a van der Waals gas. Using a straight aortic line assumption, a centered expansion is used to generate an inviscid wall contour of minimum length. The van der Waals results are compared to previous perfect gas results to show the real gas effects on the flow properties and inviscid wall contours.
Rocket engine design follows three phases: systems design, parameter design, and tolerance design. Systems design and parameter design are most effectively conducted in a concurrent engineering (CE) environment that utilize methods such as Quality Function Deployment and Taguchi methods. However, tolerance allocation remains an art driven by experience, handbooks, and rules of thumb. It was desirable to develop and optimization approach to tolerancing. The case study engine was the STME gas generator cycle. The design of the major components had been completed and the functional relationship between the component tolerances and system performance had been computed using the Generic Power Balance model. The system performance nominals (thrust, MR, and Isp) and tolerances were already specified, as were an initial set of component tolerances. However, the question was whether there existed an optimal combination of tolerances that would result in the minimum cost without any degradation in system performance.
There are many multi-stage optimization problems that are not easily solved through any known direct method when the stages are coupled. For instance, we have investigated the problem of planning a vehicle's control sequence to negotiate obstacles and reach a goal in minimum time. The vehicle has a known mass, and the controlling forces have finite limits. We have developed a technique that finds admissible control trajectories which tend to minimize the vehicle's transit time through the obstacle field. The immediate applications is that of a space robot which must rapidly traverse around 2-or-3 dimensional structures via application of a rotating thruster or non-rotating on-off for such vehicles is located at the Marshall Space Flight Center in Huntsville Alabama. However, it appears that the development method is applicable to a general set of optimization problems in which the cost function and the multi-dimensional multi-state system can be any nonlinear functions, which are continuous in the operating regions. Other applications included the planning of optimal navigation pathways through a transversability graph; the planning of control input for under-water maneuvering vehicles which have complex control state-space relationships; the planning of control sequences for milling and manufacturing robots; the planning of control and trajectories for automated delivery vehicles; and the optimization and athletic training in slalom sports.
The Phillips Laboratory at the Edwards Air Force Base has developed the Advanced Space Structures Technology Research Experiment (ASTREX) facility to serve as a testbed for demonstrating the applicability of proven theories to the challenges of spacecraft maneuvers and structural control. This report describes the work performed on the ASTREX test article by Texas A&M University under contract NAS119373 as a part of the Control-Structure Interaction (CSI) Guest Investigator Program. The focus of this work is on maneuvering the ASTREX test article with compressed air thrusters that can be throttled, while attenuating structural excitation. The theoretical foundation for designing the near minimum-time thrust commands is based on the generation of smooth, parameterized optimal open-loop control profiles, and the determination of control laws for final position regulation and tracking using Lyapunov stability theory. Details of the theory, mathematical modeling, model updating, and compensation for the presence of 'real world' effects are described and the experimental results are presented. The results show an excellent match between theory and experiments.
We show that uncertainty relations, as well as minimum uncertainty coherent and squeezed states, are structural properties for diffusion processes. Through Nelson stochastic quantization we derive the stochastic image of the quantum mechanical coherent and squeezed states.
The bound quadratic Hamiltonian system is analyzed explicitly on the basis of quantum mechanics. We have derived the invariant quantity with an auxiliary equation as the classical equation of motion. With the use of this invariant it can be determined whether or not the system is bound. In bound system we have evaluated the exact eigenfunction and minimum uncertainty function through unitary transformation.
The interference susceptibility of a serial-minimum-shift-keyed (SMSK) modulation system to an interfering signal transmitted through a satellite link with cascaded nonlinear elements was investigated through computer simulation. The satellite link evaluated in this study represented NASA's Advanced Communications Technology Satellite (ACTS) system. Specifically, nonlinear characteristics were used that had specified amplitude-modulation to amplitude-modulation and amplitude-modulation to phase-modulation transfer characteristics obtained from the actual ACTS hardware. Two measurement scenarios were analyzed: degradation of an MSK satellite link from cochannel interference and from adjacent-channel interference. Interference was evaluated in terms of the probability of bit error rate (BER) versus energy per bit over noise power density Eb/No.
A new simulation model of the mesosphere, thermosphere, and ionosphere with coupled electrodynamics has been developed and used to calculate the global circulation, temperature and compositional structure between 30-500 km for equinox, solar cycle minimum, geomagnetic quiet conditions. The model incorporates all of the features of the National Center for Atmospheric Research (NCAR) thermosphere-ionosphere- electrodynamics general circulation model (TIE-GCM) but the lower boundary has been extended downward from 97 to 30 km (10 mb) and it includes the physical and chemical processes appropriate for the mesosphere and upper stratosphere. The first simulation used Rayleigh friction to represent gravity wave drag in the middle atmosphere and although it was able to close the mesospheric jets it severely damped the diurnal tide. Reduced Rayleigh friction allowed the tide to penetrate to thermospheric heights but did not close the jets. A gravity wave parameterization developed by Fritts and Lu (1993) allows both features to exist simultaneously with the structure of tides and mean flow dependent upon the strength of the gravity wave source. The model calculates a changing dynamic structure with the mean flow and diurnal tide dominant in the mesosphere, the in-situ generated semi-diurnal tide dominating the lower thermosphere and an in-situ generated diurnal tide in the upper thermosphere. The results also show considerable interaction between dynamics and composition, especially atomic oxygen between 85 and 120 km.
The isotopic composition of C, N, O, Ne, Mg, Si cosmic ray nuclei has been measured in the energy range 50-200 MeV per nucleon using data collected by the High-Energy Telescope of the cosmic-ray subsystem experiment on the Voyager 1 and 2 spacecraft. These data were collected during the period of minimum solar activity in 1986-1988 at an average distance of 27 AU with an effective solar modulation that was much less than at the Earth. The isotope analysis, based on the energy loss - total energy method, has a mass resolution of 0.2 amu for carbon and 0.4 amu at silicon. We find a (C-13)/(C-12) ratio slightly lower and a (O-18)/(O-16) ratio slightly enhanced over their solar system value. We also observe the previously reported enhancement of the (Ne-22)/(Ne-20) ratio relative to solar at the cosmic-ray source but only a weak, if any, enhancement of the (Mg-25)/(Mg-24), (Mg-26)/(Mg 24), and (Si-30)/(Si-28) ratios.