Download or read book Flight Motion of a Continuously Elastic Finned Missile written by Charles H. Murphy and published by . This book was released on 2002-06-01 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The motion of elastic finned projectiles has been analyzed by various approximate theories. In this report the exact equations of small amplitude motion are derived for a symmetric missile. The aerodynamic and elastic symmetries are used to allow the use of complex variables to describe the lateral motion in a non-rotating coordinate system. Although the resulting equations are both ordinary and partial differential equations, frequencies and damping rates of free oscillations are obtained from an ordinary differential equation with boundary conditions. Equations for a permanently deformed bent missile are derived, and an ordinary differential equation for the forced motion of a bent missile is obtained. Sample calculations for a finned projectile with a fineness ratio of 20 show resonant motion at the aerodynamic frequency as well as at each elastic frequency. The nonlinear roll moment associated with a bent missile is computed and the location of possible spin-yaw lock-in is determined. The flight motion of an elastic missile is shown to be the sum of two elliptical motions: a low frequency pitching motion and a higher frequency flexing motion. The induced drag coefficients for both motions are computed as functions of the missile's elasticity.
Download or read book Flight Mechanics of an Elastic Symmetric Missile written by Charles H. Murphy and published by . This book was released on 2000-04-01 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The free-flight motion of an elastic missile is approximated with three bodies connected by two massless elastic cantilever beams. If the mass distribution of the three bodies is 1-2-1, the frequency of the symmetric oscillation of the outer bodies is within 5% of the classical frequency of the oscillation of a free-free beam. A second combined pitching antisymmetric flexing motion can occur with a frequency that is almost twice that of the symmetric flexing motion. As the beam stiffness is reduced, the symmetric flexing motion frequency approaches the rigid body aerodynamic zero-spin frequency, and the flight zero-spin aerodynamic frequency is considerably reduced. Moderate beam damping can cause dynamic instability for spins greater than the zero-spin aerodynamic frequency. Resonance mode amplification can occur when the spin is equal to the zero-spin aerodynamic frequency, but more importantly it can occur when the spin is equal to the two elastic flexing frequencies. Spin-yaw lock-in occurs at the lower elastic frequency.
Download or read book Mathematical Theory Of Rocket Flight written by Barkley Rosser and published by Read Books Ltd. This book was released on 2013-04-18 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the official final report to the Office of Scientific Research and Development concerning the work done on the exterior ballistics of fin-stabilized rocket projectiles under the supervision of Section H of Division 3 of the National Defense Research Committee at the Allegany Ballistics Laboratory during 1944 and 1945, when the laboratory was operated by The George Washington University under contract OEMsr-273 with the Office of Scientific Research and Development. As such, its official title is “Final Report No. B2.2 of the Allegany Ballistics Laboratory, OSRD 5878.” After the removal of secrecy restrictions on this report, a considerable amount of expository material was added. It is our hope that thereby the report has been made readable for anyone interested in the flight of rockets. Two slightly different types of readers are anticipated. One is the trained scientist who has had no previous experience with rockets. The other is the person with little scientific training who is interested in what makes a rocket go. The first type of reader should be able to comprehend the report in its entirety. For the benefit of the second type of reader, who will wish to skip the more mathematical portions, we have attempted to supply simple explanations at the beginnings of most sections telling what is to be accomplished in those sections. It is our hope that a reader can, if so minded, skip most of the mathematics and still be able to form a general idea of rocket flight.
Download or read book The Flight of Uncontrolled Rockets written by F. R. Gantmakher and published by Elsevier. This book was released on 2014-05-17 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs on Aeronautics and Astronautics, Division VII, Volume 5: The Flight of Uncontrolled Rockets focuses on external ballistics of uncontrolled rockets. The book first discusses the equations of motion of rockets. The rocket as a system of changing composition; application of solidification principle to rockets; rotational motion of rockets; and equations of motion of the center of mass of rockets are described. The text looks at the calculation of trajectory of rockets and the fundamentals of rocket dispersion. The selection further focuses on the dispersion of finned rockets. Topics include the critical section of the trajectory; standard formula for calculating angular deviation; dispersion of actual rockets; and effective launcher length. The text also describes the dispersion of finned rotated rockets and of finned anti-tank rockets. The book also examines the effect of wind on the flight of rockets. Topics include correction to the coordinates of the point of impact for finned rockets; general effect of wind on dispersion; and general treatment of powered flight in the presence of wind. The text is important for readers interested in the ballistics of uncontrolled rockets.
Download or read book On the Free Flight Motion of Missiles Having Slight Configurational Asymmetries written by John Dudley Nicolaides and published by . This book was released on 1953 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theories for the free fligbt motion of miseiles, as generally considered by the aerodynamicist and the ballistician, are combined to yield a single theory for the basically symmetrical missile. The force and moment system contains not only the usual aerodynamic forces and moments but also the effects of slight configurational asymmetries and the effects of rolling velocity. The theory yields the condition for the dynamic stability of both statically stable and statically unstable missiles, and alco predicts that the presence of configurational asynnetries together with rolling velocity may result in resonance instability. Numerical integrations of the differential equations for the pitching and yawing motion are carried cut for three variations in the rolling motion. The results indicate that the rapidity of passage through the resonance region is a significant factor affecting the nagnitude of the pitch and yaw of the missile. rWo models of a simple arrow type missile having control surface deflection are gun launched at supersonic velocity in the Aberdeen Spark Photography Range and the free flight pitching and yawing motion and the transverse displacement are measured. The tricyclic theory is fitted to the experimental data. The results indicate tbat the theory accurately represent. the actual motion of the two models and that the associated static and dynamic aerodyamic derivatives are accurately determined.
Download or read book Transactions of the Seventh Symposium on Ballistic Missile and Space Technology Held at the United States Air Force Academy on 13 16 August 1962 written by Charles T. Morrow and published by . This book was released on 1962 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book THE STABILITY AND REPONSE OF AN AERODYNAMIC MISSILE IN PLANE MOTION written by and published by . This book was released on 1949 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Free Flight Motion of a Symmetric Missile Acted on by Nonlinear Forces and Moments written by Charles H. Murphy and published by . This book was released on 1957 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Computer Modeling in Engineering Sciences written by and published by . This book was released on 2009 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Explosive Shocks in Air written by Gilbert F. Kinney and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: A purpose of science is to organize diversified factual knowledge into a coherent body of information, and to present this from the simplest possible viewpoint. This is a formidable task where our knowledge is incomplete, as it is with explosions. Here one runs the risk of oversimplification, naivete, and incom pleteness. Nevertheless a purpose of this work is to present as simply as possible a general description of the basic nature of explosions. This treatise should be of interest to all who are working with explosives such as used in construction or in demolition work, in mining operations, or in military applications. It should also be of interest to those concemed with disasters such as explosions or earthquakes, to those involved in civil defense precautions, and to those concemed with defense against terrorists. That is, this material should be of interest to all who wish to utilize, or to avoid, the effects of explosions as weil as to those whose interest is primarily scientific in nature.
Download or read book Spin Yaw Lockin of an Elastic Finned Projectile written by Charles H. Murphy and published by . This book was released on 2004-08-01 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supersonic finned projectiles carrying very long dense metallic rods have been observed to have significantly large flexing motion. The appropriate Lagrangian for a pitching, yawing, rolling, and flexing missile is derived and the powerful finite element method used to construct differential equations for finite element parameters. These differential equations for constant spin are used to calculate frequencies and damping rates of transient motion and trim response motion to missile-fixed inertia and aerodynamic forcing terms associated with inelastic deformations. The results agree with earlier results based on a much more difficult iterative integration of a complex differential equation with unusual boundary conditions. Only three elements were necessary for reasonable accuracy, although codes for five and seven elements have been prepared and exercised. The finite element ordinary differential equations allowed calculation of the time history of missile motion with varying spin and demonstrated the occurrence of spin-yaw resonance at the aerodynamic frequency and at the lowest elastic frequency.
Download or read book Free Flight Motion of Symmetric Missiles written by Charles H. Murphy and published by . This book was released on 1963 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linearized angular motion of a symmetric missile is developed in some detail with some consideration of the rolling motion, drag, aerodynamic jump and the effect of varying coefficients. The tricyclic motion of a missile with misaligned control surfaces in briefly considered. This linear theory is, then, applied to the analysis of ballistic range data. Next, simple cubic nonlinearities in static moment and Magnus moment are treated by a quasi-linear analysis and these cubic coefficients obtained from ballistic range flight data. More generalized relations for arbitrary symmetric nonlinear terms are derived and their use in the construction of "amplitude" planes indicated. These amplitude planes have proven to be quite useful for the prediction of missile flight performance. Finally, the influence of strongly nonlinear static moments is determined by a perturbation method which makes use of two quasi-constants of the motion--total energy and angular momentum.
Download or read book Motion of a Ballistic Missile Angularly Misaligned with the Flight Path Upon Entering the Atmosphere and Its Effect Upon Aerodynamic Heating Aerodynamic Loads and Miss Distance written by H. Julian Allen and published by . This book was released on 1957 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis is given of the oscillating motion of a ballistic missile which upon entering the atmosphere is angularly misaligned with respect to the flight path. The history of the motion for some example missiles is discussed from the point of view of the effect of the motion on the aerodynamic heating and loading. The miss distance at the target due to misalignment and to small accidental trim angles is treated. The stability problem is also discussed for the case where the missile is tumbling prior to atmospheric entry.
Download or read book Analysis of Non linear Longitudinal Motion of a Missile in Supersonic Flight written by Morito Ii and published by . This book was released on 1956 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dictionary of Guided Missiles and Space Flight written by Grayson Merrill and published by Princeton, N.J. : Van Nostrand. This book was released on 1959 with total page 746 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U S Government Research Reports written by and published by . This book was released on 1963 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Missile Aerodynamics written by Jack Norman Nielsen and published by AIAA (American Institute of Aeronautics & Astronautics). This book was released on 1988-01-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The similarities between the airplane and the missile extend beyond their flying capabilities, and at higher operational speeds, the configuration distinctions become even less apparent. " Missile Aerodynamics," a classic now available from AIAA and Nielsen Engineering and Research, Inc., combines the best of missile and airplane aerodynamics, drawing extensively from numerous technical papers to present a rational and unified account of the principles behind missile projection. Evaluate the missile versus the airplane in a multitude of areas, from longitudinal acceleration, wing loading, roll and dynamic stability, guidance and navigation, and more. J.N. Nielsen covers every aspect of missile aerodynamics, from the classification of missiles and basic formulas to innovative aerodynamic controls. In one reliable reference, readers will find hundreds of schematics, equations, and tables with practical applications in missile design and engineering. Originally published by Nielsen Engineering and Research, Inc.
