Pitch Oscillations Research Articles

重力傾度を利用する人工衛星の姿勢制御

Abstract The gravity gradient stabilization provides a passive, long-lived and earth pointing satellite attitude control system. The fundamental principles of the gravity stabilization are showed, and then the equations of motions are derived by applying the Lagrangean equations to the proposed system which is composed of the main rod, damping rods and damper-spring mechanisms. As a result of linearization, these equations are expressed in two groups, one describing the pitch motions and the other the roll-yaw motions. The equations for pitch have two oscillatory transient modes; one is symmetric, and the other antisymmetric, and the characteristics are represented by three non-dimensional parameters related to the moment of inertia, spring constant and damping constant. Orbital eccentricity introduces a driving torque to cause the steady harmonic oscillations in pitch. There exist a cross-coupling between the roll and yaw motions due to the Coriolis forces, but if these cross terms are neglected and the time base transformation is performed, the roll equations reduce to the pitch equations. Therefore the results for pitch are applicable for roll. The effect of the coupling torque is to provide damping of the yaw motions. The method for selecting the parameters to yield optimum results is examined and the performance of the system for thus obtained parameters is that the time to half-amplitude is within 0.3 orbit and that the orientation error due to the orbital eccentricity is below 1.8° for the eccentricity of 0.01.

Ablation effects on vehicle dynamics.

The effects of ablation on re-entry body dynamics is a problem that during recent years has advanced from one of general interest to one of general concern. An exploratory analysis shows that ablation will have opposite effects on static and dynamic stability. Thus a slender, conical re-entry body may experience increased static stability but severely decreased dynamic stability at low angles of attack and oscillation amplitudes when ablation is concentrated to the blunted nose and the cone trailing edge. At high angles of attack and/or high oscillation amplitudes, statically destabilizing, but dynamically stabilizing, effects may result when windward-side ablation occurs over the whole vehicle length. These qualitative results apply both to a rigid body describing single-degree-of-freedom pitch oscillations and to an elastic body describing single-degree-of-freedom bending oscillations. During the portion of re-entry where the boundary-layer transition moves from the base forward to the oscillation center, the undamping effect of ablation is greatly aggravated.

Steady and Unsteady Motions and Wakes of Freely Falling Disks

The motions and wakes of freely falling disks were studied and it was found that the diverse motions of the disks exhibit a systematic dependence on the Reynolds number Re, and the dimensionless moment of inertia I*. The relation between I* and Re along the boundary separating stable and unstable pitching oscillations of the disk was determined. The Reynolds number for stable motion of a disk with large I* is 100, in agreement with the Reynolds number for stability of the wake of a fixed disk. Slightly unstable disks of large I* were stabilized by reducing the moment of inertia. The highest Reynolds number for stable disk motion was 172. At higher Reynolds numbers the disks exhibited periodic pitching and translational oscillations. The laminar wake behind certain of the oscillating disks consisted of a staggered arrangement of two rows of regularly spaced vortex rings similar to the wake observed behind liquid drops by Margarvey and Bishop. The dependence of the dimensionless frequency of oscillation on I* and Re was determined along the boundary for stable motion and at higher Reynolds numbers when the wake was turbulent. Tumbling motions of the disks were observed when the Reynolds number was large, Re > 2000, and I* was greater than a certain value, I* =̇ 10−2.

The Effect of a Root Gap on the Aerodynamic Forces of a Slender Delta Wing in Oscillatory Pitching Motion

SummaryAn investigation of the effect of a root gap is extended to the oscillatory pitching motion of a slender wing. Potential theory is used and the unsteady forces are shown to be reduced by the gap as drastically as the steady. These results cast doubt on measurements made by the technique of half-model testing. Viscous flow in the gap is discussed with reference to the possible types of model mount. The effect of viscosity may be to reduce the gap loss, but the extent of the improvement is uncertain.

Quasi-Steady Nonlinear Pitching Oscillations in Transonic Flight

Quasi-Steady Nonlinear Pitching Oscillations in Transonic Flight

Oscillating Airfoils at High Mach Number

A simple formula is given for the pressure distribution on an oscillating airfoil in two-dimensional flow at high Mach Number. The formula is expected to be reasonably accurate if the pressure on the surface remains within the range 0.2 to 3.5 times the mainstream pressure. To illustrate the application of the formula, some results for symmetrical airfoils performing pitching oscillations are obtained and compared with results obtained from existing theories in the case of high Mach Number.

Nonstationary Motion of Purely Supersonic Wings

A general theory is presented for the calculation of the total forces acting on purely supersonic wings. The method applies to wings having an arbitrary downwash distribution (stationary or non-stationary) and is valid whenever all of the wing edges are supersonic. The general three-dimensional non-stationary problem is reduced to an equivalent two-dimensional problem. In the case of harmonic oscillations the aerodynamic coefficients are expressed in terms of known or tabulated functions. The specific example of an oscillating delta wing is considered and values of the aerodynamic coefficients for plunging, pitching, and rolling oscillations are calculated for two Mach numbers.

The Instability of Pitching Oscillations of an Airfoil in Subsonic Incompressible Potential Flow

A theoretical study is carried out to determine the conditions under which steady-state pitching oscillations of an airfoil in one degree of freedom are possible in two-dimensional subsonic incompressible potential flow. The results show that such oscillations can occur if the airfoil moment of inertia is sufficiently great and if the axis of rotation is located at a point that is forward of the airfoil quarter-chord but not too far forward of the airfoil leading edge. The practical significance of these results with respect to flutter and airplane stability problems is briefly examined.

Societies and Academies

Societies and Academies