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The Star 48 upper stage rocket motor and payload system appears to precess in a coning motion which affects the flight path. The coning motion has been attributed to side forces generated because of deviations of the rocket nozzle entrance flow from truly axisymmetric conditions. In this report, an experimental investigation is described in which intentional nozzle entrance flow misalignment was produced and consequent side force was measured on a model at a simulated altitude of 170,000 ft. Side forces generated with an approximately 1/50th scale Star 48 rocket nozzle were quite small when compared to the predictions and measurements of previous investigators, but the difference was attributed to the difference where the flow inclination or misalignment occurs. When the flow is inclined at the nozzle throat, the downstream effect of the inclination is predictably large. When the flow is inclined in the plenum upstream of the nozzle entrance, the downstream effect is smaller by an order of magnitude. The observed side forces show a dependence on the nozzle length, as indicated by earlier investigators. Keywords: Rocket nozzles; Nozzle gas flow; Liquid propellant rockets; Rocket nozzles.

The asymmetric steady-state, inviscous, adiabatic flow of a perfect gas through a subsonic/supersonic nozzle is considered. The nozzle itself is either of rectangular cross section or is axisymmetric. A first-order small asymmetry induced by an entrance flow which is oblique to the nozzle axis and has a transverse pressure gradient is allowed. The cross section of the nozzle is assumed to vary only slowly as a function of the axial distance; the case considered here is therefore an extension of the well-known theory of the quasi- one-dimensional flow of a perfect gas treated in standard textbooks. An integral method is used to obtain approximate results. The method is simple, yet in a test case (supersonic flow at an angle of attack through a rectangular channel) where the exact first-order result is known, a comparison shows surprisingly good agreement. Numerical results are tabulated for axisymmetric nozzles with polynomial Mach number dependence.

The electrical conductivity of air in thermodynamic equilibrium at temperatures up to about 7,000 deg K is known with considerable reliability from shock tube experiments reported by Lamb and Lin. These data have been used to compute the conductivity directly as a function of temperature and density. In this case, the contribution of the positive ions to the total electron collision probability is still relatively small, but becomes increasingly important at higher temperatures. In this paper estimates of the conductivity up to 24,000 deg K are computed. This upper limit was decided upon because it coincides with the limit of Gilmore's computations of the equilibrium composition of air.

The basic equations and some fundamental concepts of magnetoaerodynamics are discussed. As an application, the problem of the flow near the stagnation point of a body of revolution is reviewed and an exact solution is given. Data are presented for the heat transfer coefficient at the stagnation point, and for its gradient in the stagnation point region. The magnetic field strength required to accomplish an appreciable reduction of aerodynamic heating in hypersonic flight is discussed, for the case in which ionization is due to thermal motion. Alternatively, methods which involve electrical breakdown of the air are considered.

Some basic aspects of ion beam neutralization in the presence of magnetic fields are investigated. The problem leads to an integro-differential equation for the electrostatic potential. This equation is solved numerically for several values of the electron-ion mass ratio. Of more interest for practical applications is the limit as the mass ratio tends to zero. In this case, the governing equation becomes linear and the problem reduces to finding the inverse of a Hilbert transform. The solution can be expressed in terms of elementary functions. Among the results obtained are the distribution of the charge densities for electrons and ions in the beam, and the electron trajectories. The limiting condition for beam reversal, which applies when the magnetic field is sufficiently strong to prevent the electrons from being drawn into the beam, is determined. Also computed is the loss in propulsive efficiency due to 'electron-swirl.' Finally, it is pointed out that this loss can be entirely avoided if a magnetic field is employed whose transverse component changes direction. (Author)

Initial results of an experimental investigation of the electrostatic acceleration of cesium ions in the presence of a transverse magnetic field are reported. No accelerating electrodes are employed. Their function is assumed by a magnetically confined electron sheath which is produced by thermionic emission from a tungsten filament located outside the ion beam. Cesium ions are accelerated in the small gap between the surface of a porous tungsten ionizer and the magnetic field surface intersecting the filament. The magnetic field strength is such that the electron cyclotron radius is small or, at most, comparable to the length of the accelerating gap (1 mm or less), whereas the motion of the cesium ions is essentially unaffected by the magnetic field. Measurements have indicated that a well-collimated ion beam can be obtained. Potential advantages in applying this new concept to electric propulsion may include high perveance and relative freedom from ion sputtering (since no accelerating electrodes are used). The main difficulty with this approach, however, is a strong possibility that at high current densities an excessive leakage of electrons to the ionizer could take place through Bohm diffusion. (Author)

The surface waves produced by a hydrofoil of infinite aspect ratio operating in water of large depth are computed. The foil is replaced by a single lifting line parallel to the free surface. An equation gives the surface elevation in dimensionless form. The numerical calculation has been carried out for two different values of the Froude number. In both cases it is found that the waves behind the foil are nearly sinusoidal, provided that the distance from the foil is approxametly larger than one-quarter wave length.

Results of tests with hydrofoils, conducted by the NACA, are analyzed and it is found that the profile drag of hydrofoils agrees very closely with wind-tunnel measurements of the same sections. An approximate method is employed in order to reduce the measured drag to pure profile drag. The range of applicability of this method is discussed. (Author)

A particular solution of the general expression for the bound vortex drag of a hydrofoil with finite span, operating in water of great depth, can be obtained for infinitely large Froude Numbers and uniform load distribution. This solution can be used as an approximation for large, but finite, Froude numbers provided that the ratio of submergence and half-span of the hydrofoil is large. At a ratio of submergence and half-span equal to unity, the approximative solution gives values that are only 23% smaller than the correct value for F = (V sq)/gf equal to 10.85. Therefore, the bound vortex drag increases very little between F = 10 and F = infinity. (Author)

The pressure distribution produced by a hydrofoil of high aspect ratio at the bottom of a shallow basin of constant depth is computed. The different character of the solution in the 2 cases of subcritical and supercritical speed is discussed. In the subcritical case, the pressure distribution is approximately sinusoidal, whereas it decreases exponentially with the distance from the foil in the case of supercritical speed. The effect of a hydrofoil upon mines of the pressure-sensitive type is considered. For ordinary operating conditions of a hydrofoil craft, it appears that the duration and amplitude of the pressure signature are of similar orders of magnitude as those of ordinry sea waves. In this case, therefore, the signature of the craft is of a type with respect to which mines are insensitive. However, if a hydrofoil craft is operated close to critical speed, it is possible to produce signatures of longer duration, approaching those resulting from ordinary vessels. A numerical example is calculated and some of the difficulties arising in employing hydrofoils as a mine-sweeping device are pointed out. In general, the discussion is restricted to the case of a single hydrofoil. The case of 2 or more foils, however, can be obtained by superposition of the results derived for a single foil. Equations are given which permit calculation of the load applied by a ship model to false bottoms in towing tank tests.

Recent experimental results obtained with a laboratory model of the space-charge-sheath thrustor are reported. The principal feature of this thrustor is the electrostatic acceleration of ions in a space-charge sheath formed on the ionizer. Operating conditions were a specific impulse of 2700 to 5500 sec, a magnetic field strength of 800 to 2500 G, an accelerating gap of 1 to 3 mm, an ionizer surface if 13.8 sq cm, a cesium vapor pressure of 5 to 40 mm Hg, and an ion-beam current density of 4 to 14 mA/sq cm. The resulting ion-beam was surprisingly well collimated, with an estimated half-angle of 1.5 deg. Under best operating conditions, the electron drain current to the anode (ionizer) was 31% of the total current. (Author), Formerly available as Aerospace rept. no. TR-0200(4220-01)-1.