# Showing papers in "AIAA Journal in 1970"

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TL;DR: In this article, the authors considered the early stages of the formation of a train of vortex rings and found that their stability depends on the products of vortex separation 6 and cutoff distance d times the perturbation wavenumber.

Abstract: x(/3) Trailing vortices do not decay by simple diffusion. Usually they undergo a symmetric and nearly sinusoidal instability, until eventually they join at intervals to form a train of vortex rings. The present theory accounts for the instability during the early stages of its growth. The vortices are idealized as interacting lines; their core diameters are taken into account by a cutoff in the line integral representing self-induction. The equation relating induced velocity to vortex displacement gives rise to an eigenvalue problem for the growth rate of sinusoidal perturbations. Stability is found to depend on the products of vortex separation 6 and cutoff distance d times the perturbation wavenumber. Depending on those products, both symmetric and antisymmetric eigenmodes can be unstable, but only the symmetric mode involves strongly interacting long waves. An argument is presented that d/b = 0.063 for the vortices trailing from an elliptically loaded wing. In that case, the maximally unstable long wave has a length 8.66 and grows by a factor e in a time 9.4(^4#/CL)(6/F0), where AR is the aspect ratio, CL is the lift coefficient, and V0 is the speed of the aircraft. The vortex displacements are symmetric and are confined to fixed planes inclined at 48° to the horizontal.

1,092 citations

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TL;DR: In this article, panel flutter theory applied to aeroelastic stability of flat unloaded plates and cylindrical shells is applied to the stability of aero-elastic vehicles.

Abstract: Panel flutter theory applied to aeroelastic stability of flat unloaded plates and cylindrical shells

459 citations

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TL;DR: In this article, a multi component diffusion coefficient and thermal conductivity of a mixture of species was investigated, where the number of components in the mixture was determined by the multi component Lewis-Semenov number of the mixture.

Abstract: multi component diffusion coefficient, ft/sec binary diffusion coefficient, ft/sec thermal diffusion coefficient, Ib sec/ft enthalpy, z^ h^Ci, ft/sec i enthalpy of species i, ft/sec thermal conductivity of mixture, lb/(sec° R) density-viscosity product, piJL/(pn)r multi component Lewis-Semenov number, Cpp binary Lewis-Semenov number Cpp^a/k thermal Lewis-Semenov number, cpDi/k molecular weight of the mixture, 1 / ( Z-j Ci/

393 citations

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TL;DR: In this paper, a model describing the combustion of ammonium perchlorate (AP) composite propellants has been developed based on a flame structure surrounding individual oxidizer crystals; the relationship between crystals and the binder matrix was evaluated statistically.

Abstract: A model describing the combustion of AP composite propellants has been developed. The model is based on a flame structure surrounding individual oxidizer crystals; the relationship between crystals and the binder matrix being evaluated statistically. Three separate flame zones are considered: 1) a primary flame between the decomposition products of the binder and the oxidizer, 2) a premixed oxidizer flame, and 3) a final diffusion flame between the products of the other two flames. Simple global kinetics are assumed for gas-phase reactions, and the surface decomposition of the propellant ingredients is assumed to be adequately described by simple Arrhenius expressions. The oxidizer decomposition is taken as being the over-all controlling factor in the combustion process. The results obtained show that the calculated surface temperature and the effect of oxidizer concentration predicted by the model are in agreement with observed experimental trends. The predicted effect of particle size is somewhat greater than observed experimentally while the temperature sensitivity is in excellent agreement with experimental data. The results of the calculations indicate a relatively strong exothermic reaction taking place at the propellant surface. Apparently the ammonium perchlorate (AP) partially decomposes exothermically in the thin surface melt previously reported in AP deflagration studies.

382 citations

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TL;DR: In this article, a new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented, which is of the same type as those encountered in the treatment of similarity boundary layers.

Abstract: A new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented. The governing equations generated by the local nonsimilarity solution method are of the same type as those encountered in the treatment of similarity boundary layers. In addition to its local applicability, the utility of the new method is enhanced by its simplicity and directness, both in concept and in actual computations. Several nonsimilar velocity boundarylayer problems are solved herein with a view to illustrating the method, the participating nonsimilarities stemming from the freestream velocity distribution, surface mass transfer, and transverse curvature. On the basis of comparisons with available published information as well as of comparisons internal to the method itself, it may be concluded that the local nonsimilarity method provides results of high accuracy at all streamwise locations, except those near a point of separation.

243 citations

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TL;DR: In this paper, an exact integral formula defined on the boundary of an arbitrary body is obtained from a fundamental singular solu- tion to the governing differential equation, such that the Laplace transformed temperature field may subsequently be generated by a Green's type integral identity.

Abstract: This paper develops a numerical treatment of classical boundary value problems for ar- bitrarily shaped plane heat conducting solids obeying Fourier's law. An exact integral formula defined on the boundary of an arbitrary body is obtained from a fundamental singular solu- tion to the governing differential equation. This integral formula is shown to be a means of numerically determining boundary data, complementary to given data, such that the Laplace transformed temperature field may subsequently be generated by a Green's type integral identity. The final step, numerical transform inversion, completes the solution for a given problem. All operations are ideally suited for modern digital computation. Three illustra- tive problems are considered. Steady-state problems, for which the Laplace transform is un- necessary, form a relatively simple special case. A FORMULATION of the various transient boundary value problems associated with isotropic solids obeying Fourier's law of heat conduction is developed. An exact in- tegral formula is derived relating boundary heat flux and boundary temperature, in the Laplace transform space, that corresponds to the same admissible transformed temperature field throughout the body. Part of the boundary data in the formula is known from the description of a well posed bound- ary value problem. As is shown, the remaining part of the boundary data is obtainable numerically from the formula it- self regarded as a singular integral equation. Once both trans- formed temperature and heat flux are known everywhere on the boundary, the transformed temperature throughout the body is obtainable by means of a Green's type integral identity. This identity yields the field directly in terms of the mentioned boundary data. The final step, transform in- version, although done approximately also, is accomplished by a technique particularly well suited to the class of problems under investigation. The main feature of the solution procedure suggested is its generality. It is applicable to solids occupying domains of rather arbitrary shape and connectivity. Boundary data may be prescription of temperature, or heat flux, or parts of each corresponding to a mixed type problem. Also, a linear combination of temperature and flux may be given corre- sponding to the so-called convection boundary condition. The same boundary formula described previously is applicable in every case. Approximations in the transform space are made only on the boundary, in contrast to finite difference procedures, and the approximations made are conceptually simple, natural to make, and give rise, as is shown, to very ac- curate data for a relatively crude boundary approximation pattern. Problems posed for composite bodies, i.e., two or more heat conducting solids bonded together, are particularly amenable to the present treatment. One computer program is employed which utilizes only data describing the domain geometry, boundary temperature or flux, material properties, and a sequence of values of the transform parameter neces- sary for the inversion scheme. Output is the transformed temperature at any desired field point. A second program in-

206 citations

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TL;DR: In this paper, the authors used the direct simulation Monte Carlo method to study the breakdown of translational equilibrium in steady cylindrical and spherical expansions of hard sphere and Maxwell molecules, and extended it to the combined translational and rotational breakdown in a gas of rough sphere molecules.

Abstract: The direct simulation Monte Carlo method has been used to study the breakdown of translational equilibrium in steady cylindrical and spherical expansions of hard sphere and Maxwell molecules. The study of spherical expansions was extended to the combined translational and rotational breakdown in a gas of rough sphere molecules. The breakdown of translational equilibrium in a complete one-dimensional rarefaction wave in a hard sphere gas was also investigated. In all cases, the breakdown of equilibrium was found to coincide with a constant value of the ratio of the logarithmic time derivative of density following the motion of the fluid to the collision frequency in the gas. This value is proposed as an empirical breakdown criterion for use in engineering studies of systems which involve low-density expansions from continuum to highly rarefied conditions. The onset of nonequilibrium was marked by the divergence of the separate kinetic temperatures based on the molecular velocity components parallel and normal to the flow direction. The parallel temperature in a steady expansion gradually froze to a constant value, in qualitative agreement with experiment and with analytical studies employing the BGK model. The rate of decay of the temperature based on the normal velocity components was greater than the isentropic rate for hard sphere molecules, but less than it was for Maxwell molecules.

202 citations

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Virginia Tech

^{1}TL;DR: Viscous shock layer equations of laminar hypersonic flow past blunt body at moderate to high Reynolds numbers were given in this article, where the body was assumed to have a blunt body.

Abstract: Viscous shock layer equations of laminar hypersonic flow past blunt body at moderate to high Reynolds numbers

196 citations

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TL;DR: In this article, a Fourier series method was used to obtain a solution to the governing equations of simplysupported laminated plates in which coupling occurs between bending and in-plane extension.

Abstract: Using a Fourier series method, a solution is obtained to the governing equations of simplysupported laminated plates in which coupling occurs between bending and in-plane extension. Results are presented for bending under transverse load, natural frequencies of flexural vibrations, and buckling under uniform biaxial compression. Coupling is shown to reduce the effective stiffness of a laminate compared to analogous homogeneous orthotropic plates.

139 citations

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TL;DR: Cresci et al. as mentioned in this paper investigated the effect of Laminar, Transitional, and Turbulent Heat Transfer on Blunt-Nosed Bodies in Hypersonic Flow.

Abstract: Atmosphere," Izvestiya Akademii Nauk SSSR, Otdelenie Tekhnicheskikh Nauk, Mekhanika i Mashinostroenie, No. 4, 1965, pp. 36-40. 7 Benjamin, A. S., "The Effect of Albative Geometry Change on the Heating and Recession Characteristics of Sphere-Cones," AIAA Paper 66-992, Boston, Mass., 1966. 8 Cresci, R. J., MacKenzie, D. A., and Libby, P. A., "An Investigation of Laminar, Transitional, and Turbulent Heat Transfer on Blunt-Nosed Bodies in Hypersonic Flow," Journal of the Aerospace Sciences, Vol. 27, No. 6, June 1960, pp. 401-414. 9 Schlichting, H., Boundary Layer Theory, McGraw-Hill, New York, 1955, pp. 447-449. 10 Dippree, D. F. and Sabersky, R. H., "Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers," International Journal of Heat and Mass Transfer, Vol. 6, No. 5, May 1963, pp. 329-353. 11 Ames Research Staff, "Equations, Tables, and Charts for Compressible Flow," Rept. 1135, 1953, NACA. 12 Dunlap, R. and Kuethe, A. M., "Effects of Cooling on Boundary Layer Transition on a Hemisphere in Simulated Hypersonic Flow," Journal of the Aerospace Sciences, Vol. 29, No. 12, Dec. 1962, pp. 145^1461. 13 Fay, J. A. and Riddell, F. R., "Theory of Stagnation Point Heat Transfer in Dissociated Air," Journal of the Aerospace Sciences, Vol. 25, No. 2, Feb. 1958, pp. 73-85. 14 Sutton, G. W., "On the Stable Shape of a Slender Ablating Graphite Body," Journal of the Aerospace Sciences, Vol. 26, No. 10, Oct. 1959, pp. 681-682.

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TL;DR: In this article, the control error is expressed as a quaternion and all coordinate system transformations are performed using quaternions, which can reduce computation time by more than 40% over the equivalent direction cosine matrix solution.

Abstract: Space vehicle attitude control system performance is often limited by the computational speed of airborne digital computer hardware. The application of quaternions to digital atti- tude control problems involving coordinate system transformations can reduce computation time by more than 40% over the equivalent direction cosine matrix solution due to a new method of treating quaternions which allows the order of multiplication to be interchanged so as to isolate the most rapidly varying parameters. This paper presents a formulation for control equations in which the control error is expressed as a quaternion and all coordinate system transformations are performed using quaternions. The new principle of "quaternion algebra" which allows interchanging the order of multiplicatio n is developed and used to simplify the control equations. The quaternion control equations are applied to a three- gimbal IMU example and the results are compared to an equivalent direction cosine matrix solution. T HE problem of describing the relationship between two coordinate systems is one of the most basic concepts en- countered in the field of navigation and guidance. Until re- cently Euler angles formed the most widely used method of describing the rotation between two coordinate systems. The use of three Euler angles to fix the attitude of a body with re- spect to an inertial or reference coordinate system has the advantage of being well-defined geometrically and fairly simple to visualize. The 3X3 direction cosine matrix, how- ever, was more readily adaptable to high-speed digital com- putation and has replaced the Euler angle method in the solution of all but the most simple navigation problems. The direction cosine matrix approach is particularly useful to de- scribe several successive rotations of a body with respect to a fixed reference system. A third, but infrequently applied, approach to establishing body orientation utilizes the qua- ternion, first devised by Hamilton. The quaternion ap- proach makes use of Euler's Theorem which states that any real rotation of one coordinate system with respect to another may be described by a rotation through some angle about a single fixed axis. The quaternion is a compact form for rep- resenting the single fixed axis and angle referred to by Euler's Theorem. The quaternion may be handled much the same as the direction cosine matrix, in that successive rotations result in successive quaternion multiplication. The ad- vantage of the quaternion lies in its ability to define the ro- tational relationship between two coordinate systems using only four numbers as opposed to the nine elements of a direc- tion cosine matrix. This results in a similar simplification when the effect of several successive rotations is being com- puted. The principal impediment to use of quaternions has been that the direction cosine matrix, rather than the qua- ternion, is the desired end product of computation. Usually, the computation saved by using quaterion multiplication to perform successive coordinate system rotations is lost when the resultant quaternion must be put in the form of a direction cosine matrix. When the object of the computation is to obtain the control error it is not necessary to define the direction cosine matrix explicitly. In fact, optimum control, in the least angle sense, is performed by defining the control error in terms of the single axis and angle of Euler's Theorem. This may be done by formulating the problem completely in terms of quater- nions. The quaternion formulation is shown to be particu- larly advantageous due to a new method for treating quater- nions which allows the order of multiplicatio n to be inter- changed.

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TL;DR: In this article, a single crystal self-deflagration of pure ammonium perchlorate single crystal was studied, determining energy transfer mechanisms from pressure effects, combustion characteristics and subsurface profile.

Abstract: Pure ammonium perchlorate single crystal self deflagration, determining energy transfer mechanisms from pressure effects, combustion characteristics and subsurface profile

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TL;DR: In this article, a method of solution of the compressible turbulent boundary-layer equations for twodimensional and axisymmetric flows, with transverse-curvature effects, is presented.

Abstract: A method of solution of the compressible turbulent boundary-layer equations for twodimensional and axisymmetric flows, with transverse-curvature effects, is presented. The Reynolds shear-stress term is eliminated by an eddy-viscosity concept and the time mean of the product of a fluctuating velocity and temperature term appearing in the energy equation is eliminated by an eddy-conductivity concept. An implicit finite-difference method is used in the solution of both momentum and energy equations after they are linearized. Results are presented for several adiabatic compressible flows, with and without pressure gradients for Mach numbers up to 5. The results show that the method is quite accurate and fast; a typical flow can be calculated in one or two minutes on the IBM 360/65 computer.

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General Dynamics

^{1}TL;DR: In this paper, a procedure is presented to calculate steady supercritical planar flows over lifting airfoils using an unsteady approach, where the steady flow is obtained as the asymptotic flow for large times.

Abstract: A procedure is presented to calculate steady supercritical planar flows over lifting airfoils using an unsteady approach, where the steady flow is obtained as the asymptotic flow for large times. The unsteady flow is generated by impulsively imposing the airfoil boundary condition in an initially uniform flow. The resulting flow is calculated by a finite difference analogue to the unsteady Euler equations using a diffusing second-order difference scheme. Here an artificial viscosity appears by which shock waves acquire a steep profile. The procedure is used to calculate the flows over one of the nonlifting symmetrical shockless profiles derived by Nieuwland, using the hodograph method, and over a lifting NAG A 64A-410 profile. Results agree well with experiments, with local differences accountable by a BusemannGuderley instability in the first case, and by viscous effects in the second case.

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TL;DR: In this paper, a technique was developed for explicitly eliminating the constraint torques from a canonical system of n vector equations for the attitude dynamics of a satellite consisting of n arbitrarily interconnected rigid bodies.

Abstract: A technique is developed for explicitly eliminating the constraint torques from a canonical system of n vector equations for the attitude dynamics of a satellite consisting of n arbitrarily interconnected rigid bodies. This elimination reduces the number of scalar second order differential equations from 3n to r, the number of degrees of rotational freedom of the satellite. At the same time, the number of dependent variables in these equations is reduced from the full set of 3n angular velocity components to just 3 such components for one body, together with r — 3 relative angular rates. This elimination and reduction saves computer time when the equations are integrated, and also avoids a possible build-up of numerical errors violating the constraints. The final equations resemble those obtained from a Lagrangian approach, but are simpler to derive and to modify to account for additional effects.

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TL;DR: Local axisymmetric dimple imperfection effects on buckling load of circular cylindrical shell under axial compression were studied in this paper, where the authors showed that axiomatic imperfection has a strong effect on the buckling of the shell.

Abstract: Local axisymmetric dimple imperfection effects on buckling load of circular cylindrical shell under axial compression

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TL;DR: The application of quasi-steady state plasma acceleration to development of pulsed plasma jet engines has been investigated in this article, where the authors propose an approach to accelerate pulsed plasmas.

Abstract: Applications of quasi-steady state plasma acceleration to development of pulsed plasma jet engines

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TL;DR: Flutter analysis of plates with inplane boundary support flexibility exposed to transverse pressure loading or buckled by uniform thermal expansion is presented in this paper, where the authors show that these plates are vulnerable to thermal expansion.

Abstract: Flutter analysis of plates with inplane boundary support flexibility exposed to transverse pressure loading or buckled by uniform thermal expansion

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TL;DR: In this paper, an algebraic fit is made to the results of a numerical analysis describing the collisionless current attracted to cylindrical Langmuir probes whose ratios of probe radius to Debye length are of moderate value.

Abstract: An algebraic fit is made to the results of a numerical analysis describing the collisionless current attracted to cylindrical Langmuir probes whose ratios of probe radius to Debye length are of moderate value. The probe currents indicated by these expressions are compared to some numerically computed values and to values obtained using an approximate analytical solution. This algebraic description of the single-probe response is then used to derive the double-probe characteristics in the region where the current attracted to the probe is potentialdependent. Equations are derived and methods are discussed for accurately determining both electron temperature and number density from these double-probe characteristics. The analogous results for double-probe operation in the region of orbital-motio n-limited current collection are also included.

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TL;DR: The use of film cooling for protecting a surface exposed to high temperature air at hypersonic speeds is investigated experimentally in this paper, where the effect of injection on the velocity, temperature and Mach number profiles is studied.

Abstract: The use of film cooling for protecting a surface exposed to high temperature air at hypersonic speeds is investigated experimentally. The tests were conducted in a Mach 6 contoured axisymmetric nozzle with a streamlined centerbody. The Reynolds number in the test section was in the range of 1-3.6 X 10 6/in.; and a wall to freestream temperature ratio of 0.635. Heat-transfer distributions downstream of the slot were obtained for various mass flow rates and the effect of injection on the velocity, temperature and Mach number profiles was studied. Correlations for the cooling lengths with the blowing rate parameters X = pjUj/peUe for the various coolants-—air, helium, hydrogen, and argon were obtained. Correlations for the heattransfer rates in the form (1 — q/go.») an

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TL;DR: In this paper, the steady-state free and forced response and stability for large amplitude motion of a beam with clamped ends is investigated, and a multimode analytical and numerical technique is used to obtain theoretical solutions for both response and stabilisation.

Abstract: The steady-state free and forced response and stability for large amplitude motion of a beam with clamped ends is investigated. Elastic restraint of the ends is included in order to relate theory with experiment. A multimode analytical and numerical technique is used to obtain theoretical solutions for both response and stability. Experimental results largely confirm the results of the analysis. It is concluded that, while single mode analyses are adequate in some cases, there are circumstances where a multimode analysis is essential to predict the observed results. Nomenclature Am = amplitude of the rath mode E = Young's modulus F = transverse force FQ = generalized force h = beam thickness I = second moment of area of the cross section Ks = axial spring factor k = axial spring constant ki = rotational spring constant L = beam length PO = initial axial tension Pom = nondimensional amplitude of the generalized harmonic force t = time w = transverse displacement x = axial coordinate Mmkin,Fim, = modal constants GmrsjGmgrs

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TL;DR: In this paper, a new method of detecting boundary layer transition at supersonic speeds is described, which is based on measuring the change in the root mean square of the voltage fluctuation across surface thin film gauges operated at constant temperature.

Abstract: A new method of detecting boundary layer transition at supersonic speeds is described. rity of methods such as schlieren and those of maximum surface temperature and peak surface pitot pressure,locate positions near the end of transition, which, as will be shown in the paper, have a strong Mach number and unit Reynolds number dependence. A more complete picture of transition dependence on these parameters has been obtained by measuring the change in the root mean square of the voltage fluctuation across surface thin film gauges operated at constant temperature. effects of Mach number and unit Reynolas number on the beginning and length of transition to be established more precisely than with previously used methods. The use of thin film gauges to infer local laminar and turbulent skin friction a t supersonic speeds is also described. The majoThis technique enables the

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TL;DR: In this paper, the performance of a 25kw, lithium fueled, applied field MPD arcjet with an open-ended heat-pipe vaporizer and a hollow cathode was reported.

Abstract: The performance is reported of a 25-kw, lithium fueled, applied field MPD arcjet which incorporates a unique feed system with an "open-ended heat-pipe" vaporizer and a hollow cathode. The arc typically operates at currents of 250-500 amp, voltages of 40-60 v, magnetic field strengths between 500 and 3000 gauss, and produces a highly ionized lithium beam which transports 70% of the input electrical power to the beam stop. The ambient tank pressures range as low as 2 X 10 ~" torr. A comparison of hollow cathode and conventional MPD arc performance is made and it is concluded that the hollow cathode arc is superior to the conventional design. Diagnostic experiments performed in the exhaust plume include the determination of axial ion and atom velocities by measurements of Doppler shifts with a scanning Fabry-Perot interferometer and of ion energies by use of electrostatic energy analyzers; the determination of ion temperatures by comparison of experimental and calculated spectral line profiles; the determination of electron temperatures and densities with electrostatic probes; and the determination of current densities by Rogowski loops. These measurements indicate that at a station 25 cm downstream of the arc head the directed ion velocity exceeds 2 X 10 cm/sec. At a station 90 cm downstream the plasma typically has an electron temperature of about 2.3 ev, a density of approximately 1.5 X 10 cm~, and under certain operating conditions more than 40% of the arc current extends 90-cm downstream of the arc head. The efficiency of a process that converts input electrical power into kinetic energy is discussed in terms of a model which sets the plasma into rotation with subsequent expansion in a magnetic field.