A new, more precise and simple semi-empirical formula has been obtained for the prediction of the rotational velocity of magnetically driven arcs in air and nitrogen. The formula is based on the balance between the motive Lorentz force and the aerodynamic drag force and takes into account changes in the gas density value due to the arc rotation and the axial gas velocity. The formula enables the calculation of the arc velocity in electric arc heaters as a function of current, magnetic field, axial gas velocity and gas density. Experimental results are presented for arcs in air and nitrogen, for currents in the range 100-1760 A, magnetic induction values of 0.005-3.9 T and axial gas velocities of 0.2-33 ms-1. The formula can be useful for the study of cold electrode erosion and engineering calculations of electric arc heaters.332025912597Roman, W.C., Myers, T.W., Experimental investigation of an electric arc in transverse aerodynamic and magnetic fields (1967) AIAA J., 5, pp. 2011-2017Kukekov, G.A., Investigations of direct current arc in magnetic field (1941) J. Tekhn. Phys., 11, pp. 229-234. , in RussianKukekov, G.A., Investigations of direct current arc in magnetic field (1941) J. Tekhn. Phys., 11, pp. 972-978. , in RussianMyers, T.W., Approximation to the electrical conductivity of a magnetically balanced arc in transverse argon flow (1966) AIAA J., 4, pp. 1459-1460Szente, R.N., Munz, R.J., Drouet, M.G., Effect of the arc velocity on the cathode erosion rate in argon-nitrogen mixtures (1987) J. Phys. D: Appl. Phys., 20, pp. 754-756Szente, R.N., Munz, R.J., Drouet, M.G., Arc velocity and cathode erosion rate in a magnetically driven arc burning in nitrogen (1988) J. Phys. D: Appl. Phys., 21, pp. 909-913Koroteev, A.S., Mironov, V.M., Svirchuk, J.S., (1993) Plasmotrons - Design, Characteristics, Calculations, , (Moscow: Mashinostroenie) in RussianYas'ko, O.I., (1977) Electric Arc in Plasma Torch, , (Minsk: Nauka i Tekhnika) in RussianSharakhovsky, L.I., Experimental investigation of an electric arc motion in annular ventilated gap under the action of electromagnetic force (1971) J. Eng. Phys., 20, pp. 306-313Marotta, A., Sharakhovsky, L.I., A theoretical and experimental investigation of copper electrode erosion in electric arc heaters: I. The thermophysical model (1996) J. Phys. D: Appl. Phys., 29, pp. 2395-2403Sharakhovsky, L.I., Marotta, A., Borisyuk, V.N., A theoretical and experimental investigation of copper electrode erosion in electric arc heaters: II. Experimental determination of arc spot parameters (1997) J. Phys. D: Appl. Phys., 30, pp. 2018-2025Sharakhovsky, L.I., Marotta, A., Borisyuk, V.N., A theoretical and experimental investigation of copper electrode erosion in electric arc heaters: III. Experimental validation and prediction of erosion (1997) J. Phys. D: Appl. Phys., 30, pp. 2421-2430Marotta, A., Sharakhovsky, L.I., Heat transfer and cold electrode erosion in electric arc heaters (1997) IEEE Trans. Plasma Sci., 25, pp. 905-912Kopainsky, J., Schade, E., Rotating high current arc (1979) Appl. Phys., 20, pp. 147-153Lapedes, D.N., (1978) McGraw-Hill Dictionary of Physics and Mathematics, , New York: McGraw-HillWutzke, S.A., Pfender, E., Ecken, E.R.G., Symptomatic behaviour of an electric arc with a superimposed flow (1968) AIAA J., 6, pp. 1474-1482Desaulniers-Soucy, N., Meunier, J.L., A study of magnetically rotating arc stability using fluctuations in voltage, velocity and emission line intensity (1995) J. Phys. D: Appl. Phys., 28, pp. 2505-2513