We study the acceleration of magnetosheath plasma using a semi-analytical magnetic string approach for a range of solar wind Alfvén Mach numbers, MA, between 2 and 20. We work with an IMF vector perpendicular to the solar wind velocity, Vsw, and pointing north. We do not invoke magnetic reconnection. Our results indicate that magnetosheath speeds can exceed the solar wind speed, and the ratio V/Vsw increases with decreasing MA. Analyzing the dependence of this ratio on MA, we find that for MA = 2, maximum V/Vsw ≈ 1.6, and for MA = 10–20, maximum V/Vsw varies from 1.21 to 1.13. Maximum speeds occur a few Earth radii (RE) tailward of the dawn-dusk terminator. The thickness of the accelerated flow layer varies as MA−2. Taking the magnetopause subsolar distance as 10 RE, we find typical values for the thickness of ∼4 RE for MA = 3 and 0.35 RE for MA = 10. The physical mechanism is that of draping of the magnetic field lines around the magnetosphere, and the associated magnetic tension and total pressure gradient forces acting on the flow. For lower MA the plasma depletion is stronger, and thus the acceleration produced by the pressure gradient is larger. An additional acceleration is produced by the magnetic tension, which is stronger for smaller MA. At the dayside the pressure gradient and magnetic tension forces both act in the same direction. But tailward of the terminator the magnetic tension starts to act in the opposite direction to the pressure gradient. When the resulting force vanishes, the highest speed is attained.