mass, (m/s) is the velocity of ions perpendicular to the magnetic field, (C) is the elementary charge of the ion, (T) is the magnetic field strength at the point of reference and is a constant that differs by source with and . In the solar plasma wind at 1 AU with (kg) the proton mass, = 500 km/s, = 36 nT with =0.5 at from equation at magnetopause and =2 then 72 km. The MHD applicability test is the ratio . The figure plots on the left axis and lost thrust on the right axis versus the ratio . When , is maximum, at , , a decrease of 25% from the maximum and at , , a 45% decrease. As increases beyond one, decreases meaning less thrust from the plasma wind transfers to the spacecraft and is instead lost to the plasma wind. In 2004, Fujita published numerical analysis using a hybrid PIC simulation using a magnetic dipole model that treated electrons as a fluid and a kinematic model for ions to estimate the coefficient of drag for a magnetic sail operating in the radial orientation resulting in the following approximate formula:The lost thrust is . Coil attack angle effect on thrust and steering angle In 2005 Nishida and others published results from numerical analysis of an MHD model for interaction of the solar wind with a magnetic field of current flowing in a coil that momentum is indeed transferred to the magnetic field produced by field source and hence to the spacecraft . Thrust force derives from the momentum change of the solar wind, pressure by the solar wind on the magnetopause from equation and Lorentz force from currents induced in the magnetosphere interacting with the field source. The results quantified the coefficient of drag, steering (i.e., thrust direction) angle with the solar wind, and torque generated as a function of attack angle (i.e., orientation) The figure illustrates how the attack (or coil tilt) angle orientation of the coil creates a steering angle for the thrust vector and also torque imparted to the coil. Also shown is the vector for the interplanetary magnetic field (IMF), which at 1 AU varies with waves and other disturbances in the solar wind, known as space weather. For a coil with radial orientation (like a Frisbee) the attack angle = 0 degrees and with axial orientation (like a parachute) =90 degrees. The