File:Magsail ISM deceleration distance and time comparison.jpg

English: For deceleration in the Interstellar Medium (ISM) the figure plots distance traveled while decelerating ${\displaystyle x_{d}}$ (ly) and time required to decelerate ${\displaystyle t_{d}}$ (yr) given a starting relative velocity ${\displaystyle \beta _{0}=v_{0}/c}$ and a final velocity ${\displaystyle v_{f}=0.013c}$ (m/s) for the coil radius ${\displaystyle R_{c}}$=100 km an Interstellar medium (ISM) plasma density of 1.7x10^-22. The magsail mass is 197 tonnes assuming ${\displaystyle J_{e}}$ = 10¹¹ (A/m²) and ${\displaystyle \delta _{c}}$=6,500 (kg/m³) for the superconducting coil. Force is defined in the Magnetic sail article for the magsail using the Andrews/Zubrin MHD model and the Gros kinematic model assuming C_d=4. Acceleration is force divided by mass, velocity is the integral of acceleration over the deceleration time interval ${\displaystyle t_{d}}$ (yr) and deceleration distance traveled ${\displaystyle x_{d}}$ (ly) is the integral of the velocity over ${\displaystyle t_{d}}$ (yr). Numerical integration resulted in the lines plotted in the figure with deceleration distance traveled plotted on the primary vertical axis on the left and time required to decelerate on the secondary vertical axis on the right. Note that the MHD Zubrin model and the Gros kinematic models predict nearly identical values for stopping distance up to ${\displaystyle \beta _{0}}$~ 5% of light speed, with the Zubrin model predicting less deceleration distance and shorter deceleration time at greater values of ${\displaystyle \beta _{0}}$. This is consistent with the above figure where the Gros model predicts a smaller effective area ${\displaystyle A(v)}$ for larger values of ${\displaystyle \beta _{0}}$.