Earth's bow shock is the result of interaction between the supersonic solar wind and Earth's magnetopause. However, data limitations mean the model of the shape and position of the bow shock are based largely on near-Earth satellite data. The model of the bow shock in the distant magnetotail and other factors that affect the bow shock, such as the interplanetary magnetic field(IMF) B_y, remain unclear. Here, based on the bow shock crossings of ARTEMIS from January 2011 to January 2015, new coefficients of the tail-flaring angle a of the Chao model(one of the most accurate models currently available) were obtained by fitting data from the middle-distance magnetotail(near-lunar orbit, geocentric distance -20R_E>X>-50R_E). In addition, the effects of the IMF B_y on the flaring angle a were analyzed. Our results showed that:(1) the new fitting coefficients of the Chao model in the middle-distance magnetotail are more consistent with the observed results;(2) the tail-flaring angle a of the bow shock increases as the absolute value of the IMF B_y increases. Moreover, positive IMF B_y has a greater effect than negative IMF B_y on flaring angle. These results provide a reference for bow shock modeling that includes the IMF B_y.
