This paper conducts a parametric trade study to establish and understand the relationship between the sonic boom/aerodynamic efficiency and the design parameters for supersonic bi-directional flying wing(SBiDir-FW). The mission requirements for this supersonic plane include the cruise Mach number of 1.6, range of 4000 nm, payload of 100 passenger and flight altitude of 50k ft. An advanced geometry model is employed to construct the SBiDir-FW configurations. The geometry model can freely vary airfoil meanline angle distribution to control the expansion and shock waves on the airplane surface in order to mitigate sonic boom and improve aerodynamic efficiency. The trade study has several very important findings: 1) The far field ground sonic boom signature is directly related to the smoothness of the wave distribution on the airplane surface. The meanline angle distribution is a very effective control methodology to mitigate surface shock and expansion wave strength, and mitigate compression wave coalescing by achieving smooth loading distribution chord-wise. Compared with a linear meanline angle distribution, a design using non-monotonic meanline angle distribution with reversed cambering in the mid-chord region is able to reduce the sonic boom ground loudness by over 20PLdB. 2) Decreasing sweep angle within the Mach cone will increase L/D as well as sonic boom. A design with variable sweep from 84° at the very leading edge to 68° at the tip achieves a very high L/D of 10.4 at Mach number 1.6 due to the low wave drag. If no sonic boom constraint is considered, the L/D can be further increased. 3) The round leading edge and trailing edge under high sweep angle are beneficial to improve aerodynamic performance, sonic boom, and to increase volume of the airplane. The qualitative and quantitative findings in this paper give better understanding of physics and provide the path to achieve the ultimate high performance design. The final design with refined mesh achieves sonic boom ground loudness of 72PldB and aerodynamic dynamic efficiency L/D of 8.3. If increasing the cruise altitude from 50kft to 56kft, the ground sonic boom loudness will be decreased to 68PLdB and 65PLdB respectively. All the design in this study are created manually. It is believed that a systematic automated design optimization will significantly improve the design.