## 4 Aerodynamic Characteristics
### Aerodynamic Force Coefficients  
The aerodynamic force coefficients are calculated via the pressure field test results. \(\overline{C}_{D}^{t}\), \(\overline{C}_{L}^{t}\), \(\overline{C}_{M}^{t}\), \(\widetilde{C}_{D}^{t}\), \(\widetilde{C}_{L}^{t}\), and \(\widetilde{C}_{M}^{t}\) are the mean and fluctuating drag, lift, and moment coefficients of the train model, whereas \(\overline{C}_{D}^{b}\), \(\overline{C}_{L}^{b}\), \(\overline{C}_{M}^{b}\), \(\widetilde{C}_{D}^{b}\), \(\widetilde{C}_{L}^{b}\), and \(\widetilde{C}_{M}^{b}\) are the mean and fluctuating drag, lift, and moment coefficients of the bridge-deck model, respectively. The detailed definitions about the above force coefficients are available in [34]. Figures 8 and 9 present the aerodynamic force coefficients of the train and bridge-deck models, respectively. For verification, the experimental results of the train-only case, bridge-only case, [37; 38; 39] are also illustrated here. As demonstrated in Figure 8a,b,e and Figure 9b,c, the results of the train-only and bridge-only cases show good agreements with those from previous studies when taking into consideration differences of the experimental models. Because all the present cases were carried out under similar conditions, the above comparisons verify the present investigation. As shown in Figure 8a, \(\overline{C}_{D}^{l}\) in the train-only and train-bridge cases is in good consistency with each other in \(\alpha=[-12^{\circ},-6^{\circ}]\), while \(\overline{C}_{D}^{l}\) in the train-bridge case is much smaller than that in the train-only case in \(\alpha=[-4^{\circ},12^{\circ}]\), suggesting a strong bridge-deck shielding effect. The above two typical behaviors of \(\overline{C}_{D}^{l}\) in different ranges of \(\alpha\) are in fair agreement with the other two cases. Figure 8: Aerodynamic force coefficients of the train model: **(a)** Mean drag coefficients; **(b)** Mean lift coefficients; **(c)** Mean moment coefficients; **(d)** Fluctuating drag coefficients; **(e)** Fluctuating lift coefficients; and **(f)** Fluctuating moment coefficients. Figure 9: Aerodynamic force coefficients of the bridge-deck model: **(a)** Mean drag coefficients; **(b)** Mean lift coefficients; **(c)** Mean moment coefficients; **(d)** Fluctuating drag coefficients; **(e)** Fluctuating lift coefficients; and **(f)** Fluctuating moment coefficients. with the flow visualization and flow profile test results as shown in Section 3.1.2. As demonstrated in Figure 8d-f, \(\widetilde{C}^{t}_{D}\), \(\widetilde{C}^{t}_{L}\), and \(\widetilde{C}^{t}_{M}\) in the train-bridge case are much smaller than those in the train-only case, which shall be attributed to the underbody flow restraining effect as concluded in Section 3.1.1. In comparison with the study of [34] the effects caused by the occupied track variation on the aerodynamic force coefficients of the train model can be concluded by the following two aspects as shown in Figure 8:  
1. In \(\alpha=[0^{\circ},12^{\circ}]\), no abrupt changes, i.e., drag crisis (Figure 8a), jumping and recovering of lift, moment, and three fluctuating force coefficients (Figure 8b-f), can be observed in the present study. As concluded in Section 3, these differences shall be chiefly caused by the disappearance of the quasi-Reynolds number effect. 2. In \(\alpha=[-12^{\circ},0^{\circ}]\), the \(\overline{C}^{t}_{D}\), \(\overline{C}^{t}_{L}\), and \(\overline{C}^{t}_{M}\) in the two cases with train model mounted on the upstream and downstream tracks share almost the similar behaviors, as described in Figure 8a-c. However, the \(\overline{C}^{t}_{L}\) in the present study is reduced by 0.23 in the range of \(\alpha=[-12^{\circ},0^{\circ}]\). As demonstrated in Figure 9b-f, the stall angle of the bridge-deck model in the train-bridge case is about \(\alpha=-4^{\circ}\), which is about \(4^{\circ}\) larger than that of the bridge-only case as highlighted by two blue arrows in Figure 9b,c.