# Blockage Effects in Wind Tunnel Tests for Tall Buildings with Surrounding Buildings
## 6 Proposed Calculation Method of Equivalent Blockage Ratio
### The Drag Coefficient Error Caused by Surrounding Models  
Taking some test conditions as examples, Table 6 shows the blockage ratios of the target pressure models and surrounding models while Table 7 shows the error of the drag coefficient caused by the pressure model and surrounding models. This error is equal to the relative error of the drag coefficient minus the relative error caused by the target pressure model itself, in other words, the calculation formula of the error in Table 7 is \(\Delta C_{D}-\Delta(R_{t})\). In Tables 6 and 7, the height of the surrounding models is classified into equal height or half height, and the location is classified into upstream, lateral, and downstream.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & **Scale** & \multirow{2}{*}{**Surrounding Model**} & \multirow{2}{*}{**Pressure Model**} & \multirow{2}{*}{**Upstream Model**} & \multirow{2}{*}{**Lateral Model**} & \multirow{2}{*}{**Downstream Model**} \\  & **Ratio** & & & & & \\ \hline
1b & 1/300 & H & 2.38\% & 0.00\% & 4.76\% & 0\% \\
1b & 1/200 & H & 5.36\% & 0.00\% & 10.72\% & 0\% \\
2b & 1/300 & H & 2.38\%  
According to the analysis results in Section 4 of this paper, it is necessary to consider the overlapping projected parts of the upstream models and lateral models, but it is not necessary to consider the overlapping parts of the downstream models and lateral models. According to this characteristic and the results in Tables 6 and 7, the multivariable equations can be obtained as follows:  
\[\left\{\begin{aligned} & R_{uug}k_{uug}+R_{leq}k_{leq}+R_{deq}k_{dqq}+R_{ oqg}k_{oqq}=\Delta_{qe}\\ & R_{uhg}k_{uhq}+R_{lhq}k_{lhq}+R_{dhq}k_{dhq}+R_{ohq}k_{ohq}= \Delta_{qh}\end{aligned}\right. \tag{10}\]  
In Equation (10), the subscripts \(u\), \(l\), \(d\), \(e\), \(h\), and \(o\) represent the upstream, lateral, downstream, equal, half, and overlap effects, respectively. The subscript \(q\) represents the \(q\)-th equation. \(R\) and \(k\) represent the blockage ratio and influence coefficient of the unit blockage ratio, \(\Delta\) represents the error of the drag coefficient.  
By solving Equation (10) using regression analysis, each coefficient value can be obtained (see Table 8). It can be seen from Table 8 that: (a) the influence coefficient of the blockage effect of downstream models was at the minimum, while that of lateral models was at the maximum (i.e., the blockage effect caused by the lateral model with each unit blockage ratio was larger than that of the upstream model and that of the downstream model); (b) the influence coefficient of the blockage effect of surrounding models of equal height was greater than that of models of half-height; and (c) in addition to the condition where the surrounding models were at the downstream end, the influence coefficient of blockage effect of surrounding models was greater than that of the target pressure model. These conclusions are entirely consistent with the analysis results in Section 4.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Condition** & **Scale Ratio** & **Surrounding Model** & **Total Error** & **Pressure Model** & **Surrounding Models** \\ \hline  
\hline \hline \end{tabular}
\end{table}
Table 7: The error of the drag coefficient caused by the pressure model and surrounding model.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Surrounding Location** & **Equal Height** & **Half Height** \\ \hline Upstream \(R_{u}\) & 3.8 & 3.2 \\ lateral \(R_{l}\) & 4.3 & 3.7 \\ Downstream Rd & 1.4 & 1.5 \\ Overlap Ro & 1.4 & 1.6 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Th regression results of the influence coefficient of the blockage effect.