**3. Definitions of symbols and calculation formula on this paper**

The wind pressure coefficient was calculated based on *The Building Standard Law of Japan* (The building Center of Japan, 2004)*, Recommendations for Load on Buildings 2004* (Architectural Institute of Japan, 2004) and *ASCE Manuals* (Cermak & Isyumov, 1998). Definitions of the symbols in this paper are shown in figure 4. As for the signs of wind pressure coefficient, the positive (+) means positive pressure against the roof and the negative (-) means negative pressure against the roof.

**Figure 3.** Form finding method on the horn-shaped membrane structure

**Figure 4.** The definitions of symbols in this paper

The wind pressure coefficient is obtained from follows;

$$\mathbf{C}\_{p\dot{\jmath}} = \mathbf{C}\_{p\dot{\imath}} - \mathbf{C}\_{p\dot{\imath}} \tag{1}$$

$$\mathbf{C}\_{p\text{\%}} = \frac{\mathbf{P}\_{\text{\%}} - \mathbf{P}\mathbf{s}}{qz}, \mathbf{C}\_{p\text{\%}} = \frac{\mathbf{P}\_{o\text{\%}} - \mathbf{P}\mathbf{s}}{qz} \tag{2}$$

$$
\overline{q\_z} = \frac{1}{2} \rho \overline{v\_z}^2 \tag{3}
$$

in which *C pj* is the wind pressure coefficient at measurement pressure tap *j*, *C poj* is the external wind pressure coefficient at measurement tap *j*, *C pij* is the internal wind pressure coefficient at measurement tap *j*, *P ij* is the internal pressure at measurement tap *j*, Po is the external pressure at measurement tap *j*, *P <sup>s</sup>* is the static, or the barometric, pressure at a reference location, *q*¯ *<sup>z</sup>* is the mean value of dynamic pressure at the reference location *z*, *ρ* is the density of the air, and *v*¯ *<sup>z</sup>* is the mean value of wind velocity at the reference location *z*. In this paper, the reference location *z* with the uniform flow means the position of the pitot tube. On the other hand, the reference location *z* with the turbulent boundary layer flow was obtained from the following equations;

$$z = h + \frac{H}{2} \tag{4}$$

in which *h* is the eave height of the roof, and *H* is the rise of the horn-shaped roof.

Particularly, the mean value of wind pressure coefficient *C p\_mean* and the peak value of wind pressure coefficient *C p\_peak* are expressed respectively as follows;

$$\mathbf{C}\_{p\\_mean} = \mathbf{C}\_{p\nu\\_mean} - \mathbf{C}\_{p i\\_mean} \tag{5}$$

$$\begin{cases} \mathbf{C}p\\_\text{peak}, \text{max} = \mathbf{C}\_{p\text{0\\_peak}, \text{max}} - \mathbf{C}\_{p\text{1\\_peak}, \text{min}}\\ \mathbf{C}p\\_\text{peak}, \text{min} = \mathbf{C}\_{p\text{0\\_peak}, \text{min}} - \mathbf{C}\_{p\text{1\\_peak}} \end{cases} \tag{6}$$

in which *C po\_mean* and *C pi\_mean* are the mean value of external and internal wind pressure coefficient, *Cpo\_peak* and *Cpi\_peak* are the tip value of external and internal wind pressure coefficient.

Additionally, *C pi\_mean*, *C po\_mean*, *C po\_peak* and *C pi\_peak* are given by the following equations;

**Figure 4.** The definitions of symbols in this paper

The wind pressure coefficient is obtained from follows;

**Figure 3.** Form finding method on the horn-shaped membrane structure

128 Wind Tunnel Designs and Their Diverse Engineering Applications

, *ij oj pij poj*

*z z P Ps P Ps C C q q*

> 1 <sup>2</sup> <sup>2</sup> *q v z z* <sup>=</sup> r

*CC C pj poj pij* = - (1)


(3)

$$\mathbf{C}\_{pi\\_peak} = \frac{P i\_{-\\_mean}}{qz}, \mathbf{C}\_{po\\_peak} = \frac{P o\_{-\\_mean}}{qz} \tag{7}$$

$$\mathbf{C}\_{pi\\_mean} = \frac{P\_{i\\_mean}}{qz}, \mathbf{C}\_{po\\_mean} = \frac{P\_{o\\_mean}}{qz} \tag{8}$$

in which *P i\_mean* and *P o\_mean* are the mean value of internal and external wind pressure on the pressure measurement tap respectively, and *P i\_peak* and *P o\_peak* are the tip value of internal and external wind pressure on the tap. In case of the enclosed type which is constructed with side walls, *P <sup>i</sup>* is neglected on these calculations.
