# Linear wind

The Linear wind can be selected in the Atmosphere part. A linear wind is defined by the following parameters:
• Start speed
$$V_0$$

• End speed
$$V_e$$
• Start-up duration
$$T_0$$

• Duration
$$T$$
The role of these parameters is illustrated in the following figure:

The magnitude of the wind speed at the hub
$$V_{hub}$$
is defined as follows:
$$V_{hub}=\left\{\begin{array}{lll} V_0&\text{for}&t{<}T_0\\V_0+ (t-T_0)\cdot\frac{V_e-V_0}{T}&\text{for}&T_0\leq t {<} T_e\\ V_e&\text{for}&t\geq T_e\\ \end{array}\right.$$

The same equation applied for the Wind angle
$$\alpha$$
, replacing the start speed
$$V_0$$
and the end speed
$$V_e$$
with the start angle
$$\alpha_0$$
and the end angle
$$\alpha_e$$
, respectively:
$$\alpha=\left\{\begin{array}{lll} \alpha_0&\text{for}&t{<}T_0\\\alpha_0+ (t-T_0)\cdot\frac{\alpha_e-\alpha_0}{T}&\text{for}&T_0\leq t {<} T_e\\ \alpha_e&\text{for}&t\geq T_e\\ \end{array}\right.$$