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:
$$\alpha=\left\{\begin{array}{lll} \alpha_0&\text{for}&t{<}T_0\\\alpha_0+ (t-T_0)\cdot\frac{\alpha_e-\alpha_0}{T}&\text{for}&T_0\leq t {<} T_e\\ \alpha_e&\text{for}&t\geq T_e\\ \end{array}\right.$$