Читать книгу Flight Theory and Aerodynamics - Joseph R. Badick - Страница 22

Vector addition is more complicated than scalar addition. Vector quantities are conveniently shown by arrows. The length of the arrow represents the magnitude of the quantity, and the orientation of the arrow represents the directional property of the quantity. For example, if we consider the top of this page as representing north and we want to show the velocity of an aircraft flying east at an airspeed of 300 kts., the velocity vector is as shown in Figure 1.3. If there is a 30‐kts. wind from the north, the wind vector is as shown in Figure 1.4.

To find the aircraft’s flight path, groundspeed, and drift angle, we add these two vectors as follows. Place the tail of the wind vector at the head of the arrow of the aircraft vector and draw a straight line from the tail of the aircraft vector to the head of the arrow of the wind vector. This resultant vector represents the path of the aircraft over the ground. The length of the resultant vector represents the groundspeed, and the angle between the aircraft vector and the resultant vector is the drift angle (Figure 1.5).

Figure 1.3 Vector of an eastbound aircraft.

Figure 1.4 Vector of a north wind.

Figure 1.5 Vector addition.

The groundspeed is the hypotenuse of the right triangle and is found by use of the Pythagorean theorem :

The drift angle is the angle whose tangent is V_w/V_a/c = 30/300 = 0.1, which is 5.7° to the right (south) of the aircraft heading.