Blade Element Angle of Attack Change Owing to Flapping Motions

The blade angle of attack change +Да depends on the vertical flapping velocity on шг> and on V sin ip, i. e., on the azimuth angle, which we

see from the formula

The sign of the vertical flapping velocity is determined by the direction of the flapping motion: a minus sign for upward blade flapping, a plus sign for

downward flapping. Since the maximal upward blade flapping velocity occurs at the 90° azimuth, the negative angle of attack increment will be greatest at this azimuth and the angle of attack of a given blade element will be minimal. The highest downward vertical flapping velocity occurs at the 270° azimuth, and the positive angle of attack increment Да will be maximal at this azimuth. This means that a given blade element has its maximal angle of attack at the 270° azimuth (Figure 42). Moreover, in analyzing the curve we see that the maximal magnitude of the negative angle of attack increment at the 90° azimuth is less than the maximal magnitude of the positive angle of attack increment at the 270° azimuth.

This variation of the angle of attack increment is explained by the fact that in (17a) for ф = 90° the second term of the denominator is positive, and tg Да will decrease as a result of increase of the resultant flow velocity over the blade.

0°.. S0° 130а 270а 350° V*

1) with rigid mounting;

2) with hinged support.

For ф = 270° the second term of the denominator is negative, and this means that the angle of attack increment Aa will increase as a result of reduction of the resultant velocity of the blade element. Moreover, at the 90° azimuth the vertical upward flapping velocity Vq will be less than at the 270° azimuth, when the blade flaps downward. But the blade element angle of attack does not change only in azimuth. It also varies along the main rotor radius (Figure 43). We see from the figure that the angles of attack will be highest for the tip elements at an azimuth close to 270°, and lowest at the 90° azimuth, with the angles of attack being nearly the same for elements at different radii.

The following azimuthal variation of the angle of attack is characteristic: from the 0° azimuth the angles of attack, remaining nearly constant along the length of the blade, decrease up to about the 110° azimuth and then begin to increase.

The following angle of attack variation along the radius is characteristic of the retreating blade: from the root to the tip of the blade the blade

element angles of attack increase by 4-5°, with the variation being less at the root elements than at the tip. The angle of attack variation equalizes the blade thrust force azimuthally (Figure 44), and the blade flapping motions are reduced.