Variation of Circumferential and. Resultant Velocities along Main Rotor Radius

Let us examine the velocity diagram of different blade elements of a two – bladed rotor when the blades are at the 90° – 270° azimuths. We shall consider the vectors of the reversed flow, i. e., the velocity vectors of the flow which approaches the blade element as a result of the circumferential velocity and the flight velocity. The velocity vectors of the motion of a point on the blade element were shown previously in Figure 32a, b.

In the diagram of Figure 33 we examine the reversed vectors. We see the following from the figure.

1. The circumferential velocities increase from zero at the hub axis.

The variation of the circumferential velocities of the various elements up to the maximal value at the tip elements is shown along the line OD or OE.

2. All the blade elements travel with the velocity of the helicopter.

If we draw the line FG parallel to the line ED at the distance V, we obtain the diagram of the resultant velocities of the various elements.

3. At the 90° azimuth the resultant velocity of all the elements is u + V = шг + V; at the point 0, W = V.

4. At the 270° azimuth the resultant velocity is cor – V.

5. At the outboard blade elements, located between points A and C, the circumferential velocity is greater than the flight velocity and, consequently,

the difference u – V is positive, i. e., W > 0. Therefore, the air flow /47

approaches the outboard elements from the leading edge. There is direct flow over the blade elements just as at the 90° azimuth, but with a lower velocity.

6. The blade element located at the point A has a circumferential velocity equal to the flight velocity u = V. Since these velocities are directed oppositely, the resultant velocity of this element is zero.

7. For the inboard elements between points A and 0 the circumferential velocity is less than the flight velocity (u < V), i. e., for these elements the difference u – V = – W. This means that the flow approaches these elements from the trailing edge. There is reversed flow over the inboard elements at azimuths close to 270°.

8. The reversed flow zone has the diameter d, which can be determined from the similar triangles ODC and OBA. In these triangles OC = R; OA = d;

CD = u = U)R; AB = V. From the basic property of similar triangles

OA AB (JIT ~ CD » or

‘ d ___ V.

7? ~ ’

hence

Cl

Knowing that

V _ .

~ JA’

we finally have d = Ry.

Conclusion: the dia­

meter of the reverse flow zone is larger, the larger the main rotor radius and the larger the main rotor operating regime coefficient y, i. e., the higher the flight velocity for a given rotor rpm.

As a result of the reverse flow, negative thrust develops on the portion of the blade located in this zone; this negative thrust is reduced by the blade root cutout.