Down wash Angle

The estimation of a representative angle at the tail that allows for the downwash from the wing is a difficult task. The vortex system shed from the wing is unstable and rolls up into two trailing vortices, so the model for the trailing vortex system is not well defined. Even if one could circumvent this problem, the downwash in the region of the horizontal tail will not be uniform over the tail. Thus, to use a simple correction to the tail angle of attack leaves something to be desired.

With these reservations in mind, the simple model illustrated in Figure 8.5 is proposed to calculate e«. The wing is replaced by a single bound vortex with a vortex trailing from each tip. As the vortex sheet rolls up, the edge moves in toward the centerline, so that the span between the two trailing vortices, b’, is less than the wingspan. For an elliptic wing, it can be shown that

_ 7Г

b ~ 4

Using the model shown in Figure 8.5 and the Biot-Savart law (Equation 2.64), the graphs of Figure 8.6a and 8.6b were prepared. To obtain ea from these graphs, one first determines the distance, /ac, from the quarter-chord of the tail to the quarter-chord of the wing, b’ is calculated from Equation 8.18 to give /ac/b’. Figure 8.6a is then entered interpolating for hjb’. Note that h, is the height of the tail above the plane containing the wing and parallel to V. The value of ea obtained from Figure 8.6a is then multiplied by the factor presented in Figure 8.6b to correct for sweepback.

With the use of these graphs, an estimate of ea can now be made for the light plane of Figure 3.62. In this case,

/ac = 159 in.

b = 360 in.

S = 160 ft2

Because of the dihedral and at an angle of attack, h, is approximately zero. Using Equation 3.74 and a value for a0 of 6.07/rad leads to a value for a of 4.19/rad. From Figure 8.6a,

= 0.6

ea = 0.447