Our heavyweight helicopter equal in the world does not have
In Rostov started production of the most load-lifting rotary-wing car The Russian holding «Helicopt[...]
Inclined Wing at Subsonic Incident Flow
General formulas The local lift coefficient of a wing section is obtained through integration of the pressure distribution over the wing chord according to Eq, (2-Ю). By taking into account Eq. (4-69), the transformation formulas for the local lift coefficient and, accordingly, for the local pitching-moment coefficient are thus given as
For incompressible flow, the wing theory of Sec. 3-3-5 produces the dimensionless lift distribution 7inc (i? inc) and the dimensionless pitching-moment distribution from Eqs. (3-115fl) and (3-115b). By introducing Eqs. (4-67д), (4-672?), (4-70/z), and (4-702?), the dimensionless distributions for subsonic flow become
ctc
7 ~ 2b~ 7inc
_ cmc___
22? ~Minc
These equations show that the dimensionless lift and moment distributions remain unchanged during transition from incompressible to compressible flow. It should be noted, however, that the distributions 7 and 7inc, and fi and qinc belong to different planforms (Fig. 4-44).
The transformation of the coefficients of total lift and pitching moment, taking into account Eqs. (4-66), (4-67й), (4-672?), and (4-69), results in
The coefficient of induced drag in incompressible flow for elliptic lift distribution is, from Eq. (3-312?), cDi-mc =сь-1ПС1пЛ[пс. Introducing cL inc and /linc into the above transformation formulas yields the relationship
Hence, the formula for the coefficient of induced drag in relation to the lift coefficient is independent of the Mach number. The transformation formulas for the remaining aerodynamic coefficients are compiled in Table 4-4.
Elliptic wing Simple closed formulas for the lift slope as a function of the Mach number can be established for wings with elliptic planform. For incompressible flows, computations follow Eq. (3-98) of the extended lifting-line theory. Applying the subsonic similarity rule yields
dc^ 2 пЛ
У(1 – Mai,) Л2 + 4 + 2
|
Table 44 Transformation formulas for the aerodynamic coefficients of an inclined wing of finite span in subsonic flow (Prandtl, Glauert, Gothert), Q! — ®inc
|
Figure 445 Ratio of lift slopes at subsonic and incompressible flow fox elliptic wings of various aspect ratios л vs. Mach number of incident flow according to Eq. (4-74).
from which the limiting values
^=~Л (Л->0) (4-750
da 2 v ‘
= … 2?… — (Л -> oo) (4-75b)
da yi _ Mai,
are obtained. Equation (4-75д) is identical to Eq. (3-101b). For very small aspect ratios, the dependence of the lift slope on the Mach number thus disappears. Equation (4-75b) is identical to the expression of the plane problem from Table
4- 1.
For the case Ma„ — 1, the lift slope becomes
^ = v Л (Л&. = 1) (4-75c)
Contrary to the airfoil of infinite span (A =°°), for which (dcL/da)00 = °°, the lift slope of wings of finite span has finite values. The significance of this result will be investigated more closely in Sec. 4-44.
The ratio of the lift slopes for Маж Ф 0 and Ma„ = 0 is shown in Fig. 445 for several aspect ratios against the Mach number. This figure shows that the compressibility influence on the lift slope becomes smaller when the aspect ratio is reduced. This fact was first pointed out by Gothert [28].
Wings without twist The aerodynamic coefficients will be computed for the same wings for which the lift distribution was determined in Sec. 3-3. These were a trapezoidal, a swept-back, and a delta wing, with aspect ratios between A = 2 and /1=3. These three given wings are depicted in the upper boxes of Fig. 446. The geometric data for the wings are compiled in Table 34. The second and third rows of boxes show the wings transformed with the subsonic similarity rule for Ma„ = 0.4 and 0.8, respectively. The lift distributions of these wings have been
|
Figure 4-46 Planforms of given and transformed ‘wings for the examples of lift distribution at subsonic incident flow. Given wings: see Table 34. (a) Trapezoidal wing: y?=0°, л =2.75, X = 0.5. (b) Swept-back wing: tp = 5Q°, л=2Л5, Л = 0.5. (c) Delta wing: ^> = 52.4°, л = 2.31, Л = 0. |
computed according to the wing theory for incompressible flow of Sec. 3-3-5.
The results of these computations for the lift distribution of the wing without twist (a= 1) are presented in Fig. 4-47. The lower figures give the dimensionless lift distributions 7 according to Eq. (4-71 a) for Mach numbers Max = 0 and Маж = 0.8. The curves for Ma<* = 0 are identical to curve 3 of the distributions in Fig. 3-33. In the upper figures, the local neutral points and the total neutral points N are plotted on the wing planform. At the upper part of Fig. 4-48, the lift slopes are plotted against the Mach number; at the lower part, the neutral-point displacements with respect to the geometric neutral point. The points for Маж = 1, shown as open circles, are theoretical values of an approximation method that will be explained in Sec. 4-4-4. They agree with Eq. (4-75c) for trapezoidal and delta wings. In addition, in all six diagrams, measurements by Becker and Wedemeyer [5] are included. The measured lift slopes agree well with theory in all cases. In general, the dependence on Mach number of the neutral-point positions is given satisfactorily by theory.
|
Figure 448 Lift slopes and neutral-point displacements for the three wings of Fig. 446 vs. Mach number. (—— ) Subsonic similarity rule (wing theory, Sec. 3-3-5); approximation theory for Маи = 1; Sec. 44-3. (———- ) measurements from Becker and Wedemeyer, profile thickness 6 = 0.05. (a) Trapezoidal wing, (b) Swept-back wing, (c) Delta wing. |
Certain discrepancies between theory and experiment of the neutral-point positions can be explained mainly by the effect of the finite profile thickness disregarded in the theory; compare also Fig. 4-13b. It is noteworthy that the neutral point of the trapezoidal wing shifts considerably upstream under the compressibility influence. However, this theoretical result is only partially confirmed by measurements, because shock waves form when the drag-critical Mach number is exceeded. On the two other wings, the swept-back and the delta wings, the neutral points are displaced toward the rear.
No more detailed statements are needed on the induced drag, since, as shown by Eq. (4-73), the quotient С£ц1с is independent of Mach number and thus equal to that of incompressible flow (see Table 34).
Further results on the aerodynamic coefficients of delta wings of various aspect ratios are compiled in Fig. 4-82, together with results for supersonic incident flow.
Data for the compressibility effects on the flight mechanical coefficients at subsonic incident flow, for example, of the rolling, pitching, and yawing wing, are found in Kowalke [5] and Krause [5].
