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TABULATION OF RESULTS—INCOMPRESSIBLE FLOW
Formulas and numerical tables of the aerodynamic coefficients for an airfoil with flap and tab, whose hinge lines do not necessarily coincide with their respective leading edges, have been published by many authors. The most important references are:
Dietze:13Л1,1312 Luftfahrt-Forsch. 16, 84-96 (1939); 18, 135-141 (1941). W. P. Jones:1316,1317 Aeronaut. Research Council R. & M. 1948 (1941); R. & M. 1958 (1942).
Kiissner and Schwarz:13-23 Luftfahrt-Forsch. 17, 337-354 (1940). Translated as NACA Tech. Memo. 991.
Theodorsen13-32 and Garrick:13-33 NACA Rept. 496 (1934); Kept. 736 (1942).
The most comprehensive numerical tables are published by Kiissner and Schwarz in the reference named above. The relations between the special functions tabulated by various authors are listed in a paper by W. P. Jones.1317
For flutter calculations, Smilg and Wasserman’s tables of Lh, La, etc., which are derived from Kiissner and Schwarz’s results, are widely used. These tables are contained in the following references:
AAF Tech. Rept. 4798, U. S. Air Force, by Smilg and Wasserman,6-20 (1942).
Introduction to the Study of Aircraft Vibration and Flutter, book by Scanlan and Rosenbaum.619
While both sealed and unsealed gaps between the main wing and the flap and the control tab are considered in Kiissner and Schwarz’s paper, only unsealed gaps are considered in Smilg and Wasserman’s. Furthermore, the tab hinge line is assumed to be located at the tab leading edge in
|
(b) Kiissner and Schwarz’s airfoil Fig. 13.6. Comparison of Dietze’s aerodynamically balanced flap with Kiissner’s. |
|
Reference |
Duncan, Collar. Ref. 13.34 |
Theodorsen. Ref. 13.32 |
Kussner, Schwarz, Ref. 13.23 |
Dietze, Ref. 13.11. 13.12 |
Frazer, Ref. 7.31 |
Cicala, Ref. 13.7, 13.8 |
Lyon, Ref. 15.3 |
Kassner, Fingado, Ref, 6.15 |
Jones, Ref. 13.17 |
Scanlan, Rosenbaum. Smilg, Wasserman, Ref. 6.19. 6.20 |
* This Book |
|
Chord |
c |
2b |
21 |
/(= Iri> |
с |
I£= 2/) or/ |
£([38]=20 |
t |
c |
2b |
c = 2b |
|
Free-stream velocity |
W |
V |
V |
V |
V |
V |
F |
V |
V |
V |
17 |
|
Circular frequency |
P |
kv b |
V |
о |
о*= |
п |
V |
V |
ш(= 2w/) |
a> |
a> |
|
Reduced frequency |
A 2 |
к |
– ito |
(Of |
А 2 |
a> |
а> |
2V |
a> T |
к |
к |
|
Translational motion at reference point |
z |
h |
Aleivt |
6 |
Z |
rjL оті] |
Й/ |
z |
h |
h |
|
|
Rotational motion of airfoil |
0 |
a |
BeiH |
p |
в |
а |
0 |
ф |
0 |
а |
a |
|
Lift vector (circulation function) |
C |
l – h T 2 |
і 4- г 2 |
– 1C |
і – А |
1 – А |
P |
C |
C |
C |
|
|
Real part of C(Ar) |
-! |
F |
І + r 2 |
1 + Г 2 |
А |
і — А’ |
1 – А’ |
A |
A |
F |
F |
|
Imaginary part of C(k) |
AG 2 |
G |
T" 2 |
T” 2 |
– В |
– А* |
А’ |
– В |
– В |
G |
G |
|
Lift (+ upward) |
-Z |
– P |
К |
— Р |
-Z |
А» |
А* |
– |
– z |
-L’ |
L |
|
Pitching moment (+ nose up) |
M |
Ma |
– Me |
М |
м |
– М |
М |
— |
M |
M’ |
Mx0* |
|
414 |
AAF Tech. Rept. 4798. The tables in AAF Tech. Kept. 4798 for tab oscillations and tables for aileron with e < 0, where eb is the coordinate of the aileron leading edge aft the mid-chord point, are not reproduced in Scanlan and Rosenbaum’s book.
Dietze’s results for the aerodynamic overhang of the control surfaces differ from those of other authors by the assumption that the overhang part of the flap is bent and faired with the main wing, and that of the tab is faired with the flap. See the comparison in Fig. 13.6.
The notations used by several authors are listed in Table 13.1.
