REG NACA-TN-1854-1949 APPROXIMATE CORRECTIONS FOR THE EFFECTS OF COMPRESSIBILITY ON THE SUBSONIC STABILITY DERIVATIVES OF SWEPT WINGS.pdf

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1、;/*fc. o o $ developed in reference 6, is _jA 3a0 tan A sin A cL2/M=0 o I 2an cos A A(A + -_ ) The corresponding Mach numher equation “becomes CY 3_o tan A sin A :L2/M TA/A + fo 2_cosA B IT J By letting a = 2ir, the compressibility factor i CL2/M = A + U cos A ?CYR AB + k cos A VcL/M=0 (9) Provided

2、by IHS. No reproduction or networking permitted without license from IHS. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TW No. 185 15 Pitching Flight Lift due to pitching.- Beference 6 presents the following equation for lift due to pitching:

3、VCLJM=0 (2 + 2c)Lc WM=0 The compressible-flow equation, therefore, is (%)M - (I + 2f )K)v then _2 cos A (1 + 2?) and 1E = - CT a _c B 1 +22f_A irk B cos A =- cos A 1 + ao cos A Bp 7rA =- sin A o cos A 1 + 2 a, *R TTA (-) where, from reference 6. = - 2Y t| + (-i an A Provided by IHS. No reproduction

4、or networking permitted without license from IHS. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-18 NACA TN No. 185 Therefore, - Cn = 2CT “R rb 2V 75 2 + 1 - 3C B 7 an cos B + + tan A aQ cos A 7TA B + 2aQ cos A TTA W2 y b72 I) tan A (IM After substi

5、tuting this value of c1 _ c-, from equation (Ik) into J_j -K equation (12), integrating across the span, differentiating the result with respect to the yawing-velocity parameter , and replacing aQ by 27T, the Mach number value of the derivative of rolling moment due to yawing “becomes 2 + A(l-B2) B(

6、AB + 2 cos A) + AB + 2 cos A /x tan A tan2A AB + k cos A I 5 2A “2T At zero Mach number this equation reduces to the equation presented in reference 6: _ 1 A + 2 cos A (x tan A tan A CLAI=0 3 A + k cos A Vc 2A 2k 0 Therefore, 1 Z 2 + Af 1 B2) T B + 2 cos A (x tan A 2A (I B( AB + 2 CQ3 A)J AB + k cos

7、 A x tan A tan2 A tan2/v 2T7 1 A + 2 cos A 3 A + U cos A 2A 2k J Tf x/c is restricted to zero, Provided by IHS. No reproduction or networking permitted without license from IHS. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. l85*t- 19 A(

8、l - B ) + AB + 2 cos A tan2A 2B(AB + 2 coe A) B + cos A 8 1 + A + 2 cos A tan2A A + k cos A 5 Yawing moment due to yawing and lateral force due to yawing- The contribution of a wing alone to either Cn or Cy is small compared to the contribution of the yertical tail. For this reason, these two deriva

9、tives were not deemed as “being of sufficient importance to warrant consideration similar to that given the derivative C The derivatives may “be corrected for compressibility effects on a similar basis; however, the procedure used for these derivatives could not be expected to be very reliable “beca

10、use the drag and the drag distribution are important “but can- not be handled in a logical manner. Perhaps the most reliable procedure for the derivative Cn is the use of the incompressible-flow equation of reference 6 with the wing profile-drag coefficient appropriate to the Mach number in question

11、. Provided by IHS. No reproduction or networking permitted without license from IHS. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 HACA TW Wo. lSt- PEFEREWCES 1. Goldstein, So, and Young, A.D.: The Linear Perturbation Theory of Compressible Flow

12、, with Applications to Wind-Tunnel Interference. H. Q Qi V A V 1 I I l 1 1 0 n . 1 .? N A b- vX N j l 1 II *p -p 3 H -C) H & p o- m o O P H cd p p 35 vo “ cv / 1 , / / / / / / / / 7 / / V / / 1 /, 1 / x - / / / ill i I, 1 ! Si 1 1 55 K) h H H o u o -p (D s to H I o o II P Ato H H EQ m /y H Provided

13、by IHS. No reproduction or networking permitted without license from IHS. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-26 KA.CA TE No. I85U I / / / ill 1 1/ / I 0 %3 / / Wo) Wh. Id, fo/%) o I ff o u o -p CD CD H CO U CD -P CO H CD +3 o -P * H? H 5

14、c 03 O ta -H (D -P 5 & $ Pi H H m o -P * 5|ss . s N Y ) A I ll % o 1 Q ! 1 ll $ 53 *M 51 0 o p H P4 O P -P 1 a to H -P H P4 -P s p H H H 2 O II IH|lo I O -P o P o ta s H P o CO 3) H 3 g H s Provided by IHS. No reproduction or networking permitted without license from IHS. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-