1、NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTENo. 1187f_A,t_(shtL) .s,_; _! _-T _-t,.)FLt_!_ENGIN_:_ _r,:G DC eART_NTFORMULAS FOR ADDITIONAL MASS COP_ECTIONSTO THE MOMENTS OF INERTIA OF AII:_PLANESBy Frank S. Malvestuto, 7r. and Lawrence 7. GaleLangley Memorial Aeronautical LaboratoryVa.Wa
2、shingtonFebruary, 1947 _ O0Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AFRONAUTICSTECHNICAL NOTF NO. 1187FORMULAS FO
3、R ADDITIONAL-MASS CORRECTIONSTO THE.,MOMENTS OF INERTIA OF AIRPIANESBy Frank S. Mzlvestuto, Jr. and Lawrence J. GaleFormulas are presented for the calculation of the additional-mass corrections i,o the reorients of inez*ia of airplane. _. Theseformnlas are of particular value “n con_,erting the v_rt
4、ual momentsof “ _-_znero.,a of aJrplane_ or models exTJerimentally deter_,1Jned Jnair to the true moments of inertia. A correlation of a_ditionalmoments of ._nerta calculated by these fo:cmu.!as with exper3mentala_ditJonal moments of iuertJa obtained from vacuum-chamber testsof 40 soin-tunnel models
5、 indicates that the fo_nulas gSve satJsfactaryestimations of the additional moments of inertia.II_R ODUCTI OI_“In stab_lltv investi_Lat!ons _nvolvng free-flight tests ofdynamically scaled models or of full-scale airplanes it is necessaryto know accurately the true moments of inertia o_ the mode_ ora
6、rplane. In order to _tain the true moments of Inertia c_ themode, or airplane the experimental moments of inertia, determinedby the T_endulu_:!method, must be corrected for the effect of thesurrounding air. The effect of thi_ ambient air on the apparentmomeuts of inertia is usually small but mal_ be
7、 as large as 25 per-cent of the true moments of inertia for a_rplames with low wYngloading.The fundaz_ental basis of the effect of t_e amb:_ent-a._r mass onbodies undergoing acceleration has been de_reoped in references 1and 2. I_ofer_nca_ -_, 4, and 5 present ex-perJmental data on theeffect, of the
8、 amb_ent-aJr ma_s on the moments o_ Jnertla oF flatplates obtaffned by swinglnc the plates as an integral part of apendulum. Pet?erence 3 pre_ents a method of correctrig the momentsof inertia of a ful.-scale airplane for the amb:ent-_ir mass effectby cons!_der_ng the projected areas of various compo
9、nents of thealrplan,7 _n planes normal and parallel to the plane of ssm_etry and.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 _,_ACATN No. !197applying to these projected areastbe experim(_nfo.ily dete_minedf=_, plates of finitea_,ditional mcmen
10、of-iner+_a corrections for _ _aspect ratio.In the presc_,_tpaper_ for_,ulas are presr-nC_-dfcr the ra_idevaluaticn of the ac_dit_ona!-_ss and moment-of-_n vD_euT _o _uau;oulIvuoD_.pp_ _o _usl.0_.I_eooII6,-4_moo*,-4om_90_0o_O_0_ oo_ o_o_ (1)b.OProvided by IHSNot for ResaleNo reproduction or network
11、ing permitted without license from IHS-,-,-NACA TN No. 1187 Fig. 5“DHA/.2“_ .8Z_X 0o 2 4ZCo/z_2INATIONAL ADVISORYCOMMITTEE FOIl AERONAUTICSi 1 i 16Dihedral angle, degFigure 5.- Variation of the additional moments of inertia of asingle plate with dihedral angle; A = 4 (reference 5).Provided by IHSNot
12、 for ResaleNo reproduction or networking permitted without license from IHS-,-,-Fig. 6 NACA TN No. 1187/.2o“.8.6.4Figure 6.-2 3crTaper ratio,ctNATIONAL ADVISORYCONNITTEE FORAERONAUTICSI ! L I4 5 6Dependence of the additional moment of inertia on taperratio (reference 5).Provided by IHSNot for Resale
13、No reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1187 Fig. 73.0OO_Q,-4oa)o2.6 -_/_/_./fyz,6- RQI/o5 shown on curves _rcma v/_vm de/_h o/e2u/vo/cntc/_so_d2.4Z20/2/0.6,6rnaxlmum Wld/k o/c2,d/vulent c/_5o/d/dW/f/JJI/JI jII4.2JNATIONAL ADVISONYCOIqNITTEE FOE AEIIOIIAUTICS
14、 I I I0 I Z 3 4 .5 _ 7 _ 9 /0Fineness ratio of equivalent ellipsoidFigure 7.- The variation of the coefficients of additional masskfy and kfz with the fineness ratio of an equivalent ellipsoidActual length LfMaximum width w,/-_ “Provided by IHSNot for ResaleNo reproduction or networking permitted w
15、ithout license from IHS-,-,-Fig. 8 NACA TN No. 1187NoBoBr-4o.r-4O_)r-Ior-It_(DOZ2-/.8x_/4LZLo,6.20I I_ofo5 #hown onmOXli“rTum depfh7_OXl/_un? W,dP/_CUfV_5 Qf_.“Of e2u)vai_n,+ _,/“D3old_ dof cqzllVOlCntelli,osold _ w _._/Fineness ratio of equivalent ellipsoidFigure 8.- The variation of the coefficien
16、ts of additional momentof inertia k fZ and k fy with fineness ratio of an equivalentellipsoid Actuallength = LfMaximum width ,-6-“W/0Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1187 Fig. 9oo32O62400200OIbO0/2O08_9D4_(DO (D/ OsoC?0O“00
17、/“0./co/0r(9(9NATIONAL ADVISORY0, COMNITTE FOIl AERONAUTICSi !0 4DO dt)O /200 1600 2000 24DD 2800 J200Experiments/Ixa, g r-ln 2.Figure 9.- Comparison of the experimental and calculated model valuesof the additional moments of inertia about the X swinging axis for40 free-spinning models.Provided by I
18、HSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Fig. I0 NACA TN No. 1187IhoQ oor_o8OO40O0 00 4OO 8ooNATIONAL ADVISORYCOHI41TTEEFOIl AERONAUTICS1200 1600 2000/Experimental , g r-in. 2IY aFigure 10.- Comparison of the experimental and calculated model valuesof the additional moments of inertia about the Y-swinging axis for 40free-spinning models.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
