1、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-1. Report No. 2. Government Accession No. 3. Recipients Catalog No. NASA TR R-433 4. Title and Subtitle 5. Report Date EXPERIMENTAL DETERMINATION OF AIRPLANE MASS AND INERTIAL CHARACTERISTICS October 19
2、74 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. Chester H. Wolowicz and Roxanah B . Yancey 9. Performing Organization Name and Address NASA Flight Research Center P. 0. Box 273 Edwards, California 93523 H-814 IO. Work Unit No. 501-06-05 11. Contract or Grant No.
3、 13. Type of Report and Period Covered * Technical Report 14. Sponsoring Agency Code 12. Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington, D . C . 20546 I 15. Supplementary Notes 16. Abstract - This report reviews and evaluates current practices for experi-
4、 mentally determining airplane center of gravity, moments of inertia, and products of inertia. The techniques discussed are applicable to bodies other than airplanes. In pitching- and rolling-moment-of-inertia investigations with the airplane mounted on and pivoted about knife edges, the non- linear
5、 spring moments that occur at large amplitudes of oscillation can be eliminated by using the proper spring configuration. The single-point suspension double-pendulum technique for obtaining yawing moments of inertia, products of inertia, and the inclination of the principal axis provides accurate re
6、sults from yaw- mode oscillation data, provided that the sway-mode effects are minimized Ir y proper suspension rig design. Rocking-mode effects in the data an be isolated. The conduct of the experiments, as well as the test setup used, is a major factor in obtaining accurate results. 17. Key Words
7、(Suggested by Author(s) ) Experimental techniques Inertia determination Mass and inertia characteristics 18. Distribution Statement Unclassified - Unlimited Category: 02 22. Price“ 21. No. of Pages 19. Security Classif. (of this report) 20. Security Classif. (of this page) Unclassified Unclassified
8、64 $3.75 *For sale by the National Technical Information Service, Springfield, Virginia 22151 , Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-EXPERIMENTAL DETERMINATION OF AIRPLANE MASS AND INERTIAL CHARACTERISTICS Chester H . Wolowicz and Roxanah
9、B . Yancey Flight Research Center INTRODUCTION Mass and inertial characteristics-the location of the center of gravity, the moments of inertia, and the inclination of the principal axis-must be known to pre- dict the performance and limiting flight conditions of new airplane configurations. The accu
10、racy of such predictions is particularly important for unconventional ve- hicles like the lifting bodies, Furthermore, after a flight test program begins, the accuracy of the predicted mass and inertial characteristics affects the precision with which the stability and control derivatives can be det
11、ermined from the flight data. Estimates of airplane mass and inertial characteristics are made and refined during the design process. To verify the calculated characteristics, the mass dis- tribution characteristics of a new configuration are frequently determined experi- mentally. However, in any e
12、xperimental investigation there are limitations on the experimental setups and precautions to be observed. In these respects, the experi- mental techniques have continuously improved. At first, experimental mass characteristics were determined from overhead sus- pensions (refs. 1 to 4) . The vertica
13、l center-of-gravity position was obtained by tilting the airplane through large pitch angles and sighting the point of intersection of the line of suspension in the XZ-plane. The pitching and rolling moments of inertia were obtained by suspending the airplane as a compound pendulum. The yawing momen
14、t of inertia was obtained with the airplane suspended as a bifilar pendulum. The inclination of the principal axis was obtained from the experimen- tally determined ellipsoid of the inertias. However, structural, handling, and accu- racy problems make it impractical to apply these methods to airplan
15、es that weigh more than approximately 45,000 newtons. Improved and simpler techniques were reported in reference 5. The pitching and rolling moments of inertia were obtained by the compound-pendulum method, but the airplane was supported on and pivoted about knife edges, and the restoring moments we
16、re provided by springs. The yawing moment of inertia and the inclina- tion of the principal axis were determined by suspending the airplane support system from a vertical torsion tube in a way that permitted freedom in pitch but restrained -. Provided by IHSNot for ResaleNo reproduction or networkin
17、g permitted without license from IHS-,-,-the airplanes rolling motion by the bending of the tube. Reference 5 is the first reported instance of finding the roll-to-yaw ratio of the response to yaw excitation as a function of pitch attitude to obtain the inclination of the principal axis. Evi- dently
18、, there were practical problems that precluded further use of the torsion tube, such as difficulty in providing rigid restraint at the fixed end of the tube. In current practices of determining mass and inertial characteristics, the ver- tical center-of-gravity position is obtained by tilting the ai
19、rplane through a range of pitch attitudes while it is mounted on weighing scales located at jack points or the landing gear. Reference 6 considers this method to be accurate to within 5 per- cent. An overhead suspension method that provides more precise results is in use at the NASA Flight Research
20、Center. To determine pitching and rolling moments of inertia, the airplane is supported on and pivoted about knife edges. To determine yawing-moment inertias and the inclination of the principal axis , a single-point sus- pension double-pendulum technique is used. The elementary principles of this t
21、echnique are described in reference 7. Reference 8 expands on the discussion in reference 7 and provides a comprehensive theoretical treatment to insure proper rig design for the condition where the restoring-moment springs are in planes parallel to the YZ-plane. At the NASA Flight Research Center t
22、he same technique is used, but the springs are in planes parallel to the XZ-plane. Although the literature has been concerned with improved techniques for the experimental determination of airplane mass and inertial characteristics , little mention has been made of the effects of amplitudes of oscil
23、lation on the degree of nonlinearity in the gravity-force and spring moments in pitching- and rolling- moment-of-inertia determination. This report reviews current practices for experimentally determining the air- plane center of gravity , moments of inertia, and products of inertia. The techniques
24、discussed are applicable to bodies other than aircraft. The method used at the NASA Flight Research Center to obtain the vertical center-of-gravity position accurately is described , along with the more conventional method which involves tilting the air- plane at jack points. The report provides inf
25、ormation to facilitate the assessment of proposed experimental setups for pitching- and rolling-moment-of-inertia tests in terms of the amplitude of oscillations permissible for the accuracy desired. Finally , the NASA Flight Research Centers application of the single-point suspension double- pendul
26、um method to determine yawing moment of inertia and product of inertia is described, and the interaction of the modes of oscillation and the requirements to suppress or minimize the undesired modes are reviewed, SYMBOLS Physical quantities in this report are given in the International System of Unit
27、s (SI). Details concerning the use of SI are given in reference 9, Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a length of the line of action of the spring, in yawing-moment- of-inertia tests, from the attachment point at the aircraft to the tieb
28、ack stanchion (fig. 11) , m 0 Q2 - 22 Q B=t h Cs=4k(Qj)2(+cos6 SP -q1sin6 SP ),N-m d dl ES EW horizontal distance between the front and rear loading points used in obtaining the horizontal center-of-gravity position by the methods shown in figures l(a) , l(b) , and 2, m horizontal distance between t
29、he center-of-gravity datum and the rear loading point used in obtaining center-of- gravity positions by the method shown in figure 2, m ratio of the nonlinear increment in the change in spring moment to the linear change for the aircraft oscillating about a pivot moment to the linear change for the
30、inverted-pendulum concept of the aircraft oscillating about a pivot - ratio of the nonlinear increment in the change in weight g acceleration due to gravity, m/sec2 Ix 9 Iy 9 Iz moments of inertia of the aircraft about the X-, Y-, and Z-body axes, respectively, kg-m2 IYo IZ0 moment of inertia of the
31、 aircraft about its Y-axis passing through its center of gravity, kg-m2 moments of inertia of a test-setup component (such as cradle) about the Y- and Z-axes passing through the components center of gravity, respectively, kg-m2 moments of inertia of a test-setup component (such as cradle) about the
32、X- and Y-pivots of oscillation, respectively, kg-m2 IXZ IX z ss product of inertia relative to aircraft X- and Z-body axes, kg-m2 product of inertia of an aircraft relative to the X- and Z- axes passing through the line of suspension, kg-m2 3 Provided by IHSNot for ResaleNo reproduction or networkin
33、g permitted without license from IHS-,-,-(IXSZS) ts IXoZo ec (IY) am S IZ kt with test-setup components included, kg-m2 IX z ss product of inertia of a test-setup component relative to the X- and Z-axes passing through the components center of gravity, kg-m2 product of inertia of a test-setup compon
34、ent relative to the X- and Z-axes passing through the line of suspension, kg-m2 change in pitching moment of inertia due to apparent additional air mass effects, kg-m2 yawing moment of inertia of an aircraft about the line of suspension, kg-m2 change in yawing moment of inertia of an aircraft about
35、the line of suspension due to apparent additional air mass effects, kg-m2 yawing moment of inertia of an aircraft in the test setup about the line of suspension, kg-m2 - linear spring constant of an individual spring, N/m spring constants of springs used in single-point suspen- sion test setup (fig.
36、 17), N/m torsional spring constant, N-m/rad k =Wy Q; (2; + 2;) + kt sin2 6 , N-m/rad SP QO Cp sinusoidal forcing rolling-moment input, N-m , and side force input, N, respectively L ”F Ls ,Ns ,Ys spring rolling moment, N-m, yawing moment, N-m, and side force, N, respectively distance from the center
37、 of gravity of airplane and com- ponent weight, respectively, to the pivot of oscillation normal to pivot axis, m a/c”W length of suspension beam (used in appendix B) , m b Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-r Q Q0,Q1Q2 Q =Q1cos61, m h A
38、MW W m = -, kg g m =- Wa/c , kg a/c g distance between reference rivets, defining reference dimensions used in pitch and roll configurations, defined longitudinal body axis (fig. 3), m in table 1 and figure 6, m dimensions used in single-point suspension method for Ixz , and E, defined in figures ll
39、(a) Z determining I and 13, m change in spring moment, N-m change in weight moment due to perturbation of inverted AMW when pendulum arm is horizontal, N-m pendulum action of weight, N-m P period of oscillation, sec Pnl ,Pn2 ,Pn3 spring configurations in pitch tests with springs normal to moment arm
40、 extending from spring attachment point on airplane to pivot of oscillation (fig. 6) Pvl ,Pv2 spring configurations in pitch tests with springs vertical roll rate, rad/sec , and roll acceleration, rad/sec2 , respec- tively amplitude of roll rate and yaw rate, respectively, rad/sec amplitude of rocki
41、ng-mode roll rate in total roll response to yaw-mode excitation (fig. 15 (b) , rad/sec yaw-mode amplitude ratio of roll-to-yaw rate kt cos ti sin 6 j P1=(% SP SP 5 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-R 9R Rnl t W (WQ sin sW) Wa/ c ec ( Wa
42、/ - wb Wbal W x:z X P xs ,Ys ,zs , 6 vertical reaction loads on main landing wheels and nose- wheel, respectively, in center-of-gravity determination (figs. l(a) and l(b) , N spring configuration in roll tests with springs normal to moment arm extending from spring attachment point on airplane to pi
43、vot of oscillation (fig. 6 (c) yaw rate, rad/sec, and yaw acceleration, rad/sec2 , r3spec- tively time, sec weight, N gravity-force moment of experimental component, N-m weight of the aircraft with test-setup components removed, N weight of the aircraft with the weight of the test-setup components i
44、ncluded, N weight of suspension beam (fig. 3), N weight of ballast (fig. 3), N weight of outrigger (fig. 3), N loading weight in the determination of the vertical center- of-gravity position using the single-point suspension method, N axes of the airplane through its center of gravity (fig. 17) long
45、itudinal and vertical reference axes, respectively, through the suspension bolt (fig. 3) longitudinal principal axis of the airplane axes of the airplane (with test-setup components included) passing through the center of gravity located on the line of suspension (fig. 17) horizontal and vertical di
46、stances, respectively, of the center of gravity of the suspension beam relative to the XZ/-axes (fig. 31, m Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-X or X ref xs Y, Y zs Ax, A; Y - YFRo Yst - w ym IYI I yst I I -yly - Z Z Z r -1 Z ts horizont
47、al and vertical distances, respectively , of the center of gravity of the leveling ballast relative to the XZ-axes (fig. 31, m horizontal and vertical distances, respectively, of the center of gravity of the spring attachment outrigger relative to the XZ-axes (fig. 3) , m horizontal distance from li
48、ne of suspension to the body reference station (fig. 3) , m horizontal , lateral , and vertical distances, respectively , of the center of gravity of an experimental component from the XsYsZs-axes, m horizontal and vertical distances, respectively, of the loading weight , w , relative to the XZ-axes
49、 (figs. 1 (c) and 3) , m distances parallel and normal , respectively, to the center of gravity of the aircraft from the datum used in ground- based determinations of the center of gravity (fig. 1 (b) ) , m - shift in x and y, respectively, due to the removal of test- setup components, m lateral displacement , m sway-mode amplific
