1、IS0 1151-3 89 W 4851903 Ob53854 549 W INTERNATIONAL STANDARD IS0 11513:1989 TECHNICAL CORRIGENDUM 1 Published 199643-15 Flight dynamics - Concepts, quantities and symbols - Part 3: Derivatives of forces, moments and their coefficients TECHNICAL CORRIGENDUM 1 Mcanique du vol - Concepts, grandeurs et
2、symboles - Partie 3: Drives des forces, des moments et de leurs coefficients RECTIFICATF TECHNIQUE 1 Technical corrigendum 1 to International Standard IS0 1151-3:1989 was prepared by Technical Committee ISOflC 20, Aircraft and space vehicles, Subcommittee SC 3, Concepts, quantities and symbols for f
3、light dynamics. Page 5, subclause 3.3.2.4 Read: instead of: ICs 01.060.20; 49.020 Ref. No. IS0 1151-3:199/Cor.l:1996E) Descriptois: aircraft, aerodynamics, flight, flight dynamics, force, moments, concepts, definitions, symbols, quantities. Q IS01996 Printed in Switzerland 6 . INTER NATIONAL * STAND
4、ARD IS0 1151-3 Second edition 1989-04-01 Flight dynamics - Concepts, quantities and symbols - Part 3 : Derivatives of forces, moments and their coefficients Mcanique du vol - Concepts, grandeurs et symboles - Partie 3 : Drives des forces, des moments et de leurs coefficients Reference number IS0 115
5、1-3 : 1989 (E) IS0 1151-3 : 1989 (E) Contents Page Foreword . . . . . . . . . , , . . . , . , . . . . . . . . , , . . . , . , , . , , . , , , , , . , . , . , . . . , . , , , . , , 3.0 3.1 3.2 3.3 3.4 3.5 Introduction . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6、 . . . . . . . . . . . . , Functions and independent variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Functions and classes of derivatives. . , . , . , . , , . . . . . . , . , , . . , . . . . . . 3.1.2 Independent variables . . . . , . . . . . . . . , . . . . . . . . .
7、 . . . . , . . . . . . . . . . . . Direct derivatives . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . Specific derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Specific force derivative
8、s , , . . . . . . . . . , , . . . . . , . . . . . . . . . . . . . . . . . . 3.3.2 Specific moment derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized derivatives . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coeff
9、icient derivatives. . , , , , , , . . , , , , , . . . . . , . , . , . . . . . I , . . . . . . . . . . . . . . . . 111 1 1 1 2 2 3 4 5 6 8 6 IS0 1989 All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photoco
10、pying and microfilm, without permission in writing from the publisher. International Organization for Standardization Case postale 56 o CH-121 1 Genve 20 o Switzerland Printed in Switzerland 1151 PT 3-89 4853903 O068629 5 r IS0 1151-3 : 1989 (E) Foreword IS0 (the International Organization for Stand
11、ardization) is a worldwide federation of national standards bodies (IS0 member bodies). The work of preparing International Standards is normally carried out through IS0 technical committees. Each member body interested in a subject for which a technical committee has been established has the right
12、to be represented on that committee. International organizations, govern- mental and non-governmental, in liaison with ISO, also take part in the work. IS0 collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization. Draft Internat
13、ional Standards adopted by the technical committees are circulated to the member bodies for approval before their acceptance as International Standards by the IS0 Council. They are approved in accordance with IS0 procedures requiring at least 75 % approval by the member bodies voting. International
14、Standard IS0 1151-3 was prepared by Technical Committee ISO/TC 20, Aircraft and space vehicles. This second edition cancels and replaces the first edition (IS0 1151-3 : 19721, of which it constitutes a technical revision. Users should note that all International Standards undergo revision from time
15、to time and that any reference made herein to any other International Sfandard implies its latest edition, unless otherwise stated. iii 7- - 1151 PT 3-89 3 Y851903 0068630 1 IS0 1151-3 : 1989 (E) IC0 1151, Flight dynamics - Concepts, quantities and symbols, comprises, at present, seven parts: Part I
16、: Aircraft motion relative to the air. Part 2: Motions of the aircraft and the atmosphere relative to the Earth. Part 3: Derivatives of forces, moments and their coefficients. Part 4: Parameters used in the study of aircraft stability and control. Part 5: Quantities used in measurements. Part 6: Air
17、craft geometry. Part 7: Flight points and flight envelopes. IC0 1151 is intended to introduce the main concepts, to include the more important terms used in theoretical and experimental studies and, as far as possible, to give cor- responding symbols. In all the parts comprising IS0 1151, the term “
18、aircraft“ denotes a vehicle intnded for atmosphere or space flight. Usually, it has an essentially port and starboard symmetry with respect to a plane. That plane is determined by the geometric characteristics of the aircraft, In that plane, two orthogonal directions are defined: fore-and-aft and do
19、rsal-ventral. The transverse direction, on the perpendicular to that plane, follows. When there is a single plane of symmetry, it is the reference plane of the aircraft. When there is more than one plane of symmetry, or when there is none, it is necessary to choose a reference plane. In the former c
20、ase, the reference plane is one of the planes of symmetry. In the latter case, the reference plane is arbitrary. In all cases, it is necessary to specify the choice made. Angles of rotation, angular velocities and moments about any axis are positive clockwise when viewed in the positive direction of
21、 that axis. All the axis systems are three-dimensional, orthogonal and right-handed, which implies that a positive rotation through n/2 around thex-axis brings the y-axis into the position previously occupied by the z-axis. The centre of gravity coincides with the centre of mass if the field of grav
22、ity is homogeneous. If this is not the case, the centre of gravity can be replaced by the centre of mass in the definitions of IS0 1151; in this case, this should be indicated. Numbering of sections and clauses With the aim of easing the indication of references from a section or a clause, a decimal
23、 numbering system has been adopted such that the first figure is the number of the part of SO 1151 considered. iv 3353 PT 3-89 I4853903 0068633 3 r _ _ INTERNATIONAL STANDARD IS0 1151-3 : 1989 (E) Flight dynamics - Concepts, quantities and symbols - Part 3: Derivatives of forces, moments and their c
24、oefficients 3.0 Introduction This part of IS0 1151 deals with derivatives of forces, moments and of other quantities characterizing such forces and moments. The term “derivative“ designates the partial derivative of a function with respect to an independent variable. These derivatives appear in the
25、terms of the Taylor series representing the variations of functions with the independent variables. This part of IS0 1151 is restricted to first-order terms. Terms of higher order would require additional definitions for derivatives of higher order. The aircraft is assumed to be rigid. However, most
26、 of the definitions can be applied to the case of flexible aircraft. Aerolastic effects would require the introduction of further quantities. 3.1 Functions and independent variables A set of derivatives is characterized by the set of the functions and the set of the independent variables, with respe
27、ct to which dif- ferentiation takes place. 3.1.1 Functions and classes of derivatives Different classes of derivatives are used in flight dynamics studies. This part of IS0 1151 includes the following classes of derivatives: I I Ciause Class I Distinguishing I mark I 3.2 I Direct derivatives I I I I
28、 3.3 I Specific derivatives I - I I 3.4 I Normalized derivatives I A I 3.5 I Coefficient derivatives I I The distinguishing marks may be omitted if no confusion is likely. In each class, the specific term for a particular derivative shall refer to the function and to the independent variable. The fu
29、nctions used in a given problem refer to only one axis system. In the chosen axis system, the components are numbered as follows: 1 Component with respect to the x-axis 2 Component with respect to the y-axis 3 Component with respect to the z-axis 1 p_ _I_ 3L53 PT 3-87 -l 4853703 00b8632 5 I- No. 3.2
30、.1 IS0 1151-3 : 1989 (E) Term (Direct) resultant force derivative matrix 3.1.2 Independent variables The independent variables considered are - variables representing the aircraft motion relative to the air (1.2 and 1.3); - variables representing the motivator deflections (1.8.3). NOTE - It may be n
31、ecessary to introduce additional types of independent variables, for example parameters relating to the aircraft propulsive system. It is necessary to specify the set of independent variables used. The value of the derivative of a given function with respect to a given independent variable depends,
32、generally, in fact, on the choice of the other independent variables. If different sets of independent variables are used simultaneously, each set of derivatives corresponding to a given set of independent variables shall be characterized by an appropriate distinguishing mark. 3.2 Direct derivatives
33、 A direct derivative is the partial derivative of a component of a force or a moment with respect to a variable included in a given set of independent variables. A direct derivative has the dimension of the ratio of the function to the independent variable. The symbol for a direct derivative is the
34、symbol of the function to which the symbol of the independent variable is added as a subscripti). EXAMPLE ax - = x, all The symbols of direct derivatives do not contain a distinguishing mark. The direct derivatives of the components of the resuitant force R (1.5.2) and of the components of the resul
35、tant moment the elements of matrix R (3.2.1) and matrix Q (3.2.2). The symbols of the matrixes shall, preferably, be printed in bold type. -+ (1.5.51 are Definition The matrix consisting of the direct derivatives of the com- ponents of the resultant force (1.5.21. The rows of the matrix are ordered
36、according to the conven- tion given in 3.1.1. The ith row contains the derivatives of the ith function. Thejth element in a row of the matrix is the direct derivative, with respect to thejth variable in the set of independent variables (3.1.2). The matrix has the following structure: 1 R11 RI2 RI3 -
37、 - * RI, R = R21 Rz RB . Ra i RN R32 * *R3n with, for example R1 = x R2 = Y R3 = Z NOTE - An analogous matrix RA can be defined with regard to the components of the airframe aerodynamic force (1.6.2.2). Symbol R 1) The independant variable is sometimes indicated in the symbol by a superscript, for e
38、xample ax all - - xu 2 D No. 3.2.2 Term (Direct) resultant moment derivative matrix IS0 1151-3 : 1989 (E) Definition The matrix consisting of the direct derivatives of the com- ponents of the resultant moment (1 -5.5). The rows of the matrix are ordered according to the conven- tion given in 3.1.1.
39、The ith row contains the derivatives of the ith function. Thejth element in a row of the matrix is the direct derivative, with respect to thejth variable in the set of independent variables (3.1-21. The matrix has the following structure: with, for example NOTE - An analogous matrix QA may be define
40、d with regard to the comDonents of the airframe aerodvnarnic moment (1.6.2,lO). Symbol Q 3.3 Specific derivatives A specific derivative is the derivative of a component of the specific resultant (1.5.10) or of the specific resultant moment (1.5.12) with respect to a variable contained in a given set
41、 of independent variables. The inertial characteristics of the aircraft, - mass (1.4.11, and - moments of inertia (1.4.2) and products of inertia (1.4.3) with respect to the body axis system, are assumed to be constant. If the inertial characteristics of the aircraft cannot be assumed to be constant
42、, the parameters required for their definition shall be in- cluded in the set of independent variables. A specific derivative has the dimension - of the quotient of a linear acceleration by the independent variable, in the case of a specific force derivative, or - of the quotient of an angular accel
43、eration by the independent variable, in the case of a specific moment derivative. The symbol of a specific derivative consists of - the basic alphabetical symbol used for the corresponding resultant force componen? (1.5.2) or resultant moment component (1 -5.51, - the symbol of the independent varia
44、ble as a subscript, and - the distinguishing mark - above the basic alphabetical symbol. Subclauses 3.3.1 and 3.3.2 give general definitions illustrated, for each type of specific derivative, by a particular example. Specific derivadves of other forces or other moments, or with respect to other inde
45、pendent variables, can be defined in an analogous manner. 3 IS0 1151-3 1989 (EI 3.3,l Specific force derivathes A specific force derivative is the product of the reciprocal of the aircraft mass (1.4.1) (l/m) by the corresponding direct force derivative (3.2). The matrix notation of the specific forc
46、e derivative matrix, 8, is -1 R=-R m where m is the aircraft mass (1.4,l); R is the direct force derivative matrix (3.2.1). The elements of matrix i are 1 where is the derivative of the ith component of the specific resultant with respect to thejth independent variable; Ru is the direct derivative o
47、f the ith component of the resultant force with respect to thejth independent variable; m is the aircraft mass (1.4.1). No. 3.3.1.1 3.3.1.2 3.3,1.3 3.3.1.4 Term Specific force derivative with respect to an aircraft velocity component Specific force derivative with respect to an angular velocity comp
48、onent Specific force derivative with respect to a linear acceleration component Specific force derivative with respect to a motivator deflection Definition The partial derivative of a component of the specific resul- tant (1.5.11) with respect to an aircraft velocity component (1.3.4). EXAMPLE - I a
49、y yw=- m aw The partial derivative of a component of the specific resul- tant (1.5.1 1) with respect to an angular velocity component (1.3.6). EXAMPLE - i ay y=- m ar The partial derivative of a component of the specific resul- tant (1.5.11) with respect to the derivative of an aircraft velocity component (1.3.4) with respect to time. EXAMPLE - i ay dw Qv = - - where W = - m aw dt The partial derivative of a component of the specific resul- tant (1.5.11) with respect to a motivator deflection (1.8.3.11 to 1.8.3.13). EXAMPLE Ysn=- I ay m a& Symbol - r,V
