Pub Date : 1957-02-01DOI: 10.1017/S0368393100130901
E. A. Winn
A method of solution of linear differential equations is derived which requires no special starting procedure, and which is, in principle at least, capable of extension to any order of accuracy. Further advantages of the method are that boundary conditions are easy to satisfy, and that the solution of families of equations differing only in the input function requires little extra computation. The method requires the reciprocation of a matrix of order equal to the number of points for which a solution is to be obtained, but this can be much simplified by suitably partitioning the matrix, and with most automatic high-speed computers the reciprocation of a matrix is in any case an easily programmed operation.
{"title":"A Matrix Method for the Numerical Solution of Linear Differential Equations with Variable Coefficients","authors":"E. A. Winn","doi":"10.1017/S0368393100130901","DOIUrl":"https://doi.org/10.1017/S0368393100130901","url":null,"abstract":"A method of solution of linear differential equations is derived which requires no special starting procedure, and which is, in principle at least, capable of extension to any order of accuracy. Further advantages of the method are that boundary conditions are easy to satisfy, and that the solution of families of equations differing only in the input function requires little extra computation. The method requires the reciprocation of a matrix of order equal to the number of points for which a solution is to be obtained, but this can be much simplified by suitably partitioning the matrix, and with most automatic high-speed computers the reciprocation of a matrix is in any case an easily programmed operation.","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1957-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100130901","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56963348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1957-02-01DOI: 10.1017/S0368393100130895
Bertram Klein
The determination of effective column end fixity by means of vibration testing has been established for the case when the rotational end restraints of the column are equal. It is the purpose of the present work to present solutions for the general case. The method of solution is straightforward. Results are listed in a convenient tabular array.
{"title":"Determination of Effective End Fixity of Columns with Unequal Rotational End Restraints by Means of Vibration Test Data","authors":"Bertram Klein","doi":"10.1017/S0368393100130895","DOIUrl":"https://doi.org/10.1017/S0368393100130895","url":null,"abstract":"The determination of effective column end fixity by means of vibration testing has been established for the case when the rotational end restraints of the column are equal. It is the purpose of the present work to present solutions for the general case. The method of solution is straightforward. Results are listed in a convenient tabular array.","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1957-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100130895","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56963339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1956-12-01DOI: 10.1017/S0368393100129542
E. Shepherd
{"title":"The Quick and the Dead. The story of a chief test pilot. By Squadron Leader W. A. Waterton, G.M., A.F.C. and bar. Muller, London 1956. 237 pp. Illustrated. 15s.","authors":"E. Shepherd","doi":"10.1017/S0368393100129542","DOIUrl":"https://doi.org/10.1017/S0368393100129542","url":null,"abstract":"","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1956-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100129542","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56963255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1956-12-01DOI: 10.1017/S0368393100129475
J. Pritchard
{"title":"Balloons. With an Introduction and Notes by C. H. Gibbs-Smith, Companion, R.Ae.S. Twelve coloured plates 16 in. by 11 in. The Ariel Press, London, 1956. 25s.","authors":"J. Pritchard","doi":"10.1017/S0368393100129475","DOIUrl":"https://doi.org/10.1017/S0368393100129475","url":null,"abstract":"","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1956-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100129475","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56963237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1956-11-01DOI: 10.1017/S000192400012785X
J. Pritchard
{"title":"Annual Reports of the Aeronautical Society of Great Britain, 1866-1893. Facsimile reprint in 4 Volumes. Peter Murray Hill (Publishers) Ltd., London, 1956. £50.","authors":"J. Pritchard","doi":"10.1017/S000192400012785X","DOIUrl":"https://doi.org/10.1017/S000192400012785X","url":null,"abstract":"","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1956-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S000192400012785X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57256443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1956-01-01DOI: 10.1017/S0368393100132420
J. Lockwood Taylor
Each small stage of the expansion starts with a uniform supersonic stream and finishes with a similar stream accelerated, expanded and turned through a small angle. We are therefore justified in applying to each stage the linear (Ackeret) approximation for small departures from uniform flow, according to which where U = air velocity M = Mach number α = inclination of flow.
{"title":"Derivation of the “Prandtl-Meyer” Expansion Solution from the Linear Approximation","authors":"J. Lockwood Taylor","doi":"10.1017/S0368393100132420","DOIUrl":"https://doi.org/10.1017/S0368393100132420","url":null,"abstract":"Each small stage of the expansion starts with a uniform supersonic stream and finishes with a similar stream accelerated, expanded and turned through a small angle. We are therefore justified in applying to each stage the linear (Ackeret) approximation for small departures from uniform flow, according to which where U = air velocity M = Mach number α = inclination of flow.","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1956-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100132420","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56962934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-10-01DOI: 10.1017/S0368393100128019
S. J. Peerless, D. B. Spalding
Boundary layer problems may be divided into two classes: (a) those for which similar solutions can be found, i.e. where the boundary conditions are such that similar profiles differing only in scale factor exist at different sections; and (b) those where the boundary conditions do not effect similarity, so that the development of the boundary layer must be calculated in stages. The latter class are known as “continuation problems,” and very few numerical solutions have been obtained because of the labour involved. Approximate methods of solving continuation problems are known, using the Karman momentum integral method (e.g. Ref. 1) or variants. Some of these methods make use of velocity profiles calculated for “similar” boundary layers. This note presents a new approximate method which uses “similar” profiles but avoids using the momentum integral. Instead of characterising the boundary layer thickness by the “momentum thickness,” which needs to be calculated yet is of less direct interest, the wall shear stress is used; this stress usually has to be calculated in any case and the present method is therefore comparatively simple.
{"title":"An Approximate Solution of the Laminar Boundary Layer on a Flat Plate with Uniform Suction","authors":"S. J. Peerless, D. B. Spalding","doi":"10.1017/S0368393100128019","DOIUrl":"https://doi.org/10.1017/S0368393100128019","url":null,"abstract":"Boundary layer problems may be divided into two classes: (a) those for which similar solutions can be found, i.e. where the boundary conditions are such that similar profiles differing only in scale factor exist at different sections; and (b) those where the boundary conditions do not effect similarity, so that the development of the boundary layer must be calculated in stages. The latter class are known as “continuation problems,” and very few numerical solutions have been obtained because of the labour involved. Approximate methods of solving continuation problems are known, using the Karman momentum integral method (e.g. Ref. 1) or variants. Some of these methods make use of velocity profiles calculated for “similar” boundary layers. This note presents a new approximate method which uses “similar” profiles but avoids using the momentum integral. Instead of characterising the boundary layer thickness by the “momentum thickness,” which needs to be calculated yet is of less direct interest, the wall shear stress is used; this stress usually has to be calculated in any case and the present method is therefore comparatively simple.","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1955-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100128019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56963182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-08-01DOI: 10.1017/S0368393100120401
W. J Goodey
Summary: This paper is concerned with the problem of the skin–and–stringer–covered conical fuselage of circular cross section, having flexible frames and being subjected to an arbitrary distribution of loads applied in the planes of these frames or on the end cross sections. The skin thickness and stringer cross section may vary from bay to bay but are assumed to be constant in a bay, i.e. between any two consecutive frames. The stringers are assumed to be uniformly spaced round the circumference. The frames are assumed to be of uniform cross section (circumferentially) but their stiffnesses are arbitrary, as is also their spacing along the fuselage. This paper is a sequel to one previously published in the Journal, but the method of analysis is now by minimum strain energy instead of by deflections. Owing to the generality of the investigation it is impossible to present the solution—in terms of the known loads and stiffnesses—in any explicit form, and attention has therefore been concentrated on the technique of numerical computation. A scheme of tabulation has been evolved, and its use is illustrated by a fully–worked numerical example of a moderately complex type.
{"title":"The Stress Analysis of the Circular Conical Fuselage with Flexible Frames","authors":"W. J Goodey","doi":"10.1017/S0368393100120401","DOIUrl":"https://doi.org/10.1017/S0368393100120401","url":null,"abstract":"Summary: This paper is concerned with the problem of the skin–and–stringer–covered conical fuselage of circular cross section, having flexible frames and being subjected to an arbitrary distribution of loads applied in the planes of these frames or on the end cross sections. The skin thickness and stringer cross section may vary from bay to bay but are assumed to be constant in a bay, i.e. between any two consecutive frames. The stringers are assumed to be uniformly spaced round the circumference. The frames are assumed to be of uniform cross section (circumferentially) but their stiffnesses are arbitrary, as is also their spacing along the fuselage. This paper is a sequel to one previously published in the Journal, but the method of analysis is now by minimum strain energy instead of by deflections. Owing to the generality of the investigation it is impossible to present the solution—in terms of the known loads and stiffnesses—in any explicit form, and attention has therefore been concentrated on the technique of numerical computation. A scheme of tabulation has been evolved, and its use is illustrated by a fully–worked numerical example of a moderately complex type.","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1955-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100120401","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56962513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1955-06-01DOI: 10.1017/S0368393100118747
C. L. Amba Rao
Reinforced rectangular plates find frequent application in the field of aeroplane structures, ship structures and allied fields. The stability of a structural element, if its critical load in compression is rather low, is normally influenced by its own weight. Usually the ratio of the body forces of the stiffened plate to the critical load is a considerable amount and the influence of the body forces of the plate and the ribs on the critical load of the stiffened plate is discussed here. In this note (following Timoshenko), the extensional deformation of the middle surface during buckling is neglected, which greatly simplifies the analysis. Although it leads to an under-estimation of the critical load (of the order of 10 per cent at most) it is not likely to influence the general conclusions. Strain energy method of analysis is used.
{"title":"The Influence of Body Forces on the Stability of a Reinforced Rectangular Plate","authors":"C. L. Amba Rao","doi":"10.1017/S0368393100118747","DOIUrl":"https://doi.org/10.1017/S0368393100118747","url":null,"abstract":"Reinforced rectangular plates find frequent application in the field of aeroplane structures, ship structures and allied fields. The stability of a structural element, if its critical load in compression is rather low, is normally influenced by its own weight. Usually the ratio of the body forces of the stiffened plate to the critical load is a considerable amount and the influence of the body forces of the plate and the ribs on the critical load of the stiffened plate is discussed here. In this note (following Timoshenko), the extensional deformation of the middle surface during buckling is neglected, which greatly simplifies the analysis. Although it leads to an under-estimation of the critical load (of the order of 10 per cent at most) it is not likely to influence the general conclusions. Strain energy method of analysis is used.","PeriodicalId":50846,"journal":{"name":"Aeronautical Journal","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"1955-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/S0368393100118747","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56962900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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