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The proof of the validity of the Reynolds law of similitude for the surface resistance of planes has been developed with an accuracy hitherto unattained and for a large range of lengths and speeds. It has been shown that, in addition to the form resistance, the resistance of the longitudinal edges must be taken into account.
Model design for simulation of space capsule landing on soils using similitude law
This presentation afforded the opportunity to look back in the literature to discover scaling effects in nature that might be relevant to composites. Numerous examples were found in nature's approaches to wood, teeth, horns, leaves, eggs, feathers, etc. Nature transmits tensile forces rigidly with cohesive bonds, while dealing with compression forces usually through noncompressible hydraulics. The optimum design scaling approaches for aircraft were also reviewed for comparison with similitude laws. Finally, some historical evidence for the use of Weibull scaling in composites was reviewed.
This paper deals with the development and use of scaled-down models in order to predict the structural behavior of large prototypes. The concept is fully described and examples are presented which demonstrate its applicability to beam-plates, plates and cylindrical shells of laminated construction. The concept is based on the use of field equations, which govern the response behavior of both the small model as well as the large prototype. The conditions under which the experimental data of a small model can be used to predict the behavior of a large prototype are called scaling laws or similarity conditions and the term that best describes the process is structural similitude. Moreover, since the term scaling is used to describe the effect of size on strength characteristics of materials, a discussion is included which should clarify the difference between "scaling law" and "size effect". Finally, a historical review of all published work in the broad area of structural similitude is presented for completeness.
Aircraft and spacecraft comprise the class of aerospace structures that require efficiency and wisdom in design, sophistication and accuracy in analysis and numerous and careful experimental evaluations of components and prototype, in order to achieve the necessary system reliability, performance and safety. Preliminary and/or concept design entails the assemblage of system mission requirements, system expected performance and identification of components and their connections as well as of manufacturing and system assembly techniques. This is accomplished through experience based on previous similar designs, and through the possible use of models to simulate the entire system characteristics. Detail design is heavily dependent on information and concepts derived from the previous steps. This information identifies critical design areas which need sophisticated analyses, and design and redesign procedures to achieve the expected component performance. This step may require several independent analysis models, which, in many instances, require component testing. The last step in the design process, before going to production, is the verification of the design. This step necessitates the production of large components and prototypes in order to test component and system analytical predictions and verify strength and performance requirements under the worst loading conditions that the system is expected to encounter in service. Clearly then, full-scale testing is in many cases necessary and always very expensive. In the aircraft industry, in addition to full-scale tests, certification and safety necessitate large component static and dynamic testing. Such tests are extremely difficult, time consuming and definitely absolutely necessary. Clearly, one should not expect that prototype testing will be totally eliminated in the aircraft industry. It is hoped, though, that we can reduce full-scale testing to a minimum. Full-scale large component testing is necessary in other industries as well, Ship building, automobile and railway car construction all rely heavily on testing. Regardless of the application, a scaled-down (by a large factor) model (scale model) which closely represents the structural behavior of the full-scale system (prototype) can prove to be an extremely beneficial tool. This possible development must be based on the existence of certain structural parameters that control the behavior of a structural system when acted upon by static and/or dynamic loads. If such structural parameters exist, a scaled-down replica can be built, which will duplicate the response of the full-scale system. The two systems are then said to be structurally similar. The term, then, that best describes this similarity is structural similitude. Similarity of systems requires that the relevant system parameters be identical and these systems be governed by a unique set of characteristic equations. Thus, if a relation or equation of variables is written for a system, it is valid for all systems which are similar to it. Each variable in a model is proportional to the corresponding variable of the prototype. This ratio, which plays an essential role in predicting the relationship between the model and its prototype, is called the scale factor.
The establishment of similarity conditions between two structural systems is discussed. Similarity conditions provide the relationship between a scale model and its prototype and can be used to predict the behavior of the prototype by extrapolating the experimental data of the corresponding small-scale model. Since satisfying all the similarity conditions simultaneously is difficult or even impossible, distorted models with partial similarity (with at least one similarity condition relaxed) are more practical. Establishing similarity conditions based on both dimensional analysis and direct use of governing equations is discussed, and the possibility of designing distorted models is investigated. The method is demonstrated through analysis of the cylindrical bending of orthotropic laminated beam-plates subjected to transverse line loads.
The establishment of similarity conditions between two structural systems is discussed. Similarity conditions provide the relationship between a scale model and its prototype and can be used to predict the behavior of the prototype by extrapolating the experimental data of the corresponding small-scale model. Since satisfying all the similarity conditions simultaneously is difficult or even impossible, distorted models with partial similarity (with at least one similarity condition relaxed) are more practical. Establishing similarity conditions based on both dimensional analysis and direct use of governing equations is discussed, and the possibility of designing distorted models is investigated. The method is demonstrated through analysis of the cylindrical bending of orthotropic laminated beam-plates subjected to transverse line loads.
The laws of comparison of dynamically similar fluid motions are derived by three different methods based on the same principle and yielding the same or equivalent formulas. This report outlines the three current methods of comparing dynamically similar motions, more especially of fluids, initiated respectively by Newton, Stokes (or Helmholtz), and Rayleigh. These three methods, viz., the integral, the differential, and the dimensional, are enough alike to be studied profitably together. They are treated in succession then compared. (author)
Similarity laws for bodies maximizing lift-to-drag ratio at hypersonic speeds, considering longitudinal and transversal contours
Experiments in thermal similitude - thermal scale modeling
Geometries, construction, materials, and other criteria derived for thermal models
The feasibility of using scale model testing for predicting full-scale behavior of composite beams loaded in tension and flexure was investigated. Classical laws of similitude were applied to fabricate and test replica model beams to identify scaling effects in the load response, strength, and mode of failure. Experiments were conducted using graphite-epoxy composite beams having different laminate stacking sequences and a range of scaled sizes. Results indicated that the elastic response of scaled composite beams was independent of specimen size. However, a significant scale effect in strength was observed. In addition, a transition in failure mode was observed among scaled beams of certain laminate stacking sequences. Weibull statistical and fracture mechanics based models were applied to predict the strength scale effect since standard failure criteria cannot account for the influence of absolute specimen size in failure.
The feasibility of using scale model testing for predicting the full-scale behavior of flat composite coupons loaded in tension and beam-columns loaded in flexure is examined. Classical laws of similitude are applied to fabricate and test replica model specimens to identify scaling effects in the load response, strength, and mode of failure. Experiments were performed on graphite-epoxy composite specimens having different laminate stacking sequences and a range of scaled sizes. From the experiments it was deduced that the elastic response of scaled composite specimens was independent of size. However, a significant scale effect in strength was observed. In addition, a transition in failure mode was observed among scaled specimens of certain laminate stacking sequences. A Weibull statistical model and a fracture mechanics based model were applied to predict the strength scale effect since standard failure criteria cannot account for the influence of absolute specimen size on strength.
This report presents the attempt to develop a law which will permit the use of results obtained on small models in a tunnel for the calculation of full-sized airplanes, or if it exists, a law of similitude relating air forces on a full-sized plane to those on a reduced scale model.
The plans for the wind tunnel at Issey-les-Moulineaux are discussed in relation to concerns about the Law of Similitude and propeller speed.
The problems of using models in planing tests are addressed. If one passes from the model to a hull of linear dimensions n times greater, the speeds are connected by the law of mechanical similitude. The normal forces given by the hydrodynamic equations (perfect fluid) also follow the law of dynamic similitude (Reech's method) and are multiplied by n(exp 3). A series of tests were performed and the actual results were compared to theoretical results.
Dimensional analysis, and similitude and scaling laws for structural dynamics model testing of spacecraft dynamic stability
Ranges of validity for the continuum-beam model, the length-scale effects and continuum assumptions are analyzed in the framework of scaling analysis of NT structure. Two coupled criteria for the applicability of the continuum model are presented. Scaling analysis of NT buckling and geometric parameters (e.g., diameter and length) is carried out to determine the key non-dimensional parameters that control the buckling strains and modes of NT buckling. A model applicability map, which represents two classes of NTs, is constructed in the space of non-dimensional parameters. In an analogy with continuum mechanics, a mechanical law of geometric similitude is presented for two classes of beam-like NTs having different geometries. Expressions for the critical buckling loads and strains are tailored for the distinct groups of NTs and compared with the data provided by the molecular dynamics simulations. Implications for molecular dynamics simulations and the NT-based scanning probes are discussed.