A Teaching Experiment in Modelling through Scale Reduction Methods： A Bridge to Later Trigonometric Methods

In a teaching experiment, Japanese Grade 9 students investigated how to measure the height of an aerial balloon using different models involving angles and distances, and also to evaluate the models they developed. As novices to mathematical modelling, they needed to decide which of several possible models were both valid and practicable, and the errors in measurement that are likely to arise. Opportunities to construct and use paper models, as scale reductions of the real situation, and discussing their results in small groups were effective in moving forward the thinking of many students on the dimensions mentioned above. While students were less able to identify different sources of errors, many came to appreciate the need to learn trigonometric techniques that are more suitable in dealing with problems of this kind.

Modeling Technology in Finite Element Analysis of Electrostatic Proximity Fuze Problem

In order to analyze the electrostatic field concerned with electrostatic proximity fuze problem using the available finite analysis software package, the technology to model the problem with a scale reduction object and boundary was presented. The boundary is determined by the maximum distance the sensor can detect. The object model is obtained by multiplying the terms in Poisson's equation with a scale reduction factor and the real value can be reconstructed with the same reverse process after software calculation. Using the finite element analysis program, the simulation value is close to the theoretical value with a little error. The boundary determination and scale reduction method is suitable to modeling the irregular electrostatic field around air targets, such as airplane, missile and so on, which is based on commonly used personal computer (PC). The technology reduces the calculation and storage cost greatly.

Water-trapping and drag-reduction effects of fish Ctenopharyngodon idellus scales and their simulations

In the last decades, surface drag reduction has been re-emphasized because of its practical values in engineering applications,including vehicles, aircrafts, ships, and fuel pipelines. The bionic study of drag reduction has been attracting scholars' attentions. Here, it was determined that the delicate microstructures on the scales of the fish Ctenopharyngodon idellus exhibit remarkable drag-reduction effect. In addition, the underlying drag-reduction mechanism was carefully investigated. First,exceptional morphologies and structures of the scales were observed and measured using a scanning electron microscope and3-dimensional(3D) microscope. Then, based on the acquired data, optimized 3D models were created. Next, the mechanism of the water-trapping effect of these structures was analyzed through numerical simulations and theoretical calculations. It was determined that there are many microcrescent units with certain distributions on its surface. In fact, these crescents are effective in generating the "water-trapping" effect and forming a fluid-lubrication film, thus reducing the skin friction drag effectively.Contrasting to a smooth surface, the dynamics finite-element analysis indicated that the maximum drag-reduction rate of a bionic surface is 3.014% at 0.66 m/s flow rate. This study can be used as a reference for an in-depth analysis on the bionic drag reduction of boats, underwater vehicles, and so forth.