Estimating sea vessel’s braking distance influenced by wind and waves

The article considers the methods of estimating the wind effect on the braking characteristics and the vessel behavior under the wind and waves. A model with regular sea waves is illustrated, in which the wave ordinate changes according to the sine law. It is stated that in reality the wave ordinate varies approximately by the sum of an infinite number of harmonics, the so-called irregular excitation. There are given differential equations of wind effect on the inertial-braking characteristics, of braking, of calculating the braking distance, etc. There has been estimated the braking distance of the motor vessel “Yuri Maksarev” with four rows of containers in headwinds up to 15 m/s. The wind has been proved to influence greatly the length of the braking distances, with the length of braking distance becoming two cables less after three minutes. The diagram of the apparent wind influencing the ship is presented. The apparent wind impacts the vessel’s hull above the waterline. Drift angle estimating is performed using a programmable calculator, a table or a nomogram. There is proposed a nomogram that greatly simplifies preliminary calculating and reduces the time costs. There have been compiled the programs for calculating the wind drift angle and constructing the corresponding nomogram in the application Microsoft Excel 97 using the programming language Visual Basic. The developed programs allow automating the most frequently performed calculations for determining the angle of wind drift, for which little time is needed during the maneuvering process. The arrangement of the diagram on the paper is illustrated, the process of building a nomogram is presented in stages. A case of the calculated nomogram for the motor ship “Yuri Maksarev” has been presented.

Some Somos’s theta function identities of level 6 and application to partitions

M. Somos discovered around 6200 theta function identities using PARI/GP scripts without offering the proof. He runs PARI/GP scripts and it works as a sophisticated programmable calculator. These identities highly resemble those of Ramanujan?s identities. Here we prove a few theta-function identities of level 6 discovered by Somos by using modular equations of degree 3 given by Ramanujan and further we extract some interesting combinatorial interpretations of colored partitions.

Simplified approach to DFT computation for nonprogrammable scientific calculators

Fourier analysis is an important tool used as it is or it’s different variants in many fields of sciences and engineering. It’s importance is due to it’s simplicity with which it expands a given function in terms of circular or complex exponents. Further it is quite versatile to handle many functions of practical interest, specifically, the functions with several mathematical disabilities that are hard to be handled with tools like Taylor series. Discrete Fourier Transform (DFT) is a form of Fourier analysis where the discrete function and it’s transform are both of finite length. This processing requires lot many computations. Here in this work a simplified and non programmable calculator based scheme is presented with which one can easily determine the DFT of the given function by feeding in the DFT equation once and a few presses of the calculator keys. DOI: http://dx.doi.org/10.3126/bibechana.v12i0.11681BIBECHANA 12 (2015) 13-19

Technology Tips: Don't Curve It, Convert It! Translating Assessment Score Languages with a Graphing Calculator

In this month's tip, Jay Walgren, a physics teacher from Vernon Hills High School in Vernon Hills, Illinois, introduces his method of using a programmable calculator to convert grades that are based on learning objectives and mastery of content to a standard grading scale. Although he could use a spreadsheet for this practice, Walgren prefers the convenience and portability of a programmable calculator.

The Postage–Stamp Problem, Number Theory, and the Programmable Calculator

The “postage-stamp problem” is a classic question in the area of Diophantine equations. Students can explore this rich and accessible problem to deepen their understanding of linear equations.