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    <title>Transport Research International Documentation (TRID)</title>
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    <copyright>Copyright © 2026. National Academy of Sciences. All rights reserved.</copyright>
    <docs>http://blogs.law.harvard.edu/tech/rss</docs>
    <managingEditor>tris-trb@nas.edu (Bill McLeod)</managingEditor>
    <webMaster>tris-trb@nas.edu (Bill McLeod)</webMaster>
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      <title>Transport Research International Documentation (TRID)</title>
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      <link>https://trid.trb.org/</link>
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    <item>
      <title>Use of Prolate Spheroidal Wave Functions in the Time Domain First Order Reliability Method</title>
      <link>https://trid.trb.org/View/1974231</link>
      <description><![CDATA[The paper consider the use of prolate spheroidal wave functions as basic orthogonal functions in the wave description in the time domain first order reliability method applied to wave response statistics in stationary sea states. Intact stability of a ship in beam sea is considered as an example and the results for the most probable response and the associated statistics are evaluated and compared to the usual procedure using trigonometric functions]]></description>
      <pubDate>Mon, 20 May 2024 14:02:21 GMT</pubDate>
      <guid>https://trid.trb.org/View/1974231</guid>
    </item>
    <item>
      <title>A new formulation for dynamics finite element</title>
      <link>https://trid.trb.org/View/1814562</link>
      <description><![CDATA[The subject of this paper is to present a new family of dynamic finite element, which has a formulation based on a simple expansion of trigonometric functions such as sine and cosine. This formulation allows to generating unconditionally stable elements and to excluding both spurious wave reflection and evanescent effect. Also, it is shown how to elevate the error order associated with the dynamic finite element. The finite elements analyzed here are the rod and beam (according to Timoshenko beam theory) elements. These types of elements have gained even more importance in the automotive industry engineering due to its low computational cost. Today, the structural conception of a vehicle is resumed to a wireframe modeling, which accelerates considerably the optimization process by using morphing operations over the geometry. The new formulation proposed in this work, for the beam element specifically, has lower computation cost then the classic formulation, which is based on energy criteria (the minimum potential theory) leading to a consistent (full) mass matrix.]]></description>
      <pubDate>Thu, 29 Sep 2022 16:58:21 GMT</pubDate>
      <guid>https://trid.trb.org/View/1814562</guid>
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    <item>
      <title>Using trigonometric functions and E.D.R. data to solve velocity vector triangles</title>
      <link>https://trid.trb.org/View/1957134</link>
      <description><![CDATA[The Law of Conservation of Linear Momentum is one of the most used methods of reconstructing of motor vehicle crashes. However, of evidence at the scene is lacking and the reconstructionists is unable to discover necessary pieces of information for the vehicles, they may abandon speed analysis at the start. Data from the data event recorders (EDRs) should still be collected to gain a different perspective. Velocity vectors from each vehicle, the unique triangle, can be constructed to represent the whole picture of the collision. This article demonstrates the use of trigonometric functions to solve velocity vector triangles.]]></description>
      <pubDate>Wed, 25 May 2022 09:40:10 GMT</pubDate>
      <guid>https://trid.trb.org/View/1957134</guid>
    </item>
    <item>
      <title>A novel aerodynamic modeling method for an axisymmetric missile with tiny units</title>
      <link>https://trid.trb.org/View/1713243</link>
      <description><![CDATA[This article investigates the aerodynamic modeling problem of an axisymmetric missile with tiny units. Three aerodynamic force models for an axisymmetric air-to-air standard model missile are established. The mathematical model of trigonometric series model, response surface model, and kriging model for roll moment coefficients are developed. An error reduction approach is presented to determine the configuration of the proposed aerodynamic force models. In this approach, the minimum residual sum of the square criterion is acquired to determine the desired sample data point. Moreover, the modeling accuracy of the three models is further discussed. Finally, a model missile with four control surfaces and a cable cover was applied to test the proposed modeling approach in a transonic wind tunnel named as CARDC FL-24.]]></description>
      <pubDate>Fri, 21 May 2021 10:54:11 GMT</pubDate>
      <guid>https://trid.trb.org/View/1713243</guid>
    </item>
    <item>
      <title>Derivation of Formulas in Spherical Trigonometry Based on Rotation Matrix</title>
      <link>https://trid.trb.org/View/1672544</link>
      <description><![CDATA[The formulas of spherical triangle, which are widely used to solve various navigation problems, are the important basic knowledge of nautical mathematics. Because the sine rules and the cosine rules for the sides are the fundamental formulas to derive the other spherical triangle formulas, they are also called the genetic codes of the spherical triangle formulas. In the teaching process, teachers usually use the geometric method to derive and prove these fundamental formulas. However, the derivation of geometric methods is complicated and difficult to understand. To improve the teaching process, this paper proposes the three-dimensional rotation method, which is based on conversion of two cartesian coordinate frames using the rotation matrices. This method can easily and simultaneously derive the sine rules, the cosine rules for the sides, and the five-part formulas (I), and is also helpful to solve different kinds of spherical navigation problems.]]></description>
      <pubDate>Mon, 27 Jan 2020 09:23:10 GMT</pubDate>
      <guid>https://trid.trb.org/View/1672544</guid>
    </item>
    <item>
      <title>Steady-state response of a curved beam on a viscously damped foundation subjected to a sequence of moving loads</title>
      <link>https://trid.trb.org/View/1351936</link>
      <description><![CDATA[In this paper, an analytical solution to the steady-state response of a curved beam resting on a viscously damped foundation and subjected to a single or sequence of moving loads is presented. Trigonometric functions are employed as the trial functions in approximating the displacement of the curved beam. The accuracy of the solution is gauged through comparison against available analytical results in the literature. To further examine the accuracy of the proposed analytical method, a computational study of the problem was carried out using the moving element method based on piecewise straight beam elements. Excellent agreement is found between all these results.]]></description>
      <pubDate>Tue, 28 Apr 2015 15:08:10 GMT</pubDate>
      <guid>https://trid.trb.org/View/1351936</guid>
    </item>
    <item>
      <title>An Evaluation Model Based on Grey Trigonometry Whitening Weight Function for Logistic Center</title>
      <link>https://trid.trb.org/View/1270609</link>
      <description><![CDATA[In order to locate logistic centers and improve the scientific evaluation of logistic centers, the connotation and extension of the logistic center was analyzed. Analysis results show that the logistic center is a grey system. According to the classical grey theory, the grey number was adopted to express the evaluation indices and clustering thresholds. Furthermore, a grey number formula was presented and a clustering model was built based on the trigonometry whitening weight function. Then, the possibility of comparing interval number was introduced into the grey number comparison. At last, an empirical study was conducted to prove the effectiveness and reasonableness of the presented model.]]></description>
      <pubDate>Sat, 21 Jun 2014 16:42:12 GMT</pubDate>
      <guid>https://trid.trb.org/View/1270609</guid>
    </item>
    <item>
      <title>The generalization of the quadrantal zenith angle counting rule</title>
      <link>https://trid.trb.org/View/1308901</link>
      <description><![CDATA[Calculating the azimuth of a star can be achieved by using spherical trigonometry formulas "sinZC", "ctgZS" or with A.B.C. tables using D.H-90 tables or Norrie’s Nautical Tables. The quadrantal zenith angle counting rule can be achieved only for the positive heights of a star. In this paper the authors developed the generalized quadrantal zenith angle counting rule for the cases in which the heights are negative.]]></description>
      <pubDate>Thu, 29 May 2014 17:19:51 GMT</pubDate>
      <guid>https://trid.trb.org/View/1308901</guid>
    </item>
    <item>
      <title>Approximation Models of Orthodromic Navigation</title>
      <link>https://trid.trb.org/View/1264030</link>
      <description><![CDATA[The paper deals with two different approaches to orthodromic navigation approximation, the secant method and the tangent method. Two ways of determination of orthodromic interposition coordinates will be presented with the secant method. In the second, tangent method unit change of orthodromic course will be used.]]></description>
      <pubDate>Mon, 28 Oct 2013 09:47:04 GMT</pubDate>
      <guid>https://trid.trb.org/View/1264030</guid>
    </item>
    <item>
      <title>Floating Car Data Based Travel Time Prediction with Lomb Periodogram</title>
      <link>https://trid.trb.org/View/906780</link>
      <description><![CDATA[Accurate travel time estimations are needed in many intelligent transportation systems (ITS) applications. This work describes a prediction and smoothing algorithm, based on the calculation of the power spectrum of the daily courses from floating car data (FCD). The so called Lomb Periodogram delivers the frequencies, which are needed to describe the daily course with a simple trigonometric function, the function parameters are approximated with the help of singular value decomposition fit (SVD-fit).]]></description>
      <pubDate>Tue, 15 Dec 2009 15:01:13 GMT</pubDate>
      <guid>https://trid.trb.org/View/906780</guid>
    </item>
    <item>
      <title>10-FOOT PORTABLE SUBTENSE BAR</title>
      <link>https://trid.trb.org/View/93478</link>
      <description><![CDATA[THE SUBTENSE BAR HAS LONG BEEN ACCEPTED THEORETICALLY AS A BASE FOR TRIANGULATION. WHEN USED WITH PRECISE SURVEY INSTRUMENTS, VERY ACCURATE RESULTS CAN BE OBTAINED. IN RECOGNITION OF THE POTENTIAL OF THIS DEVICE, EUROPEANS HAVE DESIGNED AND USED SUBTENSE BARS FOR MANY YEARS. THEIR SUBTENSE BARS, AT LEAST THOSE USED COMMERCIALLY IN THIS COUNTRY, ARE LIMITED TO A 2-METER LENGTH. IT WAS REASONED THAT COMPUTATIONS WOULD BE SIMPLIFIED AND THE RANGE OF OPERATIONS WOULD BE PROPORTIONATELY INCREASED IF THE BAR LENGTH COULD BE INCREASED TO 10 FT. TO RETAIN ITS VALUE FOR FIELD USE, 10 FT WAS ARBITRARILY SELECTED AS THE OPTIMUM FOR PORTABILITY AND WIND RESISTANCE. A WORKING MODEL HAS ANSWERED ALL THE REQUIREMENTS OF PORTABILITY AND ACCURACY. TO HOLD THE COST TO A MINIMUM, THE BASIC PARTS OF THE INSTRUMENT WERE CONSTRUCTED FROM OBSOLETE SURVEYING INSTRUMENTS. A GRADUATED CENTERING ROD WAS INCORPORATED SO THE EXACT HEIGHT OF INSTRUMENT COULD BE EASILY DETERMINED. ALTHOUGH THE PRIMARY PURPOSE OF THE SUBTENSE BAR IS FOR HORIZONTAL TRAVERSE, IT WAS REASONED THAT IT WOULD ALSO BE VALUABLE FOR TRIGONOMETRIC LEVELING. /AUTHOR/]]></description>
      <pubDate>Fri, 16 Sep 1994 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/93478</guid>
    </item>
    <item>
      <title>PROGRESS REPORT - STUDY OF EFFECT OF NEW VEHICLE WEIGHT LAWS ON STRUCTURES</title>
      <link>https://trid.trb.org/View/101849</link>
      <description><![CDATA[THE REPORT CONSISTS OF TWO VOLUMES. IN VOLUME I, THE DEVELOPMENT OF ORTHOTROPIC PLATE EQUATIONS IS PRESENTED AND APPLIED TO BRIDGE STRUCTURES. A TRIGONOMETRIC SERIES SOLUTION AND A FINITE DIFFERENCE SOLUTION OF THE PLATE EQUATIONS ARE COMPARED. AN ORTHOTROPIC BRIDGE DESIGN EXAMPLE IS GIVEN, USING TWO ALTERNATE METHODS, SLOPE DEFLECTION AND FINITE DIFFERENCE METHODS. AN EXTENSIVE BIBLIOGRAPHY ON ORTHOTROPIC PLATES, LOAD DISTRIBUTION ON BRIDGES, BRIDGE DECKS AND SLABS AND RELATED TOPICS IS GIVEN. VOLUME II CONTAINS THIRTY COMPUTER PROGRAMS AND THEIR DESCRIPTION.]]></description>
      <pubDate>Fri, 01 Jul 1994 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/101849</guid>
    </item>
    <item>
      <title>TRIGONOMETRIC CONSTRUCTION STAKING (TRIGSTAK)</title>
      <link>https://trid.trb.org/View/97119</link>
      <description><![CDATA[TRIGSTAK (ACRONYM FOR TRIGONOMETRIC STAKING) IS A METHOD OF CONSTRUCTION STAKING BY HORIZONTAL AND VERTICAL INTERSECTION LINES OF SIGHT FROM TWO OR MORE THEODOLITES STRATEGICALLY LOCATED AT THE CONSTRUCTION SITE OR ROAD ALIGNMENT. IT IS ACTUALLY AN EXTENSION OF THE AUTOMATION ALREADY ACHIEVED IN THE MAPPING AND DESIGN OF MOUNTAIN HIGHWAYS. PHOTOGRAMMETRIC DIGITIZING IS USED TO OBTAIN A MATHEMATICAL MODEL OF THE EARTH'S SURFACE OVER THE ENTIRE AREA OF THE PROPOSED CONSTRUCTION. THIS DIGITAL TERRAIN MODEL IS STORED IN A COMPUTER ALONG WITH THE HORIZONTAL AND VERTICAL GEOMETRY AND ROADBED TEMPLET OF THE PROPOSED HIGHWAY TO OBTAIN A MASS DIAGRAM AND AN EARTHWORK SUMMARY. INPUT OF THE TRIGSTAK PROGRAM ITSELF INCLUDES COORDINATES OF THE TRIANGULATION STATIONS, THE STATION (PLUSES) OF SLOPE STAKES TO BE SET FROM EACH TRIANGULATION STATION, AND VERTICAL CONTROL DATA. TRIGSTAK IS ALSO USED TO CHECK PHOTOGRAMMETRIC MAPS AND DIGITIZING USING THE TERRAIN DATA ONLY. /AUTHOR/]]></description>
      <pubDate>Thu, 26 May 1994 00:00:00 GMT</pubDate>
      <guid>https://trid.trb.org/View/97119</guid>
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