The Representation of Ship Hulls by Conformal Mapping Functions

1969 ◽  
Vol 13 (04) ◽  
pp. 284-298
Author(s):  
C. von Kerczek ◽  
E. O. Tuckk
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Design Procedure ◽  
Mapping Function ◽  
Polynomial Functions ◽  
Mapping Functions ◽  
Ship Hulls ◽  
Longitudinal Coordinate ◽  
Hydrodynamic Calculations ◽  
Hull Design

A method is described by which an arbitrary hull surface may be approximated by ananalytic function. The cross sections of the ship are represented by conformal mapping functions whose coefficients are polynomial functions of the longitudinal coordinate of the ship. Such a representation is intended to be used primarily for hydrodynamic calculations. However, the procedure used in generating the mapping function representation of the hull surface can, with some slight modifications, be used to freely form a hull surface. This could possibly be the basis of a mathematical hull design procedure.

Streamlines and Pressure Distribution on Arbitrary Ship Hulls at Zero Froude Number

1968 ◽  
Vol 12 (03) ◽  
pp. 231-236
Author(s):  
E. O. Tuck ◽  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Froude Number ◽  
Potential Flow ◽  
Hydrodynamic Pressure ◽  
Polynomial Functions ◽  
Forward Motion ◽  
Mapping Functions ◽  
Ship Hulls ◽  
Longitudinal Coordinate ◽  
Quantities Of Interest

A method is presented for computing the streamlines and the hydrodynamic pressure along the streamlines on a slender ship in steady forward motion at zero Froude number. The ship is represented by conformal mapping functions whose coefficients are polynomial functions of the longitudinal coordinate of the ship. The potential flow about the ship is obtained in terms of the coefficients of the surface equation of the ship and all flow quantities of interest are computed directly from these coefficients.

The Representation of Ship Hulls by Conformal Mapping Functions: Fractional Maps

1983 ◽  
Vol 27 (03) ◽  
pp. 158-159
Author(s):  
C. von Kerczek
Keyword(s):  
Conformal Mapping ◽  
Cross Sections ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Longitudinal Direction ◽  
Interpolation Scheme ◽  
Mapping Functions ◽  
Ship Hulls ◽  
The Cross ◽  
High Degree

The method for analytically representing ship hulls by conformal mapping functions of the cross sections and lengthwise polynomial interpolation of the mappings, which was developed by von Kerczek and Tuck [1], has found useful applications to ship hydrodynamics (see references [2] and [3]) as well as ship design [4]. In both such applications, however, there have been two major criticisms of this type of representation of the underwater portion of the ship hull. The first criticism concerned the occurrence of undesirable waviness in the longitudinal direction of the cross sections of the ship. This waviness is due to fitting high-degree polynomials to very slowly varying data. This defect of the surface representation can be removed easily by abandoning the polynomial interpolation and substituting some form of spline interpolation. It has been found that interpolation by simple Hermite cubic splines works very well. Such modifications of the lengthwise interpolation scheme are well known and need no elaboration.

scholarly journals Evaluation of Wet Mapping Functions Used in Modeling Tropospheric Propagation Delay Effect on GPS Measurements

2017 ◽  
Vol 11 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Sobhy Abdel-Monam Younes
Keyword(s):  
A Priori ◽  
Mapping Function ◽  
Propagation Delay ◽  
Radiosonde Data ◽  
Tropospheric Delay ◽  
Delay Effect ◽  
Gps Measurements ◽  
Mapping Functions ◽  
Significant Bias ◽  
Mapping Techniques

Background:The author compares several methods to map the a priori wet tropospheric delay of GNSS signals in Egypt from the zenith direction to lower elevations.Methods and Materials:The author compared the following mapping techniques against ray-traced delays computed for radiosonde profiles under the assumption of spherical symmetry: Saastamoinen, Hopfield, Black, Chao, Ifadis, Herring, Niell, Moffett, Black and Eisner and UNBabc mapping functions. Radiosonde data were computed from radiosonde stations at the Egyptian stations; in the south of Egypt, near the Mediterranean Sea, and near the Red Sea over a period of 5 years (2000-2005), most of the stations launched radiosonde twice daily, every day of the year. Moreover, data is received from the Egyptian Meteorology Authority.Results and Conclusion:The results indicate that currently, the saastamoinen mapping function should be used for all geodetic applications in Egypt, and if necessary, the Chao and Moffett mapping functions can serve as an acceptable replacement without introducing a significant bias into the station position.

scholarly journals Sensitivity of GNSS tropospheric gradients to processing options

2019 ◽  
Vol 37 (3) ◽  
pp. 429-446 ◽  
Author(s):  
Michal Kačmařík ◽  
Jan Douša ◽  
Florian Zus ◽  
Pavel Václavovic ◽  
Kyriakos Balidakis ◽  
...  
Keyword(s):  
Real Time ◽  
Elevation Angle ◽  
Mapping Function ◽  
Global Navigation Satellite Systems ◽  
Gradient Estimates ◽  
Post Processing ◽  
Data Set ◽  
Mapping Functions ◽  
Gradient Mapping

Abstract. An analysis of processing settings impacts on estimated tropospheric gradients is presented. The study is based on the benchmark data set collected within the COST GNSS4SWEC action with observations from 430 Global Navigation Satellite Systems (GNSS) reference stations in central Europe for May and June 2013. Tropospheric gradients were estimated in eight different variants of GNSS data processing using precise point positioning (PPP) with the G-Nut/Tefnut software. The impacts of the gradient mapping function, elevation cut-off angle, GNSS constellation, observation elevation-dependent weighting and real-time versus post-processing mode were assessed by comparing the variants by each to other and by evaluating them with respect to tropospheric gradients derived from two numerical weather models (NWMs). Tropospheric gradients estimated in post-processing GNSS solutions using final products were in good agreement with NWM outputs. The quality of high-resolution gradients estimated in (near-)real-time PPP analysis still remains a challenging task due to the quality of the real-time orbit and clock corrections. Comparisons of GNSS and NWM gradients suggest the 3∘ elevation angle cut-off and GPS+GLONASS constellation for obtaining optimal gradient estimates provided precise models for antenna-phase centre offsets and variations, and tropospheric mapping functions are applied for low-elevation observations. Finally, systematic errors can affect the gradient components solely due to the use of different gradient mapping functions, and still depending on observation elevation-dependent weighting. A latitudinal tilting of the troposphere in a global scale causes a systematic difference of up to 0.3 mm in the north-gradient component, while large local gradients, usually pointing in a direction of increasing humidity, can cause differences of up to 1.0 mm (or even more in extreme cases) in any component depending on the actual direction of the gradient. Although the Bar-Sever gradient mapping function provided slightly better results in some aspects, it is not possible to give any strong recommendation on the gradient mapping function selection.

Reducing Damage to Low-Volume Roads by Using Trucks with Reduced Tire Pressures

1997 ◽  
Vol 1589 (1) ◽  
pp. 9-18 ◽  
Author(s):  
Maureen A. Kestler ◽  
Richard L. Berg ◽  
Thomas L. Moore
Keyword(s):  
Cross Sections ◽  
Design Procedure ◽  
Army Corps ◽  
Army Corps Of Engineers ◽  
Tire Pressure ◽  
Low Volume Roads ◽  
Minimal Damage ◽  
Allowable Load ◽  
Low Volume ◽  
Pavement Damage

Heavy-volume highways in seasonal frost areas are designed to resist the effects of spring thaw. However, timber access roads, county roads, and other low-volume roads with thin bituminous surfaces can be quite susceptible to pavement damage during midwinter- and spring-thaw periods. To reduce damage to low-volume roads, towns, cities, and states typically either post reductions in allowable load or completely prohibit hauling during damage-susceptible periods. Associated economic impact can be significant. To evaluate the effects of tire pressure on cumulative road damage, a mechanistic pavement design procedure developed by the U.S. Army Corps of Engineers for use in seasonal frost areas was used on a matrix of tire pressures, low-volume pavement cross sections, and environmental conditions. A series of computer simulations showed ( a) trucks operating with conventional tire pressures can cause excessive damage, particularly in the form of cracking, to low-volume roads with thin bituminous surfaces during relatively short thaw periods; ( b) pavement damage could be reduced substantially by restricting hauling to trucks operating with reduced tire pressures; and ( c) there are “threshold” tire pressures under which only minimal damage occurs, even during critical spring thaw. These results could influence guidelines for hauling restrictions and, in turn, associated economics.

Simplified Hydrodynamic Design Procedure of a Submerged Floating Tube Bridge Across the Digernessund of Norway

2017 ◽  
Author(s):  
Xu Xiang ◽  
Arianna Minoretti ◽  
Mathias Egeland Eidem ◽  
Kjell Håvard Belsvik ◽  
Tale Egeberg Aasland ◽  
...  
Keyword(s):  
Cross Sections ◽  
Present Model ◽  
Design Procedure ◽  
Analysis Procedure ◽  
Hydrodynamic Coefficients ◽  
Bending Moments ◽  
Vortex Induced Vibrations ◽  
Simplified Method ◽  
Hydrodynamics Coefficients ◽  
The Given

The paper will look into the hydrodynamic loads and responses on the proposed Submerged Floating Tube Bridge (SFTB) through the Digernessund by the Norwegian Public Roads Administration (Statens vegvesen, NPRA). The aim is to show how different hydrodynamics aspects during the prelimiary design can be simply addressed under the given environmental conditions. Different SFTB systems are introduced as the first step. A simplified method based on modal analysis is introduced and implemented for evaluation of the motions and stress, bending moments along the bridge. Firstly, a 2D Boundary Element Method (BEM) solver is developed and verified, which is further used for solving the hydrodynamics coefficients of different bridge cross sections. The 3D hydrodynamic coefficients of pontoons are solved by the commercial software AQWA. The analysis procedure of the simplified method for the global SFTB responses is presented. The Eigen periods of the Bjørnefjord SFTB is re-calculated by the present model as a first validation of the implementation. The loads and responses of the bridge under given wave conditions are then estimated. The evaluation of the possibility of vortex induced vibrations of the current SFTB design is given.

Single station GNSS tomography as a replacement of mapping function for high precision troposphere radio wave delay correction

2020 ◽  
Author(s):  
Feng Peng ◽  
Li Fei ◽  
Jean-Pierre Barriot ◽  
Yan Jianguo ◽  
Zhang Fangzhao ◽  
...  
Keyword(s):  
Radio Wave ◽  
Time Resolution ◽  
Mapping Function ◽  
Satellite Tracking ◽  
Tropospheric Delay ◽  
High Time Resolution ◽  
Signal Delay ◽  
Mapping Functions ◽  
Single Station ◽  
Delay Correction

<p>With its relatively low cost, high availability and continuous observation ability, zenith delays from GPS combined with mapping function have been used in satellite tracking media calibration since early 2000. The mapping functions are used to model elevation dependency of radio wave delays in the troposphere. It assumes that the ratio of signal slant delay over zenith delay is less variable w.r.t time and location than the signal delay itself. Thus the parameters of signal delay elevation dependency can be modeled and unknowns of the tropospheric delay were reduced. However, the parameterization comes with a loss of accuracy. For example, the state-of-art VMF series mapping functions have a time resolution of 6 hours, which means variations that took place in less than 6 hours are smoothed. Nowadays GPS has evolved to multi-constellation GNSS with many more satellites in visibility. Here we propose a single station GNSS tomography algorithm for radio wave delay correction by directly using slant delays. This algorithm can extract the information of the troposphere variations in all the signal directions of GNSS observations with high time resolution. Thus it will be beneficial to the radio wave delay correction of precise satellite tracking. We assess the performance of this algorithm with a collocated water vapor radiometer.</p>

Design of cold-formed compression web members with periodically varying section properties

2007 ◽  
Vol 34 (2) ◽  
pp. 253-265
Author(s):  
Serge Parent ◽  
Joseph J Pote ◽  
Kenneth W Neale
Keyword(s):  
Cross Sections ◽  
Design Method ◽  
Design Procedure ◽  
Effective Length ◽  
Cross Sectional ◽  
The North ◽  
Stub Column ◽  
Flexural Torsional Buckling ◽  
Open Face

In this paper, a design procedure for cold-formed channels periodically closed on their open face and utilized as joist web members is detailed. The design method for periodically closed sections is based on the representation of the cross-sectional properties using Fourier series introduced in Timoshenko quotients for the determination of the buckling loads about each of the three member axes. Once those loads are computed, they are used in the current framework of the North American Specification for the design of cold-formed structures with appropriate effective length coefficients. The proposed design methodology is compared with test results obtained from 36 stub column samples and 21 full-scale joist specimens, also presented in this paper.Key words: cold-formed struts, periodically varying cross sections, steel joists, flexural–torsional buckling, effective length coefficients.

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