Analogues between 2D Linear Equations and Great Circle Sailing

Tseng, Wei-Kuo; Chang, Wei-Jie

doi:10.1017/s0373463313000532

Cited by 14 publications

(7 citation statements)

References 7 publications

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“…In a next step, the position where the track of the probed air mass (assuming to arrive from the average wind direction) intersects the (past or future) track of the vessel candidate (see Fig. 2) was calculated by means of trigonometric navigational equations (Veness, 2019;Tseng and Chang, 2014;Eqs. (S2) to (S12)).…”

Section: Identification and Determination Of Ship Emission Plumes Thmentioning

confidence: 99%

Influence of vessel characteristics and atmospheric processes on the gas and particle phase of ship emission plumes: In-situ measurements in the Mediterranean Sea and around the Arabian Peninsula

Celik¹,

Drewnick²,

Fachinger³

et al. 2019

Preprint

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Abstract. 252 emission plumes of ships operating in the Mediterranean Sea and around the Arabian Peninsula were investigated using a comprehensive dataset of gas and submicron particle phase properties measured during the two-month shipborne AQABA field campaign in summer 2017. The post-measurement identification of the corresponding ship emission events in the measured data included the determination of the plume sources (up to 38&#8201;km away) as well as of the plume ages (up to 115&#8201;min) and was based on commercially available historical records of the Automatic Identification System. The dispersion lifetime of chemically inert CO2 in the ship emission plumes was determined as (70&#8201;&#177;&#8201;15)&#8201;min, resulting in levels indistinguishable from the marine background after (260&#8201;&#177;&#8201;60)&#8201;min. Emission factors (EFs) as quantities that are independent of plume dilution were calculated and used for the investigation of influences on ship emission plumes caused by ship characteristics and the combustion process as well as by atmospheric processes during the early stage of exhaust release and during plume aging. Combustion efficiency and therefore emission factors of black carbon and NOx were identified to depend mostly on the vessel speed and gross tonnage. Moreover, larger ships, associated with higher engine power were found to use fuel with higher sulfur content and have higher gas phase SO2, particulate sulfate, particulate organics and particulate matter EFs. Despite the independence of EFs on dilution, significant influence of the ambient wind speed on the particle number and mass EFs was observed that can be traced back to enhanced particle coagulation in case of slower dilution and suppressed vapor condensation on particles in case of faster dilution of the emission plume. Atmospheric reactions and processes in ship emission plumes were investigated that include NOx and O3 chemistry, gas-to-particle conversion of NOx and SO2 and the neutralization of acids in the particle phase through the uptake of ambient gas phase ammonia, the latter two of which cause the inorganic particulate content to increase and the organic fraction to decrease with increasing plume age. The results enable identification of the most important influences on (or processes in) ship emission plumes and to describe those quantitatively by parameterizations, which could be used for further refinement of atmospheric models.

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Section: Identification and Determination Of Ship Emission Plumes Thmentioning

confidence: 99%

Influence of vessel characteristics and atmospheric processes on the gas and particle phase of ship emission plumes: In-situ measurements in the Mediterranean Sea and around the Arabian Peninsula

Celik¹,

Drewnick²,

Fachinger³

et al. 2019

Preprint

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show abstract

“…In contrast, using the formulae of the divided spherical triangle can directly yield waypoints without calculating the initial great circle course angle ( C ). Some great circle track studies have also presented this type of method (Holm, 1972; Miller et al, 1991; Tseng and Chang, 2014).…”

Section: Applying the Formulae Of The Combined Spherical Trianglesmentioning

confidence: 99%

New Formulae for Combined Spherical Triangles

et al. 2018

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Spherical trigonometry formulae are widely adopted to solve various navigation problems. However, these formulae only express the relationships between the sides and angles of a single spherical triangle. In fact, many problems may involve different types of spherical shapes. If we can develop the different formulae for specific spherical shapes, it will help us solve these problems directly. Thus, we propose two types of formulae for combined spherical triangles. The first set are the formulae of the divided spherical triangle, and the second set are the formulae of the spherical quadrilateral. By applying the formulae of the divided spherical triangle, waypoints on a great circle track can be obtained directly without finding the initial great circle course angle in advance. By applying the formulae of the spherical quadrilateral, the astronomical vessel position can be yielded directly from two celestial bodies, and the calculation process concept is easier to comprehend. The formulae we propose can not only be directly used to solve corresponding problems, but also expand the spherical trigonometry research field.

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“…Navigators usually adopt Napier's rule or spherical triangle formulae to solve the GCS problems (Bowditch, 2002; Cutler, 2004; Royal Navy, 2008). To reduce the number of solution steps and to apply to more different conditions, the studies of GCS have mainly focused on formula derivation with different approaches, such as vector algebra methods (Chen et al, 2014; Chen, 2016), linear combination methods (Miller et al, 1991; Nastro and Tancredi, 2010; Tseng and Chang, 2014) and the rotation transformation method (Chen et al, 2015). In order to improve the accuracy and to comply with the WGS 84 geodetic datum, the Earth is regarded as a spheroid.…”

Section: Introductionmentioning

confidence: 99%

Evaluation and Execution of Great Elliptic Sailing

Hsu

Hsieh

2017

J. Navigation

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The Great Elliptic Sailing (GES), which can reduce sailing distance, is important to navigators. Whether a Great Ellipse (GE) is worth using depends on whether the distance saved is significant. Otherwise, the Rhumb Line (RL) is easier to steer. We propose a simple criterion to evaluate the difference in distance between the GE and the RL. The criterion is that the GE is worth using when the vertex lies between the departure and destination. In order to take the advantage of shorter distance, the GE is usually approximated as a series of waypoints. Unlike currently practised methods, we propose the Longitude Bisection Method (LBM) which determines waypoints with varying intervals. This approach can establish the appropriate number of waypoints to approximate the GE effectively. The proposed criterion and the LBM are demonstrated in practical examples.

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Analogues between 2D Linear Equations and Great Circle Sailing

Cited by 14 publications

References 7 publications

Influence of vessel characteristics and atmospheric processes on the gas and particle phase of ship emission plumes: In-situ measurements in the Mediterranean Sea and around the Arabian Peninsula

Influence of vessel characteristics and atmospheric processes on the gas and particle phase of ship emission plumes: In-situ measurements in the Mediterranean Sea and around the Arabian Peninsula

New Formulae for Combined Spherical Triangles

Evaluation and Execution of Great Elliptic Sailing

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