Rothe–Hagen identity: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>Giftlite
wlink
 
en>Yobot
m →‎References: WP:CHECKWIKI error fixes - Replaced endash with hyphen in sortkey per WP:MCSTJR using AWB (9100)
 
Line 1: Line 1:
Hi there, I am Alyson Boon even though it is not the name on my birth certification. To climb is something I really appreciate performing. Mississippi is the  clairvoyance, [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 www.010-5260-5333.com], only place I've been residing in but I will have to move in a year or two. Credit authorising is how she makes a residing.<br><br>Feel free to visit my web page ... online [http://modenpeople.co.kr/modn/qna/292291 accurate psychic predictions] chat - [http://Www.Familysurvivalgroup.com/easy-methods-planting-looking-backyard/ http://Www.Familysurvivalgroup.com/],
[[File:Lod Schema.png|thumb|right|Gross tonnage is calculated by measuring a ship's volume (from keel to funnel, to the outside of the hull framing) and applying a mathematical formula.]]
'''Gross tonnage''' (often abbreviated as '''GT''', '''G.T.''' or '''gt''') is a unitless index related to a ship's overall internal volume.  Gross tonnage is different from [[gross register tonnage]].<ref>The gross register ton (GRT) is a unit of volume defined as 100 cubic feet (about 2.83&nbsp;m³).</ref>  Neither gross tonnage nor gross register tonnage is a measure of the ship's displacement (mass) and should not be confused with terms such as [[deadweight tonnage]] or [[Displacement (ship)|displacement]].
 
Gross tonnage, along with [[net tonnage]], was defined by ''The International Convention on Tonnage Measurement of Ships, 1969'', adopted by the International Maritime Organization in 1969, and came into force on July 18, 1982.  These two measurements replaced gross register tonnage (GRT) and [[net register tonnage]] (NRT). Gross tonnage is calculated based on "the moulded volume of all enclosed spaces of the ship" and is used to determine things such as a ship's manning regulations, safety rules, registration fees, and port dues, whereas the older gross register tonnage is a measure of the volume of certain enclosed spaces.
 
==History==
The International Convention on Tonnage Measurement of Ships, 1969 was adopted by IMO in 1969.<ref name="imo1982">International Maritime Organization, 2002.</ref>  The Convention mandated a transition from the former measurements of [[gross register tonnage]] (grt) and [[net register tonnage]] (nrt) to gross tonnage (GT) and net tonnage (NT).<ref name="imo1982"/> It was the first successful attempt to introduce a universal tonnage measurement system.<ref name="imo1982"/>
 
Various methods were previously used to calculate merchant ship tonnage, but they differed significantly and one single international system was needed.<ref name="imo1982"/>  Previous methods traced back to [[Moorsom System|George Moorsom]] of [[Great Britain]]'s [[Board of Trade]] who devised one such method in 1854.<ref name="imo1982"/>
 
The tonnage determination rules apply to all ships built on or after July 18, 1982.<ref name="imo1982"/>  Ships built before that date were given 12 years to migrate from their existing gross register tonnage (GRT) to use of GT and NT.<ref name="imo1982"/>  The phase-in period was provided to allow ships time to adjust economically, since tonnage is the basis for satisfying manning regulations and safety rules.<ref name="imo1982"/>  Tonnage is also the basis for calculating registration fees and port dues.<ref name="imo1982"/>  One of the Convention's goals was to ensure that the new calculated tonnages "did not differ too greatly" from the traditional gross and net register tonnages.<ref name="imo1982"/>
 
Both GT and NT are obtained by measuring ship's volume and then applying a mathematical formula.<ref name="imo1982"/>  Gross tonnage is based on "the moulded volume of all enclosed spaces of the ship" whereas net tonnage is based on "the moulded volume of all cargo spaces of the ship".<ref name="imo1982"/>  In addition, a ship's net tonnage is constrained to be no less than 30% of her gross tonnage.<ref name="imo1982"/>
 
==Calculation==
The gross tonnage calculation is defined in Regulation 3 of Annex 1 of ''[http://www.admiraltylawguide.com/conven/tonnage1969.html The International Convention on Tonnage Measurement of Ships, 1969]''.  It is based on two variables:
 
* ''V'', the ship's total volume in cubic meters (m<sup>3</sup>), and
* ''K'', a multiplier based on the ship volume.
 
The value of the multiplier ''K'' varies in accordance with a ship's total volume (in cubic metres) and is applied as a kind of reduction factor in determining the gross tonnage value - which does not have a unit such as cubic metres or tons.  For smaller ships, ''K'' is smaller, for larger ships, ''K'' is larger.  ''K'' ranges from 0.22 to 0.32 and is calculated with a formula which uses the [[common logarithm|common or base-10 logarithm]]:
 
:<math> K = 0.2 + 0.02 \times \log_{10}(V)\,</math>
 
Once ''V'' and ''K'' are known, gross tonnage is calculated using the formula, whereby GT is a function of V:
 
:<math> GT = K \times V\,</math>
 
As an example, we can calculate the gross tonnage of a ship with 10,000 m<sup>3</sup> total volume.
:<math> K = 0.2 + 0.02 \times \log_{10}(V)\,</math>
::<math> = 0.2 + 0.02 \times \log_{10}(10,000)\,</math>
::<math> = 0.2 + 0.02 \times 4\,</math>
::<math> = 0.2 + 0.08\,</math>
::<math> = 0.28\,</math>
 
Then the gross tonnage is calculated:
 
:<math> GT = K \times V\,</math>
::<math>  = 0.28 \times 10,000\,</math>
::<math>  = 2,800\,</math>
 
==See also==
{{Portal|Nautical}}
* [[Tonnage]]
* [[Moorsom System]]
* [[Gross register tonnage]]
* [[Compensated gross tonnage]]
* [[Ton]]
* [[List of world's largest ships by gross tonnage]]
 
==Notes==
{{Reflist}}
 
==References==
*{{cite web
|url= http://www.admiraltylawguide.com/conven/tonnage1969.html
|title= International Convention on Tonnage Measurement of Ships, 1969
|accessdate= 2008-03-23
|author=
|last=
|first=
|authorlink=
|coauthors=
|date=1969-06-23
|year=
|month=
|work=
|publisher=
|pages=
|language=
|doi=
|archiveurl=
|archivedate=
|quote=
}}
*{{cite web
|url= http://www.imo.org/Conventions/contents.asp?topic_id=259&doc_id=685
|title=International Convention on Tonnage Measurement of Ships, 1969
|accessdate= 2008-03-23
|author=International Maritime Organization
|last=
|first=
|authorlink= International Maritime Organization
|coauthors=
|date=
|year= 2002
|month=
|format=
|work=
|publisher= International Maritime Organization
|pages=
|language=
|doi=
|archiveurl=
|archivedate=
|quote=
}}
* {{cite book |last=Hayler |first=William B. |title=American Merchant Seaman's Manual |year=2003 |publisher= Cornell Maritime Press |isbn= 0-87033-549-9 }}.
* {{cite book
| last = Turpin
| first = Edward A.
| authorlink =
| coauthors = McEwen, William A.
| editor =
| others =
| title = Merchant Marine Officers' Handbook
| origdate =
| origyear =
| origmonth =
| url =
| format =
| accessdate =
| edition = 4th
| series =
| date =
| year = 1980
| month =
| publisher =Cornell Maritime Press
| location = Centreville, MD
| language =
| isbn = 978-0-87033-056-8
| oclc =
| doi =
| id =
| pages =
| chapter =
| chapterurl =
| quote =
}}
 
{{Ship measurements}}
 
{{DEFAULTSORT:Gross Tonnage}}
[[Category:Shipbuilding]]
[[Category:Nautical terms]]
 
[[de:Schiffsmaße#Brutto- und Nettoraumzahl (BRZ, NRZ)]]

Latest revision as of 18:42, 20 April 2013

Gross tonnage is calculated by measuring a ship's volume (from keel to funnel, to the outside of the hull framing) and applying a mathematical formula.

Gross tonnage (often abbreviated as GT, G.T. or gt) is a unitless index related to a ship's overall internal volume. Gross tonnage is different from gross register tonnage.[1] Neither gross tonnage nor gross register tonnage is a measure of the ship's displacement (mass) and should not be confused with terms such as deadweight tonnage or displacement.

Gross tonnage, along with net tonnage, was defined by The International Convention on Tonnage Measurement of Ships, 1969, adopted by the International Maritime Organization in 1969, and came into force on July 18, 1982. These two measurements replaced gross register tonnage (GRT) and net register tonnage (NRT). Gross tonnage is calculated based on "the moulded volume of all enclosed spaces of the ship" and is used to determine things such as a ship's manning regulations, safety rules, registration fees, and port dues, whereas the older gross register tonnage is a measure of the volume of certain enclosed spaces.

History

The International Convention on Tonnage Measurement of Ships, 1969 was adopted by IMO in 1969.[2] The Convention mandated a transition from the former measurements of gross register tonnage (grt) and net register tonnage (nrt) to gross tonnage (GT) and net tonnage (NT).[2] It was the first successful attempt to introduce a universal tonnage measurement system.[2]

Various methods were previously used to calculate merchant ship tonnage, but they differed significantly and one single international system was needed.[2] Previous methods traced back to George Moorsom of Great Britain's Board of Trade who devised one such method in 1854.[2]

The tonnage determination rules apply to all ships built on or after July 18, 1982.[2] Ships built before that date were given 12 years to migrate from their existing gross register tonnage (GRT) to use of GT and NT.[2] The phase-in period was provided to allow ships time to adjust economically, since tonnage is the basis for satisfying manning regulations and safety rules.[2] Tonnage is also the basis for calculating registration fees and port dues.[2] One of the Convention's goals was to ensure that the new calculated tonnages "did not differ too greatly" from the traditional gross and net register tonnages.[2]

Both GT and NT are obtained by measuring ship's volume and then applying a mathematical formula.[2] Gross tonnage is based on "the moulded volume of all enclosed spaces of the ship" whereas net tonnage is based on "the moulded volume of all cargo spaces of the ship".[2] In addition, a ship's net tonnage is constrained to be no less than 30% of her gross tonnage.[2]

Calculation

The gross tonnage calculation is defined in Regulation 3 of Annex 1 of The International Convention on Tonnage Measurement of Ships, 1969. It is based on two variables:

  • V, the ship's total volume in cubic meters (m3), and
  • K, a multiplier based on the ship volume.

The value of the multiplier K varies in accordance with a ship's total volume (in cubic metres) and is applied as a kind of reduction factor in determining the gross tonnage value - which does not have a unit such as cubic metres or tons. For smaller ships, K is smaller, for larger ships, K is larger. K ranges from 0.22 to 0.32 and is calculated with a formula which uses the common or base-10 logarithm:

Once V and K are known, gross tonnage is calculated using the formula, whereby GT is a function of V:

As an example, we can calculate the gross tonnage of a ship with 10,000 m3 total volume.

Then the gross tonnage is calculated:

See also

Sportspersons Hyslop from Nicolet, usually spends time with pastimes for example martial arts, property developers condominium in singapore singapore and hot rods. Maintains a trip site and has lots to write about after touring Gulf of Porto: Calanche of Piana.

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

Template:Ship measurements

de:Schiffsmaße#Brutto- und Nettoraumzahl (BRZ, NRZ)

  1. The gross register ton (GRT) is a unit of volume defined as 100 cubic feet (about 2.83 m³).
  2. 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 International Maritime Organization, 2002.