## Plotting Sheets
Plotting sheets are "charts" designed primarily for open ocean navigation,
where shorelines, visual aids to navigation and water depths are of no
importance to navigation. Plotting sheets are also used for plotting positions
and Lines-of-Position obtained by methods of Celestial Navigation. ## Constructing Small-Area Plotting Sheets
A plotting sheet with a Mercator scale for a specific Latitude ## Plotting Sheet with selected latitude scalemay be produced as described in the following procedure:## Plotting Sheet with selected longitude scalemay be produced as described in the following procedure:## Remarks
The above procedures differ only in the way the initial scale of the chart is defined.
The first procedure has a predefined vertical spacing of the Parallels, whereas
the second procedure allows for a predefined horizontal spacing of the Meridians. ## Constructing Large-Scale Plotting SheetsIn order to construct a plotting sheet, which is also valid for a large range of Latitudes, the basic characteristics of the Mercator grid must be understood: - Meridians are straight lines running North-South and are spaced a fixed distance
**dX**from each other.
- Parallels are also straight lines running East-West (perpendicular to the Meridians) and are spaced a distance
**dY**from the next one. The value for**dY**depends on the value of the current Latitude**Lat**:**dY**=**dX**/ cos(**Lat**). At the Equator, the Parallels are spaced at the same distance as the Meridians (dY = dX). The closer to the Poles, the larger the spacing of the Parallels (dY > dX).
Constructing the appropriate Mercator grid valid also for a large range of Latitudes
may then be done by repeating the above procedure of constructing a plotting sheet
## The Universal Plotting Sheet
The elaboration of a celestial fix according to the method of St. Hilaire does
not necessarily require a Mercator style plotting sheet.
I am indebted to Tony for sending me the following method, he found in an old
marine textbook. Latitude_Difference_in_Minutes = NS_Distance_in_Nautical_Miles For the Longitude however, the correct ratio between Latitude and Longitude scales must be taken into account. Numerically, the ratio is equal to the cosine of the local Latitude (LatAP): Longitude_Difference_in_Minutes = EW_Distance_in_Nautical_Miles / cos(LatAP) At higher Latitudes, the Meridians are "closer" than they are at the Equator, so at higher Latitudes, there are more "Minutes of Longitude per Mile" than there are at low Latitudes. Graphically, the correct Longitude difference can be obtained from the East-West distance with the following simple trigonometric construction: The scale of the plotting sheet is used to translate the Latitude and Longitude offsets (shown in red in the sketch above) to Minutes-of-Arc with one Nautical Mile corresponding to one Minute-of-Arc. |

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