{"id":437,"date":"2024-06-06T21:44:45","date_gmt":"2024-06-06T20:44:45","guid":{"rendered":"https:\/\/sailorvikas.com\/?p=437"},"modified":"2024-06-06T21:45:26","modified_gmt":"2024-06-06T20:45:26","slug":"plane-and-parallel-sailing-without-traverse-tables","status":"publish","type":"post","link":"https:\/\/sailorvikas.com\/index.php\/2024\/06\/06\/plane-and-parallel-sailing-without-traverse-tables\/","title":{"rendered":"Plane and parallel sailing (without traverse tables) –"},"content":{"rendered":"\n

Some important definitions:<\/mark><\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n


Rhumb line: <\/mark>is a line on the earth\u2019s surface, crossing all meridians at the same angle. It is the most convenient track to follow as the course of the ship remains constant for the entire passage.
Departure: <\/mark>The departure between two places is the east-west distance between them in nautical miles.
1. If the two places are on the same latitude, the departure is the distance
between them in nautical miles.
2. When the two places are in different latitudes, the departure between them is taken as the east west distance between their meridians measured along the mean latitude. This will hold good if the latitudes of both the places are fairly close to each other and this concept is used without any appreciable loss of accuracy in mean latitude problems.<\/mark>
3. When the latitudes of two places are widely separated, the mean latitude concept will be technically incorrect and in this case the departure is taken as the east west distance measure along the middle \u2013 latitude. Here, the middle latitude is defined as the latitude on which the true departure lies. This concept is used in middle latitude sailing calculations, which are generally discouraged for the purpose of practical navigation.<\/p>\n\n\n\n

Parallel sailing calculations<\/mark><\/strong> –
Example I: <\/mark>
A vessel in latitude 50N longitude 004W steers a course of 090 (T) for a distance of 90 miles. Find the position arrived.
To convert departure in to D\u2019long or vice versa, the parallel sailing formula is used which is
Dep \/ D\u2019long = Cos M\u2019lat D\u2019long = Dep \/ Cos M\u2019lat = Dep x Sec M\u2019lat
Since the vessel is travelling east \u2013 departure is the same as distance travelled which is 90 miles
D\u2019long = 90 x sec 50
= 90 x 1.55 57
= 140.02\u2019 East
= 2\u00b0 20\u2019E
Longitude arrived = 004 \u00b0 W + (2\u00b0 20\u2019E)
= 00400\u2019W \u2013 220\u2019 = 01 40\u2019W<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n


7) Plane sailing calculations<\/mark><\/strong>
Example II:<\/mark> Find the course and distance from
Position A : 490 35\u2019N 004000\u2019W to
Position B : 500 10\u2019N 0020 55\u2019W
Solution:<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Position A 49\u00b0 35\u2019N 004\u00b0 00\u2019W
Position B 50\u00b0 10\u2019N 002\u00b0 55\u2019W
D\u2019lat 00\u00b0 35\u2019N D\u2019long 1\u00b0 05\u2019E
D\u2019 lat = 35\u2019N D\u2019long =65\u2019 E
M\u2019 Lat = 49\u00b052.5
Dep = D\u2019long x cos M\u2019lat
= 65 x cos 49\u00b0 52.5
= 41.89\u2019
Tan course = Dep \/ D\u2019lat = 41.89 \/ 35 =1.19686 Course = N 50\u00b0 E
Distance = D\u2019lat x sec co.
= 35 x sec 50
= 35 x 1.55 57
= 54.5 N miles
<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

We will now work out another example on plane sailing where by the initial position, the course and distance travelled is given and we will have to find out the arrival position.<\/p>\n\n\n\n


Example III: <\/mark>
Your vessel was in position 04\u00b020\u2019S 040\u00b0 50\u2019E. She sailed on a Rhumb line course of 185\u00b0 T for a distance of 260 miles. Assuming there has been no effect of wind and current, what will be your arrived position?

Distance = 260 M
Course = 185 T i.e. S05\u00b0W
D\u2019lat = Distance x Cos course.
= 260 x cos 05
= 259.01 259\u2019
D\u2019lat = 259 = 4\u00b0 19.0\u2019S<\/mark>

Dep Latitude : 04\u00b0 20\u2019S
D\u2019lat : 04 19\u2019S
Arrived Latitude : (Add) 08\u00b0 39\u2019S
Mean Latitude: 06\u00b0 29.5\u2019 S<\/mark>
Dep = Distance x sin co = 260 x sin 05 = 22.66\u2019
D\u2019long = dep x sec M\u2019lat = 22.66 x sec 06 29.5\u2019 = 22.8\u2019 W
Departure Longitude: 040\u00b0 50\u2019 E
D\u2019long: 0\u00b0 22.8\u2019 W
Arrival longitude: 040\u00b0 27.2\u2019 E<\/mark>
Position arrived: 50\u00b0 00\u2019N, 001 \u00b0 40\u2019W<\/mark>
Course and distance:
050(T) distance 54.5\u2019
Position Arrived:
08\u00b0 39\u2019 S, 040\u00b0 27.2\u2019 E<\/p>\n\n\n\n

8) Calculations using traverse tables<\/mark><\/strong>
The above examples were worked out without the use of the traverse tables. Now let us solve few examples using traverse tables:
Some notes regarding use of traverse tables:
a) Traverse tables are made for calculations for distances only up to 600 nautical miles. If the distance exceeds 600 miles, calculations are to be done by mercator sailing method.
b) All three-figure courses are to be converted into quadrantal ones for e.g. 165(T) should be converted to S15E.
c) When entering courses and mean latitudes in the traverse tables \u2013 if the value is less than 45 then the table is entered from the top of the page and if the value is more than 45 then the table is entered from the bottom of the page.<\/p>\n\n\n\n

    \n
  1. When departure = d\u2019lat then the course will be 45.<\/li>\n\n\n\n
  2. When dep > d\u2019lat then the quadrantal course is more than 45.<\/li>\n\n\n\n
  3. When dep < d\u2019lat then the quadrantal course is less than 45<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Some important definitions: Rhumb line: is a line on the earth\u2019s surface, crossing all meridians at the same angle. It is the most convenient track to follow as the course of the ship remains constant for the entire passage.Departure: The departure between two places is the east-west distance between them in nautical miles. 1. If […]<\/p>\n","protected":false},"author":1,"featured_media":473,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ocean_post_layout":"","ocean_both_sidebars_style":"","ocean_both_sidebars_content_width":0,"ocean_both_sidebars_sidebars_width":0,"ocean_sidebar":"","ocean_second_sidebar":"","ocean_disable_margins":"enable","ocean_add_body_class":"","ocean_shortcode_before_top_bar":"","ocean_shortcode_after_top_bar":"","ocean_shortcode_before_header":"","ocean_shortcode_after_header":"","ocean_has_shortcode":"","ocean_shortcode_after_title":"","ocean_shortcode_before_footer_widgets":"","ocean_shortcode_after_footer_widgets":"","ocean_shortcode_before_footer_bottom":"","ocean_shortcode_after_footer_bottom":"","ocean_display_top_bar":"default","ocean_display_header":"default","ocean_header_style":"","ocean_center_header_left_menu":"","ocean_custom_header_template":"","ocean_custom_logo":0,"ocean_custom_retina_logo":0,"ocean_custom_logo_max_width":0,"ocean_custom_logo_tablet_max_width":0,"ocean_custom_logo_mobile_max_width":0,"ocean_custom_logo_max_height":0,"ocean_custom_logo_tablet_max_height":0,"ocean_custom_logo_mobile_max_height":0,"ocean_header_custom_menu":"","ocean_menu_typo_font_family":"","ocean_menu_typo_font_subset":"","ocean_menu_typo_font_size":0,"ocean_menu_typo_font_size_tablet":0,"ocean_menu_typo_font_size_mobile":0,"ocean_menu_typo_font_size_unit":"px","ocean_menu_typo_font_weight":"","ocean_menu_typo_font_weight_tablet":"","ocean_menu_typo_font_weight_mobile":"","ocean_menu_typo_transform":"","ocean_menu_typo_transform_tablet":"","ocean_menu_typo_transform_mobile":"","ocean_menu_typo_line_height":0,"ocean_menu_typo_line_height_tablet":0,"ocean_menu_typo_line_height_mobile":0,"ocean_menu_typo_line_height_unit":"","ocean_menu_typo_spacing":0,"ocean_menu_typo_spacing_tablet":0,"ocean_menu_typo_spacing_mobile":0,"ocean_menu_typo_spacing_unit":"","ocean_menu_link_color":"","ocean_menu_link_color_hover":"","ocean_menu_link_color_active":"","ocean_menu_link_background":"","ocean_menu_link_hover_background":"","ocean_menu_link_active_background":"","ocean_menu_social_links_bg":"","ocean_menu_social_hover_links_bg":"","ocean_menu_social_links_color":"","ocean_menu_social_hover_links_color":"","ocean_disable_title":"default","ocean_disable_heading":"default","ocean_post_title":"","ocean_post_subheading":"","ocean_post_title_style":"","ocean_post_title_background_color":"","ocean_post_title_background":0,"ocean_post_title_bg_image_position":"","ocean_post_title_bg_image_attachment":"","ocean_post_title_bg_image_repeat":"","ocean_post_title_bg_image_size":"","ocean_post_title_height":0,"ocean_post_title_bg_overlay":0.5,"ocean_post_title_bg_overlay_color":"","ocean_disable_breadcrumbs":"default","ocean_breadcrumbs_color":"","ocean_breadcrumbs_separator_color":"","ocean_breadcrumbs_links_color":"","ocean_breadcrumbs_links_hover_color":"","ocean_display_footer_widgets":"default","ocean_display_footer_bottom":"default","ocean_custom_footer_template":"","ocean_post_oembed":"","ocean_post_self_hosted_media":"","ocean_post_video_embed":"","ocean_link_format":"","ocean_link_format_target":"self","ocean_quote_format":"","ocean_quote_format_link":"post","ocean_gallery_link_images":"on","ocean_gallery_id":[],"footnotes":""},"categories":[1],"tags":[],"class_list":["post-437","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-celestial-navigation","entry","has-media"],"_links":{"self":[{"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/posts\/437","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/comments?post=437"}],"version-history":[{"count":5,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/posts\/437\/revisions"}],"predecessor-version":[{"id":472,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/posts\/437\/revisions\/472"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/media\/473"}],"wp:attachment":[{"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/media?parent=437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/categories?post=437"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sailorvikas.com\/index.php\/wp-json\/wp\/v2\/tags?post=437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}