Determining Angle on Bow - reliable mathematical approach found

B_K · 05-17-17, 02:14 PM

Hello to all Kaleuns!

I was wondering about how to mathematically determine (in)famous Angle on Bow. That is what i found out.

First, major assumptions, very simple:
- we know exactly what target we are facing, we know its length (L) and mast height (H) - easy with our Recognition Book
- we know how to use our periscope reticle - field of view and angular scale based on magnification, both in vertical and in horizontal direction
- we can figure out if the target is closing to us or goes away

So lets start with situational drawing which is here:

http://s000.tinyupload.com/index.php...86106294144239

right part is just magnified left part of the drawing. All is drawn to scale.

We observe a ship of which length L is known from recognition book. Since it travels with unknown AoB, observable length is shorter and equals Lx (perpendicular projection of L in our scope view).

L-length of a target ship
D-distance (determined by stadimeter)
greek alpha - observable horizontal angular width of a target ship

The rest of the drawing is self explanatory.

Next we move into some maths - very basic trigonometry, based on again a few assumptions - self explanatory.

http://s000.tinyupload.com/index.php...61349984728719

For those who are not interested in math method, the final answer as we see is:

AoB=arc sin [(D tan alpha)/L]

remember that sine function is symmetrical to 90 degrees, so you must check if target is closing or gets away. sin alpha = sin (180-alpha) so you get the same results for acute and obtuse angle and must choose the right one.

As drawing is to scale, you can easy check equations.

Please, give me some feedback and tell me what do you think about it.

05-17-17, 02:14 PM	#1
B_K Bosun Join Date: Nov 2011 Posts: 68 Downloads: 63 Uploads: 0	Determining Angle on Bow - reliable mathematical approach found Hello to all Kaleuns! I was wondering about how to mathematically determine (in)famous Angle on Bow. That is what i found out. First, major assumptions, very simple: - we know exactly what target we are facing, we know its length (L) and mast height (H) - easy with our Recognition Book - we know how to use our periscope reticle - field of view and angular scale based on magnification, both in vertical and in horizontal direction - we can figure out if the target is closing to us or goes away So lets start with situational drawing which is here: http://s000.tinyupload.com/index.php...86106294144239 right part is just magnified left part of the drawing. All is drawn to scale. We observe a ship of which length L is known from recognition book. Since it travels with unknown AoB, observable length is shorter and equals Lx (perpendicular projection of L in our scope view). L-length of a target ship D-distance (determined by stadimeter) greek alpha - observable horizontal angular width of a target ship The rest of the drawing is self explanatory. Next we move into some maths - very basic trigonometry, based on again a few assumptions - self explanatory. http://s000.tinyupload.com/index.php...61349984728719 For those who are not interested in math method, the final answer as we see is: AoB=arc sin [(D tan alpha)/L] remember that sine function is symmetrical to 90 degrees, so you must check if target is closing or gets away. sin alpha = sin (180-alpha) so you get the same results for acute and obtuse angle and must choose the right one. As drawing is to scale, you can easy check equations. Please, give me some feedback and tell me what do you think about it.