SUBSIM Radio Room Forums - View Single Post - Single Observation Firing Solution Procedure

cleverusername · 12-26-06, 11:55 PM

SINGLE OBSERVATION FIRING SOLUTION PROCEDURE

Since almost everyone is familiar with determining target range using the stadimeter tool, that will not be covered. Instead, I will focus on the two remaining variables: AOB and Speed.

Part I: AOB

Theory: A ship at 90 degrees AOB will appear to be as long as it's reported literature length. As the AOB increases or decreases from 90 degrees, the ship will appear narrower. This length contraction is directly related to the deviation from 90 degrees AOB. Therefore, if we can measure the apparent length of the ship, and read off it's actual length from the Target Recognition Handbook, then the target's deviation from 90 degrees AOB can be calculated. By adding or subtracting this deviation amount from 90 degrees, the target's true AOB can be determined.

Workup

Knowing the range from stadimeter readings, as well as the angular size of the ship, measured using the periscope, the apparent target length can be calculated as:

(1) Apparent Length == Range * tangent[Angular Length]

Using the calculated Apparent Length, the deviation from 90 AOB can be calculated:

(2) Cosine[Deviation from 90 AOB] == Apparent Length / Actual Length
(3) Deviation from 90 AOB == Inverse Cosine[Apparent Length / Actual Length]

Putting equations (1) and (3) together...

(4) Deviation from 90 AOB == Inverse Cosine[(Range / Actual Length) * Tangent[Angular Length]]

Execution:

Suggested Method: Calculation

1) Identify Target Ship visually using Ship Recognition Handbook
2) Note down Target Ship Length (L)
3) Resolve Target Range (R) using Stadimeter Tool
4) Point periscope at Target Bow, note bearing.
5) Point periscope at Target Stern, note bearing.
6) Subtract 4 and 5 to resolve Target Angular Length (A)

7) Calculate deviation from 90 AOB using formula:

Deviation == Inverse Cosine[(R/L)*Tangent[A]]

8a) If target ship is heading towards you, subtract that deviation from 90 AOB. e.g. if Deviation == 20 degrees, target AOB is 70 degrees.
8b) If target ship is heading away from you, add that deviation to 90 AOB. e.g. if Deviation == 20 degrees, target AOB is 110 degrees.

Result: Target AOB is known.

Alternative Method: Graphical

1) Replicate the image shown, using ruler and protractor tools to draw the real lengths and angles.
2) Instead of drawing in target actual length with the ruler, use a compass with the radius set to the target's length, with center placed on the non-vertical arm.
3) Measure the angle from the horizontal to where the compass circle intersects the vertical line. That is your deviation.
4) Proceed using steps 8a or 8b as outlined above.

Note: This method takes longer, and is more susceptible to error than the calculation method. If you believe that it is "unrealistic" that a WW2 captain would be able to calculate tangents and inverse cosines, keep in mind that the stadimeter tool, which did not exist in real life, does exactly that. This does not depart from realism any more than using the stadimeter.

12-26-06, 11:55 PM	#2
cleverusername Seaman Join Date: Jan 2006 Location: Durham, NC Posts: 38 Downloads: 0 Uploads: 0	SINGLE OBSERVATION FIRING SOLUTION PROCEDURE Since almost everyone is familiar with determining target range using the stadimeter tool, that will not be covered. Instead, I will focus on the two remaining variables: AOB and Speed. Part I: AOB Theory: A ship at 90 degrees AOB will appear to be as long as it's reported literature length. As the AOB increases or decreases from 90 degrees, the ship will appear narrower. This length contraction is directly related to the deviation from 90 degrees AOB. Therefore, if we can measure the apparent length of the ship, and read off it's actual length from the Target Recognition Handbook, then the target's deviation from 90 degrees AOB can be calculated. By adding or subtracting this deviation amount from 90 degrees, the target's true AOB can be determined. Workup Knowing the range from stadimeter readings, as well as the angular size of the ship, measured using the periscope, the apparent target length can be calculated as: (1) Apparent Length == Range * tangent[Angular Length] Using the calculated Apparent Length, the deviation from 90 AOB can be calculated: (2) Cosine[Deviation from 90 AOB] == Apparent Length / Actual Length (3) Deviation from 90 AOB == Inverse Cosine[Apparent Length / Actual Length] Putting equations (1) and (3) together... *(4) Deviation from 90 AOB == Inverse Cosine[(Range / Actual Length) Tangent[Angular Length]] Execution: Suggested Method: Calculation 1) Identify Target Ship visually using Ship Recognition Handbook 2) Note down Target Ship Length (L) 3) Resolve Target Range (R) using Stadimeter Tool 4) Point periscope at Target Bow, note bearing. 5) Point periscope at Target Stern, note bearing. 6) Subtract 4 and 5 to resolve Target Angular Length (A) 7) Calculate deviation from 90 AOB using formula: Deviation == Inverse Cosine[(R/L)Tangent[A]]* 8a) If target ship is heading towards you, subtract that deviation from 90 AOB. e.g. if Deviation == 20 degrees, target AOB is 70 degrees. 8b) If target ship is heading away from you, add that deviation to 90 AOB. e.g. if Deviation == 20 degrees, target AOB is 110 degrees. Result: Target AOB is known. Alternative Method: Graphical 1) Replicate the image shown, using ruler and protractor tools to draw the real lengths and angles. 2) Instead of drawing in target actual length with the ruler, use a compass with the radius set to the target's length, with center placed on the non-vertical arm. 3) Measure the angle from the horizontal to where the compass circle intersects the vertical line. That is your deviation. 4) Proceed using steps 8a or 8b as outlined above. Note: This method takes longer, and is more susceptible to error than the calculation method. If you believe that it is "unrealistic" that a WW2 captain would be able to calculate tangents and inverse cosines, keep in mind that the stadimeter tool, which did not exist in real life, does exactly that. This does not depart from realism any more than using the stadimeter. __________________ Visual. Tally. Press! Last edited by cleverusername; 12-27-06 at 08:57 PM.