Interested in plotting a contact-course, position and speed only using hydrophones? Read on!
U 42 is hunting for single merchants in the Western Approaches. It's 2300 hours, the sea is calm. The sky is cloudy and two hours ago a light fog came up.
The Kaleun has ordered all engines stop at periscope-depth, Heinz is listening at the hydrophone for contacts.
"Contact! Freighter, inbound. Bearing 60°."
Konrad - our WO - activates the stopwatch and orders Heinz to report the bearings exactly all 8 minutes. Konrad notes the contact on the map. He draws a line of 20 km length from our position - bearing 60° to our bow.
Additionally he grabs a green pencil and draws a perfect circle (he's a genius!) on a free area of the map and marks the center with M. He draws the horizontal diameter and marks the ends with P1 and P2. The contact is reported on the starboard side, therefore he marks the right point P1. The line P1-M shall represent the distance the contact will travel in 8 minutes, the line M-P2 shall represent the distance for the following 8 minutes. Logically the length of both lines is equal as long as we assume the contact is moving with constant speed on a straight course.
8 minutes have passed, Heinz reports: "Contact now at 50°."
Again Konrad starts the stopwatch and notes the bearing on the map - a line of 20 km length - 50° to our bow. He notes the angle of the bearinglines - 10° - and names it A1.
He calculates: (180° - 2A1) : 2 = 80°. He grabs a blue pencil and the protractor to construct an isosceles triangle under the P1-M baseline - both angles read 80° - the sides meet in Point C1. The angle at C1 reads 20° (2A1).
Konrad - a golden colour pencil in his hand - draws a circle using C1 as center and the line C1-M as radius.
"Contact at 34°."
Our WO orders "Full speed, Heading 270" and reactivates the stopwatch. He notes the new bearingline carefully on the map. The new angle reads 16° - marked as A2.
To complete his auxiliary drawing he calculates again: (180° - 2A2) : 2 = 74°.
Using the blue pencil he constructs the second triangle similar to the first procedure, but now under the M-P2 baseline. Both baseangles read 74° - the sides meet under an angle of 32° (2A2) - the point is marked as C2 and used as center for a circleline - golden coloured - which meets M.
The two golden circles show two points of intersection - one is already marked M - Konrad names the other one U using the black pencil.
"U" represents the position of an U-Boot that locates a moving contact under the bearingangles A1 (10°) and A2 (16°).
Konrad draws the angle U-P1-P2 in red - it reads exact 33°.
He transfers this angle to the first bearingline representing the first contactreport at 60°. The new arm reads the quite exact courseDIRECTION of the freighter.
Fat chance the freighter doesn't move along this line but on a parallel courseline.
The intersectionpoints of the transfered courseline with the three bearinglines cut the courseline into two equal parts. They represent the distance our freighter moved in 8 minutes.
Konrad extends the courseline by 50% ("s") to mark the theoretical fourth bearing Heinz would have reported after 8 minutes without changing the position of the U-Boot.
He draws the bearingline to meet the new end of the courseline.
Seven minutes have passed since Heinz's last bearingreport. Our WO orders all engines stop to enable Heinz a proper report after 8 minutes.
"Contact! Freighter at ..."
Konrad notes the new bearing on the map. The line meets the theoretical fourth bearing in the freighters current position.
All necessary information to start an optimal attack is collected: position, course and speed (well you have to do some calculations on your own!) of the contact.
"Kessler! Wake up our Kaleun! We've got a job to do."
To confuse you even more - this shows Konrads auxiliary drawing. The colours are used in the correct chonological order. Well therefore it's in german.
And here Konrads NavMap notes.
Good Hunting, Gentlemen.