Formulas concentrate ? ... from my archives ( reminder )

[JMV]

I know, I know this has been told over and over, but that might be usefull for the newbies as well as for the not so ... in a form of a concentrate. IYSWIM

Please, eventhough it's exerts from my looooooong hours of reading since thread 1, any correction would be welcome. I' m asking the experts and the Mathoholics here ! THANKS ALL for your numerous answer ( I wish )

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TARGET SPEED
================================================
1 )

1. Identify the ship first to obtain its length - very important. For this example lets say its 200 metres.

2. Be at full-stop ideally (or no more than 1 kt) and try to be side-on to the vessel about 1000m - it doesn't work from straight ahead, but 90 degrees + or - 50 degrees is usually fine.

3. Turn your periscope so the vertical line is ahead of the bow of the approaching ship. Don't move the periscope any more - very important.

4. Now wait until the ship's bow reaches the vertical line and start a stopwatch.

5. Its safe to lower the periscope whilst you are waiting for the ship to cross the peri's path, but don't turn it left or right.

6. OK, as the ship passes the vertical line stop the stopwatch the moment the stern passes the line. For this example lets say it took 55 seconds.

7. Now the mathematics....

Take the figure of 1.943844 multiply it by ships length (200) then divide by the time to cross the line in seconds (55).
(Meters per Second * 1.943844 = knots)

So we have 1.94 x 200 / 55

= 7.05 knots or

Divide the traget's length by the amount of time it took. This gives you the target's speed in meters per second. Divide by .514 to get speed in knots. If you don't have a calculator handy (it makes things easier) you can use a nomograph

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2 )
Simplest way is to range and mark the target on the map, wait 6 minutes and range and mark the target again. Measure the distance between the two marks (in nautical miles) and multiply by 10. You now have the target's speed in knots. This is made even simpler with the addition of target icons and/or a nomograph.
-----------------------------
1852m / 3600s = .51 (constant). 1/.51 = 1.96 (constant)

When the answer is in meter per second we can either multiply by 1.96 or divide by .51 to get knots.

therefore,

2.3 mps / .51 = 4.5 knots

Imperial: 2026 yds. / 3600 s = .56 (constant). 1/.56 = 1.78 (constant). Either divide yds. per second by .56 or multiply by 1.78 to get speed in knots
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3 )
Ok here is my manner of calculating the speed.

- Recogn the target.
- Set the crosshair at the beginning of the target.
- set on the stopwatch
- set it off when the crosshair is at the end of the target.
- take a look in you recognbook how long your target is.
- Calculate: time divided by the metres of the ship multiply the outcome with 0,1942.

Now you have the speed.

So for example a ship of 90 metres with a time of 30 secs

30/90 = 0,33 x 0,1942 - 0,06. So the speed of the ship is 6 knots.
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4 )
"It's fairly easy to work out speed by hand (as long as you have calculator handy).
It does require a bit of trigonometry though, and it's most accurate if you are stationary or at least very slow while doing it.

1) Having got range etc, lock the target in the scope (or for more "realism" you can do it without locking the target).

2) Note the bearing to the target as displayed at the top of the scope view and then start your clock (Let's say for example it was 320 degrees when you started the clock).

3) Wait 10 secs. (You can use any time you like, but 10 secs is as good as any).

4) As soon as the 10 secs is up check the new bearing of the target (it should have changed). Anyway, let's say the ending bearing was 325 degrees.

5) Ok take the difference in the two bearings 320 - 325 = 5 degrees brg change in 10 secs.

6) Using our stadimeter range, and our noted time and bearing change, a bit of trigonometry will give us the speed.

There is One important thing here - the stadimeter will give you a range in Yards - there are 3 feet to a yard! Personally I prefer to work in feet so I do a conversion from Yards to feet (just multiply the range from the Stadimeter by 3).

So let's say we have

Range - 1020yds
Brg Change - 5 degrees
Time - 10 secs

a) 1060 yds = 3060ft

b) Use -- Tan Brg Change x Range (in feet) = Distance travelled by target in feet

So using the numbers above :

Tan 5 x 3060 = 267.71ft

The target travelled 267.6ft in 10 secs. To determine speed in Knots we do :

c) 267.7 x 6 = 1606.3ft (we multiplied by 6 because we used 10 secs as our time period, there are '6 lots of 10' in a minute). The target is doing 1606.3ft per minute.

d) 1606.3 x 60 = 96377.5ft - This gives us the distance in feet the target travels in an hour.

e) Last step, convert 96377.5ft to Knots. Simply divide by 6076 (that's the number of feet in a Nautical Mile). So 96377.5 / 6076 = 15.86. Call it 16 Knots.


Important note on all of this, if you are not perpendicular to the track of the target, this system will not be accurate since the trigonometry in use is for right angle triangles. However, as long as you're more or less in the right place this should be accurate enough.

It looks like a lot of work, but you can get through the maths quickly enough and come out with an accurate result. If you're struggling for time, just pause the game when you've got the time and bearing change and you can take as long as you like going through the numbers.

For the training mission you should find this kind of data (depending on where/when in to the mission you take the data)

Range 1020 yds
Bearing change ~ 3 degrees in 10 secs

Doing the maths again ((Tan 3 x 3060) x 360)/6076 = 9.5 Kts
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5 )
Ships length past the vertical graticule / seconds x (3600/1852) = speed.

caveat: ship AOB should be between 60 & 120°, and the sub setting still or No faster than 1 kn.

i.e., T2 = 152.7m / 40 sec. x 1.94 = 7.4 kn.

I never worry about 'range' if the target fills half the scope @ x6 it's close enough for a kill. Speed & AOB are the only things of concern.
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6 )
One decree is equal to 17.7 mils.

if you saw the GTA (graphic training aid) that i put as a pic in the
tread sh3 grid protractor, you will see a square protractor, i and
many use for indirect fire, and land navigation.

the outside edge is in mils, there are 6400 mils in a 360 degree
circle.

there are 360 decrees in a circle.

the math to find how many mils in one decree is,

6400 / 360 = 17.7 mils.
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7 )
I would however state that the speed calculator in the notepad is
very buggy and hard to get to work. The only real way to get the
speed without using the Weapons Officer is to do it manually.

I use the equation:
(d/t) x 30.866 = Knots

Where d= distance travelled in kilometers, and t= time in minutes.

so if he travels 800 meters in 3 minutes you'd write the equation as:

(0.8/3) x 30.866 = 8.2 Knots

The longer the time generally the more accurate it is.

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8 )
For contact speed calculation you need two factors:
travelled distance and time used to travel that distance.
To find speed we have to divide distance by time (v = s / t).
I.e. we get 926 meters per 6 minutes = 154,333 meters/mins

But we are used to km/h - kilometers per hour.
That's 154,333 x 60 = 9260 meters/hour or 9,260 km/h

SH3 doesn't use km/h but knots.
Therefore we have to convert our calculated speed into knots.

1 knot is 1,852 km/h or 1852 meters/60 minutes.

9,260 km/h : 1.852 km/h = 5 (knots)
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METERS TO KNOTS
================================================
9 )
The m/s-to-knot factor is simply the division of 3600 seconds by
1852 meters: 1.943844= 3600/1852
Meters per Sec * 1,9438444924406047516198704103672 =knots
----------------------------------
Conversions
1 (international) knot is exactly equal to 1.852 kilometres per
hour (km·h-1), and is approximately equal to the following:

101.268591 feet per minute
1.687810 feet per second
0.5144444 meters per second (m·s-1)
1.150779 mile (statute) per hour (mph)
0.99936 Admiralty knot

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10 )
1 knot is 0.5144 m/s (=1852m/3600s). Then 100meters take :
100/0.5144=194.4 seconds. That's 3m14.4s, but 3m15s is easier
to use quickly.

As for the original 3-minute rule: 1 nautical mile is usually
rounded off to 2000 yards (Wiki says it actually is 2025.372 yards)
So 1 knot is 0.5555 yards/second (=2000yds/3600s) Then 100yds
take 180 seconds, which is 3 minutes. Since the exact
2025.372 yards case leads to a time of 2m58s for every 100 yards
movements you can use 3 minutes as a good approximation.

The 15-odd seconds difference is because a yard is not equal to
a meter.

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THE 3:15 RULE
================================================
11 )
the 3 min rule is to yards as the 3.25 min rule is to meters, i.e.,

distance (yds.) traversed in 3 min. / 100 = speed in knots.
distance (m.) traversed in 3.25 min. / 100 = ditto
-----------------------------

Mariners use these rules to determine the speed of another
vessel under their observation.

E.g. If it is determined that an observed vessel travels 0.8 km in
3:15 min., then,

the observed vessel's speed = 8 kn. If 1.5 km, then 15 kn. etc.

Imperial: Distance (yds) in 3:00 / 100 = speed in knots.
------------------------------
12 )
An Alternate to the 3-minute 15-second Method ( Von Zelda )

Using the following equation you can track targets for longer
times and distance to determine estimated speed:

Kilometers x 32.5 divided by minutes = knots

Example: 2.8 kilometers traveled x 32.5, divided by 13 minutes = 7 knots
---------------------------------
13)
And alternatives to the 3 15 rules are many. I personally love
the nomograph. Lets you take your raw range and time data and
turn out a speed. Very useful for 1 minute calculations. Or long
term ones too.

Also you should note that [1 knot = 1.852 km/h] or [1 km/h =
0.539 Knots] or [1 knot = 30.866 meters per minute]. With that
in mind you could take any distance travelled and form an equation.

Remember that lovely triangle? The D on top, the S and T on the
bottom? Speed is equal to Distance divided by Time. I just figured
this one out.

(distance travelled in KM / time in minutes) x 30.866 = speed in
knots.

Using von Zelda's example. (2.8/13) = 0.215*. That is the
number of meters that are taversed in one minute.
0.215 x 30.866 = 6.6, rounded down. Thats a pretty accurate one
I think.

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14 )
What I found out after going back over some right angle stuff, is
that the cosine of 60 degrees is 0.5 and means that whatever the range is at that moment in the periscope will be the double of the range at 0 degrees. I tested this to make sure the game follows this principle and it's been working out great for all my recent shots. I had a Small Merchant show a range of 1300 meters when the periscope was at 60 degrees (I was on its port side, 300 degrees if I were starboard) and so I went ahead and entered 650 meters for the range and let the torp fly at 0 degrees. I ended up with a shot right at the middle of the ship.
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RANGE TO TRACK
================================================
15 )
And if you would like to find out the range to the track, you can
use this, it's enough precise:

Range to the track = AOB/60 x R,
where "R" is range to the target sighted.

...also,

Range x sin(AOB) = Distance to track
------------------------------------
16 )
use this formula to calculate the angle you need to turn from to
intercept the contact. You should use knots as the the u-boat
and ship's speeds.

Angle to intercept = Sin-1 ( speed of contact * Sin (angle you
measured / your u-boat speed )

now use this formula to calculate the angle you need to turn from
to intercept the contact. You should use knots as the the u-boat
and ship's speeds.

If my u-boat is traveling at 12 knots and the contact is traveling
at approximately 5 knots :

Sin-1 ( 5* Sin (123) / 12 ) = 20.4534 Degree

And so the angle I need to turn to intercept the ship is 20.4534
degrees
-----------------------------------
17 )
I wanted to add other useless formulas :

distance traversed by the ship =
(d*sin(angle you measured)*V2)/(V1*sin(180-angle to intercept-angle you measured))

time of the crossing = distance traversed by the ship/(.5144*V2)

distance traversed by the sub = V1*0.5144*time of the crossing


d is the distance between the sub and the ship in meters.

v1 the speed of the sub in knots
v2 the speed of the ship in knots

Now you can make a good program on your graphical calculator...
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18 )
Does anyone know how far a typical merchant would have to be
before it disapears below the horizon? How far before its smoke
would also be below the horizon?

It all depends upon the height of the observer and the height of
the object being observed. For a rough geometric solution, the
square of the distance to the horizon from your eye is equal to
the height of the eye above the water times (2 x the radius of the
Earth); the Earth's radius may be averaged as ~6372 km). The
distance from the observed object to its horizon works on the
same principle. Note this approach does not take into account
the effects of atmospheric refraction, which "bends" light around
the earth's curvature, thus extending the range at which objects
can be seen; nor does it take into account the curvature of the
earth, which has only a small effect unless you're almost in space.

For example, assume the observer's eye is 5 meters above sea
level (maybe he is standing next to the UZO), and he is trying to
observe a column of smoke just over 50 meters tall, under which
chugs a coastal steamer.
distance (U-boat to horizon) = sqrt(0.005 km x 2 x 6372 km) =
roughly 7.98 km
distance (horizon to top of smoke) = sqrt(0.05 km x 2 x 6372 km)
) = roughly 25.24 km
total distance = (U-boat to horizon) + (horizon to top of smoke) = 7.98 km + 25.24 km = about 33.2 km
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CONVERSION CHART
================================================
19 )
100 M 00328 Ft / 0109 Yrd / 0.05 Nm

500 M 01640 Ft / 0547 Yrd / 0.3 Nm

1000 M 03280 ft / 1093 yrd / 0.5 Nm

2000 M 06561 Ft / 2187 Yrd / 1.1 Nm

3000 M 09842 Ft / 3280 Yrd / 1.6 Nm

4000 M 13123 Ft / 4374 Yrd / 2.2 Nm

5000 M 16404 Ft / 5468 Yrd / 2.7 Nm

6000 M 19685 Ft / 6000 yrd / 3.2 Nm

7000 M 22965 Ft / 7655 yrd / 3.8 Nm

8000 M 26246 Ft / 8748 Yrd / 4.3 Nm

9000 M 29527 Ft / 9842 Yrd / 4.9 NM
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20)
If so, why do I need to use a 20 degree bearing if I'm using a
slower torpedo?

Think of it this way. A slower torpedo will take longer to reach
the intercept point (the target's track), so the target will travel further during that time. Therefore, you need to lead the target more.

And don't get hung up on the 10 or 20 degrees given in the
example. You can calculate (or use tables like the real kaleuns
did) the exact lead angle with the equation...

Lead Angle = Arctan (target speed/torpedo speed)

So if the target is making 12 knots, and you wish to fire a 30
knot T-III electric, then your lead angle is...

Lead Angle = Arctan (12/30) = 21.8 degrees

And as long as you're within 5000 metres of the target track,
you should get a hit!
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21 )
c^2 = a^2 + b^2 - 2 * a * b * cos C
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22 )
its a format for working out a solution

R=range
B=bearing rate
R=RSA(relative speed across)
O=OSA(own speed across)
T=TSA (targets speed across)
S= speed
A=ATB
R=reciprocal bearing
C=course

and DOT which distance off track which is always handy

range = 2x RSA /BEARING RATE
BEARING RATE = 2X RSA/ RANGE
RSA= BEARING RATEXRANGE/2
OSA =SIN REL BRG X OWN SPEED
TSA = SIN ATB X TGT SPEED
SPEED =TSA/SIN ATB
ATB =TSA/SPEED INV SIN
DOT = RANGE X SIN ATB


THIS IS HOW WE GET TO A BEARING RATE ONLY
SOLUTION IN THE RN SOMETIMES YOU NEED TO
GUESTIMATE SPEED AND RANGE HERES AND EXAMPLE
own course 030 speed 8 tgt range 16k bearing rate 1.0L bearing
060 speed 16 find tgt course ( if you go down the tote same
directions add different subtract opposite if you go up the tote
differnt add same subtract)

RANGE 16000YDS
BEARING RATE 1.0L
RSA 8L
OSA 4L
TSA 12L
SP 16
ATB 48PT
RECIP BRG 240
COURSE 288 (pt atb plus stb subtract)
DOT 12k
you can do this on a calculator using the formulae or on the old
bearing rate widger standard issue on RN subs or if you good
enough in your head


for intance sin atb 30 =.5 or half so if the range is 10k then the
dot =5k( dot is a estimate of how close the target is going to come it dosent take into account own speed so it may come closer but its a quick way of making sure your safe)
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23 )
If the target moves 5 degrees, and you don’t move at all, the
angle on bow increases by that amount (or decreases if the
target is moving away.)
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24 )
Sin target AOB : Own Speed = Sin target Speed : Enemy bearing
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25 )
So here's the simplified relation to find merchie speed, even
when the sub is moving.

DM=distance merchant traveled (unknown)
DS=distance sub traveled --> (sub speed in knots / 1.777) x seconds
B1=bearing 1
R1= range 1
B2= bearing 2
R2= range 2

[ ((Sin B1) x R1) - ((Sin B2) x R2) ]squared
+
[(DS)- ((Cos B1) x R1) - ((Cos B2) x R2) ]squared
=
[DM] squared
solve for DM, (remember to take the square root of everything...) divide by seconds, mulitply by 1.777, there's your speed. Thats actually a pretty simple equation, and works if the sub is moving or not
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TARGET AOB
================================================
26 )
AoB method #1: The sine of 30 degrees is 0.5, so if you compare
the view in the periscope to the side view in the recognition
manual, a target at 30 degrees AoB will look half as long as it
does at 90 degrees. The same way, a target at 45 degrees looks
70% as long, and at 60 degrees, about 85%.

AoB Method #2: Once you know range to target, and the length
of the target, the rest is just simple trig.
First, figure out the apparent length of your target. Do this by
measuring the width of the target in degrees from your periscope
/binoculars. Remember, each TIC mark is 1 degree, .25 degrees
, and .2 degrees for the attack scope zoomed out, zoomed in, and
the binoculars respecively. Multiply this number by 174500 and
divide by the range to the target (in feet) that you calculated
before. The result is the apparent length of your target in feet.

[For those that care about the math, there are 17.45 milliradians
per degree. A milliradian = 1 foot of distance at 1000 foot range.
Thus, 1745*apparent length in degrees/range to target in feet =
apparent length in feet]
Divide the apparent length by the actual length (all in feet of
course). Ship length is found in your manual for the given ship
type, and is also found in the in-game ship ID book (the scale
bar is in hundreds of feet).
Take the inverse cosine of this ratio, and you have the exact
angle off bow of the target ship. The result will always be 0-90
degrees, so you will have to visually determine if the ship is
moving towards or away and make adjustments to the angle.
For example if you result is 70 degrees, but you know the ship is
looking back at you, the actual AOB is 110, not 70 (i.e. 20
degrees aft of 90)

Also, this will not work well with extremely low angles (which
don't result in high PK torpedo shots anyway). You must be able
to clearly see the length of the ship. If a ship is coming directly
at you, or going directly away, you will not see both ends of the
ship to get a good view of its length.

Example: A juicy European built liner is steaming at me around
50-70 AOB. I will throw in his approximate speed, AOB, and
calculate his range to get the position keeper going so that I am
ready for my AOB calculation. Initially his range is 3,000 feet.
In the periscope I can see that he appears to be 4.5 degrees in
length. I know his length is 520 feet from the books, and now I
have all I need to calculate.

invcos[(4.5*174500)/(521*3000)] = 60 degrees
-------------------------------
27 )
Calculate AoB via formula.

AoB = 180 - (Target Course) + (True Bearing to Target)
[if the AoB value from the above formula is greater than 360
then subtract 360 from it.]

To find the true bearing to the target use the following:

True Bearing to Target = (U-boat Heading + Bearing to Target)
[if the "True Bearing to Target" value from the above formula is
greater than 360 then subtract 360 from it.]
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AOB (ASPECT RATIO METHOD)
================================================
28 )
Each ship has its own "Aspect ratio", which means the difference
of its length versus its heigth. For example, a 100 yards long
ship with a mast of 33 yards has an aspect ratio of 3,33:1. Now,
because what you can see of the ship’s height remains constantly
proportional (The mast) at any given distance, while the length
you can see will change also proportionally depending on the
AOB, you can read from your scope or TBT the new Aspect
Ratio the ship shows you, and by comparing it with the standard
aspect ratio at 90º, get the AOB directly.


You just have to do this:

1.- Note the target’s Standard Aspect Ratio (F.e. 3.95 in a
Medium Modern Composite). You can get it from the
recognition manual (length 103.6 metres divided by a heigth of
26.2 metres in our Medium Modern Composite) and have it
listed already for faster consulting.

2.- Pause the game (You are now a Tracking Party member), and
count the scope marks until the top of her mast, and the marks
from her bow to her stern (Hint: The scope locks at the exact
centre, so just count from the centre to the bow fairwater and
multiply by two). It is easier to do if you raise the reticle to
align the horizontal division with the mast top, like the next
image shows.

Divide the number of lentgh marks by the number of heigth
marks, directly (No need to convert them to anything else). In
our example, we see aprox 13.25 marks to the bow (26.5 marks
total length of the ship) and almost exact 7 marks to mast top.
Dividing it, the resulting value is 3,78

3.- Use following formula to determine the percentual variation
of the aspect ratio:

New Aspect Ratio (3,78 in this case) x 100
Variation = _____________________________________

Old Aspect Ratio (3,95 in this case)

Variation in this case would be 95,8 %, i.e. nearly 96%


4.- Use this ruler (It is simply a Sinus scale) to determine the
AOB:

In this case, 96% in the lower scale represents a 75º AOB, as
you can see in the upper scale. Easy, isn’t it?
Now unstop the game, plug that value in your tool and send it to
the TDC.
NOTE: If the target is heading away from you (No converging
course) the result in degrees must be added to 90º. The aspect
ratio variation will be the same if the target has an angle on the
bow of 45º or of 135º, i.e. you will see 70% change towards the
original Standard Aspect Ratio in both cases, so it is up to you to
correct that. But its is fairly easy to see in general terms if the
target is moving away or converging, and the masts of the ship
will always provide you an orientation in the most difficult cases.

The aspect ratio approach outlined above takes the range into
account indirectly - since the apparent mast height also changes
with range like the apparent length, by using the ratios of the
two you don't need to actually determine or know the range to
solve for AOB - you only need the apparent height and apparent
length (to compare against the known values from the recognition
manual or pre-determined aspect ratios from a chart), and both
of those can be obtained from the 'scope

In the german method indicated by WernerSobe you must have
at least one range readout, otherwise you have nothing because
the same ship can f.e. extend 24 scope marks in horizontal at 90º
AOB at 2000 yards or at 45º AOB at 1200 yards (Numbers not
calculated precisely ). With my method that's not needed at all.
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RELATIVE AND TRUE COURSE
================================================
29 )
it really is adding or subtracting the bearing from your current
heading. Bearings from 0-180 degress you add, from 181 to 360
you subtract.

for example: i'm heading 299 degrees and get a hearing heading
at 347. i'd subtract 347 from 360, which is 13 and subtract that
from 299, which is 286. so my new heading would be 286. or you
can do the long math: 299 plus 347 = 646 minus 360 = 286.

another: i'm heading 137 degress and get a hearing heading
179. if i add 179 to 137 i get 316 and that's my new heading.

Old pilots trick here...

When it comes to calculating a reciprical bearing, the quickest
way to do it is use the plus2/minus2 method (or vice versa).

Eg, if you are heading 035 then Plus 2 = 235, Minus 2 = 215

If the reverse is true, then 215 Minus 2 = 015, Plus 2 = 035
-------------------------------
30 )
If you have a certain compass heading you want to turn to there's
an equation you can do to get the proper bearing to look at
before hitting the '=' key.

New course - Current Heading (+ 360 if negative)

This means that you take the course you want to turn to and
subtract the direction you're currently heading in. Your current
course can be found by turning the periscoe/uzo to 0 degrees
and hitting '='. Then if that result is negative just add 360.

So let's say you want to set a course to 045 degrees, and you find
your current heading to be 128. 45-128= -83. Since it's negative
we add 360 and get 277. Now just point your perscope/uzo at
bearing 277 and hit '='. You'll now turn to the course you want.

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31 ) JOKE
What do on on long, boring patrols

Prepare for action by getting to know your boat and the
environment.
How far can your boat go at xx speed before the batteries are
at 50%?
How long does a recharge take?
When is daylight around here?
When is sundown?
Where is the bottom? If you are not using external views, crash
diving in shallow water can be quite an interesting experience.
Examine your crew before fatigue causes you to change their
positions. They will be more efficient if placed in their original
positions. This becomes easier after some courses earn them
badges, but in action you want the best men on the job.
What types of torpedoes have you got loaded in the tubes?
What are the characteristics of them?
Do you have a plan of action or just sail to your patrol area and
back?
Where will daylight find you? Right in the enemy air patrol zone?
Where do you want to be when night falls? When your batteries
need recharging?
Examine the ship register ahead of time. Knowing the basic
information about the common types will help later in the stress
of a contact/approach.
What's your crush depth? Check in the manual for your type.
When low on fuel, is there an alternate port closer than home,
and how far away is that?
Even if you miss a sound contact or reported contact, make note
of the locations because the unit will cycle back through those
spots again. Hunt the hot spots.
I also read a book during daylight because it and the sound of
the waves are SO relaxing.
Just don't trust the crew to spot everything!!
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32 )
asin = ((target speed/torpedo speed) x sin(AOB)) to determine
the angle of lead, aka, Offset Angle of Collisioin.
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33 )
Mainly I use my "heading" to calculate target heading and AOB.
I try and guesstimate the AOB from visual, then use the
following formula to get target heading:

x = 180 - AOB - bearing to target

where x is the number of degrees you need to turn port or
starboard to be on an equal heading to the target = target
heading.

What I then do is plot a course line for the target, and then
compare and adjust it to the course lines generated by
range/bearing measurements. This allows me over time to fine
tune the AOB in situations where fast 90 isn't practical, and also cross-checks my range/bearing plots as well. Basically, I need the sub heading to plug into the trig above...
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34 )
failing that, you could make your own Lat/Long plotting sheets
using 10ths of inch as Lat increments for nautical miles, then
simply multiply the number of minutes of Longitude by the Cos
of Lat to get the number of miles and plot at the desired scale.
For example, to plot your position W20° 16.5' on N40°, at a
scale of 10 tenths of an inch per 10 nm, multiply 16.5 x cos 40°
= 16.5 x 0.766 = 12.6 tenths of an inch.
----------------------------------------------------------------------------------------

RANGE TO TARGET
================================================
35)
The manual says that the small marks = 1° @ 1x or 1.5x in the
scopes & the large marks = 5°
small marks = 0.25° @ 4x or 6x & the large marks = 1.25°

UZO (7x) small marks = 0.2° & large marks = 1°.

This is extremely hard to measure during foul wx. What I've
learned since my first day in the "Academy" 2 yrs ago is when
the C2 Cargo fills the scope viewfinder above in 6x
magnification, it is close enough for a kill.

However, if you'll note in the above thumbnail the MHH =
23.2 m in the recognition manual and measures ~2.3° in the
1.5x marks...doing the math: Range = 23.2m / tan 2.3° =
578 m (rounded up)

that tramp steamer on the right...

MHH = 22.7m measure ~1.2°: math: Range = 22.7 / tan 1.2° =
1084 m (rounded up)
----------------------------------------------------------------------------------------
36 )
Optical magnification at Attack and Observation Periscopes,
UZO and Binoculars was increased
up to 10X, now minimun marks at maximun magnification (10X)
is 0.1 degrees in Observation
Periscope, and 0.075 in Attack Periscope.
----------------------------------------------------------------------------------------
37 )
the range to the target was measured with a trigonometric equation involving a right-angle triangle. starting with the periscope head at the bottom end, the known height of the ship as the vertical line, one must find the length of the hypotenuse to determine range (the horozontal line in a right-angle triangle)only knowing how tall the ship is.

sine alpha = opposite/hypotenuse

alpha being angle subtended on periscope

opposite = mast height
hypotenuse = range

so range = mastheight / sine angle subtended

but the earlier scopes with the split prism had this calculation automated, as the american scopes do in sh4

Hitman fairly recently demonstrated that the telemetry markings on the periscope reticule were in radians rather than degrees, which apparently makes the range calculation easier

------------------------------
38 )
-Don't we use the two catheti and tangens of the angle to calculate the range?

range = height / tangens (angle)

Anyway, for such a small angle the difference between the hypotenuse and longer cathethus is minimal.

-Maybe so.
However, it is correct physics.
A torpedo travels about 1000m/min
A 300 meter ship at ten knots travels about 300m/min
If a sub at 1000m, perpendicular to the target fires a torpedo at the middle of the ship, the middle of the ship will have traveled 300 meters by the time the torpedo arrives at the spot at which it was aimed, missing the ship by 150 meters.
If the sub is at 2000 meters, and it fires a torpedo at the center of the ship, it will miss the ship by 450 meters.
Etc.
It appears prudent to lead the ship.

The AOB calculation corrects the equation for the sub not being perpendicular, by adjusting the amount that you lead the ship with your torpedo.

This is done by the torpedo computer when you feed the data into it.
If the torpedo doors are not open when the fire order is given, there will be a delay in the firing of the weapon by several seconds, making the torpedo arrive late and perhaps missing the ship.

The only time range is not important is if both the sub and the target are stopped, and the ship is at least 350 meters away, and no further than the range of the torpedo (?5Km).

-this is still not correct physics

innit, and the difference is in fact vanishingly small except at very close ranges. with sine you are measuring range to top of mast, with tangent you measure range to waterline.

e.g 25m mast subtends 1 degree
range to mast top (using sin) = 1432.47m
range to waterline (using tan) = 1432.25 m

a difference of 22 cm

e.g. 25 m mast subtends 10 degrees
range to masttop (using sin) = 143.97m
range to waterline (using tan) = 141.78m

a difference of just over 2 m, and in either case within minimum torpedo range.

Using sine is more practical for the simple reason that the same circular sliderule can be used to solve this calculation as for all the other sine-based calculations you may need to solve!

-basically the firing solution is a triangle, which is why trig is so useful. One side of the triangle is made up of the target speed, and another the torpedo speed. All that is then needed is the lead angle. Range is not important. The angle deals with it.

test it yourself. Set the TDC up to show an AOB of say port 80 and a bearing of say 10 and a speed of between 3 and 15 and see what happens to the calculated gyro with different ranges. Try with different speeds.

But it is only really a triangle with straightfire - say gyros between +-15

more than that, it becomes curved fire and to make the torpedo meet the aiming point requires factoring in another triangle, which is the difference between the line of sight between the scope and the target, and the fact that the torpedo exits from the front of the submarine, goes straight until it has cleared the boat, then begins a turning circle to the new gyro. This requires range to provide the necessary information.
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TORPEDO SPREAD ANGLE
================================================
39 )
I would like to know , what is the spread of my torpedos ( how far apart ) in meters from each other , of a 2 torpedo shot , with a 5° angle set in the TDC , at a distance of say 2.3kms , would be .

spread in meters = tangens of spread angle * distance in meters
In this case it would be 200m.

----------------------------------------------------------------------------------------

END & Thank you for your attention

Your beloved archivist JMV

[Pisces]

For part 1, 2 and 3 (measuring speed by using stopwatch and watching it pass the periscope line) it is good enough to just double the meter/second value. Only at speeds above 17 knots are you beginning to overestimate the speed by a halve knot.

[Hanomag]

OMG! I am sooo glad I use weapons officer assistance...

[makman94]

nice effort JMV ! (i really believe it)

I didn't read whole of it and probably you will be right at most of them (if not to all of them) but remember this: there are two ways to leave people in nescience ,the first way is not to give them data at all (logical) and the second way is to start 'bombing' them with data in very shot time! then the mind just....'close the store'
i doubt if anyone will read whole of this....

[JMV]

Pisces :
Why 17 knots precisely ? Thanks for your answer anyway.

Makman

I know I'm useless, after 2 years, I'm still playing 74%, ( Sunk 80.000 T in this 14th mission today end 41, but I know it counts for nothing ) but I know with all the doc I have, I should do better... I'll get there one day. Some are gifted, some are not, you know...
Anyway, I just meant not to be selfish, that's all. And if I'm not as good as you with math and trigo, at least I'm trying, and try to be usefull for others with what I gather here and there. I know, I am certainly a better archivist than the math guy...

Your beloved archivist. JMV

[java`s revenge]

Or you use the OLC Gui..:rotfl:

[Pisces]

Originally Posted by JMV

Pisces :
Why 17 knots precisely ? Thanks for your answer anyway.

Well, not precisely. The conversion factor from meters/second to knots is 3600s/1852m= 1.944 . As I suggested we take the easy conversion factor of 2 (just doubling it). Then, if the real speed is 17 knots we somehow measure is as being 8.75 m/s (the real speed is 8.7456 m/s), we overestimate it as 2*8.75 m/s= 17.5

Since most civilian traffic is much slower than that, doubling the m/s value is easy yet accurate enough. It's allways off by less than 3% of the real speed.

[makman94]

Originally Posted by JMV

Makman

.....I know I'm useless.....
......not to be selfish...... not as good as you with math and trigo.....

i think that you are ....overacting a little bit here JMV. you didn't understand the point of my post.i was not against you ! on the contrary....
anyway,sorry if you felt insulted by me.it wasn't my intention

[JMV]

To Makman94 :
Sorry to have misunderstood the true meaning of your post, but my intentions were not to bomb anybody with this load of formulas, but since they are scattered all aver the forums, I thought it would be usefull to write down these formulas as a reminder for whoever has a brain for that, rather than keeping it for myself. No hard feelings.

Pisces :
Thank you for your always very detailed explanations.

[h.sie]

JMV: Thank you for that collection.

[Bent Periscope]

You must be on a long patrol to take the time to type all this. Thanks for the summation of the information.

[JMV]

Yep ! Spent a loooooong time reading the forums for the past 3 years.
But little by little, One here one there...

[DevlinParson]

old thread, I know, but thanks for this!

[CTU_Clay]

Thanks for your work JMV

[bstanko6]

I like how you use 1.852m as the knot. technically this is not accurate (by a small degree, as I have been told). But it was accurate before the 1950's. I use still, and used it in my how to videos.

I do agree with Mak, I stopped reading it because there was an overload of info, but lots of good stuff.