Normal approach course?

[razark]

I'm just starting to read the old instructions, and trying to get a better grasp on how this was done during the war. I've got a question, and hopefully someone can give me some insight.

From http://www.ibiblio.org/hyperwar/USN/...SS-Doct-4.html:

Normal approach course -- The course which, at right angles to the bearing of target, closes the range.

Also mentioned in http://www.hnsa.org/doc/attack/index.htm#platei

Can someone explain why? Is there something in the geometry of the approach that makes the normal approach course better than another method? Why 90 degrees, instead of 80, or 70, or any other value?

Also, in what situation is the NAC used? Would the NAC be constantly recalculated to keep the target on the 90 degree bearing, or would it be calculated once?

[Armistead]

I'll let others delve into the math, but I hate 90 degree approach in game, usually leaves you broadside to an escort. That's not saying I don't prefer to shoot with a 90 angle, although I use any angle I can get a bearing, but I certainly don't plot that way.

[WernherVonTrapp]

I've used a 45° angle on approach sometimes. It all depends on the situation; whether a slow convoy or fast TF, position of escorts, early/late detection of target, weather conditions, etc..

I prefer a 90° angle (more like 80 - 110 range) not because it offers a better firing solution but because it facilitates more options for my escape. E.G., along the 90° angle range, I can turn port or starboard in about the same amount of time than if I was approaching at 45° (relative to target's approach) which would make turning to port more time consuming. At least, this is what I've come to feel comfortable with.

[Rockin Robbins]

You have to realize that when a target is first sighted you don't know its course very accurately at all. So setting up your course relative to his just isn't possible. You need information.

One way to accumulate that info is to use the "normal approach course." Just put the target off your starboard or port beam and see if the range opens up or closes. The odds of being on parallel courses, where you would remain at the same bearing and range, is just about zero.

So you put him on your 90 and watch him. If his bearing increases toward 180 that means that if you are on a converging course you will arrive on his track first. You might not be able to get accurate ranges, but you can find out if the range is increasing or decreasing. Decreasing range on a normal approach course means you are on converging courses.

If you are gaining on him your job is to produce enough range to do the end around and not be seen. You may have to open up the bearing for awhile and put him on your 120 bearing to gain enough distance. Then continuously keeping a 90 degree bearing will eventually put you on his track. That will give you his exact course.

You will plan to be there in enough time to safely pick a spot 500 to 1000 yards off the track to plug him from.

[razark]

Originally Posted by Rockin Robbins

You have to realize that when a target is first sighted you don't know its course very accurately at all. So setting up your course relative to his just isn't possible. You need information.

So this is something one does very early in the attack, before you have good speed and course information? During the approach, you gather more/better information and then close on the target's projected track by any appropriate method?

[TorpX]

Originally Posted by razark

............
Can someone explain why? Is there something in the geometry of the approach that makes the normal approach course better than another method? Why 90 degrees, instead of 80, or 70, or any other value?

I worked out the geometry related to the "normal approach course", some time ago when I started getting serious with SHCE. I can't remember the trigonometric particulars, but suffice it to say, it is indeed a matter of geometry. You probably already know this, but the word "normal" relates to the course being normal (perpendicular) to the target, not the course being usually or always used.

The course allows an interception to be made at a minimum of speed, provided an interception is possible. It is not a tactically optimum course or a default plan. There are too many unknowns to allow for this. The NAC is more a product of math, than tactics, if you get my meaning.

Also, in what situation is the NAC used?

If a sub is operating on the surface, it would normally have a speed advantage and has many options for making an intercept and attack. The same is true, if it is submerged, but on, or very close, to the target's track. When the target is detected in a less than optimum situation (a distance off the target's track), where the sub must operate submerged, and with a very limited speed, the NAC is often very valuable. ( I've made use of it many times.)

I can think of 5 general cases:

Case 1.
You start on a NAC, but the range is steadily increasing (the target is on a divergent course). This means you were caught napping and the target basically, "got by". You would have to chase after it (at considerable speed) or let it go. The NAC will not help you here.

Case 2.
You start on a NAC, but the range is holding steady, (the target is on a parallel course). Interception is impossible at this speed, (but can be achieved at a greater speed).

Case 3.
You start on a NAC. Range is steadily decreasing. The target is loosing bearing. This means interception is assured (unless the target changes speed or course). If you continue at this speed and course you will pass in front of target.

Case 4.
You start on a NAC. Range is steadily decreasing. The target is holding bearing. Interception is assured. You are on a collision course.

Case 5.
You start on a NAC. Range is steadily decreasing. The target is gaining bearing. Interception is not possible at this speed, but an attack may be possible. Target will pass in front of you.

Case 2 is mathematically improbable. If you are searching continuously and are alert, so is case 1.

Would the NAC be constantly recalculated to keep the target on the 90 degree bearing, or would it be calculated once?

It could be done either way. If you are gaining bearing [Case 3], and you hold the same course you will reach the target's track and pass in front of him. You could do this in order to make use of stern tubes or simply reach the area first and slow to minimum speed and wait. However, you could also adjust bearing once or more times. In this way, you would intercept sooner. If you were gaining bearing, you could also reduce speed, and still make an interception.



BTW, There is also, a Normal Evasion Course. (I think that is what it is called.) In this case, taking a course 90 deg. going away from the "target" allows one to get as far away as possible at a given speed. This can be very useful at times.

[joegrundman]

There seems to be a bit a bit if confusion about what the Normal Approach Course is, and what it is for. here's the plate of diagrams in the Torpedo Fire Control Manual. We are interested in Figure 1.



what armistead seems to describe is the normal course, not the normal approach course. The normal course is perpendicular to the target track. the normal approach course is perpendicular to the bearing to target.

If you are on the surface, or surfacing is an easy option, you can go generally go faster than your target. If you can go faster than your target then you can end around any target (land and ports and enemy warships/planes not withstanding). It's just a matter of time.

If you need to remain submerged then most targets travel faster than you.

In cases where you know the target range, speed and course, you can calculate an intercept course and point with some precision, and optimised to meet at the earliest opportunity.

In cases where you do not know the target details, it can be mathematically proven that the normal approach course will successfully intercept the greatest possible range of target speeds and courses.

If your angle of approach is anything other than 90, then more possible combinations of target aob and speed will escape your intercept attempt.

[joegrundman]

to make a perfect intercept on normal approach is to make a right angle triangle.

in the case of a perfect intercept (collision course)

your speed, a = sin target aob x target speed.

if sin target aob x target speed is greater than our speed, then we cannot make the intercept. if it is equal or less than we can make the intercept.

E.g. our speed 5 kts, enemy speed 10 knts, aob 50 - we cannot make this

sine 50 (approx 0.75) x 10 = 7.5 which is greater than our speed of 5. we can only make this intercept by increasing speed.

if target aob was 30 and at 10 knots, then the intercept is possible

sine 30 (0.5) x 10 = 5 knots, which is our speed.

incidentally this formula means, that yes, if you are on a collision course and you can eyeball target aob, then you can calculate speed. in itself this is a good reason for following a normal course, but this is not actually the matter in hand.

since the target aob and speed are unknown at this time, but it is assumed that the target speed is faster than ours, the question is what bearing to target gives us the best chance of making an intercept. The answer is 90.

If your target is at a different bearing than 90, the equation changes from

our speed, a =< sine aob x target speed

to

our speed, a, x sine bearing to target = < sine aob x target speed

since sine 90 = 1, and the sine of any other bearing is less than 1, it is clear that a 90 degree bearing to target allows interception of the greatest possible variety in target aob and speed for whatever speed you have.

[joegrundman]

Optimal Approach Course

that was the Normal Approach Course

however, since we are not attempting to ram the target, we don't need to optimise our interception chances for colliding with the target itself.

we are interested in the best chance of getting into a torpedo attack position, which let us say is about 800 yards off the target beam.

therefore to find the approach course that absolutely maximises our chances against a faster, unknown target, we need our normal approach course not to be relative to the target, but relative to a 'virtual' target that is 800 yards nearer to us, and exactly on the target's beam.

This is not possible to solve exactly without other information, but will account to an offset of a few degrees forward of 90. E.g an intercept bearing to target of around 85 degrees will marginally improve your chances over a bearing of 90.

This is the Optimal Approach Course.

Note: having established this course, and you are pulling ahead of the target, you may of course narrow the bearing to target in order to speed up the intercept, or you may slow down in order to save batteries.

but if it is pulling ahead, you can only speed up if you are already on the optimal approach course.

It is therefore sound practice to begin the approach at the highest speed that is practical - you may slow down if it's possible, but if you start slower, you may have lost your opportunity to hit a target without surfacing.

[Daniel Prates]

Excellent thread! I am rating it so we all can remember how to find it in the future. I would suggest everybody else doing the same.

[TorpX]

@ joegrundman,

Your explanation and advice are excellent.

This part deserves added emphasis:

...but if it is pulling ahead, you can only speed up if you are already on the optimal approach course.

It is therefore sound practice to begin the approach at the highest speed that is practical - you may slow down if it's possible, but if you start slower, you may have lost your opportunity to hit a target without surfacing.

I will usually go to standard bell and turn on a NAC, as soon as I see which way the contact is moving. When I am on the proper course, I drop down to 2/3 speed. Then I start plotting. By checking the bearing, you can adjust from there.

This will work when you can only see the mast tops and don't know the AOB, and even be done when all you have to go on is sound bearings.


This illustrates why the practice of periodic periscope searches gave way to continuous searches (or even surface searches). The farther away you spot the contact, and the more time you have to approach the target's track, the fewer contacts will get by.

[razark]

Thanks for the info y'all. I'll have to read over it a couple of times to let it all sink in.

[Daniel Prates]

I say again, indeed an excellent thread. This kind of discussion is what makes this forum AWESOME.

[virtualpender]

Thank you everyone - fascinating stuff.