A theory on the subject of Manual targeting solutions

[msumpsi]

I have been thinking leatly about the problems with the optics and the information of reference heights on targets and as i was thinkin on the equations of motion and the trigonometry of collisions it ocurred to me that it is very posibble that there is no need to be very precise as long as the measuremets are gauge incorrectly by the same amount. I have not done yet the mathematical calcullations to confirm that the equiations of motion are correct, maybe i will give it a go if a have time.

The idea on the subject is that no matter how wrong the gauge is in the measurements, as long as you take them with the same device they will still give you the correct course of the travelling target if it is going on a strait line. The differences that one will get when the gauge is incoorect will be in range and speed of the target.

But, since these two measurements are correlated to priovide the firing solution, it is very possible that the torpedo solution is correct despite the wrong measuremets.

To illustrate this, lets think of a target that is travelling acros the bow of the submarine at a certain speed which we do not know yet. We estimate the identification of the target, lock and take a range measure. Input in to the TDC will send both range and bearing. Lets assume that we misestimated as bad as measuring twice the real range to the target, so if the real value is for example 1000 yards, we measure 2000 yards.

After a certain amount of time, depending on the situation circumstances we make a second measurement of the target and send it to the TDC, which will send again range and bearing.

Now the TDC has two points of information and can draw the line that crosses them both, thus the course. Since it keeps track of the time passed in beteen measrues, it is straigh forward to calculate the speed.

Now we have the range, the course and the speed. The course of the target is correct since the two measuremts are incoorect by the same gauga, thus given as a solution that is parallel to the real course, which in terms if of course the course.

The data input that is wrong to the TDC are the range which in this case would be double of the real range, and the speed which also will be double of the true speed of the target. The reason for that is that the two triagnles made of points A (submarine), B (measure 1), and C (measure 2) will be equivalent, one the real one and the other one the one we have measured, and thus all the sides being in the same relation, so if one side of the triangle is double, then all the others are so. In this case the distance travelled by he target as measured will be double and thus double the speed.

Now we have a solution that is wrong in range and speed of the target, but here is where the theory cames into place. That the course of the torpedo in order to intercept the measured target, will also intercept the real target, only at a different time and bearing. Now, I have not made the mathematical calculations in order to cornfirm the theory (which takes time and effort, or a good mathematician) but it seems to me that it is very possible that is coorect because of the key correlation between the speed and the range in the measurements.

[msumpsi]

Originally Posted by msumpsi

I have been thinking leatly about the problems with the optics and the information of reference heights on targets and as i was thinkin on the equations of motion and the trigonometry of collisions it ocurred to me that it is very posibble that there is no need to be very precise as long as the measuremets are gauge incorrectly by the same amount. I have not done yet the mathematical calcullations to confirm that the equiations of motion are correct, maybe i will give it a go if a have time.

The idea on the subject is that no matter how wrong the gauge is in the measurements, as long as you take them with the same device they will still give you the correct course of the travelling target if it is going on a strait line. The differences that one will get when the gauge is incoorect will be in range and speed of the target.

But, since these two measurements are correlated to priovide the firing solution, it is very possible that the torpedo solution is correct despite the wrong measuremets.

To illustrate this, lets think of a target that is travelling acros the bow of the submarine at a certain speed which we do not know yet. We estimate the identification of the target, lock and take a range measure. Input in to the TDC will send both range and bearing. Lets assume that we misestimated as bad as measuring twice the real range to the target, so if the real value is for example 1000 yards, we measure 2000 yards.

After a certain amount of time, depending on the situation circumstances we make a second measurement of the target and send it to the TDC, which will send again range and bearing.

Now the TDC has two points of information and can draw the line that crosses them both, thus the course. Since it keeps track of the time passed in beteen measrues, it is straigh forward to calculate the speed.

Now we have the range, the course and the speed. The course of the target is correct since the two measuremts are incoorect by the same gauga, thus given as a solution that is parallel to the real course, which in terms if of course the course.

The data input that is wrong to the TDC are the range which in this case would be double of the real range, and the speed which also will be double of the true speed of the target. The reason for that is that the two triagnles made of points A (submarine), B (measure 1), and C (measure 2) will be equivalent, one the real one and the other one the one we have measured, and thus all the sides being in the same relation, so if one side of the triangle is double, then all the others are so. In this case the distance travelled by he target as measured will be double and thus double the speed.

Now we have a solution that is wrong in range and speed of the target, but here is where the theory cames into place. That the course of the torpedo in order to intercept the measured target, will also intercept the real target, only at a different time and bearing. Now, I have not made the mathematical calculations in order to cornfirm the theory (which takes time and effort, or a good mathematician) but it seems to me that it is very possible that is coorect because of the key correlation between the speed and the range in the measurements.

It occurs to me that the answer to this question lies on the answer to the next question: will a torpedo set to hit a ship trravelling in a straight line given bearing, course, speed and range hit another ship on the same course, and bearing but but which range and speed (both) are a constant factor multiplyier of the original one? For example at hlaf range and half speed. If the anwer is yes, and i think it is, then the theory exposed before is correct.

[TorpX]

Well, after the internet ate my post, I took another look at this problem. Perhaps it is just as well. On closer examination, I diagramed two cases.

In the first case, I have a moving sub and the plot has two sub positions and two target positions. So, you have a trapezoid in which range errors change 3 sides, but the sub travel is unchanged. Here the calculated target speed will change, but will not necessarily double. Thus, the range errors will break the solution. This is not a surprise; otherwise there would be no need to fuss about estimating range and speed like we do.

In the second case, I diagramed a plot with the sub being stationary. Here you have a triangle with all sides doubled. Your theory seems to work here. At least I can't find any flaws in it, at the moment. It does seem odd to me, though.

[Hene]

If you have the wrong speed, you wont hit. if you have a target moving at 5 knts and are using a torpedo that moves at 30 knts, and you have positioned yourself so that the torpedo strikes after 30 seconds, and you then double the range, i will take one minute for the torpedo to reach the impact point, but also for the ship, because it will also have doubled its distance to the impact point, and you will hit. If the ship would double its speed it would reach the impact point faster than the torp and you would miss. if you have misjudged the range to the target so that it is double the actual distance, and are using it to calculate the speed you will get a result two times higher than actual because it would have travelled double the distance it actually has, and you will miss. The range doesnt matter, because at right angle the torpedo will always hit the ship as long as you have right speed. The only things that matter are the torpedo speed, ship speed and ships bearing. hope I explained this well enough

[msumpsi]

Originally Posted by Hene

If you have the wrong speed, you wont hit. if you have a target moving at 5 knts and are using a torpedo that moves at 30 knts, and you have positioned yourself so that the torpedo strikes after 30 seconds, and you then double the range, i will take one minute for the torpedo to reach the impact point, but also for the ship, because it will also have doubled its distance to the impact point, and you will hit. If the ship would double its speed it would reach the impact point faster than the torp and you would miss. if you have misjudged the range to the target so that it is double the actual distance, and are using it to calculate the speed you will get a result two times higher than actual because it would have travelled double the distance it actually has, and you will miss. The range doesnt matter, because at right angle the torpedo will always hit the ship as long as you have right speed. The only things that matter are the torpedo speed, ship speed and ships bearing. hope I explained this well enough

You guya re right, i did the calculations and they will no intercept, you have to get right the measurements.