Guided Missile.

[mfgoode]

Originally Posted by Jacob Visser

I was submited this same problem some 20 years ago by my grandfather, its setting was more pacific: it was about a doc running in pursuit of his human :-).

To really solve the problem according to premisses (the direction of travel of the pursuer is always towards the pursued, you need to compute a curvilign integral. I searched "Pursuit Curve" in MathWorld found Pursuit Curve and related links.

Thanks to you axn1 and Whacky for your support :-) I started doubting.

I would have given you a no nonsense solution which has no argument as to the path.

I have given you a hint in my post to maybeso and since I dont think ANY of you mentioned deserve to know the simple but rigorous solution I will refrain once more from presenting it.

When I say 'once more' this is not the only solution or theory of mine which will make waves in future which I have actually withdrawn from this forum for lack of support from the members.

It awaits publication in a prestigious journal very soon to be refereed by IMPARTIAL math'cians. Amen.

As I told axn1 to either take it or leave it. To be sure there are others who will do the needful.

Mally

[Wacky]

Originally Posted by mfgoode

At times the duration travelled along a curved line between two points is shorter than following a straight line.

That is true ONLY when the speed is affected by an acceleration such as that caused by gravity. Without acceleration, the time of travel is directly proportional to the distance and a straight line is always the shortest path between two points.

[S485122]

Mally,
You agree with me that initially, the missile points due North towards the plane? (Or even if it was pointing in another direction, just after departure it points towards the plane, thus due North.)

Do you agree with me that the plane after 36 seconds has travelled 10 miles due East?
Do you agree with me that at that moment the missile is 20 miles from its departure point?
Do you agree with me that at that moment the missile is pointing at a point 10 miles east of the departure place of the plane?

Do you agree with me that the plane after another 36 seconds has travelled 10 more miles due East?
Do you agree with me that at that moment the missile is pointing at a point 20 miles east of the departure place of the plane?

Do you agree that since the place the missile is pointing to is changing, that it is not travelling on a parallel to that of the plane (contrary to hypotheses) its direction of travel is changing and thus its path is not a straight line?

I have made a drawing.
On the left the solution most of the posters are proposing.
On the right the solution you are proposing. This last solution implies that from the start the plane travels North-East-North and this while the plane is due North.

[Fusion_power]

Rigorous? As in mathematically rigorous? Or real world rigorous?

In the real world, the missile takes some amount of time to accelerate to its cruise speed. I don't see mention above of this acceleration time. I presume the missile will be launched from the ship at some angle. How far will it travel up before modifying its course to be parallel to the ground?

Fusion

[Eivind]

Hi

I am woting for the 240 sec. solution - or rather 239.87 sec.

Since this is a matematical problem the turnrate can be infinit high during the last part of the interception. No problem there.

The orginal question stated clearly that:

In other words the missile is constantly pointed at the plane.

So no onboard computer to calculate the point of interception.

I did a stepwise calculation in Berekely Madonna:

METHOD RK4

STARTTIME = 0
STOPTIME=275
DT = 0.001

Speed_plane = 1000/60/60
Speed_missile = 2000/60/60

init plane_x = 0
init plane_y = 100

Next plane_y = plane_y
Next plane_x = plane_x+speed_plane*dt

Angel = if (plane_x-missile_x) > 0 then arctan((plane_y-missile_y)/(plane_x-missile_x)) else Pi/2

init missile_x = 0
init missile_y = 0

Next missile_x = missile_x + speed_missile*dt*cos(angel)
Next missile_y = missile_y + speed_missile*dt*sin(angel)

Limit missile_x <= plane_x
Limit missile_y <= plane_y

The missile starts at origin (0,0) and the plane at (0,100). X-coordinat is east and Y-coordinat is north.

Confirmed hit after 239.87 sec, the plain travels 66.63 miles + fall to the ground.

Se the graph intercept for coordinats of missile and plane vs time


Se the graph phase plot for plane_y and missile_y vs plane_x - this is the flightpath seen from above.

-Eivind

[Eivind]

Originally Posted by Fusion_power

Rigorous? As in mathematically rigorous? Or real world rigorous?

In the real world, the missile takes some amount of time to accelerate to its cruise speed. I don't see mention above of this acceleration time. I presume the missile will be launched from the ship at some angle. How far will it travel up before modifying its course to be parallel to the ground?

Fusion

Please provide:
1) Altitude difference between missile and plane.
2) Launch angel in Z-coordinat
3) Function or tabel for acceleration of the missile

This is easy to incorporate into the model.

-Eivind

-Eivind

[drew]

Originally Posted by Jacob Visser

Mally,
You agree with me that initially, the missile points due North towards the plane? (Or even if it was pointing in another direction, just after departure it points towards the plane, thus due North.)

Do you agree with me that the plane after 36 seconds has travelled 10 miles due East?
Do you agree with me that at that moment the missile is 20 miles from its departure point?
Do you agree with me that at that moment the missile is pointing at a point 10 miles east of the departure place of the plane?

Do you agree with me that the plane after another 36 seconds has travelled 10 more miles due East?
Do you agree with me that at that moment the missile is pointing at a point 20 miles east of the departure place of the plane?

Do you agree that since the place the missile is pointing to is changing, that it is not travelling on a parallel to that of the plane (contrary to hypotheses) its direction of travel is changing and thus its path is not a straight line?

I have made a drawing.
On the left the solution most of the posters are proposing.
On the right the solution you are proposing. This last solution implies that from the start the plane travels North-East-North and this while the plane is due North.

Jacob, don't waste your time. This is Mally's typical M.O. I've discovered after several such discussions with Mally that he cannot be reasoned wiith. It doesn't matter if there is a rational explanation for the proper solution to the problem, he'll stick with *his* answer no matter what arguments you present to convince him of the correct answer. Since he presented the problem himself, I think he believes his answer must be the right one irrespective of any logic or mathematics.

I have no doubt that the problem, as posed to him, has the answer Mally presented, but I believe he added the "In other words the missile is constantly pointed at the plane" comment in an attempt to clarify the problem not realizing that it intruduced an assumption that yields a vastly different answer. But he won't admit it.

In any case, I corroborate your answer. We all know what the proper solution is, so don't lose any sleep if you cannot convince Mally. It's a lost cause. I've linked below another thread in which Mally could not be reasoned with. That was my first encounter with Mally and it's put a bad taste in my mouth ever since. You can also see how rude he was to me right off the bat, despite having the wrong solution. There are more examples in this forum of the same type of behavior but I cannot be bothered to find them right now. Hopefully, this can convince you that you're fighting a losing battle:

http://mersenneforum.org/showthread.php?t=5068

Drew

[mfgoode]

Originally Posted by Wacky

That is true ONLY when the speed is affected by an acceleration such as that caused by gravity. Without acceleration, the time of travel is directly proportional to the distance and a straight line is always the shortest path between two points.

Well Richard Wackerbath old boy you must be joking. You couldn't be serious as I cant believe it. What howlers!

Please brush the cobwebs from your brain

Regards my old friend,

Mally

[mfgoode]

Originally Posted by Fusion_power

Rigorous? As in mathematically rigorous? Or real world rigorous?

In the real world, the missile takes some amount of time to accelerate to its cruise speed. I don't see mention above of this acceleration time. I presume the missile will be launched from the ship at some angle. How far will it travel up before modifying its course to be parallel to the ground?

Fusion

I have emphasized its mathematical and not a physical problem.
This is strictly not a real world problem.
Ship? from off the shore?
The vertical component is 100/sq.rt.3. It travels vertically as high as the plane no higher and horizontally as far as the plane travels dumkoff !

Mally

[mfgoode]

Originally Posted by Eivind

Hi

I am woting for the 240 sec. solution - or rather 239.87 sec.

Since this is a matematical problem the turnrate can be infinit high during the last part of the interception. No problem there.

The original question stated clearly that:

So no onboard computer to calculate the point of interception.

I did a stepwise calculation in Berekely Madonna:



The missile starts at origin (0,0) and the plane at (0,100). X-coordinat is east and Y-coordinat is north.

Confirmed hit after 239.87 sec, the plain travels 66.63 miles + fall to the ground.

Se the graph intercept for coordinats of missile and plane vs time


Se the graph phase plot for plane_y and missile_y vs plane_x - this is the flightpath seen from above.

-Eivind

Forget about step wise calculations Elvind. Thats okay for computer programmers but not in pure math.

Use an Integral if you can which is the ideal summation.

If you are at Berkeley I would expect your English to be better. As it is, its atrocious! Being from the School of Hard Knocks I believe in nipping things in the bud. Sorry!

Mally

[mfgoode]

Originally Posted by drew

Jacob, don't waste your time. This is Mally's typical M.O. I've discovered after several such discussions with Mally that he cannot be reasoned wiith. It doesn't matter if there is a rational explanation for the proper solution to the problem, he'll stick with *his* answer no matter what arguments you present to convince him of the correct answer. Since he presented the problem himself, I think he believes his answer must be the right one irrespective of any logic or mathematics.

I have no doubt that the problem, as posed to him, has the answer Mally presented, but I believe he added the "In other words the missile is constantly pointed at the plane" comment in an attempt to clarify the problem not realizing that it intruduced an assumption that yields a vastly different answer. But he won't admit it.

In any case, I corroborate your answer. We all know what the proper solution is, so don't lose any sleep if you cannot convince Mally. It's a lost cause. I've linked below another thread in which Mally could not be reasoned with. That was my first encounter with Mally and it's put a bad taste in my mouth ever since. You can also see how rude he was to me right off the bat, despite having the wrong solution. There are more examples in this forum of the same type of behavior but I cannot be bothered to find them right now. Hopefully, this can convince you that you're fighting a losing battle:

http://mersenneforum.org/showthread.php?t=5068

Drew

Etu Brute (with an accent).

What may I ask is the right answer??

Its the case of 'once bitten twice shy' for Drew who this time flew!
I'm truly sorry for you Jacob.
You are the only one taking this problem seriously.
Maybe I will PM you with the actual solution tho' Ive dropped hints here and there.
Please dont be fooled by these self made geniasses and pull out of the thread as you will be misled into a maze of confusion.

So Drew you fished out a thread to prove your point. Is Revenge that sweet ??

Mally