Guided Missile.

[drew]

Originally Posted by mfgoode

What may I ask is the right answer??

To the question you asked (as posed) the true answer is the one *everyone* in this thread except you has agreed upon...239.87 seconds.

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

No need to fish...I remember that thread well. It's not often I'm greeted so rudely in a mathematical forum.

Honestly, I don't think anyone is waiting to see your solution...we all know what a 30-60-90 triangle looks like.

Drew

[S485122]

Originally Posted by drew

To the question you asked (as posed) the true answer is the one *everyone* in this thread except you has agreed upon...239.87 seconds.

Excuse me I stand by the 240 seconds. One gets a bit less if one takes bigger steps, to get 240 seconds I computed 2²¹ steps. One gets the minimum if one takes only one step: a little bit less than 208 seconds. I played around with different speeds and came to the conclusion that the time to interception must be a simple equation involving the different speeds and the initial distance, but I haven't found which at the moment.

Because of al this fuss about the rejection of the solution I proposed I remembered that evening with my grandfather long ago. A good side effect :-)

Mally,

I find you a bit rude towards other posters.

Did you look at the diagram I posted ? If you send me your solution please take the time to answer the questions I asked you. And please forgive my typos and incorrect use of the language :-)

[99.94]

Originally Posted by mfgoode

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

When in a corner Mally's standard tactic is to turn nasty. Because he seems to be wrong more often than most, it is a regular occurrence. It is a shame because he has interesting, if idiosyncratic, things to say.

I hope that Eivind is not put off by being the latest object of Mally's insults.

In any case, I am certain Eivind's English is much better than Mally's German or Latin. "Dumkoff", Mally, is spelt Dummkopf [post 31]. "Etu" [post 33] is two words - Et tu. It means "even you" and is an expression of dismay a supposed friend's treachery. I am still trying to understand how it fits in the context in which Mally used it.

[drew]

Originally Posted by Jacob Visser

Excuse me I stand by the 240 seconds.

You're right. I took Elvind at his word because his solution appeared more precise, but now that I've worked it out myself, I agree with you. The answer is exactly 240 seconds.

Drew

[Fusion_power]

You know Mally, there is something to be said for always being polite to others.

I remind myself regularly that mathematicians as a group are usually socially inept. You have carried that trait to a new low. I am now convinced that Bob Silverman is an example of a fine human being by comparison.

Maybe you need to study the difference between discrete and discreet.

Better yet, remind me someday what a fine upstanding Christian you are.....after you have read Matthew 7:12 and Galatians 6:10.

Last, but not least, post your answer to this problem so you can either be vindicated or else proven a fool.

Fusion

[Eivind]

Hi guys

Drew and Jacob you are right - i rechecked the output, and 240 sec. is correct. Due to roundup (Glyphosate) the missile north value changed to 100 at 239.87 sec, but the east values of the plane and missile align at 240 sec. My iterations was *only* 2,7*10^6.

So please add 0.13 sec. to the previous post


99.94:

Don't worry I am not easy scared. Atleast i know my limitations

And yes - even though English nor German is my native language, I speek both quite good. Zweimal hefe weiss bitte.


Mally:

No I don't study or work at Berkeley - nor do I ever intent to do so. I am a chemical engineer working with verry nasty chemicals like PCl3 and SOCl2.

Please explain why a 4. order Runge-Kutta numerical integration is inaccurate to solve the problem. I would be glad to see the error difference between this and an algebra solution.


-Eivind

[mfgoode]

Before we continue with this interesting thread (to me at least) I would like to offer my sincere apologies to all those I sent rude and overconfident replies at several stages of its development.

These are to Wacky, Jacob Visser, Drew (post # 29 hit the nail on the head) axn1, Maybeso, Fusion Power (Matt. 7:12 : Gal. 6 :10 ) , Eivind (zweimal...), 99.94 ('wrong more often than right').

Having said that all I can say to you great guys is ' All I know is that I was blind but now I can see right'

I have re-examined the problem, which Drew guessed right that I had doctored it, and suggest we revert back to the original Jacob Visser's 'Grandfather's problem' which actually speaks of two men as referred too instead of plane and missile. Let the distance be 100 metres and the speeds x and 2x metres /sec. in a direction that always faces where B is at the moment. A is south of B.

Well its much the same but eliminates gravitational effects the missile is subjected too since we are talking on differences in decimal points.

Yes Eivind 4 order Runge-Kutta numerical integration gives as good an approximation as the actual integral generally which at present I have not derived myself

However I am happy that this problem generated more depth than what I anticipated and has amused and entertained one and all judging by the replies.

Once again I am sorry I pressed the attack button, though I learnt in Martial arts that 'attack is the best from of defence'

Regards to one and all,

Mally

[S485122]

Thanks Mally !

For the anecdote the "doc" in the problem posed by my grandfather was a dog (one more typo on my part.)

In the mean time, I did some calculations with different starting distances, speeds... It appears that the time is directly proportional to the initial distance. Then the differences in time are inversely proportionnal to the differences in speed but something else as well : if the dogs speed is an epsilon above the humans speed the factor is half that of the case where the dogs speed tends to inifinity.

T the time to interception, D the initial distance, V_P the speed of the dog, V_H the speed of the human and X some other factor depending on the relative speeds.

T=X*D/(V_P-V_H)

Where the value for X for V_P almost equal to V_H is half the value for X for V_P many times bigger than V_H. (It is not an arcsinus...)

But I got no further. The solution of the problem in MathWorld dit not enlighten me :-(

[drew]

Originally Posted by mfgoode

Before we continue with this interesting thread (to me at least) I would like to offer my sincere apologies to all those I sent rude and overconfident replies at several stages of its development.

These are to Wacky, Jacob Visser, Drew (post # 29 hit the nail on the head) axn1, Maybeso, Fusion Power (Matt. 7:12 : Gal. 6 :10 ) , Eivind (zweimal...), 99.94 ('wrong more often than right').

Thanks, Mally. I know it's difficult to swallow your pride and admit when you're wrong, and I appreciate it. Hopefully we can be more cordial with each other in future discussions.

...in a direction that always faces where B is at the moment.

I'm afraid you've made the same error again, however. The above statement is the crux of everyone's disagreement. Your solution (~108 seconds) necessitates a direct path to the point of interception. When you move towards the target's current location, you follow a curved path for which it takes longer to intercept the target (140 seconds). The acceleration of gravity isn't the issue as you said the target flies low as to eliminate the necessity to climb.

Once again I am sorry I pressed the attack button, though I learnt in Martial arts that 'attack is the best from of defence'

For what it's worth, take people's corrections as constructive criticism, so there's no reason to get defensive. They are not personal attacks, only attempts to convince everyone of the true answer. No good mathematician will tolerate errors in logic without attempting to set things straight in a constructive manner.

Drew

[Peter Nelson]

Mally I don't think this is a very realistic problem.

The missile and plane speeds are unlikely to remain constant, for example because constant thrust would have more effect on the craft as it gradually burns away its fuel reserves. Some of that fuel might be expended to indirectly offset the gravitational tendency to fall to earth, and to overcome air friction and wind and precipitation. These factors mean there is not a linear relationship between fuel burn and speed. Similar considerations apply at missile launch as to initial velocity of leaving the base.

Secondly, a plane detecting a missile launch would likely take evasive maneuvers. If it chose to head north away from the missile, the missile could well run out of fuel ie beyond its design range and crash harmlessly. If the plane was on its way to bomb a city, it might choose an alternative city to bomb as a secondary objective, making initial assumptions about its course redundant.

Any attempt to initially compute an intercept vector assumes the plane will maintain its direction and/or speed which is unlikely the case if it sees a missile coming.

I believe the missile would take a curved path, from the information given.

These are also not very sophisticated missiles.

I have worked on imaging systems ie cameras and image processing electronics, which are used for realtime analysis onboard "smart" missiles. Rather than just look at the heat of a vapour trail (where your two plane technique could avoid being hit) they actually LOOK and would IDENTIFY BOTH targets and parts of targets like a wing. They would not be fooled by such tricks so the Indian airforce had better have some new evasive techniques or be shot down in flames.

[drew]

Originally Posted by Peter Nelson

Any attempt to initially compute an intercept vector assumes the plane will maintain its direction and/or speed which is unlikely the case if it sees a missile coming.

Any missile must operate under certain assumptions regarding the trajectory of the target that won't hold steady because a maneuvering target is unpredictable. It's reasonable to chase the target vehicles current inertial state, so computing the intercept vector (using the visual feedback I described earlier) is a good approach even for a sophisticated missile.

Against a maneuvering target, it needs to be prepared to continuously re-evaluate this interception as the target maneuvers.

Drew