Surface to air missile problem.

Quote: pacomartin

The nuclear missile scenario was particularly frightening because it is feared that the crew might act on their own rather than waiting for orders. Since nuclear warfare strategy was always dependent on a certain reluctance of the highest level of command to start a nuclear war, the wishes of men who expected to die might change the outcome.

I thought the crew needed the nuclear codes, in the president's suitcase, to launch the missiles.

Quote: s2dbaker

You broke WolframAlpha. Congratulations.

Thanks, I guess.

Quote: Wizard

I thought the crew needed the nuclear codes, in the president's suitcase, to launch the missiles.

For us, but no one knows what the rules were for enemy submarines. The Soviet's had different rules, and they even had a torpedo with a nuclear warhead.



The Order of Battle always had nuclear missiles fired from submarines as a last portion of the war. The idea was that the Soviet Union might think that they could shoot down the planes, and they had good enough intelligence on the silo locations that they would risk a first strike. But they would never know the locations of the submarines, so there was always the fear of retaliatory strike. And it worked the other way around as well.

But even in a non-nuclear war the point is the same. You might still fire all your conventional guided missiles if you expected to die.

There are still 5 Oscar class submarines operating.

I just wrote a solution. Enjoy.

You assume the earth is flat.

Quote: Wizard

I just wrote a solution. Enjoy.

Good heavens. Another 3 pager. Nice mind-stretcher there, Mike; you will be forever young, with no swiss-cheese dementia. Me, I'm better at crosswords, but not giving up yet.

Quote: boymimbo

You assume the earth is flat.

Indeed I do.

Quote: beachbumbabs

Good heavens. Another 3 pager. Nice mind-stretcher there, Mike; you will be forever young, with no swiss-cheese dementia. Me, I'm better at crosswords, but not giving up yet.

I stink at crosswords. Give me the one on the back of the kid's menu at the Olive Garden and maybe I have a chance. My older daughter crushes me in word games like Scrabble and Boggle.

"Plotting a course" trivia question has been generated in another thread

https://wizardofvegas.com/forum/off-topic/off-topic/15761-civil-war-torpedo-incident-trivia-question/#post289026

Quote: pacomartin

Since an actual target is trying to do evasive manueauvers you do point ahead of them for a while, but eventually you try to get into a tail chase. As a countermeasure the pilot blows chaff to try and confuse the missile.

A torpedo strategy that would completely incapacitate a submarine on first strike meant that you had to hit something much more important than the screws. As such you need a much faster torpedo.

If you blow chaff against a heat seeker, it better be flaming chaff.

Quote: Sabretom2

If you blow chaff against a heat seeker, it better be flaming chaff.

Yeah, chaff is such a nuisance on a radar. What a mess. But no good against a heat-seeker. Helps with airborne combat radar-lock, that's about all I know of.

Quote: Wizard

I just wrote a solution. Enjoy.

Thanks much. Your step of taking the derivatives wrt y in getting eqn. [1] resolves the stumbling block I mentioned encountering before.

In discussing the arc length of s, it appears that you took a derivative (going from s to ds/dy) and wound up with a constant of integration. What's up with that?

If you publish this as a column somewhere, I suggest that you change dx²/dy² to d²x/dy².

Thanks for those corrections.

Quote: Wizard

Indeed I do.

This question is very nostalgic for me. My father worked on missile guidance systems in WW-II for the Army, and he and I discussed this very problem many years ago -- I'm guessing early 1980s, yikes!

The more general question he worked on is, if a guided missile is tracking a plane, and the missile is given both the current velocity (velocity is a vector, both speed & direction) of the missile and of the plane, what is the correct instantaneous change in velocity for the missile? I believe this is what my dad worked on, helping to create an approximate numerical solution.

This same problem applies to pacman in a discrete domain. One of the programming projects I did early on was to program a perfect monster that optimally caught Ms. Pac in a randomly generated maze (the monster moved faster than Ms. Pac). It is a cute recursive problem which is very much like what dad did.

My only nit (sorry, Mike) is that you take many notational liberties that may have no mathematical foundation. (Not that there's anything wrong with it). You cannot freely perform algebra with differentials and assume it really means something. I've long had this issue with applied mathematicians. They do this without ever once really understanding what "dx "or "dy" means, unadorned by themselves. Another foundational issue. There are books written about this topic.

Nice one Mike, thanks for the problem and the memories!

Quote: rxwine

I don't know where they actually point heat seeking missiles (if this is one), but seems like they would still try to lead the target if possible. If the target is directly overhead I would think it would still be smart to point out ahead of where the plane seems to be going. The tip of the missile in this case is pointing where the plane is definitely not going to be and has to constantly turn to follow. Seems like wasted motion, if you actually fired one that way on purpose.

Actually, this problem is well-known in math games books: it usually involves a dog (or a cat) chasing a target that moves straightly. The dog is not intelligent enough to point "ahead" of its target.
Err... So says the problem! I wouldn't dare making such assumptions on cats and dogs, personnally.

My solution involves the arctangent function in Excel but I got the same result. 2.6191 minutes or 2 minutes and 37.15 seconds.

Quote: teliot

My only nit (sorry, Mike) is that you take many notational liberties that may have no mathematical foundation. (Not that there's anything wrong with it). You cannot freely perform algebra with differentials and assume it really means something. I've long had this issue with applied mathematicians. They do this without ever once really understanding what "dx "or "dy" means, unadorned by themselves. Another foundational issue. There are books written about this topic.

To be honest, I forgot why one can do some of the things I did. For example, when I had

(s-y) du/dy = (10/11) * (1+u²)^1/2

and then put the dy on the other side...

(s-y) du = (10/11) * (1+u²)^1/2 dy

I don't see why that works. I probably understood it 30 years ago, but forgot.

Quote:

Nice one Mike, thanks for the problem and the memories!

You're welcome.

The link to the wizard's solution appears to be broken at this time. Here is another. The formula is quite simple: T = Lv/(v² - u²) where L is the altitude, v is the missile speed and u is the aircraft speed.