A wee brain teaser

[Bengal]

A friend of mine is doing a BSc Hons in Mechatronics and got given the following problem in one of his papers.

Q. Find the shortest flight path (taking into account turn radius) of a fully laden 747, travelling at max speed, which passes directly o/h Glasgow, Dundee & Edinburgh. And for extra bonus points name 3 other places over which the jet would pass.

Pondering over this killed a while at work for me, would be interested to see what other folk come up with. Bit of a bizarre question for mechatronics eh??

I look forward to some replies...

[john_tullamarine]

One gets delightful lecturers such as he/she who penned this question.

Likewise I shall be interested to see the range of attempts ...

In more boring engineer-speak, the problem would have been presented along the lines of a 3D (2D would be a bit too easy for an honours year task) design drafting exercise with a requirement to minimise the component material used.... is not the 747 tale far more interesting ?

For the exam/tute question, not something to be answered in two minutes ....


A similar one from a charming Fluid Mechanics lecturer in the dim past was along the lines of (and this related to the Faculty building which, subsequently, was cast out from within the tender care of Engineering ..... to the barbarian Humanities hordes ... )

The tealady prepares iced coffee on the ground floor without stirring and permits the cups to sit in the fridge until the liquid is still. Three weeks later she carries the cups up the spiral staircase to the third floor for distribution to the clamouring hordes. Ought she to stir the coffee

(a) before she climbs the stairs,
(b) after, or
(c) not bother ?

This was a final exam question and generated some lengthy and involved dissertations ....

He came up with a number of similar fascinating items ... and his lectures were an absolute delight .....

On a more serious note, this style of instructor (and the consideration transfers very well to flight instruction) usually is far more successful in getting the story across than the stuffed shirt/boring/pedantic/know-it-all/incompetent/etc (pick one or more) types who lose the intelligent student after 2.34 microseconds ....

[Lump Jockey]

Hmmm, ...........I got a "C" in maths!!

[cwatters]

Here's a good one to give him back. Told to me by a maths student at Southampton. I understand it's very difficult and only one student ever claimed to have an answer...

There is a cow in a circular field. It's tethered to a fence post by a rope.

Q: How long does the rope have to be so that the cow can only eat the grass on half the area of the field.

[Flap40]

Assuming you are refering to the three cities in Scotland and assuming they have to be passed in that order then I get 181km (using city centres not airports) passing over Banockburn-Perth-Dundee-St.Andrews-Leith-Edinburgh.
If they can be done in any order the Glasgow-Edinburgh-Dundee (or reverse) would be 128km and passes over Airdrie-Livingstone-Edinburgh-Leith and Buckhaven.

These answers are probable wildly out though as I found three websites with turn radius formulae/calculators and got three different answers!

As for the cow, simply plough up half the field before hand;)

[john_tullamarine]

The man/woman in the previous post is, of course, a lateral thinker .... and probably has a glorious career in business ahead of him/her.

Most of us would not have considered the quick solution of ploughing half the field ..... ?

The three different answers tale brings back a chuckle .. many years ago ... freighter at 0-dark-thirty in the morning ... out over a body of water .... ATC pops up with "can you give us a wind ?".

Not having any fancy gear on this bird .... the three of us ferreted about in our nav bags to see if any one of us had a prayer wheel ... three turned up as a matter of interest .... three heads were scratched as techniques buried in memories clawed their way to the surface.

The upshot was that we came up with three totally different answers ....while my answer was correct, of course, I declined to impose my will upon my colleagues ... so we averaged them .. and reported the W/V back to ATC as L&V .... whereupon we all promptly went back to sleep ....

(.... I may have embellished the tale ever so slightly for the purpose of the post .........)

[andrewc]

How about SQRT(1/2*PI) for normalised units...

-- Andrew

[Bally Heck]

I have enormous admiration for the author of this one.



Dr. Schambaugh, of the University of Oklahoma School of Chemical Engineering, Final Exam question for May of 1997. Dr. Schambaugh is known for asking questions such as, "why do airplanes fly?" on his final exams. His one and only final exam question in May 1997 for his Momentum, Heat and Mass Transfer II class was: "Is hell exothermic or endothermic? Support your answer with proof."

Most of the students wrote proofs of their beliefs using Boyle's Law or some variant. One student, however, wrote the following:


"First, We postulate that if souls exist, then they must have some mass. If they do, then a mole of souls can also have a mass. So, at what rate are souls moving into hell and at what rate are souls leaving? I think we can safely assume that once a soul gets to hell, it will not leave.

Therefore, no souls are leaving. As for souls entering hell, let's look at the different religions that exist in the world today. Some of these religions state that if you are not a member of their religion, then you will go to hell. Since there are more than one of these religions and people do not belong to more than one religion, we can project that all people and souls go to hell. With birth and death rates as they are, we can expect the number of souls in hell to increase exponentially.

Now, we look at the rate of change in volume in hell. Boyle's Law states that in order for the temperature and pressure in hell to stay the same, the ratio of the mass of souls and volume needs to stay constant. Two options exist:

1. If hell is expanding at a slower rate than the rate at which souls enter hell, then the temperature and pressure in hell will increase until all hell breaks loose.

2. If hell is expanding at a rate faster than the increase of souls in hell, then the temperature and pressure will drop until hell freezes over.

So which is it? If we accept the quote given to me by Theresa Manyan during Freshman year, "that it will be a cold night in hell before I sleep with you" and take into account the fact that I still have NOT succeeded in having sexual relations with her, then Option 2 cannot be true...Thus, hell is exothermic."

[john_tullamarine]

... the lovely tale about Miss Manyan (and similar names) has been doing the rounds since Pontius was a pilate ........ still puts a cute spin on thermodynamics classes .....

[Tim Zukas]

I assume the cow-in-field problem is tough-- I certainly haven't a clue how to do it analytically. But the answer is easy enough: if the cow is tethered to the edge of the field its rope should be 1.31899099 times the radius of the field.

(Or to be more precise, 1.15872 84730 18121 51783 times the radius. Wrong answer above due to emptyheadedness.)

[fireflybob]

The one about the cow (actually it's a goat) in the circular field eating half the area is one of the classic math puzzles - you need some calculus to solve it!

The solution (along with quite a few other interesting puzzles) can be seen at:-

Maths (http://mathforum.org/dr.math/index.html)

Enjoy!

[Flap40]

Come on Bengal. What was the real answer?

[Chris Vernon-Jarvis]

Never mind the damned cow, who is this pilot Pontius you are talking about?

[error_401]

As for the cow I'd rather use a Piper Arrow (My Instructor used to call it 'a flying pig' so it's closest to the cow and not as expensive as the 747) and fly the Waypoints of the question. Use GPS and GIS to cover for the mapping of the flight path :D

Or - if you're really serious use this:

Turning radius is:

Assumptions to be made (if not you'll end in hell - frozen or not)
Standard rate of turn - 2 minutes for 360 deg. equals angular speed of 3 deg per sec.

Assume either all in cruise at a given cruise speed (easy variant)
or the flight path profile from take-off to landing (have fun and a CRAY or something to calculate it ;) )

Then - radius of turn is a function of True Air Speed. Now guess the wind :cool:

Or assume that bank is given - usually 25 or 30 deg on airliners so you get the load factor - together wit Air Speed you get radius of turn.

Another solution is: Grab a 747 Hang two ropes on either Wingtip hang an anchor or plow at the end and make a low pass along the waypoints the broken houses, dead cows, funny diagonal plows (reminds the corn signs) mark the way