Planes and a brainteaster.

Morning All,
Thought to put this in the 'Aviation' thread...but there isn't one:). Then searched 'brainteaser' which came up with a thread with an invite to post them on it. So I did. Then realised I'd revived a thread which started in 2006 with the last reply being 2006:frustrated:.
Like the invite from that one, if anyone wants to contribute brainteasers and puzzles feel free.
Is there, or does this forum have/need it's own 'Brainteaser and Puzzle' thread for them?
From today's local 'comic'.
20220327_141434~2.jpg

If anyone's interested, I posted a clue on the other thread but cba to put it here:D.
 
I think you can do it with 2 x Planes.

Plane A and Plane B take off at the same time. Plane B puts half a tank into Plane A at the quarter way mark, filling Plane A back to full. Plane B flies back to the start point and only just gets back. Plane B then refuels and sets off back the opposite direction, meeting Plane A at the 3/4 way point. Plane B puts another half a tank into Plane A, leaving both planes to make their way to the finish on their half tanks. Both planes only just make it back.

No wasted time and fuel tanks used to their absolute capacity. I'm not sure you could do it any quicker or better.
 
Morning All,
Thought to put this in the 'Aviation' thread...but there isn't one:). Then searched 'brainteaser' which came up with a thread with an invite to post them on it. So I did. Then realised I'd revived a thread which started in 2006 with the last reply being 2006:frustrated:.
Like the invite from that one, if anyone wants to contribute brainteasers and puzzles feel free.
Is there, or does this forum have/need it's own 'Brainteaser and Puzzle' thread for them?
From today's local 'comic'.
View attachment 651825
If anyone's interested, I posted a clue on the other thread but cba to put it here:D.
There is an Aviation area of the site, but it's for Army Aviation, iow AAC.

This is where it belongs
 
You can do it with one aircraft. Simply fly a great circle around any parallel of latitude that gives you a track distance of < half the circumference of the earth at the equator (the quoted range for one aircraft on a full tank of fuel).

You could work this out with basic trigonometry and geometry but as a stab in the dark, it’s probably not a million miles off starting and ending in London, 50 ish degrees of latitude. It should be 45N but ISTR there’s some obscure spherical trig law that means it isn’t. And no, I’m doing my hair.

It’s still a circumnavigation.

You could take this to the extreme and taxi it around either of the poles and log hundreds of circumnavigations on a tank of fuel.
 
And don’t forget to factor in the fact the earth is slightly fatter around the equator than if measured around the the poles.

Basically the planet has a bit of a gut on it.
 
Here’s another one for you:

All Headings are in degrees True to remove any errors with Magnetic Variation.

Take off from a point on the equator.
Head north for 60 miles
Head east for 60 miles
Head south for 60 miles
Head west for 60 miles

Where are you?
 
I think you can do it with 2 x Planes.

Plane A and Plane B take off at the same time. Plane B puts half a tank into Plane A at the quarter way mark, filling Plane A back to full. Plane B flies back to the start point and only just gets back. Plane B then refuels and sets off back the opposite direction, meeting Plane A at the 3/4 way point. Plane B puts another half a tank into Plane A, leaving both planes to make their way to the finish on their half tanks. Both planes only just make it back.

No wasted time and fuel tanks used to their absolute capacity. I'm not sure you could do it any quicker or better.
Ok, I've slept on this and realised my error. Plane B would fall out of the sky whilst refuelling. I'm thinking that Plane A and B follow the same profile, but you need a Plane C to put quarter tanks into Plane B at the 1/8th point there and back both ways round. Let me get a pen and paper out...
 
Ok, I've slept on this and realised my error. Plane B would fall out of the sky whilst refuelling. I'm thinking that Plane A and B follow the same profile, but you need a Plane C to put quarter tanks into Plane B at the 1/8th point there and back both ways round. Let me get a pen and paper out...
So you haven’t actually slept on it….

………you’ve been awake all night wrestling with it and now have eyes like a greyhound’s bollocks?
 
Here’s another one for you:

All Headings are in degrees True to remove any errors with Magnetic Variation.

Take off from a point on the equator.
Head north for 60 miles
Head east for 60 miles
Head south for 60 miles
Head west for 60 miles

Where are you?
Somewhere east of your start point. Instinct says the maths is to do with the quarter polar circumference of the earth and the ratio of the great circle at that latitude vs that of the Equator.
 
Somewhere east of your start point. Instinct says the maths is to do with the quarter polar circumference of the earth and the ratio of the great circle at that latitude vs that of the Equator.
Warm
 
I’m watching this thread with mild interest and the warm knowledge I don’t have to worry about sh*te like this anymore.
Only if i have enough fuel for a bimble around the lakes and a landing on pilling sands for fish and chips for lunch.
I don’t miss that stuff one bit.
carry on!
 

theinventor

War Hero
I think you can do it with 2 x Planes.

Plane A and Plane B take off at the same time. Plane B puts half a tank into Plane A at the quarter way mark, filling Plane A back to full. Plane B flies back to the start point and only just gets back. Plane B then refuels and sets off back the opposite direction, meeting Plane A at the 3/4 way point. Plane B puts another half a tank into Plane A, leaving both planes to make their way to the finish on their half tanks. Both planes only just make it back.

No wasted time and fuel tanks used to their absolute capacity. I'm not sure you could do it any quicker or better.
I think you need a couple more, under your plan B has used 1/2 tank to get to the 1/4 point, if he gives the other half tank to A then he's got none to go home with.

Whereas, if you think of the world in terms of clock-face:

A starts from 12 o'clock and flies to 3 o'clock, he's now on half a tank
B1 and B2 lfollow him and both meet him at 3 o'clock and give him 1/4 tank each. A is now full, and flies round to 9 o'clock.
B1 and B2 both have 1/4 tank left which only gets them back as far as between 1 and 2 o'clock. At this point, they meet up with C who gives them both 1/4 tank and B1, B2 and C back home.
B1 and B2 refuel then head off to meet A at 9 o'clock. Repeat of the first half: give A 1/4 tank each which gets him home, then meet up with C at between 10-11 o'clock to top up B1 and B2 then all home for tea & medals.

Four planes in total.
 
I think you need a couple more, under your plan B has used 1/2 tank to get to the 1/4 point, if he gives the other half tank to A then he's got none to go home with.

Whereas, if you think of the world in terms of clock-face:

A starts from 12 o'clock and flies to 3 o'clock, he's now on half a tank
B1 and B2 lfollow him and both meet him at 3 o'clock and give him 1/4 tank each. A is now full, and flies round to 9 o'clock.
B1 and B2 both have 1/4 tank left which only gets them back as far as between 1 and 2 o'clock. At this point, they meet up with C who gives them both 1/4 tank and B1, B2 and C back home.
B1 and B2 refuel then head off to meet A at 9 o'clock. Repeat of the first half: give A 1/4 tank each which gets him home, then meet up with C at between 10-11 o'clock to top up B1 and B2 then all home for tea & medals.

Four planes in total.
I think you're right. I also think my method I corrected above is also right, but both yield the same answer - 3 planes.
 
Morning All,
Totally forgot to post the answers for my op. Doh!
20220327_141447~2.jpg


This one from today's local 'comic', if anyone's interested.
20220410_141950~2.jpg

Answers, when I remember to post them;).
 
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