Neal's conundrum

[EdEssery]

Neal\'s conundrum

Neal McDonald (Watch Leader on Kingfisher 2) posed the following problem to Andrew Preece (fellow crew member and YW journalist) earlier today...

"Neal's watch are always chatting and struggling to answer Neal's conundrums, such as 'does the wind instrument at the top of the mast measure wind velocity or wind force' and 'do your hair and nails stop growing in the Southern Ocean?'. This morning he asked me how much extra rope you would need if you took a rope wrapped around the earth on a diameter and moved it a metre away from the earth all the way around."

My schoolboy maths suggests the answer is 2 pie metres.

My logic goes...
Circumference of a Circle is Pie * Diameter of Circle
Let d = diameter of earth in metres
Let n = the answer we are seeking

(Pie x d) + n = Pie x (d + 2) -- [d + 2 = Diameter of earth plus one metre raised each side]

(Pie x d) + n = (Pie x d ) + (Pie x 2) -- [same equation differently quoted]

n = Pie x 2 -- [subtract Pie x d from each side]

QED
but what's wrong - it feels wrong intuitively - the answer must be a function of d but I can't see it.

Help!

 

[Jacket]

Re: Neal\'s conundrum

Nope, thats right.

 

[Twister_Ken]

Re: Neal\'s conundrum

Why worry, you'd never be able to winch it tight anyway.

 

[tcm]

pie metering, kingfisher, and Simpsonian maths

You're bit late on this, but correct. The kingfisher post illustrates. Note that pi has nothing to do with pastry, so not speeled as "pie". The increase in rope needed is indeed a function of the diameter or radius- it is 2xpi times the increase in radius- but in this case the increase is just one metre so that's it - 2 x pi metres, or about 6.28 metres.

Mmm...pie

 

[wishbone]

Re: pie metering, kingfisher, and Simpsonian maths

I see you've still go your mind working on the food subject!

Wishbone

 

[jfm]

Re: Neal\'s other conundrum

Yes, most definitely two pie-eaters, though that solution is a bit round the houses. Every circle has pi metres of circumference per metre of diameter. So add 2 meters to the dia, and you must add 2 pi to the circ.....

But a much more debatable point is the wind thingy. Does it measure wind speed or force? Imho the answer's neither, but awaiting Preece's considered analysis.

 

[Twister_Ken]

Re: Neal\'s other conundrum

Speed, if it's got a whirlygiggy thingy, coz the cups'll be whizzed round at wind speed. Won't they?

 

[jimi]

Re: Neal\'s other conundrum

But that assumes the cups whirl at the speed of the wind, if they were in liquid they'd go faster than in a gas so I reckon they measure force .. or the amount of energy required to turn the cuppy things at that speed! Ask Sinbad he knows all about cuppy things..

 

[BrendanS]

Re: Neal\'s conundrum

Force vs velocity. Velocity is a vector measurement ie.
velocity = speed in a particular direction.
Whirling cups measure force, if you couple that to an instrument that measures wind direction, then you have wind velocity

 

[kaj]

Pi squared is pie

3) pie n, vb Printing. a variant spelling of pi^2

from "Collins English Dictionary" 5th Edition first published in 2000 (c) HarperCollins Publishers 1979, 1986, 1991, 1994, 1998, 2000.

Didn't know until this morning

 

[Gunfleet]

Re: Neal\'s conundrum

<<Whirling cups measure force,>> They don't 'measure' anything. They are moved by a force. The speed at which they are moved is....(fill in the blank).

 

[Badger]

Re: Neal\'s conundrum

Do you think being at school in the 1960's and concentrating on country dancing and finger painting was at all a disadvantage to a young badger ? What on earth does all this mean and ......... whay would I want to put a rope around the earth ???

 

[snowleopard]

measuring instruments

what do you mean by 'measure'? in the case of most instruments, they respond to a physical phenomenon which is related in some way to the quantity you want to measure. to prevent us poor laymen having to apply a formula to work out what we need to know, the scale is graduated to suit us, e.g.

altimeter measures pressure, displays as height,

ammeter measures magnetic field, displays as current

mileometer measures rotations of a cable, displays as distance

anemometer measures rate of rotation of the cups, displays as wind speed.

it's what you read on the dial that counts. incidentally wind force is is proportional to the square of the velocity so the force at 10 knots is 4 times that at 5 knots while the reading of your wind meter only goes up by a factor of 2.

ask a nerdy question, get a nerdy answer.

and incidentally in the 'band round the earth' problem the diameter of the earth doesn't come into the formula so the answer is the same for a golf ball, a football, blair's head, jupiter or any other round object however large.

 

[jfm]

blair

All 2x pi mathematics agreed except for Blair's head. They dont make ropes long enough. Also most people with a loop of rope that close to him would go for the neck, not the head.

 

[graham]

Re: blair

If he knew you had that much rope he would bring in a new rope tax. Calculated by Length x Circumference x loads a money and then you wont be able to afford any pies so starve .