What Mathematics behind the Prayer Wheel?

[Blip]

I sit here looking at my Jeppesen CR-2 Computer and can't help but marvel at the... the magic that it is! :ok:

Besides all the aviation stuff on the inside of the wheel (which is also amazing), how is it that you can do multiplication and division using the round slide rule on the outside?

How is the spacing between the numbers determined? How the @%$# does it work? Is there a mathematical term for it?

Who actually invented the circular slide rule?

Was there a straight one first?

To the person who made it possible...

THANKYOU!!!

PS It comes in very handy at the shops too when you're trying to decide if the 600g box really is better value than the 375g box!!

:p

[Intruder]

How is the spacing between the numbers determined? How the @%$# does it work? Is there a mathematical term for it?

Logrithmic, my dear Blipson!

If you had attended engineering school before the turn of the 70s, you would have been intimately familiar with the "straight one"! Come to think of it, I just happen to have a slide rule (or "slipstick") in my desk drawer, for those times when I need something to fondle for nostalgia's sake.

Ah, yes... I just found my Acu-Math No. 400, a relatively cheap, single-sided version (all plastic -- no teak or mahogany cores like some of the elegant models of yesteryear). The primary C and D scales for higher-accuracy multiplication and division, the "backwards" CI (Inverse) scale, the "folded" A and B scales for quicker work, the S scale for Sines, and I may have to play a bit before I remember what the K, L and T (Tangent?) scales do...

Turn off your calculator and try one out for a while!

P.S. They're no good for addition and subtraction!

[Loose rivets]

Who was that wonderful old guy at Cass college in the 60's who had a small production run of aviation specific straight jobs commissioned? They had all sorts of cribs built in for the ATPL that helped a lot. I still used a ‘Boots special' small plastic one- cost a couple of bob - that i could pull the fuel figures off before my young P2 had warmed up his electronic multi-valent machine.

[Oktas8]

As Intruder said, logarithmic.

Log5 + log15 = log (5 x 15)

Or in CR-2 language:

5 on the outer ring "added" to 15 on the inner ring, then go around to the end of the ring (10) to get 5 x 15.

Log 15 - log 5 = log (15 / 5) using a similar idea.

You can do square roots too, but I have forgotten how...

O8.

[Blip]

OMG!!

Thankyou guys (both male and female)!

And with this information I have discovered something else (bit like re-inventing the wheel i suppose!).

I was wondering how they knew where to put the various numbers on the circle. Well if you put the "10" and think of it as a 1 at the top (or 12 O'Clock position)...

Log1 = 0

So you don't have to move the wheel at all. 1 is right there in front of you.

Log10 = 1

So if you want to find 10 you have to turn the wheel around once. ;)

Log17.8 = 1.25

So if you want to find 17.8 you have to turn the wheel around one and a quarter times Anti-clockwise. (or look at the 3 O'Clock position.)

Log31.7 = 1.5

So if you want to find 31.7 you have to turn the wheel around one and a half times anti-clockwise.( or look at the 6 O'Clock position.)

Log56.5 = 1.75

So if you want to find 56.5 you have to turn the wheel around one and three quarters times anti-clockwise.(or look at the 9 O'Clock position.)

Log0.1 = -1

So to find 0.1 you have to turn the wheel around once clockwise. ;)

Log 3.17 = 0.5 so to find 3.7 you have to turn the wheel around just half a turn anti-clockwise.

Log3170 = 3.5 so to find 3170 you have to turn the wheel around anti-clockwise three and a half times. :rolleyes:

Brilliant!!!:ok:

[Intruder]

You can do square roots too, but I have forgotten how...

Directly! A to D scale, or B to C scale!

[Bre901]

IntruderP.S. They're no good for addition and subtraction!
You can do some with the L scale (decimal logarithm)

K is the cube scale
T is the Tangent (and Cotangent)
S does both Sine & Cosine

[mcdhu]

Still by far and away the quickest way of doing currency conversions!!

Cheers,
mcdhu