I was a tool room foreman for a company in the hydraulics industry and I am well aware of this. Half an inch plus or minus a tenth (of a thou) or plus or minus the snoot of your bonnet. There is no such thing as "exactly the same size".
As for general aviation navigational tolerances. If you can see the target at the calculated time it's close enough innit? Being retired from all that is a piece of cake, though I still have my own machines to play with, plus or minus not a lot as required.

My feeble math challenged brain doesn't "get it" :confused:

Actually half an inch and .5 inch are technically the same, it is the precision of the dimension that matters, for instance, (no offence meant) a builder / bricklayer may build a wall to an accuracy of +/- 1/8 of an inch and consider it perfect, the toolmaker will cut and grind a piece of steel to an accuracy of +/- .ooo1" before being satisfied, .001" under half inch could be scrap in certain circumstances.

98 is pretty close to 100.

There are twenty four 2.5s in sixty.

24 is pretty much 25

divide 100 by 25 = 4

The "half an inch" or ".5 inch" is the precision of the dimension, and can mean that those two expressions of the dimension could represent quite different values.

"Half an inch" suggests a precision of +- "one quarter inch", because greater precision than one quarter inch either side of the value is not expressed. So something expressed as "half an inch" with no further statement of precision, would be acceptable if it was greater (just) than one quarter inch, and less than three quarters of an inch. If "half an inch, plus or minus one sixteenth of an inch" is expressed, then things are different.

".5 inch" is a much more precise dimension, and suggests a precision of +- .05". Therefore, without a further statement of precision, ".5" would be interpreted as .45" to .54", which is much more precise than the .25" to .74" which is conveyed by the word expression of "half".

To take it further, .001" means a dimension from .0995" to .0014". Parts in your engine are made and maintained to greater precision than that. If you accepted a Lycoming cylinder, with a valve guide dimensioned at "half an inch", you'd be a fool!

In aviation, this does not matter much in inches, unless you're building or maintaining the plane. But, think of it in "tanks". Would you be content to have a "half tank" of fuel put in, based upon reading the fuel quantity indicator in the instrument panel? Or, would you feel more comfortable ordering .5 of 100 liters, knowing that in doing so, you must be pumped between 45 and 54 liters. Or, request .50 of 100 liters, and you'll have to be pumped between 49.5 and 50.4 liters.....

Step:

I know where you're coming from with your statement about accuracy but in reality if you asked for .50 of a hundred litres they would probably cart you off to the local asylum...:). I think we all know if we ask for a hundred litres it's understood that we'll get a hundred litres. Unless you want to start a debate about the accuracy of the bowser meter. Which in fact would be a valid point. I flew a 172 for nearly two hours the other week and put in 37 litres of fuel to full afterwards. According to the bowser.

Arguing over the precision of a part in the engineering business used to be the norm, years ago, a tenth (.0001") often disputed depending on ones "feel" with a micrometer, now with digital comparators and all manner of technology the doubt is removed down to parts of a micron. But even then absolute yes or no is debateable . Depending on the application, one man's perfection is another man's piece of shrapnel.
I thought I had retired from this stuff!
Wasn't there an engineer a while ago remarked "the fit between the cylinder and piston was so close you couldn't get a shilling piece between them"?

The important point is that math, like English, is a language, and it is important that you use it with the precision you intend, to convey what you need to. Clarity can be vitally important, to assure that one thing works as intended with the next....

If the tower cleared you to land on runway "E", you'd expect a final approach heading somewhere between 045 to 134 degrees. Landing on runway 09, conveys much greater precision of heading. Runways aren't "090", cause no GA heading indicator is that good!

Actually this is a primary school question for a 10 year old.

I downloaded a past GCSE Maths paper for my 15 year old son for some revision and the first question was:

A picture of a clock with the big hand on the 9 and the little hand approaching the 3:

"Write down the time shown on the clock"..

I kid you not..... (When I did O level Maths I was doing calculus at 14...WTF...)

I'm clear about the precision expressed by 0.5 implying between 0.45 and 0.55, just as 0.50 implies between 0.495 and 0.505. However, I don't understand why 1/2 inch means between 1/4 and 3/4. I don't think that it would be normal in the imperial system to specify a higher level of precision by stating a dimension as, say, 2/4", or perhaps 32/64". I studied engineering as the SI system was becoming the standard, partly, I thought, because it removed some of the many uncertainties in the former systems of units. If I order a 1/2", or indeed, a 5/16" bolt, I think I would need to refer to some sort of standards document or manufacturer's spec sheet to find out the relevant tolerances. I don't think it could be inferred from the description. Actually, I guess the same is true when specifying an M10 bolt - but perhaps that's why it is described as an M10 bolt, not a 10mm bolt...:O

And I'm not sure about Step Turn's runway 'E'. If a nautical helmsman was told to steer E, I think he would be in trouble if he went anywhere close to NE or SE. I think it would rather depend on the number of points marked on the compass. Which, of course, is not necessarily linked to the precision, or the accuracy, of the compass!

Why would private pilots ask serious ATPL questions here?

CG

Well Guys, the ATPL question is.....


'How far will an aircraft travel in 2-1/2 hours with a ground speed of 380 knots?'
.

Well, the method you would use would depend on the spread of alternative answers.

If the alternative answers were:

a) 2

b) 4

c) 6

d) 8

a TLAR method would be quite adequate.

If they were:

a) 4.06

b) 4.07

c) 4.08

d) 4.09

something more accurate is required.


MJ:ok:

Ps. I've come to this a bit late. Have I missed something, or has this thread gone on far too long? :confused:

By my reckoning, 950 NM?

Clearly you lot on here need my book, Diversion Planning.....!! Got a few useful things about speed, distance and time. Near as need be, groundspeed is 100 kts, which is 5/3 of a mile per min.....multiply by the number of minutes and theres your answer. (25/6 miles or approx 4 and 1/6 miles, the approximation coming from the round up from 98 to 100 kts. In a light aeroplane you wont want to be this accurate, for the most part!! 5/3 per min is 10/6 per min, and 2.5 times this is 25/6. See, no calculator!)

What about: one aircraft leaves Goodwood heading for Edinburgh at 90 knots, another leaves Edinburgh at the same time at 120 knots heading for Goodwood, same altitude, disregarding airspace, both calculate for a wind of 290/20. Where will the crash site be?

10-up
 

When gliding I always think vertically in terms of hundreds of feet per minute, as that is what the variometers display your climb rate in. 1-up is 100' per minute, which is almost exactly 1 knot. Thus 1000' per minute is close to 10 knots, so about 4 miles in 2-2.5 mins.

At either Goodwood or Edinburgh, during a botched landing. Because both aircraft will have dutifully flown at the altitude appropriate for the direction of flight, and passed safely!

Well, the 1/2" vs 0.5" thing depends a lot on context.
if you ask for affaninch, then 1/4"-3/4" might be an acceptable thing.

As a math/engineering nerd, i read 0.5, 0.50, 0.500 etc as different tolerances unless otherwise stated. I read 1/2 to be the same number but with perfect precision- you can write 0.499 as 0.5 but not as 1/2 (well, you can. but it aint right.).