General Nav Question
 

Hi all.
im after a quick check on my answer to an ATPL gen nav question, i have got this one wrong but for the life of me cant see how!!

A straight line drawn on a mercator chart joins N (56S 002E) to P (56S 006W)
and measures 100cm. The earth distance (in Statute miles) represented by the line N-P is?........

well there are 8 degrees between the points N-P 1 degree is 60nm, so 8 degrees are 480nm. 480 nautical miles is 555nm, which im told is wrong answer!!
the possible answers are
A-309
B-500
C-895
D-555.
How can i be wrong, or am i just missing the obvious and being thick?
put me out of my misery......

Approx dist = d-long * cos mean-lat

8º * 60NM/º * cos56 = 268,412593NM = 308,9497 SM

I'd say answer A, is it?

How do you get 1 degree = 60 nm for longitude ?

Changes in longitude decrease as the latitude increases, therefore it may well be a change of 8 degrees but a minute of arc is only equal to one nautical mile at the equator. As the latitude increases the distance decreases as a function of the latitude, you need to multiply the change in arc of the longitude by the cosine of the latitude. Cosine 0 degrees= 1, cos 90= zero. Try it.:ok:

60 NM/º only applies to great circle lines (e.g. All meridians and the Equator). But when you're flying along a parallel of latitude (which is not a great circle line-except for the Equator-) you must multiply by the latitude of the parallel.

hmmm
 

yes but its a mercator chart. the distance between meridians of longitude doesnt change with change of latitude, only the scale increases.

If calculating the distance between two points using Lat/Long in the manner described, the type of projection used on the map is surely somewhat academic!

Not in this particular case, but in general the projection type is very significant.
In this case the track to be measured is a straight line on a Mercator; and is therefore a rhumb line. This one just happens to be along a parallel of lat which means that the equation chlong x cos mean lat yields the exact answer - 268.413NM.
If the projection type had been a Lamberts Conformal then the straight line would have been along the great circle and the exact distance would have been slightly shorter - 268.263NM.
Not a lot of difference and both answers still convert to the same 309SM.
The examiners were making it easy by choosing points close together.

But to illustrate the significance of projection type, take the example of say 56N000W to 56N180W and see what a difference there is between the RL distance (straight line on a Mercator) and the GC distance (straight line on a Lamberts).
RL = 180 x 60 x cos56 = 6039NM True Trk 090 or 270, take your pick.
GC = 2 x (90-56) x 60 = 4080NM Init True Trk 360 to the pole, then 180 from the pole to 56N180W.

My GNSXLs simulator tells me that the distance is 267.8nm, as does my Palm Lat Long calculator thingee, so the correct answer is A.

Agree!

Using my (don't laugh) Loran calculator box that lost its label long ago, I get 268.74nm while the computer offers 268.3.

Agree !

Google earth yields 309 statute miles

Sure, the distance on the chart doesn't change-- but that's not what they're asking for.

In any case, since the Earth isn't actually spherical the correct rhumb-line answer is 269.515 nm, 310.153 statute miles, assuming WGS84.

"If calculating the distance between two points using Lat/Long in the manner described, the type of projection used on the map is surely somewhat academic!"

True, if you're calculating "the" distance-- which he isn't.

DC8 you go it right!:D :)

Don't worry about it. It's the first and last time you'll see a mercator projection (unless you want to for some reason). It's amazing the licensing authority examines completely useless info. in this day and age. It's a wonder they switched from latin to english already.