I remember from my atpl training that to find the distance between two different longitudes on the same latitude we used the formulae for departure
ie 15w to 25w on the 60 deg lat = 600 x .5 = 300nm
This is roughly correct for a rhumb line distance.
but what if the 15w was on the 30 deg lat and the 25w was on the 60 deg lat.
how do you work out the distance??
do you take the mean lat ie 45
so 600 x cos 45(.707) = 424nm
Well the distance between 30N and 60N is 30*60=1800 nm so i think 424nm would be quite a shortcut... What you have calculated is the east-west average departure for that route, but you have forgotten to take into account the north-south component.
The rhumb line distance can be calulated by trigonometry by making a triangle on the Mercator chart between 30N15W, 60N25W and 60N15W. Since we are interested in measuring the hypotenus, let's make the chart scale equal to 1 unit = 1nm at 45N.
That gives us the short side (E/W) of the right angled triangle 424,26 units (10 degrees * 60min/degrees * cos 45). The long side (N/S) scale is not skewed so this is 1800 units.
The hypotenus is then 1849,32 units, which translates into 1849 nm rhumb line distance.
The great circle distance is always shorter than or equal to the rhumb line distance, with it being the same on a north-south route or along the equator, and the biggest difference found on east-west routes near the poles. That is to say, the great circle distance in this case is not more than 1849nm but not less than 1800nm (since this would be from 30N15W to 60N15W). Since this route is predominantly north-south in the mid-latitudes, it would be reasonable to believe that the GCD would be significantly closer to 1849nm than 1800nm.
The exact computation is best suited for fancy computers. However, using the
Great Circle Mapper, it comes to a distance of 1845 for the great circle.