Hope this helps.
Flying a great circle route - as most people know, the shortest distance between two points is a straight line and if pushed might define a straight line as a line that does not bend or deviate. When we come to look at lines on the earth we find that this definition is no good, there are lines of constant direction but they are not the shortest distance between two points.
On the surface of the earth, lines that form the shortest distance between two points have changing direction, not because they are bent but because of the way direction is measured - this is a result of the converging meridians (known as convergency). These shortest distance lines are called great circles.
It is an obvious advantage to be able to take the shortest track between two points so great circle tracks are used for navigation whenever possible. As Ryanair Boeing 737-800's are fitted with Inertial Reference Systemes and GPS, they are able to fly Great Circle Tracks with use of the Flight Management Computer. FMC LNAV guidance provides great circle courses between waypoints. (Not so during arrival/approach).
Benefits of a visual approach.
The flying of a visual approach has most benefit at an airport where no radar service is available. At such airports, normally a full instrument flight rules procedure must be flown in order to allign the aircraft on the runway centre line. However, if meterological conditions permit a visual approach, significant trackmiles can be cut from an approach. This has the benefit of saving both time and fuel, both of which help the companies bottom line.
Thus, both visual approaches and the flying of Great Circle Tracks have the benefit of saving time / fuel and therefore money.
Winglet / weight to follow.