How is range increased when flying into a HW?

[Devils Advocate]

Let’s assume the following: still air conditions, two airports (A & B) which are 500Nm apart, your aircrafts normal TAS is 500 Kts, so you can nominally fly between A & B in one hour.

Now add a 50Kt headwind component on the sector from A to B.

Accordingly your G/S from A to B is now only 450Kt, so the 500Nm trip takes 66.7 minutes – a 6.7 minute difference from the still-air time, with an effective flight distance now of 555.6Nm (i.e. 55.6 Nm further to fly than in still air)

Of course on the way back (from B to A), with a 50Kt tailwind component, the aircraft has a G/S of 550Kt, so the trip back only takes 54.6 minutes – a 5.4 minute difference from the still-air time, with an effective flight distance of 454.6Nm (i.e. 45.4 Nm less to fly)

The point here is that, on a route between two points, with a consistent TAS and head/tail wind components, a headwind always hurts you more than the tail wind helps you because you spend less time flying along in the tailwind than you do flying into the reciprocal headwind, e.g. in the above example we’re flying into the headwind for ( 6.7 – 5.4 = ) 1.3 minutes more than the we’re exposed to it as a tailwind over the same distance.

So as has been said previously, you would normally try to fly faster into a headwind, thereby lessening your exposure to it, and maybe slow down a bit in a tailwind i.e. let it help you to your destination.

HOWEVER - the above makes no correction for the relationships between fuel cost, aircraft DOC & FOC maintenance costs, fuel tankering policy, obtaining the most efficient flight level, etc, and accordingly is very general.

Hopefully of course, and if you program it correctly, your aircrafts FMC will calculate the best speed to fly at for a particular route ( though it's not aware of your ATC FltPln quoted speed, and or filed FltLvl ) - and albeit that the FMC similarly does not have your airlines financial model programmed into it w.r.t. true aircraft operating costs, i.e. it’s, not surprisingly, very fuel orientated in its calculations.