A few pages back I recall jb saying that not much time can be made up on most flights - even long sectors - without substantial wind assistance. Approx. 15mins on LAX-MEL IIRC.
Remember that wind assistance isn't just a case of picking up extra ground speed from the wind. Changing altitude to get out of adverse winds is just as important.
Does altitude make a difference to how much you can make up or does changing altitude just get you better winds?
You need to start by having a think about the way aircraft speeds are chosen. Basically, at lower levels, we fly a 'best' IAS. That IAS results in a TAS that varies with altitude. IAS and TAS are equal at sea level, but TAS is approximately double IAS at FL400. So, for a given IAS, the higher we go, the better the TAS.
But, mach number provides an upper limit to the IAS, and as we climb we'll eventually hit a point at which our constant IAS reaches our target (or limit) mach number. In most cases this happens around FL300. So, IAS below that level and then mach number above. Now though, as we climb and hold that constant mach number, the IAS starts to reduce. The upshot is that you'll normally hit your maximum TAS at the IAS/mach crossover.
So, if there were no wind, we'd have the maximum groundspeed at the point of maximum TAS. But of course, there is wind. The wind change can be quite linear as you climb, whilst at other times there are large changes over quite short level changes. That means that the altitude for maximum groundspeed could vary dramatically, and it will vary with the direction you're travelling.
On shorter sectors where MTOW and endurance aren't a big factor does taking extra fuel but flying a lower altitude allow you to go quicker?
The difference in aircraft speed will be marginal at best. For instance in the 380 we normally cruise at around mach .84. But mach .87 is as fast as you can reasonably go, and even then you'll run the risk of hitting the Vmax every now and then. That's a difference of about 18 knots of TAS, which over the course of a short sector amounts to only a couple of minutes.
If you look at Melbourne-Sydney sectors, in the 767 days it was common for the south bound aircraft to be at about FL280, whilst those going north were up around FL370. Basically, on those flights the south bound flights were being operated down low to get out of the wind, whilst those going north were maximising it. They were probably both operating at about the same mach number.
The background to the question is that last night's QF846 SYD-DRW was 44 mins late off the blocks. Along with the usual PA the Captain said he'd "added extra, we'll drop down a little lower where we can go faster and try to make up some of that time". FWIW arrival was only 10 mins late.
The winds on that sector would have a strong headwind component. Going lower should get you less wind.
If we can get maximum TAS at around FL300, then why do we go higher? Well, the aircraft has a couple of competing things happening that affect our choice of altitude and speed. The wing has a best angle of attack, so ideally we'd like to fly at a speed that gives us that AoA. As our weight reduces, the speed for that AoA will also reduce (and recall that we do reduce cruise speeds as the flight goes on). At the same time, the engines have a speed at which they are most efficient...call it about 85% thrust. So, we want to chose an altitude that will give us that best IAS/AoA whilst simultaneously requiring the engines to be at that best power setting. Ignoring ATC aspects, that pretty much defines your initial cruising level. But, as the weight reduces and you slow to hold that best AoA, you're moving the engines away from their best setting. This leads us to the step climbs that you see on most longer flights...where we'll climb again once we reach the point that the weight has reduced enough for us to get that best speed/power combination at the next level up.