[alancalverd]

I'm still thinking about  this. The problem is that you have to lift all the fuel for a journey at takeoff. For a 747 the full fuel load is around 400,000 lb. If you only took half of this, and refuelled halfway to your destination, you could carry an additional 200,000 lb of payload - almost doubling your profit!

The additional cost would be that of flying a tanker for maybe an hour. But unlike a normal refuelling stop, you wouldn't have to disembark passengers and faff about with security etc, so the handling fees and time on the ground for the tanker would be much less than for a passenger liner. The tanker wouldn't need to be based at a customs airport at all - it could fly from a company site or a military base. Unlike combat refuelling you can take your time and choose your rendezvous "somewhere quiet".  It's a potential earner for countries that are overflown by long routes,  without the need to increase their passenger handling capacity.

[syhprum]

Maybe flying into London from Japan you could refuel over Iran if you could solve the political problems

[alancalverd]

It's not such a crazy idea!

The fun with military refuelling is that you are usually trying to fly a small,  fast plane (fighter) in the wake of a big slow one (KC135 - ish) - all very unstable. But flying a 747 in the wake of a tanker would be a lot easier - much more inertia and a better performance match at 500 mph.

London-Tokyo is normally by polar route. No political problem.  The tanker base would be an interesting posting somewhere in the Arctic Circle.

This actually shows the advantage of air travel over rail! There is a serious Russian proposal for a direct rail link between London and Tokyo, but the only feasible route is about 8000 miles - 2 days by the fastest possible train, maybe 4 days by something that can cope reliably with all the weather and track conditions, and a vast carbon footprint in steel and concrete, not to mention the disruption of other transport and migration routes. By contrast, the 6000 mile 12 hour polar flight already goes several times a day with no infrastructure or surface disruption at all. Refuelling somewhere over Russia would halve the fuel consumption per passenger.

[syhprum]

`Although this would seem to offer economic advantages we must look to the example of the A380 which proved to be a failure be cause it was to big to fill up.
How would the extra load carrying capacity be used I can only think for freight if there was a need which would surely slow down the turn round time for the aircraft with loss of revenue.
As for aircraft taking a polar route from Japan to the UK let me recount my experience flying in from Korea we were scheduled to make a refuelling stop at Frankfurt taking a more southerly route (probably due to the promise of a favourable jet stream ) which took us along at a ground speed of 750 mph and made a Frankfurt stop not needed.

[alancalverd]

Every time I've flown on a 380 it's been full. Pilot friends say it is a delight to fly. The problem is that very few airports can handle it (it's BIG) and its fuel efficiency has been surpassed by the Dreamliner with pretty much the same range - more profit per seat and a smaller capital risk.

If you start with a clean sheet and design for airborne refuelling, you will end up with an even more efficient machine than the 787. Everything that flies is a box of compromises: if you reduce the takeoff weight for a given range, you have an extra degree of freedom in your design.  Hence the military value - more payload, faster, more agile, or just smaller and more fuel efficient….

[teragram (OP)]

All your statistic shows is that the UN prediction was wrong.

In that it was too optimistic?

Modern airliners are almost as efficient as gliders but clearly carry a lot more deadweight (toilets, galleys, luggage, unspent fuel...) so maybe expend about 5 - 10 kW per passenger fighting gravity and about 600 kW per passenger moving through the air.

It seems that the total drag on an aircraft is the sum of the drag due to it's frontal area and the induced drag, which is the result of deflecting airflow downwards to support the aircraft's weight. The former obviously increases with airspeed, while the latter decreases with airspeed. The optimum speed of the aircraft (in terms of energy required) is that at which the two quantities are approximately  equal. At this speed, the energy required to move forward is nearly equal to that required to maintain altitude. This is explained in:-

Sustainable Energy - without the hot air         David JC MacKay

 In "C  Planes II, page 269, available online.

[alancalverd]

Not quite. Whilst the induced drag coefficient decreases with the inverse square of speed, drag force increases with the square of lift, which is proportional to the square of speed. Thus the drag force increases with the square of speed, and as power = speed x force, the power required to move through the air increases with V³.

"Optimum speed" is a lot more complicated. Propeller planes are most efficient at low speed and altitude, but the fuel consumption of a jet at idle or taxi is pretty much the same as at Mach 0.8 and 30,000 ft. Then there's the problem of flying in the corner between stalling and exceeding Mach1 at high altitude. Plus wind: no point in flying at 60 kt into a 100 kt headwind: however efficient your Piper Cub, it will go backwards! It's not much simpler with a glider: since low-level air is always rising and falling, you want to fly slower in rising air (allowing for wind!) and faster in descending air -  counterintuitive (because the induced drag wall make you descend quicker) but a lifesaver if you get the equation right.

[teragram (OP)]

Thanks for the information, a bit over my head (pun intended), but what then is the ratio of lift power to drag power in level flight at the most economical speed? Given perhaps that conditions are perfect.

[alancalverd]

Defining "most economical speed" is the problem.

There is a speed at which the lift/drag ratio is optimised and this will give you the least power required to stay airborne, but that won't be the maximum range for a given fuel load, or the min fuel for a given destination. As an example, consider a basic trainer like a Cessna 152 ( I just happen to have the flight manual on my desk at the moment!) With a full fuel load at 6000 ft it can fly about 700 miles at 45% power, 80 kt (best L/D speed) or 650 miles at 55% power, 90 kt,  in zero wind. But if we fly into a 30 kt headwind we can only go about 435 miles at either speed - it just takes 1.5 hours longer at 80 kt!

Since the upper winds can be in excess of 100 kt in any direction, and airliner operation depends on moving stuff from A to B, not just keeping it in the air, it isn't always best to fly at optimum L/D. Typically, an airliner will be designed to cruise at around Mach 0.8 (530 kt)  but the best glide speed (max L/D) is a lot lower - around 200 kt, and unlike a piston engine, a jet is more fuel-efficient at higher speeds.