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Having read about Rutan's Voyager and more recently about Virgin Atlantic GlobalFlyer I wondered how would some modern long haul airliner such as a cargo Boeing777 (or other airliner) perform at this specific longest range flight attempt?
Assuming take off at MTOW, and carrying as a payload no passengers but only usable fuel (tanks in cabin connected to existing fuel lines) and pilots.
What would roughly be the achievable range and/or how would one proceed to estimate this range?
First, go to the Boeing Airport Planning documents website. This includes a wealth of information about most Boeing commercial aircraft. Choose the document that matches the aircraft you're interested in. I'll choose the 777F document because you mentioned a cargo 777.
Scroll through to PDF page 45. That is a payload-range diagram for the aircraft.
This chart shows the aircraft's capabilities in terms of payload, range, and fuel. The X-axis represents the range. The Y axis represents the amount of payload in terms of OEW (operational empty weight) plus Payload. OEW is used because different airlines outfit their aircraft in slightly different ways, so their starting point (OEW) is different. The 777F's OEW is about 318000lb.
The horizontal line across the top of the payload-range diagram depicts the maximum zero fuel weight (MZFW). This is typically a structural limit for maximum landing weight. You can't land heavier than this without risking breaking the gear.
The first corner of the payload-range diagram represents the maximum gross weight at brake release. In this case, 766,000 lb. I.e. 448,000 lb of payload and fuel. The upper-left corner of this line is the maximum payload choice for that gross weight -- 229000 lb payload, 219000 fuel.
Following along that line, we remove a pound of payload and replace it with a pound of fuel (to maintain constant brake release gross weight). As we do this, the aircraft can reach longer range -- same weight, but more fuel. This continues until the fuel tanks are full. I.e. we reach the second corner on the chart-- 320860 lb fuel.
At that point, we can continue reducing the payload to increase range -- but since we can't add more fuel, we don't get as much of a benefit.
If you wanted to add more fuel tanks in the cargo bays of the 777F, you could do so. The empty tanks would add to the OEW. So instead of starting from 318,000 you might start a few thousand pounds heavier.
To estimate the best achievable range, you want to extrapolate the line from the first corner on the payload-range diagram (the one at constant brake release gross weight). Extrapolate that line out down and to the right until you reach the OEW of your modified aircraft with more tanks. Performing highly accurate eyeball extrapolation, I estimate 13,000 nautical miles.
The slope (m) of this corner of the payload-range diagram represents an important fundamental aircraft performance quantity. We just have to invert it and change the sign...
The slope is (very approximately)
$m=rise / run = -100000 lb / 3000 nm$
$m=-\frac{1}{SR}$
or
$SR=-\frac{1}{m}$
Where $SR$ is the specific range of the aircraft. So about 30nm/1000lb fuel. This is a measure of fuel efficiency similar to MPG for a car.
If you look at the term in the front of the Breguet Range Equation, I think you will see the Specific Range there.
First cut numbers, working from Wikipedia's B-777 page, and using the 777-200LR, since that seems to be the longest-ranged of the models:
So that's how much more fuel weight you could carry in the new tanks without the aircraft being overweight. Which is less than half-again the existing fuel load, so we aren't going to be getting dramatic 3X increases in range.
The published range for the 777-200LR is 8,555 NM, which is stated as almost enough to connect any possible pair of airports in the world. Multiplying that times the ratio of notional fuel capacity to existing fuel capacity (i.e. 446,000 / 321,000) gives a result of 11,886 NM. Not near Voyager's 26,366 NM flight.
Disclaimers:
This leaves out a lot of factors. How much OEW you lose by stripping out seating, galleys, and so forth, and how much you add by adding fuel tanks & pumps, is one.
Also, the distance you fly per pound of fuel when an airplane is full of gas and heavy, is significantly less than the distance you fly on a pound of fuel in a light aircraft. So while the 8,555 nm range figure is presumably starting at a max-weight takeoff (the same as the notional flight), it ends heavier than the hypothetical flight -- so the "extra" gas effectively gets used more efficiently, since it's used when the aircraft is lighter than it would be in revenue service. (This dynamic is captured in Rob McDonald's answer, and his 13,000 NM range seems like about the right increase here.)
Also, the published range builds in some worst case, or 90% worst case assumptions about winds and reserves -- if you say you can fly from X to Y, you also want to be able to fly from Y to X, even when the winds are strong (i.e. a headwind on one of the two legs). If you're planning a record-setting flight, you just fly with the winds, and where they're best for you. And you'll spend the additional last hours of your flight at a maximally efficient (high) altitude because you're so light. Which probably is where you'd enjoy strong tailwinds as well. So all of that would improve on the number above by quite a bit, since you're not trying to fly in both directions between your two airports routinely, but only once when conditions are best.
Nevertheless, unless you get waivers for a far higher takeoff weight than what's published (which the performance on a cold day at Edwards AFB would probably support), you're still far, far short of being able to do what Voyager did.
