How much fuel is burned to carry the trip fuel?

Question

For rockets, there is a rule of thumb that says for each kilo of fuel put into orbit, 7 kilos is needed to get it there.

For long and ultra-long flights, it feels intuitive that some very significant proportion of the fuel, perhaps the majority, is needed to carry the fuel needed to complete the flight. In other words, imagine that the fuel was weightless and 50,000 litres were needed. But since fuel is not weightless, the requirement is actually 100,000 litres.

Of course there are a lot of variables and it's fairly easy to calculate, but is there a rough and ready rule of thumb?

Answer 1

The 7:1 rocket figure is perhaps for the unrealized single-stage-to-orbit, getting a payload to low Earth orbit (LEO) is closer to 9:1, and going to the moon and back is 23:1 (Saturn V).

If a soda can's content is the fuel, then the rocket stages that are jettisoned have better fuel to empty mass ratio compared to that soda can, so staging is not the main reason why the figures are higher than the 7:1.

• This is important because if a 5-hour flight is getting to LEO, then an ultra-long-haul 16-hour flight is the equivalent of going to the moon and back.

This already tells us there is no general rule of thumb for flight planning (or space flight). But, there is a common figure that is used when highlighting the benefits of carrying the right amount of fuel.

0. A common figure: 15%.

According to Simon Weselby, a Fuel and Emissions Performance Manager at Airbus, that figure is 15%. So to carry 1,000 kg of fuel, an extra 150 kg will be burned.

According to the famous lift-to-drag ratio graph, carrying fuel in cruise is not a big deal as the induced drag decreases with speed. The challenge is getting a heavy plane off the ground and getting it up to speed.*

If the fuel fraction mid-flight for a long-haul jet is 20%. Then that means the thrust required to carry 20% of the weight is 10% of the thrust (if the induced drag equals the form drag at the minimum drag point).

* That's why above a certain range, it becomes more economical to make stops. This takes into account the fuel alone. Not taking into account the passenger convenience, aircraft cycles, the maintenance cost of the extra takeoff thrust, etc.

That relationship is demonstrated by the graph below.

(Wikipedia) Takeoff, climb, step-climbs, etc., are accounted for, i.e., those are the averages for complete flights, not just cruise.

I've used the same 777-200 data that was used in making that graph to come up with different ways to look at your question, which can be answered in more than one way (the previous 15% figure is the easy answer).

1. If the fuel was weightless problem first.

I've used the most economical range (average fuel flow) as a baseline. And from there found out how much fuel is wasted to carry the extra fuel for the extra range.

NM      kg

2800       0    0%
3200     230    1%
3600     420    1%
4000     750    2%
4400    1130    2%
4800    1760    4%
5200    2350    4%
5600    3180    6%
6000    4060    7%
6400    4990    8%
6800    6080    9%
7200    7260   10%
7600    8590   11%
8000    9970   12%

Going from 2800 NM to 8000 NM, 9970 kg are wasted carrying the heavier fuel, or 12% of the total fuel load.

The fuel fractions for 2800 NM and 8000 NM are 18% and 40%. The aforementioned 15% figure for the A330 at 2500 NM matches that of a 777-200 at 2400 NM.

2. Problem two: carrying more fuel for the same trip distance.

This is equivalent to payload. What it does is increase the landing weight (LW). A quick and dirty way to check how much extra will be burned carrying more fuel that will not be used is to use the same fuel fraction for that distance.

This is what the Airbus presentation says, which I've been able to verify in a spreadsheet for 5 different weights 22.7 tonnes apart. (And also for the 737 for good measure.)

(Own work) Click to view full table.

For example, if our baseline flight needs 15% fuel fraction, it will still be 15% of the new higher weight (landing weight + trip fuel). In other words, if the LW goes up, the trip fuel goes up.

For the 777-200, landing weights of 136,100 and 226,800 kg need 25,400 and 37,800 kg of fuel for a 2400 NM trip. Or 15.7% and 14.3% fuel fractions.

An 8000 NM trip needs a fuel fraction of 40.3% for the lowest landing weight I calculated, and 38.8% for the heaviest.

So the quick and dirty rule of thumb is to maintain the fuel fraction for the same trip distance.

3. Percent of Landing Weight (LW) per hour.

A different way to look at it: I've constructed the graph below for the 777-200. As you can see, it matches the trend of the Wikipedia one.

(Own work)

So for a 6-hour flight, it will be 6 times 3.6, or 21.6% of the LW in fuel.

While a 0.5% is negligible for a 737 and maybe even for a 777 on short routes, it is not when it is multiplied by long flight durations.

Below is yet another way to look at the data, the average fuel flow per engine in kg per hour for the different trips.

NM      FF/eng (kg/hr)

 800    2510
1200    2460
1600    2440
2000    2450
2400    2450
2800    2450
3200    2470
3600    2480
4000    2490
4400    2510
4800    2540
5200    2560
5600    2580
6000    2610
6400    2640
6800    2660
7200    2690
7600    2720
8000    2750

Answer 2

While various operations will have various rules of thumb, I don't think that there is any one single rule of thumb, because the length of the flight (and probably, the type of aircraft) affects the result to much.

In a fairly short-haul 737, to get "another 1000 lbs" of fuel at landing, you just upload another 1000# into the tanks. You'll burn less than 10 pounds of that for a quick flight, and so uploading the extra 1000# means arriving with about 990# more, which is too small a difference to worry about. (Plus, you order fuel in 100 pound increments, so "load another 1007 lbs" would generate a puzzled look from the fueler.)

On the other hand, in a discussion with a 747 pilot who routinely flew from Minneapolis to Tokyo, when he wanted another 10,000# of fuel at arrival (that airplane uses bigger numbers than the smaller 737!), he had to upload almost 20,000#. The 737 rule of thumb wouldn't work at all for him, as his rule of thumb was based on burn rates and timeframes that totally outside of the 737 operation.