# How does flight duration affect the hourly fuel consumption in heavy aircraft?

A 15 hour flight across the Pacific obviously requires more fuel than a 7.5-hour transatlantic flight. How significant is the hourly fuel consumption increase due to the additional fuel carried at the beginning of the longer flight? Another way of asking the question would be: How much more more fuel do you need to carry (in a typical heavy plane such as the B747-400) for a flight that is twice as long?

• You could take the Breguet range equation to derive some of those numbers, at least approximately. Including takeoff&climb will be complicated (and depend on more variables). – yankeekilo Jan 12 '14 at 13:49
• @yankeekilo: care to write an answer based on these equations (w/o including T/O and LDG)? Otherwise I might take a shot at it... – abey Jan 13 '14 at 20:00
• Please be my guest, in fact I was hoping for those very words :D – yankeekilo Jan 13 '14 at 20:30

The heavier the airplane, the more fuel it will burn in a given amount of time. Therefore, if you takeoff with enough fuel to fly further, you will be burning more fuel in each corresponding hour than if you took off at a lighter weight to fly a shorter distance.

# Example

I don't have performance information for the 747, but I can give you an example for a G-IV corporate jet. Instead of comparing a short trip to a longer trip, I planned the same trip with different amounts of fuel in order to make the airplane heavier. I planned the flight for the following conditions:

## Flight Conditions

• Fly from Los Angeles to Detroit, using the same route and average Boeing winds for July
• Climb to and maintain the optimum altitude, with step climbs where appropriate
• Trip 1: Climb initially to FL450 and stay there for the entire flight (the optimum altitude for this weight)
• Trip 2: Climb initially to FL410 and then climb to FL450 2:32 into the flight (the optimum altitude the weight initially followed by a climb once the optimum altitude has changed)
• Fuel:
• Trip 1: Takeoff with enough to land with a 1:30 reserve - 59,000 lb. takeoff weight
• Trip 2: Takeoff with max fuel, landing with a 5:39 reserve - 73,000 lb. takeoff weight
• Taxi fuel is not included in the first hour burns, but climb fuel is.

## Results

          Trip 1      Trip 2
Hour     Fuel Burn    Fuel Burn     Diff
1        4,212         4,844      +13.7 %
2        2,536         3,088      +21.8 %
3        2,411         3,123      +29.5 %
4        2,163         2,103      -2.8 %
Total    11,722        13,558     +15.7 %


## Summary

As you can see, the fuel burn is significantly higher in the first 3 hours due to the additional fuel that we were carrying (and therefore the higher weight of the aircraft). Hour 4 is almost the same because of the idle power descent used in the planning software.

• When you say "Climb initially to FL450 and stay there for the entire flight". What does FL450 means? – Gabriel Brito Apr 10 '14 at 17:25
• @GabrielBrito FL450 stands for "Flight Level 450" which is (roughly) 45,000 feet. You convert a flight level to feet by multiplying by 100. The one major difference in aviation though is that a flight level is not corrected for local pressure variations while actual altitude would be. So it's "close" to 45,000 feet in this case. – Lnafziger Apr 10 '14 at 18:31

Another consideration is the fact that the center of gravity changes as the fuel burns.

Yet another is whether you have ballast fuel, fuel used to bring the zero fuel weight c.g. within the allowable envelope. Technically speaking, ballast fuel is not available to burn, although obviously if that's all that's left you're going to use it.

Then there's the matter of extra fuel to make a captain happy that's above what the flight planned fuel is. Let's say the captain wants 8,000 lbs of extra fuel. For the old 747-100 and -200 aircraft, the rule of thumb was that if you loaded extra fuel, 20% of that fuel would be used just to carry it. In other words, If you wanted an extra 8,000 pounds available, you needed to load 10,000 extra.

Another rule of thumb for the old 747s that was used as a check on whether the fuel called for in the flight plan was reasonable, was to figure 30,000 lbs burns for the first two hours, 25,000 lbs per hour after the first two.

Unfortunately I no longer have the manuals for the 747 that would allow me to accurately compare, say, a four hour flight against an eight hour flight.

On the 747-400, the general rule for extra fuel used to carry extra fuel was 4% per hour or 3% per hour depending on your requirement.

If you wish to arrive with 10,000 pounds extra after a 10 hour flight you would have to load 14,000 pounds extra before departure (the 4% rule)

If you load 14,000 pounds extra before departure for the same 10 hour flight, this is burnt at 3% per hour (the 3% rule) leaving you with about 10,000 pounds at arrival.

The sums:

$$10,000\times4\%\times10hours=4,000lbs~burnt$$ to carry it, so load 14,000 pounds.

$$14,000\times3\%\times10hours=4,200lbs~burnt$$ to carry it, leaving 9,800 at the destination.

Close enough for Government work!

• Just to put this in perspective, he was asking about catering an extra 7.5 hours of fuel. How much would that be, and how much does that increase the fuel burn overall during the first hours when it is extremely heavy? – Lnafziger Jan 14 '14 at 12:46

For every 1% reduction in fuel weight there is a .75% reduction in fuel burn, "it takes fuel to carry fuel"

• Welcome to Aviation. It would be helpful to explain where those numbers came from, and how widely that can be applied. Is your comment valid only for a 747-400, or would it equally apply to other aircraft, and if so, which? – user11516 Oct 12 '15 at 1:23