How do you calculate trip fuel based on hourly fuel burn rates?

I am working on a small personal project that uses fuel burn data about specific aircraft to calculate the total fuel required for a trip. The data looks like this:

          | 120000 kg  | 150000 kg | 180000kg
----------+------------+-----------+-----------
21,000 ft | 6250 kg/hr | 6350 kg/hr| 6450 kg/hr
22,000 ft | 6225 kg/hr | 6325 kg/hr| 6425 kg/hr
23,000 ft | 6200 kg/hr | 6300 kg/hr| 6400 kg/hr


Based on the table above, you can see that to cruise at 21,000 ft and a weight of 120,000 kg, you would burn 6250kg/hr.

The problem I am having is that in order to calculate total weight, you first need to know total fuel, which you don't have until you know the proper burn rate. What would be the proper way to calculate fuel based on this information?

• Generally, you don't! There are different charts and/or tables (and computer programs) which are used to calculate the amount of fuel needed for the flight. They generally start with your landing fuel (at the destination / alternate if required) and work backward to come up with the required ramp/takeoff fuel and cruising altitude. Mar 29 '17 at 16:53
• Do you also have the data for fuel to altitude? You can't calculate trip fuel without those. Apr 2 '17 at 12:26

This would typically be solved iteratively. You start with your mass equal to ZFW and calculate how much fuel you need based on the table:

$$\mathrm{Fuel}_1 = \mathrm{Fuel}(m=\mathrm{ZFW})$$

Then you add this fuel to your total weight and repeat the calculation:

$$\mathrm{Fuel}_2 = \mathrm{Fuel}(m=(\mathrm{ZFW} + \mathrm{Fuel}_1))$$

which will give you slightly larger result. You repeat this process until convergence, meaning

$$\mathrm{Fuel}_{i + 1} \approx \mathrm{Fuel}_i$$

and this is your final result.

I think you're using the data the wrong way round. Fuel burn does not dictate how much fuel you should carry, but it might dictate what altitude you want to cruise at to conserve the maximum amount of fuel.

The amount of fuel you need to carry is based on endurance plus contingency. If you know the endurance of your aircraft is 3hrs, and your planned route estimates at 1.5hrs having added the appropriate contingency you might decide that you need 2 hrs of fuel for the journey. That means that you need tanks 2/3 full.

Now you know that the fueld to 2/3 fill your tanks weighs x, the weight of your aircraft is y then the total weight is simply x+y.

Using your datatable, you can now calculate the optimal cruising altitude.

Obviously this is oversimplified, as you still have the problem that it might be worth carrying slightly more fuel to get a better cruise efficiency.

• Wouldn't endurance change based on fuel burn though? My endurance would be much longer if I was burning 5,000 kg/hr versus 8,000 kg/hr. Mar 29 '17 at 21:30

I ended up solving it by programmatically going through each and every weight/altitude combination, multiplying the fuel burn rate by my duration, and adding that weight to my ZFW. If I was below MTOW, I saved the fuel burn rate and altitude, otherwise I discarded it. At the end, I picked the lowest fuel burn rate out of my saved options, which also gave me my optimal cruising altitude.

• From a calculation standpoint, brute force with all values, takes more work than an iterative refinement. Jan 31 '19 at 13:20

The normal approach is to segment your flight so that you know your burn for different phases of the flight. For example, cruise after a long flight, may be at a reduced power setting, because the aircraft is lighter (having burned much of it's fuel).

Then one adds up the fuel for each segment, including reserve, to get the total load.

Manually, iterative refinement can be done to optimize things.

For the flying I do, there is no push to drop the fuel load down, so we can pick a point, and with one run at he fuel (manually when not using an aircraft with FMS or electronic aids (tablet), we can verify if the initial guess is close, and decide to use that load.

However, friends who fly for airlines say that the ops people are always cutting their fuel tight, especially when there is weather which could cause diversions. They will ask for a few more pounds "for the wife and kids." Then again, a fuel diversion can be expensive.

Another point, normally one selects cruise altitude for WX conditions, traffic, and flight duration. In other words, normally the available fuel does not drive altitude. Altitude is driven by flight conditions, routing, economy, etc.

So in summary, segment your flight, and use climb and descent burn rates and rates for your weight, power (or TAS) and altitude, to get an initial "proposal" and then iteratively refine if necessary. Obviously add reserves and a flight condition based reserve. If you will be picking your way through some weather you will want a reserve for that.