How to compute the fuel bias value with PFPX

What is the fuel bias?

A planning and dispatching software that one uses can have limitations based on the fact that plots provided by the aircraft manufacturer have to be translated into functions by using discrete values read from those plots. If the functions are linear (linear dependency on the plot) than the function fitting is quite precise, but more often than not, the dependencies are not linear, so fitting algorithms can have errors which will translate into different values found during flight for the output parameters given by the software.

Another source of differences for actual flight parameters as opposed to computed ones are the actual environment that an operator uses the plane. For example, the manufacturer provided plots may be given for ISA conditions, while the operator constantly flies the plane in a high temperatures-low density area. This will again introduce some errors into the computed values that may have to be corrected by the dispatcher. And this problem is more acute in the virtual world as developers usually learn as they go along.

One of these values is the fuel burn rate. The manufacturer (real world plane) provided extensive plots describing the fuel burn of an engine in their aircraft configuration and the model developer (virtual world plane) did his/her best to make the engine follow the manufacturer's performance plots, but as I said above, there can be differences that will arise from the actual translation of plots into continuous functions or from flying in ISA and flying in Congo all the time. Or it may just be a feature of the plane that drastically changes the fuel burn: i.e. the B737-300's auto-flight in turbulent weather that increases the ordered speed thus decreasing the climb rate => increasing climb time => burning more fuel. Whatever the case, you will see that the fuel used can differ from expected computed values.

The correction to fuel burn that a dispatcher can use is called the fuel bias. In uncorrected usage this value is 100% (or 1) as the fuel burn table used will be the one provided by the manufacturer and translated into code by the developer. When a positive fuel bias value is inserted, the software will increase fuel burn values, thus increasing the fuel needed for the trip. On the other hand, when the fuel bias value is negative, the fuel burn will be decreased and less fuel will be computed for the trip.

So how does one compute this correction value?

PFPX and fuel bias

PFPX, dear PFPX, offers simmers a way to account for these discrepancies by imploying an algorithm to compute the fuel bias for all aircraft in the database. It is as simple as reading some in-flight parameters and inserting them into PFPX. It will consequently provide the fuel bias and a drag index correction. But to have a coherent computation, the values need to be taken in stable flight as in the cruise part of a flight.

The values needed by PFPX to compute the fuel bias are:

• flight level/altitude
• true airspeed
• ground speed
• Mach number/outside air temperature
• aircraft weight
• actual fuel consumption
• (cost index)

Outside Air Temperature

The fuel bias calculation needs the outside air temperature to be known, but in a jet that is not really available because of the high mach numbers which in turn give way to air friction that heats up the air around a jet liner. So what we know in a jet is the total air temperature that is not that helpful. That is why PFPX provides alternative ways of entering/finding the outside air temperature. The most convenient way to insert the outside air temperature without ever knowing it is by means of ISA deviation and mach number. If you know the altitude, the true airspeed (easily read as all jetliners have TAS indications) and the mach number you can derive the outside air temperature directly in PFPX Bias window. First you insert the true airspeed and the altitude, which will make PFPX compute a mach number in ISA conditions at that altitude. But you know the actual mach number from the jetliner's PFD so what you need to do in the PFPX window is to modify the ISA deviation temperature window until the computed mach number matches your actual mach number. That way you will have a good estimation of the actual atmospheric conditions for your fuel bias calculation.

That is why I wrote "outside air temperature/mach number" in the requirements list - GA can give you OAT while for jets it's better to read the mach number and derive the OAT.

TAS, GS and drag index correction

So as you can see from the above list, one needs not just the true airspeed but also the ground speed. This is for wind calculation. Normally, if there would be no wind, the aircraft would always have a GS equal to the TAS. Knowing the two values will tell the algorithm what kind of longitudinal wind did the plane encounter (headwind or tailwind component). While this parameter doesn't change the fuel bias in any way, it does help PFPX compute something called drag index correction for the actual flying conditions. This is the same as the fuel bias correction in the sense that a positive value will tell the algorithm that the plane is dragging more so more engine power is required to maintain a certain speed so the actual fuel consumption shown is now higher than normal.

Actual fuel consumption

This is pretty straight forward, you read the current fuel burn rate from the screens or dials. One thing I want to point out in here is that you should make sure you understand the unit of measurement. For example, in IXEG's B737-300, the fuel burn is ALWAYS given in thousands of kilograms per hour for each engine, even if you have the fuel quantity in pounds!!! So please be sure you always know what unit you have the value in and what unit is required in PFPX window. Use Google to convert.

Cost Index

Some jets employ the use of the Cost Index concept (all turbo-fan jetliners) which is not the scope of this post to explain, but is suffice to say that CI is inversely proportional with the fuel burn so that is why PFPX needs to know what CI did the pilot actually request from the FCS before doing any computation regarding fuel burn rates. If the aircraft doesn't employ the CI logic, you won't be asked for it.

Conclusion

So if you enter all required input PFPX will come up with a fuel bias value and a drag correction value. If you apply this, all future fuel calculations will have these corrections in for this particular aircraft. While the correction values are usually low (|5%| to |8%|) I found that the IXEG model needs a larger correction (+16% to +22%). Nevertheless, after correcting the fuel bias I get more consistent fuel values when comparing PFPX flight plans with in-flight values. But one thing to point out is that a new re-computation of the fuel bias value may be needed at extreme atmospheric changes, so I would advise anyone to recompute once in the summer and once in the winter, just to cover all bases.