Author Topic: Fuel Calculation  (Read 3289 times)

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Offline Adrian Chitan

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Fuel Calculation
« on: April 22, 2014, 11:24:27 AM »
Hello again,

I think this is a subject bothering new and old pilots whenever they want to fly, so why not talk about it a bit.

I think we should first get some terms out of the way.

Cost Index
The Cost Index of a flight is an indirect ratio between flight time and fuel used. The idea behind this number is that if the amenities of a flight (personnel paycheck, catering, etc.) are more expensive that the fuel used (not necessarily fuel < personnel, but the airline has it's own algorithm of declaring a cheap fuel flight), then you would want to fly as fast as you can and finish the flight fast. That means you should put in a greater CI so that the plane gets to the maximum safe speed faster (it doesn't necessarily mean that you'll fly faster, because an A320 is flown at .78 Mach at CI 20 or CI 60, but the plane will climb faster and accelerate faster with the latter).

Air Distance
Already known by everyone, but a reminder never hurts. If you have a FP distance of 1500 NM for a 737 with a mean tailwind of 30 kts then the Air Distance is about 1400 NM. If the wind was a headwind of 30 kts then you would have 1600 NM. What does this Air Distance mean is the actual distance your plane has to fly to reach its' destination.

FuelPlanner
I guess everybody knows about fuelplanner.com. If nothing else, you use this little online tool to get a good estimate of the fuel needed for your flight. Unfortunately, the tool has some downsides. First and foremost, it doesn't take into account the real zero fuel weight of your aircraft. It uses some standard ZFW it has in its' database for every plane you choose. And it doesn't give you any fuel correction numbers for ZFW modification.

Second, it gives you something called Reserve Fuel, but it is actually based on nothing. Reserve Fuel should be the divert fuel usage and if at anytime during the flight you get the INSUFFICIENT FUEL (in the FMC equipped planes) you should divert to your alternate. But don't be to jumpy into going to your divert airfield because INSUFFICIENT FUEL can be brought up artificially by the pilot: inserting a wrong cruise wind (can make the computer calculate a longer air distance than it will actually be flown), inserting a to high reserve fuel margin (if you didn't account for diverts, but you insert a reserve fuel margin, halfway or 3/4 into your flight you may get the warning), flying at a higher fuel consumption profile than planned (higher CI or higher climb/descent speeds).

The good thing about it is that it gives you a CI for the flight and the fuel estimates are pretty good for all your flying needs. In my case, I have found that sometimes I had to much fuel at the end of the flight or the reverse, I had to little (especially because I like flying around the upper limit of the ZFW).

Now let's look at a fuelplanner result for a flight from Berlin's Tegel to Henri Coanda in an A320.



The number you are after is the TAKE OFF FUEL. It says that 18395 pounds of fuel have to be loaded into the plane to fly a direct route (!!!) with a ZFW of 125410 pounds and still have a 6897 pounds of reserve fuel in a no-wind weather at the optimal cruise altitude. The actual fuel burned will be 11498 pounds.

The bottom box can actually help you into modifying these values for the actual flight. It says that the BLOCK TIME is 2 hours and 5 minutes. It means that the 11498 pounds will last for 2 hours and 5 minutes. You know your FP and the normal TAS (TAS = GS in no-wind weather). You can account for wind now by calculating the air distance. So you find out that you'll need to fly about 2 hours and 30 minutes. We know that 2.08 (2 hours and 5 minutes) hours takes 11498 pounds and using the 3 simple rule we get that for a 2.5 hour flight we'll need about 13820 pounds.

Another problem is the Reserve Fuel. We've set our sights on Baneasa airport for the alternate so we'll have to calculate a new reserve based on the known distance from LROP to LRBS. The direct route is about 13.5 NM at a TAS of about 250 kts (we'll divert below FL100). This means that the divert will be done in about 3 minutes. So for 1 hour and 15 minutes we'll use 6897 pounds of fuel, how much will we use for 0.054 hours (3 minutes)? 298 pounds. Let's round this up to 500 pounds. So by using the simplest tool at our disposal we have found that a better guess for the flight is to load the plane with 14320 pounds of fuel.

But this contains no contingency fuel (unexpected diverts during the flight because of weather or military operations) nor a holding pattern fuel (the airport may be busy). The hold time can actually be calculated from the reserve fuel expectancy again. Holding pattern is usually done at lower FLs so we can actually consider it a divert condition. So if I want 30 minutes for my holding time I again use the 6897 pounds/1:15 combination from the fuelplanner load sheet. We find that an added 2759 pounds should suffice for the holding pattern. For the contingency fuel, you will have to add how much would you expect the maximum added distance for your trip will be because of the route divert. After knowing the distance (maybe corrected into an air distance) you can transform it into an added time and again use the 11498 pounds/2:05 combination to get the fuel needed.

The last thing you should correct for is the actual ZFW of the plane. If you have a heavier ZFW than 125410 pounds then you should add some fuel while the reversal is true for a lighter plane. The added fuel needn't be to much (+100 pounds of fuel for every added 1000 pounds of ZFW, -60 pounds for every subtracted 1000 pounds of ZFW - something like this for a A320).

Home made remedies
When I was flying FSX and PMDG planes, they have the tendency to detailing the fuel calculation so that the flight can be as real as possible. From those documents, I created fuel planner programs for different aircraft. I will share with you now the program for the PMDG 737 and the PMDG 747-8i. They both follow exactly what is said in the PMDG manuals but they are very different because the 737 uses pure formulas to get everything while the 747 uses tables to get the required information. I did them in Microsoft Visual Studio Express (C++) which is free for anyone who has Windows. If you don't have Windows, you can just copy the code sources and compile them using your C++ compiler.

The 737 program can be used after the 737 has aligned so that you get the remaining fuel at destination and at alternate. You just have to give these to the program (in the command line) along with the unit of measure (lbs/kgs), the total fuel weight that the plane calculated the remaining fuel for and the time you want to save as holding time in minutes. You'll get the gist, is not that hard. If you have questions you can ask them here, of course.

A window showing the results for a trip is shown below.



Professional Flight Planner
A few weeks ago I have bought PFPX from FlightSimSoft. I cannot even scratch the surface of the depth that this little tool brings into flight planning, but I will talk a bit about its' fuel planning. First off all, I should start by saying that PFPX accounts for wind and equipment by default. It knows the winds for your entire flight so you don't have to account for them anymore because it will. For the equipment it has different aircraft profiles to match any IFR flight you might do, and all the profiles are also modifiable. Now, the flight planning window has a special section for fuel planning as you can see in the picture bellow.



As can be seen I havve selected EU-OPS as the fuel policy (because we are an European Union VA - by the way, even if I would fly in the US I still have to use EU-OPS because it doesn't matter where I am flying but where is the plane registered). Also, I want to have a 30 minute extra time of flight (this is that contingency for a modified FP during the flight that I want to account for) and 40 minutes of hold time. The plane type can be seen in the Aircraft section (the A320-214 CFM). Also in the Aircraft section you can see my climb, cruise and descent profiles: 250 kts to FL100, then 300 kts until reaching .78 Mach and keep this Mach number for the cruise also; then the descent is the opposite of the climb. The Payload section shows the payload on the aircraft: 132 adults with 7 children adding up to a ZFW of 56184 kg. On the right map you can see the actual FP. We have a 11% increase over the great circle adding up to 776.1 NM. What is hard to see here is that I have also chosen LRBS as the alternate and I told PFPX that I won't go direct to LRBS but through FLR VOR.

Now, the picture below shows the results of the PFPX from a fuel standpoint.



PFPX gives us a release fuel weight (the fuel that needs to be in the plane before the preflight) of 9392 kg. It also gives us the detailed fuel planning sheet with the holding fuel being about 1.5 tons. We also have the alternate fuel at 626 kg. The CONT 3% UKLU is the en-route alternate (an alternate airport for diverting while en-route). The extra contingency for the 30 minutes I requested are weighted at about 1.1 tons.

In the top right you can see the ZFW of the plane. Now, if this ZFW changes (when the pilot gets into the plane he finds out that there are 10 extra passengers on-board or you have to carry more fuel in a tankering mission), PFPX helps you with what is written in the green rectangle in the above picture. It says this: if the plane's takeoff weight increases with 1 ton, then you have to add 55 kg of fuel, while in the case of a ton decrease you will have to take out 56 kg of fuel. Even more helpful is the line below that. It says that if you fly 2000 ft lower than your optimal cruise altitude than you'll have to put in an extra 28 kg of fuel.

Unfortunately, PFPX is a bit expensive, the PFPX+TOPCAT bundle going for about 55 euros (TOPCAT is a tool for calculating takeoff and landing performance - remember those V speeds and derate temperatures, that's what TOPCAT does for you). But as I said and showed, you can do a pretty good fuel estimation using fuelplanner or your home made methods.

I know this was a bit long, but you don't have to read it if you have a good fuel planning method. This just adds to the reality of virtual flying.

Offline Adrian Chitan

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Re: Fuel Calculation
« Reply #1 on: April 22, 2014, 11:29:14 AM »
Unfortunately, I got the Upload Server Full error for my attachments so I can't put in the cpp files for the "home made remedies".

Offline Adrian Chitan

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Re: Fuel Calculation
« Reply #2 on: April 22, 2014, 03:36:35 PM »
I've put the cpp files on Dropbox:

https://www.dropbox.com/sh/v0hhhrw1vnmes0b/n2d20Aderu

Cheers.

DBX024

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Re: Fuel Calculation
« Reply #3 on: April 23, 2014, 09:23:45 PM »
Multumim foarte mult pentru efortul depus  si pentru aceste informatii

 

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