When does it burn fuel to carry fuel?

[Lemurian]

Hello, Mutt

So your 40% over 11 hours appear on the high side for that aircraft!

The way you wrote, it looks as if you *tankered* an extra 27,270 Kg of fuel, of which you burned 7,770 kg. Right ?
Remember, the formula I gave is about landed weights. from that point of view, in order to land 27,270 - 7,770 = 19,500 kg, you used 7,770 / 19500 = .398 or 39.8 % of the landed fuel.

Secondly, K will increase 1/- with higher weights, 2/- with longer flights and 3/- with your cruise schedule (the higher the CI, the higher the trip fuel and the TO / LW ratio ).

Thirdly, that extra fuel takes our computation probably away from the realm of quick computation as we're coming - my estimation - some 22 to 25 % of the LW and with that extra load, the flight profile will be very different (Step climbs...) and the fuel consumption will reflect that.

But my example, for obvious reasons, did not portra an actual flight. Let's just say that betwen CDG and HKG with a 30kt tail wind, the real example came out with an 11 hr 6 mins and a K= 1.347. The airplane was some 36 T below MTOW.

Please, re-do the calc using actual weights.

Regards

[glawkshuter]

It's funny, but does anyone here besides me have a clue as to thier per gallon cost of fuel at the departure or destination point inorder to determine how much fuel to tanker here or there to figure this out..?? If you don't then it's all moot, you simply carry as little as possible to make the plane climb and fly faster, fly as high as you can to get your fuel consumption as low as possible per trip, go with long range power settings...as airliners can go 20000 hours on an engine....unlike corporate... For corporate there is a point where the engine cost out weighs the fuel cost(not lately)...so in the past we went fast, now we go slower, and really shop fuel....

[mutt]

FUEL TIME ETA NGM NAM FL COMP TEMP WEIGHTS
POA RPLL 077499 10:00 1600 4944 4898 370 P006 M35 148.77 OWE
ALT RPVM 005876 00:54 1654 0345 0350 M004 025.00 PAYLD
HLD 003100 00:30
RES 006414 01:00 112.37 TO/F
REQ 092889 12:24 ATW . . . . / 286.15 TO/WT
XTR 019489 03:09 208.65 LDGWT
BLST 000000
ETOP 000000 00:00
TOT 112378 15:32


Le Murian, these are the actual flight details. How am i expected to know the landed fuel prior to flight?

glawkshuter, our crews are advised of the fuel cost and the multiplier for carrying it on various distances. This way they have a better understand of the costs associated with tankering.

Outta here for next 6 weeks, so dont know if i will be able to continue this discussion, more the pity as it was interesting

Mutt

[mutt]

Keygrip,

I ran CFPs for a C550, 1.40hr sector.

PLD / FUEL BURN / %
500 / 686 / 4.2%
600 / 693 / 3.6%
700 / 699

So for every 100 additional KGS, its costing me circa 4% to carry. But the amounts of fuel increase are so small that they arent worth worrying about.

So to answer your original question, all aircraft burn more fuel to more fuel to carry fuel. you only need to worry about it when the financial costs are sufficient that they impact on your operation......

Mutt

[kijangnim]

correction

Greetings,
Lemurian and Mutt are both right
In fact Lemurian computed the K factor using the following ,the LANDING WEIGHT DID NOT CHANGE because the increased TAKEOFF WEIGHT is PAYLOAD,
MUTT used an increased TAKEOFF WEIGHT due to EXTRAFUEL uplift, so the LANDING WIEGHT is AFFECTED and will be LOWER, which will give a LOWER K factor.
In fact the thing to do is to use MUTT result and compare the fuel price (in percentage) difference (corrected by fuel SG) to the K factor and if fuel price is greater then TAKER FUEL.
The method used by Lemurian is the one to use incase of excess weight to be offloaded. let say that for limitation purposes we have to get rid of XXXX KG , then using K we would split the weight between pay load and fuel , which in turns will save you K % of your payload which is $$$$

[bookworm]

Interesting question. I like Lemurian's approach of using Breguet's range formula to assert that take-off weight / landing weight is effectively constant. However I'm not sure it really gets at the heart of Keygrip's question as to why this is an issue on the 777 but not the C152. Let me look at the problem from a different angle.

The key parameter is the % increase in power required per % increase in weight, which I'll call alpha. Mathematically that's

(dP/P) = alpha * (dW/W)

Knowing that, and assuming that fuel consumption is proportional to power required:

Extra fuel consumption rate / Normal fuel consumption rate = alpha * Extra fuel loaded / Weight

Rearranging that:

Extra fuel consumption rate / Extra fuel loaded = alpha * Normal fuel consumption rate / Weight

The left hand side is just the proportion of the extra fuel burned per hour. It depends on (Normal fuel consumption rate / Weight), so it's more (per hour) for a short flight than a long one, but I don't think that goes far towards explaining why it's significant for a 777 but not a C152.

What about this factor "alpha"? Well that will depend on how much of the drag is lift- (and therefore weight-) dependent. That depends very strongly on the speed you fly at.
At minimum drag speed, half the drag is weight-dependent induced drag. As you increase the speed, weight-dependent induced drag becomes a much lower proportion, and % extra power required per % extra weight is much lower.

If I take a drag polar that looks like (^2 is "squared")

drag = W^2/v^2 + v^2

then I get

alpha = 2/(1 + v^4)

where v is the speed relative to minimum drag speed. That's a really strong dependence on v. At minimum drag speed alpha is 1. At 1.4 times minimum drag speed, alpha has fallen from 1 to 0.4. At 1.7 times minimum drag speed, alpha has fallen to 0.2.

I don't fly big jets but I think that's where the difference lies between them and light aircraft.

My light twin burns about 85 lb/hr at 3400 lb, so my proportion of extra fuel burned per hour is alpha * 2.5%. But that's cruising at about 50% above minimum drag speed, so alpha is about 0.3, and it costs me less than 1% per hour to tanker fuel.

If I'm interpreting the Boeing figures I've got here for a 757, and cost index 0 is a reasonable indication of minimum drag speed, even cost index 70 suggests a cruise speed just 1.07 faster. At today's lower cost indices, that might be even 1.05 times minimum drag speed, and so alpha is going to be pretty close to 1 (say 0.9). I appreciate my naive drag polar might not be accurate at Mach 0.8, but the point stands that you're flying at a speed where weight dependent drag is a much greater proportion.

So do get back to Keygrip's question, it starts to matter to a significant extent when you start flying at speeds closer to minimum drag where weight-dependent drag is a significant proportion of total drag. That tends to apply to fuel-conscious ops in big jets, and less to the always-cruise-at-75%-power C152s.

[SNS3Guppy]

We use 5% of the load increase per hour. If we intend to tanker 50,000 lbs of fuel, at the end of 10 hours we will have consumed 50% of that above the planned burn without it. In other words, if we'd have planned to use 180,000 lbs of fuel for the flight, we'll have burned 205,000 lbs instead...tankering the extra fuel cost us half of the tankered fuel over a 10 hour flight over and above the fuel burn we'd have had without the extra fuel.

We do look closely at the cost of the fuel at departure and destination and that plays a role in determining what we can tanker. However, our chief criteria for determining how much fuel is the required fuel burn vs. the payload; we certaily won't carry extra fuel at the expense of revenue payload just to tanker cheaper fuel...because we're burn and waste much of the extra fuel. The payload pays the fuel costs...so unless the price difference is grand, or the circumstances of the flight can justify the significant cost increase of tankering the fuel (for safety), we generally don't tanker.

[glawkshuter]

So Guppy...based on what you paid for fuel at your destination, where's the cut off in price per gallon that will determine if you tanker down or back?

[BOAC]

I expect Keygrip is REALLY pleased he asked this question

We see you are back, ssg, and still 'shuting the glawk' too. If you cannot work that out from SN3's post......................

[barit1]

Early 80s, DL had a number of KLAS flights - and the fuel price there was 20-30% higher than KLAX. So they substituted a DC-8 on some of the flights simply to tanker in fuel to KLAS for their 727's, DC-9's etc. They didn't like to do so, but for a brief time the numbers made sense.

[glawkshuter]

Well color me confused by all the complicated math.....Met a Continental pilot who told me that everyone is flying around in his airline with min reserves as has been directed by management....For me, I will try to save a buck but not compromise safety doing it...

[SNS3Guppy]

So Guppy...based on what you paid for fuel at your destination, where's the cut off in price per gallon that will determine if you tanker down or back?

There isn't a cutoff point, as it doesn't work that way.

[glawkshuter]

Guppy...must be very nice not to have to worry about the actual price of fuel when considering whether to tanker or not.
In my world the price per gallon determines the actual fuel cost of the trip...but maybe you have a oil refinery at your airport...

[SNS3Guppy]

When one can save a few pennies or even twenty five percent on the cost of a gallon of fuel, that sounds great...until one burns half of the tankered fuel just to move it from A to B. In that case, the effective cost of the fuel you have remaining...that is, the fuel that wasn't wasted getting it from A to B...has just doubled. Save a dollar or a euro or a pound on a gallon of fuel...but have half of the tankered fuel remaining...and you haven't saved that dollar...you've doubled the cost on the fuel instead. Why? You just paid a little less, but got half as much. That's not economy.

Further, the airplane climbs slower, uses more runway, lands heavier, has a lower climb gradient, lands faster, may require higher power settings and thus experiences greater engine wear, yada, yada, yada.

You tanker 10,000 lbs, a purchase of 1,500 gallons. You do this because the destination has fuel at 4.00 a gallon, whereas your departure has it for 3.00 a gallon. This sounds good; you'll save 1,500 dollars on the cost of the fuel. You make a five hour flight, consuming five percent of the surplus tankered fuel, per hour. The surplus tankered fuel is 10,000 lbs, meaning you consume 25% of the tankered fuel during that five hour flight (5% per hour for five hours).

Fuel at departure would be 4,500 dollars, whereas one would have to pay 6,500 dollars at the destination for the same amount of tankered fuel. Unfortunately, because 25% of that fuel is burned on the way to the destination (fuel burn has gone up due to carrying the extra load), you have only 75% of that fuel remaining...1,125 gallons of tankered fuel. Dividing the total cost of the tankered fuel you bought, 4,500 dollars, by the amount of fuel you have remaining (1,125 gallons), you find that for the fuel you've got, you really ended up paying four dollars after all. You've saved nothing, but instead dragged ten thousand pounds of fuel across the country or internationally, for nothing. That's ten thousand pounds of revenue paying payload that one could have carried instead...or at least 75% of those ten thousand pounds...7,500 lbs of payload that would have paid and been profit.

Break even point? It's not nearly so simple as looking only at the cost of fuel at departure and destination. One needs to consider numerous other factors, including the purpose of the flight, the payload available, the conditions of flight, etc, when making such a decision. Very often tankering provides no additional benifit economically.

We do plan fuel stops where the difference in cost justifies the stop, but in that case we're tankering nothing; we carry the proper amount to reach the tech stop, then take on the proper amount to reach the destination. Even then, merely making the stop for the sake of fuel cost is more complicated than the raw cost of the fuel. Time lost when the aircraft could be on another trip making money, additional trip time and time on airframe and engines, landing and engine thermal cycles, etc, all must be factored into the justification in making the stop. Most of the time, a tech stop just for the cost of fuel isn't justifiable.

Where a tech stop must be made due to the length of the trip (which for us is sometimes the case), we'll break up two six or seven hour legs with a fuel stop selected for it's convenience to the route, it's minimal turn around times, and yes, the cost of the fuel.

You see, in the real world, it's not quite as simple as your world.

[glawkshuter]

.. the calculated formulas are for a captain to decide if taking on extra fuel for safety is worth the 'x' amount of cost to the company by carrying the extra fuel.

[Lemurian]

Guys, Oh! Guys !

I'm quite disappointed in you :
One of the uses of the transport factor is really about profitability of tankering.
Let's go back to the initial def : K = ðTOW / ðLW,
which means in layman's terms that for each landed ton of transported fuel, one needs to uplift K tons of extra fuel.
The price of that landed fuel will be Po * ðTOW = Po * ðLW * K...... ("o" for origin ).
Let's call Pd the fuel price at destination : the transported fuel, ðLW, would have been paid Pd * ðLW, had one not transported any fuel.
So, tankering will be profitable if :
Pd * ðLW > Po * ðLW * K, in other words if the cost of the extra fuel at departure is lower than the cost of the transported ( meaning "landed") fuel at destination.
Simplifying the above equation :
Tankering is profitable if : Pd/Po > K

The beauty of it is that it works, whatever the type of aircraft, whatever the distance....be it a 744 or a Cessna 150.
It allows to have a ball park figure while waiting for one's dispatch to finalise the computations.
Beware, though : for greater quantities of extra fuel on long sectors, one could alter significantly the flight profile through delayed steps... and find that one would spend some extra time in the air, adding the effects of DOC to the economics of the flight.

Mutt,
From your CFP, I only have the final burn-off of 77,499 kg.
The final figures of TOW = 286.15 T ; LW = 208.65 T give a K= 1.371
Of the extra fuel = 19.500 T you'd keep at destination 19.500 / 1.371 = 14.223 T, thus using 5.277 kg extra burn-off to land 14.223 t at destination.

[dlk111]

The MD80 that I fly used about 78 pounds of fuel for each 1000 pounds tankered on a typical trip from Seattle to Oakland. So about 7.8% was used up.The fuel price in Seattle was better than in Oakland. On a trip from Seattle to Anchorage the burn was about 125 pounds or 12.5% used up.
The price of jet is so bad now that my last trip to San Jose the entire return fuel was tankered! I left Seattle with 32000 pounds of fuel!

[kijangnim]

Greetings
Lemurian....Laisses tomber

[glawkshuter]

Maybe what needs to be specified, some of the reasons to tanker fuel:1: Total Trip cost reduction. Self Explanatory. By purchasing and carrying as much of the cheap fuel, you reduce having to use the expensive fuel. Over the total trip, the cost is less. This assumes you know the price per gallon at departure and destination airports and can actualy control the amount of fuel purchased. 2: Safety: Taking that extra fuel to eliminate putting a plane in the water, having to turn around midway, Island fuel reserves come to mind...the more fuel you have the more time you have. And more I am sure...But for the purposes of this thread, the question seems to be, when does it start costing money to carry extra fuel around....Since it's obvious that carrying one once over minimal legaly required reserves cost money to carry to the destination, the question remains for those agonizing over carrying tankered fuel: How much safety are you willing to give up, inorder to save a buck for the company?

[Lookforshooter]

I happen to agree with Glawkshuter...it's one thing to sit there and figure out the cost of tankering so as to be brow beaten into not taking any excess fuel thus making the flights just a little unsafer(Airlines) vs simply shopping fuel, discounts, and tankering fuel to make the trip cost much less.