Payload Formula

[Trader]

Anyone have software or reference to calculate the cost of each additional pound of payload?

[ft]

Check the range diagrams for the type in question. From that, you should be able to calculate the fuel needed at different weights and thus the operating costs. Then calculate the amount of payload which can be shifted along the route over n flights along the proposed route and divide the operating costs by the amount of payload. Difference in operating cost/difference in payload and there you have it.

Unless you are prepared to make quite a few rather broad assumptions regarding other factors, I’m afraid you’ll end up with a complex answer, largely saying “it depends”.

If you just want the fuel burn, the performance manuals typically have provisions to calculate the fuel used for climb at various weights, fuel flow in cruise and so on.

Or do you want to do it analytically? Then you’ll need to set up the equations of flight for different phases of flight and calculate drag and specific fuel consumption. Again, you will have to make a lot of assumptions and I suspect the answer will be largely “it depends”.

Perhaps if you give us more to work with? Are you interested in the general approach, or one specific type? Is it to be merely fuel consumption or all operating costs? What’s the purpose of the question?

Cheers,
Fred

[Thunderball 2]

I once did an exercise to determine the incremental fuel burn on DC10 operations to the Far East. I asked Flt Ops for the numbers, valid for typical weights. They took forever to come back, I remember that, and when they did I had a deputation of about five of them.

From memory, it was roughly 285 kgs per sector (flown via DXB) of fuel per additional 1,000 kgs of payload, i.e. 570 kgs right through to HKG. But this is 25 years ago...

Net result? Staff travel fares went up by 100%, from £30 round trip to £60.

But of course this is not definitive; as Fred implies, every flight will be different.

[BTW, this concept is far from academic. I'm aware of UK charter carriers lifting US-UK freight out of Florida at net/net revenue rates/kilo that won't cover marginal cost of incremental fuel burn].

[Old Smokey]

Yes, IT DEPENDS on far too many variables to come up with one simple formula. If, for example, the flight were to be conducted at one Flight Level throughout, some fairly simple formulae might emerge which were reasonably valid over a modest weight range. If, on the other hand, increased weight delayed a step climb, or prevented it altogether for a longer range flight, a whole new set of parameters emerge.

The only realistic method is to run a series of flight plans at different weights, and establish the relationships. The better computerised flight planning programmes provide data for the expected weight, and plus/minus Time and Fuel adjustments for ZFW change. Similarly, adjustments are provided for 'Off Optimum' Flight Levels.

[alatriste]

A very easy, and maybe inaccurate, " rule of thumb" that I have read some time ago, valid for a tipical airliner, is a 4% of fuel burned increased, per flight hour, when the weight is increased 1.000 Kg.
If payload or block fuel is increased 1.000 Kg for a 3 hours flight, trip fuel will be 120 Kg higher.

[Trader]

Thanks for the responses.

Basically, I am looking at how much additional fuel is burned per 1lb/kg a payload added. Working through the graphs and using some of yuor comments I am getting a good idea. I agree, if yuo want full cost there are many 'assumptions' to be made.