Cost Index

The major airlines have long recognized this and that’s why some airline flight management computers (FMC) incorporate a Cost Index (CI) as a performance initialization input. Boeing defines CI as the time cost of the airplane divided by the fuel cost. The time cost includes the crew, maintenance programs and just about everything else that is paid for by the hour. If the fuel is more expensive than everything else, it pays to slow down. If the “everything else” is more than the fuel, you may want to speed up. Few business aircraft FMCs have CI entries, but you can figure this out on your own.

I don't really have any sources for this. I read about the process in two Boeing manuals and pretty much did the math to make it work. It will give you an idea about how to attack the problem.

Consider a Gulfstream G450 cruising at 37,000 ft. in a 100-kt. headwind starting at 70,000 lb. gross weight under ISA conditions. The crew know LRC will be Mach 0.80 but are wondering if the owner will see an improved bottom line if they fly Mach 0.03 slower, or even Mach 0.03 faster.

“It depends,” is the right answer. But it depends on more than just what the aircraft’s design engineers thought; rather it depends on what the company accountant thinks. You won’t find the following equation in any aeronautical or pilot texts, but it might help answer the question, “How fast do you want to fly?”

In this equation:

D — Distance to cruise (nm, since the climb and descent fuel will be about the same, we consider only the cruise portion)

TAS — True air speed during cruise (kt.)

WF — Wind factor (kt., positive numbers for headwinds, negative for tailwinds)

FF — Fuel flow (pounds per hour), average in cruise

FC — Fuel cost ($ per gallon)

FD — Fuel density (pounds per gallon)

VA — Variable airframe costs ($ per hour)

VC — Variable crew costs ($ per hour)

VE — Variable engine costs ($ per hour)

$$\mathrm{Total\; Cost}=\left(\frac{D}{\mathrm{TAS}-\mathrm{WF}}\right)X(\mathrm{FF}X\frac{\mathrm{FC}}{\mathrm{FD}}+\mathrm{VA}+\mathrm{VC}+\mathrm{VE})$$

To compute the answer, values must be inserted. Are the pilots paid hourly or by salary? A salaried crewmember doesn’t add to variable costs and so that expense does not lend to any incentive to fly faster. Are any of the maintenance programs billed by flight hour? Some aircraft maintenance programs are fixed rate to a certain level of activity and then add per hour charges, while others count every hour from the first at one hourly rate. Is the aircraft on a lease program, and billed by flight time as opposed to calendar time? All of these variable costs can amount to $3,000 or more for a typical business jet and may overwhelm the cost of fuel, making it financially advantageous to burn more Jet-A to reduce total flight time.

Mach	No Variable Costs	$1,000 Variable Costs	$2,000 Variable Costs
0.77	$12,035	$20,828	$38,413
0.80	$12,278	$20,648	$37,389
0.83	$13,245	$21,233	$37,207

Meanwhile, the cost of fuel is always a factor. At $1.00 per gallon there are usually incentives to fly fast. But at $5.00 per gallon? Not so much!

For the sake of our example, let’s say it is an ISA day, the fuel costs $3.00 per gallon and has a density of 6.5 gal. per pound. The first hour fuel burn at Mach 0.77 will be 2,996 lb.; at Mach 0.80 it will be 3,178 lb.; and at Mach 0.83 it will be 3,593 lb. The speed up/slow down question depends entirely on those variable costs:

These numbers can be fine-tuned by adjusting fuel burn rates on an hourly basis, but for demonstration purposes the conclusion in this example is clear: It doesn’t pay to fly faster until the variable costs exceed the cost of the increased fuel burn.

In other words, when fuel costs are low, there’s a strong incentive to fly faster. Conversely, when fuel costs are high, there’s a strong incentive to fly slower. Similarly, as variable costs increase, the incentive to fly fast increases.