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AAE 451 Spring 2004

Method for Calculating Direct Operating Cost

The following is an estimation method known as DOC+I (Direct operating cost plus interest). This method is based on the work of Liebeck1 and has been applied by Ross2 for wide body commercial aircraft. By definition the DOC+I method takes into account the following operating expenditures; flight & cabin crew cost, airframe maintenance, engine maintenance, landing fees, depreciation, interest, and insurance. Flight Crew & Cabin Crew The flight deck and cabin crew cost are all based on Block Hours (BH), which is equivalent to the number of trips per multiplied by the average flight time per trip. For the flight crew there salary is a function of the maximum takeoff weight of the aircraft as seen in Equation 1. The flight attendants or cabin crew cost is based on an assumed pay rate of 60 dollars per hour.

Flight Crew = BH × (# of flight crew) × ( 440 + 0.532*(Wgross /1000 )

(Eq. 1)

Cabin Crew = BH × (# of flight crew) × 60

(Eq. 2)

Airframe Maintenance Cost of airframe maintenance is broken down into three parts; labor, materials, and burden or the cost of taking the aircraft out of operation. Airframe Maintenance Labor: Notice that for both the labor and material cost, are based on a historical curve fit developed by Liebeck1 and are dependent of the number of trips per year, average trip time and the airframe weight. 2 Wairframe Wairframe Maintenance Hrs. × Trip Time + ... = 1.26 + 1.774 - 0.1071 5 5 Trip 1×10 1× 10 (Eq. 3) 2 W W ... + 1.614 + 0.7227 airframe + 0.1204 airframe 5 5 1× 10 1× 10 Maintenance Hrs. $ Airframe Labor Cost = × ( # of trips ) × 25 (Eq. 4) Trip Hr

Airframe Maintenance Materials: 2 Wairframe Wairframe Material Cost × Trip Time + ... = 12.39 + 29.8 + 0.1806 5 5 Trip 1× 10 1×10 (Eq. 5) 2 W W ... + 15.2 + 97.33 airframe - 2.862 airframe 5 5 1×10 1× 10

Airframe Material Cost =

Material Cost × ( # of trips ) Trip

(Eq. 6)

Airframe Applied Maintenance Burden: Applied Maint. Burden = 2 × Airframe Labor Cost (Eq. 7) Thus: Total Airframe Maintenance Cost = Airframe Labor +Airframe Mat. + Airframe Burden

Engine Maintenance Engine Maintenance Labor:

0.434 Maintenance Hrs. (Eq. 0.05 × Thrust per Engine = 0.645 + × (Trip Time ) × ( # of Engines ) × 0.566 + Trip 1× 104 Trip Time

8)

Engine Labor Cost =

Maintenance Hrs. $ × ( # of trips ) × 25 Trip Hr

(Eq. 9)

Engine Maintenance Material:

0.38 Material Cost 0.05 × Thrust per Engine = 25 + × ( Trip Time ) × ( # of Engines ) × 0.62 + 4 Trip 1× 10 Trip Time

(Eq. 10)

Engine Material Cost =

Material Cost × ( # of trips ) Trip

(Eq. 11)

Engine Maintenance Burden: Applied Maint. Burden = 2 × Engine Labor Cost

(Eq. 12)

Total Engine Maintenance Cost = Engine Labor + Engine Mat. + Engine Burden (Eq. 13)

Again, notice that the labor rate for total aircraft maintenance is assumed to be 25 dollars per hour. However, this value can be changed if found that current rates differ.

Landing Fee The landing fee is based on the operational empty weight of the aircraft and an average of landing fees in the United States. They may heavily vary in Europe, with possible additional fees such as NOX emissions or community noise. However this is not captured in this method. Wgross - W fuel Landing Fee = 1.5 × (Eq. 14) 1000

Depreciation, Interest & Insurance For all of the following methods the total airframe cost must be known, which can be found using methods found in Raymer. Notice that all of the following equations are dependent on gross weight that will be found by your sizing code.

Airframe Cost Airframe Cost Airframe Cost (Eq. Depreciation = (1 - residual ) × + Airframe Spares × + Engine Spares × Period Period Period

15)

For the calculation of Depreciation the following values can be used: Period = 15 years, Residual = 0.1, Airframe Spares = 0.06, Engine Spares = 0.23. Insurance = 0.0035 × Airframe Cost (Eq. 16)

(1+Interest Rate )2× Period Future Value + Present Value × Interest = Interest Rate × -1 + (1+Interest Rate )2×Period (Eq. 17)

For the interest calculation it is ok to set the future value of the aircraft to zero since it is difficult to predict this value, especially at the very early stages of preliminary design.

Finally, from all of these the total direct operating cost of a commercial transport can be found: DOC = Flight Crew + Cabin Crew + Airframe Maintenance + Engine Maintenance + Depreciation + Insurance + Interest (Eq. 18)

References:

1 Liebeck, R.H., et. Al., "Advanced Subsonic Airplane design and Economic Studies," NASA CR-195443, April 1995. 2 Ross, T. E., "Designing for Minimum Cost: A Method to Assess Commercial Aircraft Technologies", Purdue University School of Aero. & Astro. May 1998.

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