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 )
Cabin Crew = BH × (# of flight crew) × 60
(Eq. 1)
(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. ⎛
= ⎜ 1.26 + 1.774 ⎜
⎟ − 0.1071⎜
⎟ ⎟ × Trip Time + ...
⎜
1×105 ⎠
1× 105 ⎠ ⎟
Trip
⎝
⎝
⎝
⎠
(Eq. 3)
2
⎛
⎞
⎛W
⎞
⎛ Wairframe ⎞
... + ⎜1.614 + 0.7227 ⎜ airframe
+ 0.1204 ⎜
⎟ ⎟
5 ⎟
⎜
1× 10 ⎠
1× 105 ⎠ ⎟
⎝
⎝
⎝
⎠
Maintenance Hrs.
$ ⎞
⎛
Airframe Labor Cost =
× ( # of trips ) × ⎜ 25
⎟ (Eq. 4)
Trip
⎝ Hr ⎠
Airframe Maintenance Materials:
2
⎛ Wairframe ⎞
⎛ Wairframe ⎞ ⎞
Material Cost ⎛
= ⎜ 12.39 + 29.8 ⎜
⎟ + 0.1806 ⎜
⎟ ⎟ × Trip Time + ...
⎜
Trip
1× 105 ⎠
1×105 ⎠ ⎟
⎝
⎝
⎝
⎠
(Eq. 5)
2
⎛
⎞
⎛W
⎞
⎛W
⎞
⎟
... + ⎜ 15.2 + 97.33 ⎜ airframe5 ⎟ − 2.862 ⎜ airframe
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 + ⎜
4
⎜
Trip
1
10
Trip
Time
×
⎝
⎠
⎝
⎠⎠⎠
⎝
⎝
Engine Labor Cost =
Maintenance Hrs.
$ ⎞
⎛
× ( # of trips ) × ⎜ 25
⎟
Trip
⎝ Hr ⎠
8)
(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 ⎠ ⎠ ⎟⎠
⎝
Engine Material Cost =
Material Cost
× ( # of trips )
Trip
Engine Maintenance Burden:
Applied Maint. Burden = 2 × Engine Labor Cost
(Eq. 10)
(Eq. 11)
(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
⎜
Interest = Interest Rate × Future Value + Present Value × ⎜
⎜ −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.