For a standardized DOC calculation the 'TU Berlin DOC Method' has been chosen. The formulas have been implemented into a DOC tool that calculates all DOC parts for a given CPACS file. The DOC tool as well as a summary of all DOC formulas is given in the following. Please note, that in the summary the unit of the DOC parts is [€/yr] whereas the unit used in the tool as well as in the aircraft design analysis is [$/ASK] respectively [$/100ASK].

DOC tool

With the DOC tool all DOC parts are automatically calculated for a given aircraft and mission in CPACS format and written into the CPACS file. Therefore the executable and the CPACS file have to be in the same folder. In the docTool-config.xml program settings like the name of the CPACS-file to be analyzed as well as scenario settings like the type of flight route and the corresponding unit rate for navigation have to be set.

You can dowload the DOC tool with a CPACS-file example here (.zip): docTool.zip

Summary of DOC formulas

A summary of the used DOC formulas, based on the TU Berlin DOC Method, is given in the following and can be downloaded here: DOCMethod CeRAS TUBerlin

General information

• All monetary values in 2010-€
• Overall unit: €/yr
• U.S. Dollar exchange rate: 1 USD = 0.72 €
• Fuel price [2010-USD/kg]: 1.0
• DOC cost parts:
  • Fuel
  • Fees (Navigation, Landing, Ground Handling)
  • Maintenance (Airframe, Engine)
  • Crew (Cockpit Crew, Flight Attendants)
  • Capital (Depreciation, Insurance)

$$\begin{aligned} DOC = DOC_{fuel} + DOC_{fees} + DOC_{mc} + DOC_{crew} + DOC_{c ap} \end{aligned}$$

Fuel

$$\begin{aligned} DOC_{fuel} = BF \cdot P_{fuel} \cdot FC \end{aligned}$$

• BF: Block fuel [kg]
• P_fuel Fuel price [€/kg]
• FC: Flight cycles per year [1/yr]

Fees

$$\begin{aligned} DOC_{fees} = DOC_{ldg} + DOC_{ground} + DOC_{nav} \end{aligned}$$

• DOC_nav Navigation fees [€/flight]
• DOC_ldg Landing fees [€/flight]
• DOC_ground Ground handling fees [€/flight]

Landing:

$$\begin{aligned} DOC_{ldg} = (K_{ldg} \cdot MTOW) \cdot FC \end{aligned}$$

• K_ldg Landing fee rate [€/kg] (0.01 €/kg)
• MTOW: Maximum take off weight [kg]

Ground Handling:

$$\begin{aligned} DOC_{ground} = (K_{ground} \cdot PL) \cdot FC \end{aligned}$$

• K_ground Ground handling fee rate [€/kg] (0.1 €/kg)
• PL: Payload [kg]

Navigation:

$$\begin{aligned} DOC_{nav} = (K_{nav} \cdot \frac{R}{100} \cdot \sqrt{\frac{MTOW}{50}}) \cdot FC \end{aligned}$$

• K_nav Unit rate for navigation [€/km] (domestic Europe: 100 €/km, transatlantic flights: 70 €/km, far east flights: 60 €/km)
• R: Range [km]
• MTOW: Maximum take off weight [t]

Maintenance

$$\begin{aligned} DOC_{mc} = DOC_{AF,mat} + DOC_{AF,per} + DOC_{ENG} \end{aligned}$$

• DOC_AF,mat Airframe material maintenance cost (repair and replacement)
• DOC_AF,per Airframe personnel maintenance cost (inspection and repair)
• DOC_ENG Engine total maintenance cost

Airframe Material:

$$\begin{aligned} DOC_{AF,mat} = [OWE \cdot (0.21 \cdot FT + 13.7) + 57.5)] \cdot FC \end{aligned}$$

• OWE: Operating weight empty [t]
• FT: Flight time [h]

Airframe Personnel:

$$\begin{aligned} DOC_{AF,per} = LR \cdot (1 + B) \cdot [(0.655 + 0.01 \cdot OWE) \cdot FT + 0.254 + 0.01 \cdot OWE] \cdot FC \end{aligned}$$

• LR: Labor rate [€/h] (50 €/h)
• B: Cost burden (2)
• OWE: Operating weight empty [t]

Engine:

$$\begin{aligned} DOC_{ENG} = [N_{ENG} \cdot (1.5 \cdot SLST + 30.5 \cdot FT + 10.6)] \cdot FC \end{aligned}$$

• N_ENG Number of engines
• SLST: Sea level static thrust [t]

Crew Cost

$$\begin{aligned} DOC_{crew} = C C \cdot (S_{FA} \cdot n_{FA} + S_{FC}) \end{aligned}$$

• CC: Crew complement (number of crews per aircraft: 5)
• n_FA Number of flight attendants (one flight attendant per 50 PAX)
• S_FA Average yearly salary of one flight attendant (60 000 €/yr)
• S_FC Average yearly salary of cockpit crew (300 000 €/yr for 2 pilots)

Capital

$$\begin{aligned} DOC_{cap} = [P_{OWE} \cdot (OWE - W_{ENG} \cdot N_{ENG}) + P_{ENG} \cdot W_{ENG} \cdot N_{ENG}] \cdot (a + f_{ins}) \end{aligned}$$
$$\begin{aligned} a = IR \cdot \frac{1 - f_{RV} \cdot ( \frac{1}{1 +IR})^{DP}}{1 - ( \frac{1}{1 +IR})^{DP}} \end{aligned}$$

• P_OWE Price per kg OWE (Structure, Systems, Equipement) [€/kg] (1150 €/kg)
• OWE: Operating weight empty [kg]
• P_ENG Price per engine weight [€/kg] (2500 €/kg)
• W_ENG Weight per engine [kg]
• a: Annuity rate
• f_ins Insurance rate (0.5 %)
• IR: Interest rate (5 %)
• f_RV Residual value factor (in percentage of aircraft price, 10 %)
• DP: Depreciation rate [yr] (14 years)

Utilization

Flight cycle per year from statistical data:
$$\begin{aligned} FC = \frac{OT_{p.a.}}{FT + BTS}= \frac{POT_{p.a.}-DT_{p.a.}}{FT + BTS} \end{aligned}$$

• OT_p.a. Yearly operation time [h]
• BTS: Block time supplement per flight [h] (1.83)
• POT_p.a. Potential yearly operation time [h] (365 x 24 h = 8760 h)
• DT_p.a. Yearly forced downtime [h] (2748.8 h) consisting of

* C-Checks (3.2 days p.a., 4 days per 15 month)
* D-Checks (5.6 days p.a., 4 weeks per 5 years)
* Repairs (2.6 days p.a., statistical average)
* Night Curfew (7 days p.a., from 11:00 p.m. until 6:00 a.m. at operation days)

DOC correction for additional payload

DOC correction for aircraft with cargo capacity at maximum passenger load

$$\begin{aligned} (\frac{DOC}{SKO})_{c} = \frac{DOC}{SKO} \cdot \frac{n_{PAX}}{n_{PAX} + \frac{E_{Cargo}}{E_{PAX}} \cdot R} \end{aligned}$$
$$\begin{aligned} E_{Cargo}=FR \cdot(PL-PL_{PAX}) \end{aligned}$$

• SKO: Seat kilometer
• n_PAX Maximum number of passengers
• E_Cargo Cargo revenue per flight [€]
• E_PAX Seat revenue per flight [€] (370 €)
• FR: Cargo revenue rate [€/tkm] (0.3 €/tkm)
• PL: Payload [t]
• PL_PAX Passenger payload [t]