Life cycle cost estimation for high-speed transportation systems

Abstract

This paper presents an innovative methodology and tool developed by Politecnico di Torino and the European Space Agency (ESA) to support life cycle cost (LCC) estimation for high-speed transportation systems. This ad hoc built-in tool aims at supporting engineers in cost estimations during conceptual and preliminary design phases. This includes the evaluation of research, development, test and evaluation costs (RDTE costs), production costs as well as direct and indirect operating costs (DOC and IOC). Eventually, the results of the LCC evaluation for two different high-speed transport vehicles is provided and discussed.

Appendices

Appendices

1.1 Appendix 1: Summary of TRANSCOST-modified CERs implemented in HyCost tool

1.1.1 RDTE costs

See Table 15.

• High-speed advanced aircraft

  $$ H_{\text{VA}} = 2169M_{\text{OEW}}^{0.262} f_{1} f_{2} f_{3} f_{8} f_{10}^{'} f_{11} . $$

• Turbojet

  $$ H_{\text{ET}}^{ '} = \left( {232.4M_{{\text{E}}_\text{dry}}^{0.509} + 1.12v} \right)f_{1} f_{3} . $$

• Ramjet

  $$ H_{\text{ER}} = 355M_{{\text{E}}_\text{dry}}^{0.295} f_{1} f_{3} . $$

• Combined cycle engine

  $$ H_{\text{CCE}} = C_{\text{complexity}} (k_{\text{TJ}} H_{\text{ET}}^{'} + k_{\text{RJ}} H_{\text{ER}} )f_{1} f_{3} . $$

• Fuel system

  $$ S_{{{\text{Fuel}}_{\text{dev}} }} = \left( {0.1M_{\text{OEW}}^{0.68} + 0.49M_{{\text{E}}_\text{dry}}^{0.51} } \right)f_{1} f_{3} . $$

• TPS

  $$ S_{{{\text{TPS}}_{\text{dev}} }} = \left( {0.56M_{\text{OEW}}^{0.59} + 1.8q^{0.51} } \right)f_{1} f_{3} . $$

• TEMS

  $$ S_{{{\text{TEMS}}_{\text{dev}} }} = \left( {5.73M_{\text{OEW}}^{0.26} + 0.8P^{0.17} + 0.53\dot{m}_{{_{{{\text{BO}}_{\text{LH2}} }} }}^{0.19} } \right)f_{1} f_{3} . $$

• Total development cost

  $$ C_{\text{TOT}} = f_{0} (H_{\text{VA}} + \mathop \sum \limits_{i = 1}^{{n_{E} }} H_{\text{Ei}} )f_{6} f_{7} . $$

Table 15 List of cost drivers for RDTE CERs

1.1.2 Production cost

See Table 16.

• High-speed advanced aircraft

  $$ F_{\text{VF}}^{'} = \left( {0.34M_{\text{TOEW}}^{1.75} + 7.06v_{k}^{0.4} } \right)f_{10}^{'} . $$

• Turbojet

  $$ F_{\text{ET}}^{'} = 2.29M_{{{\text{E}}_{\text{dry}} }}^{0.530} + 0.50v^{0.60} . $$

• Ramjet

  $$ F_{\text{ER}} = 5.63T^{0.35} . $$

• Combined cycle engine

  $$ F_{\text{CCE}} = C_{\text{complexity}} (k_{\text{TJ}} F_{\text{ET}}^{ '} + k_{\text{RJ}} F_{\text{ER}} ). $$

• Fuel system

  $$ S_{{{\text{Fuel}}_{\text{prod}} }} = 0.48M_{\text{OEW}}^{0.38} + 0.5M_{{{\text{E}}_{\text{dry}} }}^{0.39} . $$

• TPS

  $$ S_{{{\text{TPS}}_{\text{prod}} }} = 0.51M_{\text{OEW}}^{0.19} + 3.41q^{0.12} + 0.68Q^{0.11} . $$

• TEMS

  $$ S_{{{\text{TEMS}}_{\text{prod}} }} = 5.41M_{\text{OEW}}^{0.23} + 0.79P^{0.15} + 0.52\dot{m}_{{{\text{BO}}_{{{\text{LH}}2}} }}^{0.19} . $$

• Total production cost

  $$ C_{F} = f_{0}^{\prime N} \left( {\sum\limits_{i = 1}^{n} {F_{{V_{i} }} } f_{{4_{i} }} + \sum\limits_{j}^{{n_{e} }} {F_{{E_{j} }} } f_{{4_{j} }} } \right)f_{9} . $$

Table 16 List of cost drivers for production CERs

1.2 Appendix 2: Summary of NASA-modified ATA CERs implemented in HyCost tool

1.2.1 Fuel cost (DOC_f)

The fuel cost per ton-mile in SI units is:

$$ {\text{DOC}}_{\text{Fuel}} = \frac{{1677.78 C_{f} \left( {\frac{{m_{\text{fT}} }}{{m_{\text{GTO}} }}} \right)\left( {1 - K_{R} } \right)}}{{\left( {\text{LF}} \right) \left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)R_{T} }}, $$

where $C_{f}$ is the cost of fuel per unit mass (in kg); $m_{\text{GTO}}$ is the gross take-off mass; $m_{\text{PL}}$ is the payload mass; $K_{R}$ is the reserve fuel fraction [%]. $R_{T}$ is the range in kilometers.

1.2.2 Crew cost (DOC_C)

The crew cost per ton-mile in SI units is:

$$ {\text{DOC}}_{C} = \frac{{\frac{320}{{m_{\text{GTO}} }}}}{{0.63\left( {\text{LF}} \right) \left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right){\text{M }}\left( {\frac{{V_{\text{B}} }}{{V_{\text{CR}} }}} \right)}}, $$

where $V_{\text{CR}}$ is the cruise speed; $V_{\text{B}}$ is the block speed; M is the cruise Mach.

1.2.3 Insurance cost (DOC_I)

The insurance cost per ton-mile in SI units is:

$$ {\text{DOC}}_{I} = \frac{{\left( {\text{IR}} \right) \left( {\frac{{{\text{C}}_{\text{HST}} }}{{m_{\text{GTO}} }}} \right)}}{{0.63\left( {\text{LF}} \right) \left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right){\text{M }}\left( {\frac{{V_{\text{B}} }}{{V_{\text{CR}} }}} \right)U}}, $$

where IR is the annual insurance rate; $C_{\text{HST}}$ is the acquisition cost of the aircraft; U is the annual utilization in block hours/year.

1.2.4 Depreciation cost (DOC_D)

The depreciation cost per ton-mile in SI units is:

$$ {\text{DOC}}_{D} = \frac{{1.1\left( {\frac{{C_{\text{HST}} }}{{m_{\text{GTO}} }}} \right) + 0.3\left( {\frac{{C_{\text{TJ}} }}{{m_{\text{GTO}} }} + \frac{{C_{\text{RJ}} }}{{m_{\text{GTO}} }}} \right)}}{{0.63 \left( {\text{LF}} \right) \left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)M \left( {\frac{{V_{\text{B}} }}{{V_{\text{CR}} }}} \right)U L_{d} }}, $$

where $C_{\text{TJ}}$ is the cost of the turbojet engines; $C_{\text{RJ}}$ is the cost of the ramjet engines.

1.2.5 Maintenance cost (DOCM)

Maintenance cost is given by the sum of labor and material cost for both airframe and engines. The NASA-modified ATA CERs introduce the following four coefficients to estimate HST maintenance cost for labor and material of both turbojet and ramjet components:

• $K_{\text{LTJ}}$, turbojet maintenance labor ratio (HST turbojets to present subsonic turbojets);

• $K_{\text{MTJ}}$, turbojet maintenance material ratio (HST turbojets to present subsonic turbojets);

• $K_{\text{LRJ}}$, ramjet maintenance labor ratio (HST ramjets to present subsonic turbojets);

• $K_{\text{MRJ}}$, ramjet maintenance material ratio (HST ramjets to present subsonic turbojets).

The following six contributions shall be summed:

• 1. DOC_M/AF/L, maintenance labor effort required for the airframe (cost per ton-mile):

$$ {\text{DOC}}_{{{\text{M}}/{\text{AF}}/{\text{L}}}} = \frac{{\left( {3.70 + 2.18 t_{f} } \right)\left[ {\frac{0.05}{1000} \left( {\frac{{m_{\text{AF}} }}{{m_{\text{GTO}} }} + \frac{{m_{\text{AV}} }}{{m_{\text{GTO}} }}} \right) + \left( {\frac{3}{{m_{\text{GTO}} }} - \frac{315}{{\left( {\frac{{2(m_{\text{AF}} + m_{\text{AV}} )}}{1000} + 120} \right)m_{\text{GTO}} }}} \right)} \right]M^{{\frac{1}{2}}} \left( {r_{L} } \right)}}{{\left( {\text{LF}} \right)\left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)\frac{{R_{T} }}{1000}}}, $$

where m_AF is the mass of airframe in kilograms, m_AV is the mass of avionics in kilograms, m_GTO is the maximum take-off mass in kilograms, r_L is the average labor rate per hour for all personnel involved in maintenance activities.

• 2. DOC_M/AF/M, maintenance material cost for the airframe (cost per ton-mile):

$$ {\text{DOC}}_{{{\text{M}}/{\text{AF}}/{\text{M}}}} = \frac{{\left( {5.22 \cdot t_{f} + 10.57} \right)\left( {\frac{{C_{\text{HST}} }}{{m_{\text{GTO}} }} - \frac{{C_{\text{TJ}} }}{{m_{\text{GTO}} }} - \frac{{C_{\text{RJ}} }}{{m_{\text{GTO}} }}} \right)}}{{\left( {\text{LF}} \right)\left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)R_{T} \cdot 10^{3} }}. $$

• 3. DOC_M/TJ/L, maintenance labor effort required for the turbojet engines (cost per ton-mile):

$$ {\text{DOC}}_{{{\text{M}}/{\text{TJ}}/{\text{L}}}} = \frac{{\left( {\frac{\text{T}}{\rm{W}}} \right)_{\text{GTO}} \left( {1 + k_{TJ} \cdot t_{F} } \right)\left( {\frac{9.91}{{T_{\text{TJ}} /10^{3} }} + 0.1} \right)r_{L} K_{\text{LTJ}} }}{{\left( {\text{LF}} \right)\left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)R_{T} }}, $$

where $T_{\text{TJ}}$ is the thrust of each turbojet engine in N; t_F is the number of flight hours per flight; k_TJ is the time of operation of the turbojet engines as a ratio of t_F.

• 4. DOC_M/TJ/M, the maintenance material required for the turbojet engines (cost per ton-mile).

$$ {\text{DOC}}_{{{\text{M}}/{\text{TJ}}/{\text{M}}}} = \frac{{\left( {\frac{{C_{\text{TJ}} }}{{m_{\text{GTO}} }}} \right)\left( {0.034 \cdot k_{\text{TJ}} \cdot t_{F} + 0.042} \right) K_{\text{MTJ}} }}{{\left( {\text{LF}} \right)\left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)R_{T} }}. $$

• 5. DOC_M/RJ/L, the maintenance labor required for the ramjet engines (cost per ton-mile):

$$ {\text{DOC}}_{{{\text{M}}/{\text{RJ}}/{\text{L}}}} = \frac{{ \left( {1 + k_{\text{RJ}} \cdot t_{F} } \right)\left( {\frac{{1.01 N_{\text{RJ}} \left( {\frac{L}{D}} \right)}}{{m_{\text{GTO}} / 10^{3} }} + 0.1} \right)r_{L} K_{\text{LRJ}} }}{{\left( {\frac{L}{D}} \right)\left( {\text{LF}} \right)\left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)R_{T} }}, $$

where $\frac{L}{D}$ is the lift-to-drag ratio.

• 6. DOC_M/RJ/M, the maintenance material cost for ramjet engines (cost per ton-mile):

$$ {\text{DOC}}_{{{\text{M}}/{\text{RJ}}/{\text{M}}}} = \frac{{\left( {\frac{{C_{\text{RJ}} }}{{m_{\text{GTO}} }}} \right)\left( {0.034 \cdot k_{\text{RJ}} \cdot t_{F} + 0.042} \right) K_{\text{MRJ}} }}{{\left( {\text{LF}} \right)\left( {\frac{{m_{\text{PL}} }}{{m_{\text{GTO}} }}} \right)R_{T} }}. $$

1.3 Appendix 3: HyCost tool screenshots

See Figs. 12, 13, 14, and 15.

Fig. 12

Example of HyCost input windows: vehicle and mission data

Fig. 13

Example of HyCost input windows: development, production and operating scenario

Fig. 14

Example of HyCost DOC output window

Fig. 15

HyCost window for the evaluation of technological improvements