Engine Acquisition Cost Model Selection

Although the airframe cost is the dominant component of an aircraft’s acquisition cost, the engine will also contribute to the total cost. Section 6.4 identified that models can be split into PCM and MPCM models, and that parametric cost models are better suited to the cost estimation of preliminary designs. This conclusion also holds for the propulsion system, as detailed component design will not have been performed at the preliminary design stage. As with the airframe, there are key variables that are useful in predicting cost. For an engine, these are the thrust or weight, as both relate to engine size and hence correlate reasonably well with cost (Figure 6.8).

Two publicly available models were selected to estimate the acquisition cost of the main engines (see Appendix E):

• Birkler et al., 1982 [175] • Younossi et al., 2002 [167]

Both models are developed by the RAND corporation. However, the methods used by Birkler et al. and Younossi et al. differ in the relationships and inputs used. Birkler et al.’s model splits the cost estimate into development program and production costs [175]. The development program cost includes the costs to bring the engine to the model qualification test (MQT) stage plus additional costs to correct engine problems during service and the cost of performance

6. Acquisition Cost Estimation

and reliability improvement over time. MQT is defined as a series of tests that is used to demonstrate that the engine is production-ready. The relationships do not include the cost of demonstrator or flight test engines. The cost estimating relationships use maximum thrust and maximum turbine inlet temperature as inputs to estimate both the development, C_{development,eng}, and manufacturing cost, Cmanufacturing,eng. Maximum turbine inlet temperature in particular was

identified as a variable that closely ties to cost, as it is typically linked to an engine’s technology level. Maximum turbine inlet temperature can therefore serve as a proxy for the developmental costs of factors such as advanced materials and engine performance improvements. As with the airframe cost models, the development cost is distributed over the first lot. As there are multiple engines per aircraft, it is assumed that the first lot of engines is equal to the number of engines per aircraft, Nengines, multiplied by the number of aircraft in the first lot, Naircraft. Total

cost for the engine is the sum of the manufacturing cost and the development cost, distributed over the number of engines in the first lot:

Cengine = Cmanufacturing,eng+

Cdevelopment,eng

NenginesNaircraft

(6.11)

Younossi et al. ’s model also splits costs into relationships for the development program and the manufacture of engines [167]. Relationships are provided for the cost of developing an engine derivative versus the development cost of a new engine. The development program cost includes the costs incurred during the design, development, and testing of an engine. The method uses a learning slope to estimate the cost of the first engine and the nthengine. Hence the average manufacturing cost of engines in the first lot can be obtained:

Cmanufacturing,eng= 1 Nengines Nengines X n=1 Cmanufacturing,eng,nnb (6.12)

Where b is the learning curve exponent, with an assumed 80% learning curve for engine man- ufacture. Maximum turbine inlet temperature, maximum engine thrust, engine weight, and specific fuel consumption at sea level are used as inputs for the cost estimating relationships. As with the previous model, the total engine cost is the sum of the average manufacturing cost per engine and the development cost, distributed over the number of engines in the first lot.

Both sets of cost estimating relationships were developed using a database of military air- craft engines. As has previously been identified by Finizie, military engine costs estimates are typically higher than cost estimates for civil engines [168]. The estimates are nevertheless useful to provide a preliminary value of cost. In addition, engine cost is a reasonably small percentage of the total cost. Therefore, errors in engine cost estimates contribute a relatively smaller error to the overall acquisition cost estimate.

Publicly available engine acquisition cost estimation models are typically focused on con- ventional propulsion system configurations: turbojets and turbofans. However, the main en- gines of the N3-X are predominantly power producing, rather than thrust producing. Therefore, these models are more difficult to apply to the N3-X case study. Instead, an ‘equivalent engine’ was defined for use in the cost estimating relationships. This equivalent engine has the same design variables as the N3-X main engines (i.e. mass flow, component efficiencies, maximum temperature), however, the auxiliary power requirement is defined as 0MW. The equivalent en- gines are therefore thrust producing turbojets, as opposed to power producing turbogenerators. The maximum sea level thrust produced by the equivalent engine could then be used in the cost estimating relationships.

In addition to the above described cost models, cost estimates were produced by simple correlations of cost to engine thrust and weight. A correlation of cost to weight bypasses the

0 20 40 60 0 100 200 300 Cos t (1 00 0 U S$ ) Power (kW) Siemens GE Energy $aver GE A$D Ultra

Figure 6.9: Motor cost correlations for three commercial motor classes

requirement for an equivalent engine to be defined, and was used as a point of comparison against cost estimates from the selected models (Figure 6.8).

Miscellaneous Propulsion System Components

The N3-X propulsion system also includes the propulsor array and the superconducting elec- trical system, which will also contribute towards the total cost of the aircraft. It was assumed that the cost of the propulsors in the array could be estimated in a similar manner to the cost of a propulsor fan or propeller using relationships by Roskam [158]. The cost estimating relation- ship correlates cost to shaft horsepower and provide estimates for both composite and metal blades. Composite blades were assumed for the N3-X propulsor array, with a cost estimating relationship as follows:

Cfan = 10(0.7746+1.1432 log10Pshaft) (6.13)

The maximum power at RTO was used to determine the shaft horsepower, Pshaft, for the cost-

estimating relationship. In the absence of an alternative method for the cost of individual propul- sor fans, this relationship was used to provide a estimate, as the propulsor fans would be su- perficially similar to fans in conventional propulsion systems.

A superconducting electrical system presents the biggest challenge for a cost estimate of the N3-X, as there are currently no superconducting electrical systems available for commercial aviation. In addition, the 2–3 MW motors required for each propulsor in the array have a higher power rating than most conventional motors. There is therefore no historical data on which to base a cost estimate. As a preliminary assumption, the cost of the motors and generators was taken from a simple correlation of motor power to cost, using costs for commercially available electrical motors [176, 177]. The cost values were extrapolated out to the requisite power level, although this lies well outside of the available data set. The motor/generator cost was assumed to be the average cost estimated by the three data sets correlated to the power (Figure 6.9).

It is highly likely that there will be a significant and non-quantifiable error in the motor and generator cost estimate. However, a preliminary estimate is necessary in the absence of vali- dation data for the cost of high power superconducting systems. Cost estimates for supercon- ducting systems in aviation applications are a subject for further work as research on super- conductivity and high power electrical systems progresses.