# Cost Formulas and Results

This section provides the semi-empirical cost formulas for establishing Nacelle B costs, as well as for any aircraft component. The input required is relatively simple: (1) geometry with dimensions; (2) materials used; (3) weight breakdown; and (4) the array of manhours required to design, fabricate, and assemble an aircraft to completion. The factors and indices involved in the design and manufacture are listed in Tables 16.8 through 16.12 and obtained through DFM/A studies. The total manufacturing cost of a nacelle is the sum of individual costs of each of the four components, as follows:

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nacelle cost: Cn = ^ C = Cnc + Cfc + Ctr + Ctc + Cebu (16.5)

where CNC = cost of nose cowl CFC = cost of fan cowl CTR = cost of thrust reverser CTC = cost of tail-cone assembly CEBU = cost of EBU (e. g., anti-icing)

The nose cowl is the only component studied herein; methodologies for the other components follow the same procedure. The cost of each nacelle component is indi­vidually estimated for the six headings in Table 16.7. The nose-cowl cost, CNoseCowl, is the sum of the following six items:

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CNoseCowl — C i — C Mat + C Fab + C Asm + C Sup + C Amr + C Misc

where C Mat = cost of material C Fab = cost of fabrication C Asm = cost of assembly C Sup = cost of support CAmr = cost of amortization CMisc = miscellaneous cost

1. Nose-Cowl Material Cost, CMat.

n n

CMat = cost of material = ^ C’^raw + ^ C’^finish

ii

where n is the number of different types of materials. In general,

where Wi = weight of the material

ui = standard cost of raw material per unit weight Pi = procurement factor (for nose cowl = 1)

Table 16.9 lists seven types of raw materials. The parts weight captures the effects of size; therefore, the size factor need not be applied here.

YTi C’i_finish is the actual cost and is obtained from the bill for subcontracted materials. Therefore, the cost of material C’Mat for the nose cowl in this study is as follows (subscripts “al” and “ti” stand for aluminum and titanium alloys, respec­tively):

C Mat — ^ ^ C i_raw ‘ ^ C i.

— (Wal X ual X Pal)sheet + (Wal X ual X Pa1)forge + (Wal X ual X Pal)honeycomb

+ Wti X Uti X Pti + W’comp X Ucomp X Pcomp + (WAGS X uAGS x P4GS)fastener

+ (Wags x Uags x Pags)rivet + C’ifintsk (16.8)

Using Table 16.9, the following relationship can be worked out:

Nacelle B cost of raw material Nacelle A cost of raw material

= [(0.4778 x 1)sheet + (0.3868 x 2.25)honeycomb + (0.34254 x 3.5)ti + (0.005 x 18.44)fasteners + (0.0139 x 0.63)nvet]nacellem/[(0.2288 x 1)^

+ (0.1213 x 4.19)forge + (0.3104 x 2.25)honeycomb + (0.2752 x 3.5)ti + (0.175 X 3.62)comp + (0.0366 X 18.44)fasteners + (0.0101 X 0.63)nvert]nacelle_A = 2.6/3.14 = 0.828

The finished materials comprise a variety of items that go straight to the assem­bly line without in-house work involved. Their acquisition policies vary during each negotiation (see Table 16.6).

Table 16.9 lists 0.77 of Nacelle B as composed of raw materials and 0.23 of fin­ished materials. Using these proportions:

Nacelle B cost of material Nacelle A cost of material

2. Nose Cowl Part Fabrication Cost, C’Fab. Table 16.7 lists the number of parts fabricated in each of the six stages of both nacelles. The manhours required to fab­ricate each part are a combination of operations (e. g., machining, forming, and fit­ting). The nose-cowl part fabrication cost is expressed as follows:

manufacturing cost (C’Fab) = rates x manhours

x learning-curve factor

x size factor x manufacturing philosophy (16.9)

Table 16.7 shows that both nacelles have six stages (m = 6). Each stage has four classes of parts: structure, minor parts, AGS, and EBU. The EBU is separated from the other classes, which are classified as one (n = 1).

Although geometrically similar, in the DFM/A study, Nacelle B has fewer parts to reduce the assembly time. Although there are few parts for Nacelle B, the parts fabrication needs about the same amount of time for both nacelles. Therefore, the various factors are as follows:

• size factor Ksize = 1.133 from Equation 16.1

• geometry factor Fi = 1 (geometrically similar)

• complexity factor, F2 = 1 (functionality issues, same for both nacelles)

• parts-manufacturing philosophy factor (methods factor), F3 = 1.0

• learning-curve factor = 1.022 (slightly higher)

Engineering process sheets provide all the information for Nacelle A to compute cost; for nondimensionalizing, all the factors use 1 as the baseline value.

Therefore, using Equation 16.7, the parts-manufacturing cost of

Nacelle B = (1.133)0’5 x 1.022 = 1.0878 x Nacelle A

3. Nose-Cowl Assembly Cost, C’Asm. The manhours required for assembly at each stage are listed in Table 16.10 in nondimensional form. The nose-cowl assembly is expressed as:

assembly cost (CFab) = rates x manhours x learning-curve factor x size factor

x manufacturing philosophy (16.10)

The rate and factor for Nacelle A are 1; Table 16.2 lists them for Nacelle B:

(16.11)

In this case, m = 6 stages and n = consists of the following cost-driver factors:

• Fi = 0.735 for the tooling concept (assembly methods – Nacelle B takes less time)

• F2 = 1.0, the complexity factor (functionality – same for both nacelles)

• F3 = 1.0, aerodynamic smoothness requirements (surface tolerance is the same)

Then, Equation 16.7 reduces to:

6 Г 3 і

x (manhours x rates x learning-curve factor)

i i

To simplify, all stages are combined to obtain the Nacelle B cost. Using 1 as the baseline Nacelle A factors and indices, the Nacelle B assembly cost is expressed as follows:

assembly cost of Nacelle B = (1.133)0 25 x 0.735 = 0.759 x Nacelle A

It is interesting that considerable assembly costs can be reduced at the expense of a slightly increased parts-fabrication cost and, of course, with some increase in
the tooling cost (i. e., NRC). Establishing these factors is the main purpose of the DFM/A trade-off studies. Basically, they summarize the manhours required com­pared to the baseline manhours.

4. Nose-Cowl Support Cost, C Sup. Separate support costs are taken as a percent­age of material, fabrication, and assembly costs. Support costs arise from reworking and concessions when the build quality is not met (e. g., tolerances). In this book, the support cost is flat-rated as follows:

CSup = 0.05 x (material cost + parts-fabrication cost + assembly cost) (16.12)

5. Nose-Cowl Amortization Cost, C’Amr. Cost is amortized for 400 finished prod­ucts. It is a variant design and therefore has low amortization costs; it can be included in the manhour rates at all stages or separately at the end. In this book, the cost is accounted for in the manhour rates and is not computed separately. Typi­cally, because it is produced in twice more in number, the amortization cost is taken as 2% of material costs plus parts-fabrication costs plus assembly cost:

C Amr = cost of amortization = (design + methods + tool) cost/N (16.13)

where N = 400, or

CAmr = 0.02 x (material costs + parts-fabrication costs + assembly costs

6. Nose-Cowl Miscellaneous Costs, C’Misc Miscellaneous costs are unavoidable, as follows (taken as 3%):

CMiscp = 0.03 x (material costs + parts-fabrication costs + assembly costs)

(16.14)

Total Costs of the Nacelle B Nose Cowl. The final costs of the Nacelle B nose cowl can now be computed, in nondimensional form – that is, relative to the Nacelle A costs. Using Equation 16.4, the following is estimated (i. e., costs of amortization embedded in manhour rates and costs of support and miscellaneous cost estimated as 10% of other costs):

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where (CSup + CMisc) = 0.1 x (CMat + CFab + C’Asm) (16.15)

Nacelle B nose-cowl cost:

CNoseCowl-B °.8302CMat^acA + l-0878 CFab-NacA + °.759 Casm-NacA

+ °Л x (°.8302 CMat_NacA + ^°878 CFab_NacA + °.759 CAsm^acA = °.9132CMat_NacA + 11966CFab_NacA + °.8349CA smNacA

From company records, the Nacelle A cost fractions are as follows:

CMat-NacA/ CNoseCowl-A = °.408 CFab_NacA/ CNoseCowl_A = °.349 CA sm^NacA /‘ CNoseCowl _A °.149

Table 16.13. DOC components

 Fixed-cost elements Trip-cost elements 1. Ownership cost 3. Fuel charges (a) Depreciation 4. Maintenance (airframe and engine) (b) Interest on loan 5. Navigational and landing charges (c) Insurance premium 2. Crew salary and cost

Dividing Equation 16.15 by CNoseCowlA, the relative cost of Nacelle B is as follows:

CNoseCowi-blCNoseCowiA = 0.9132 x 0.408 + 1.1966 x 0.349

+ 0.8349 x 0.149 = 0.9146

The results show that although the two nacelles are geometrically similar, Nacelle B – with a 13.5% higher-thrust engine – could be produced at an 8.5% lower cost through DFM considerations in an IPPD environment. Changes in mate­rial, structural, tooling, procurement, and subcontracting policies contribute to cost reduction. A preliminary weight of a new design and the procurement policy for the raw materials can be established at the conceptual design stage (i. e., DFM/A studies). Accuracy improves as a project progresses. In the absence of the actual weight, approximations can be made from the geometry. If it had been costed with prevailing empirical relations using weight, size, performance, and manufacturing considerations, the cost of Nacelle B would be higher than Nacelle A. The prevail­ing equations do not capture the subtlety of DFM/A considerations. Chapter 17 describes the myriad changes that have occurred in the manufacturing technology; these benefits must be reflected in a new approach to formulation.