# A Feature-Based Cost Estimation Model for Wind Turbine Blade Spar Caps
## 3 Cost Model Methodology, Selection of Cost Modelling Approach
### Technical Cost Modelling: Tooling, Capital, Labor, Production Rate
#### 3.3.1 Resource Costs: Material, Tooling, Capital, Direct Labor, Indirect Labor, Utilities
As dedicated tooling cost is a function of part volume fraction, part complexity, and part mass, 35 m Spar Cap tooling cost is related to the Reference Standard cost (Equation (11)) by:  
\[\ell 265,000=\ell 20,000\times\text{Cost Scaling Feature Factor}\]  
\[\ell 265,000=\ell 20,000/\left(1-V_{f}\right)^{x}\left(1-\overline{C}\right)^ {y}\left(1-\overline{M}\right)^{z}\]  
where \(\left(1-V_{f}\right)=0.44\), \(\left(1-\overline{C}\right)=0.50\), and \(\left(1-\overline{C}\right)\) varies with \(m\) and \(M\). Tooling Cost, Capital Cost, Direct Labor Cost, and Production Rate are assumed the same regardless of composite. For part mass, CFRP was chosen instead of GFRP when deriving Factor Indices for cost elements, as CFRP spar caps over 50 m blade length increasingly become the norm. Should CFRP become competitive with GFRP, CFRP spar caps become more economic. Figure 3 shows material mass for CFRP and GFRP as a quadratic function of spar cap length. The Cost Scaling Feature Factor scales with spar cap mass only while volume fraction and complexity have defined values of 0.44 and 0.50, respectively. Therefore, values of Cost Factor Indices \(x\), \(y\) and \(z\) will be greater than zero. In the absence of extensive tooling cost data for spar caps 40 to 75 m, Cost Factor Indices \(x\), \(y\) and \(z\) were estimated using a mathematical iterative method. One variable is fixed while the other variables are changed until a consistent set of numbers is derived that satisfies a relationship, in this case for tooling cost and capital cost. Volume fraction plays a dominant role in composites manufacturing so index \(x\) will be assumed greater than indices \(y\) and \(z\). For \(M=10\),000 kg, Factor Index \(x\) was initially given a constant value of 2, while Factor Indices \(y\) and \(z\) were each assigned a value of 0.1. By iteration, values of \(y\) and \(z\) were varied until Equation (11) was satisfied for \(m=500\) kg. With three known values of \(x\), \(y\) and \(z\) (Table 4), Dedicated Tooling Cost was estimated from Equations (11) and (14) for spar cap lengths 35 to 75 m for a maximum molding mass \(M=10\),000 kg (Figures 4 and 6). \[F=1/\left(1-V_{f}\right)^{2}\left(1-\overline{C}\right)^{1.39}\left(1- \overline{M}\right)^{1} \tag{14}\]  
Capital Cost requirements are infrastructure costs for a plant with one spar cap production line using a nominal cost of \(\ell 387\)/sqm for land and buildings [29; 30]. Estimates for required floor space are summarized in Table 5[29; 30]. Total plant infrastructure capital expenditure (CAPEX) is depreciated over 20 years. CAPEX requirements are summarized below. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Tooling** & \multicolumn{6}{c}{**Cost Factor Indices**} \\ \cline{2-7}
**Cost (\(\ell\))** & \(x\) & \(y\) & \(z\) & **Capital Cost (\(\ell\))** & \(x\) & \(y\) & \(z\) \\ \hline
103,499 & 2 & 0.1 & 0.1 & 839717 & 1.5 & 0.1 & 0.1 \\
139,399 & 2 & 0.5 & 0.5 & 1,130,982 & 1.5 & 0.5 & 0.5 \\
229,967 & 2 & 1.2 & 0.8 & 1,865,776 & 1.5 & 1.2 & 0.8 \\
256,476 & 2 & 1.35 & 0.9 & 1,914,776 & 1.5 & 1.23 & 0.9 \\
265,000 & 2 & 1.39 & 1 & 1,935,000 & 1.5 & 1.2452 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Factor Indices for Tooling and Capital Cost resources. The capital cost for one 35 m spar cap production line is \(\varepsilon\)387 \(\times\) 5000 = \(\varepsilon\)1,935,000. The capital cost of the Reference Standard is \(\varepsilon\)227,500 [29]. As with Tooling Cost, Capital Cost will be related to the Reference Standard cost (Equation (13)) by:  
\[\varepsilon\)1,935,000 = \(\varepsilon\)227,500/\(\left(1-V_{f}\right)^{x}\left(1-\overline{C} \right)^{y}\left(1-\overline{M}\right)^{z}\]  
As for Tooling Cost, the same mathematical iterative technique was used to derive Cost Factor Indices \(x\), \(y\) and \(z\) that satisfied Equation (13) for \(m\) = 500 kg (35 m spar cap mass) with the value of \(x\) for Volume Fraction assumed greater than \(y\) and \(z\).