# 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  
Part cost increases with increasing fiber volume fraction, complexity, and mass, while production rate decreases with increasing complexity. Since tooling, capital, and direct labor costs for the spar cap range were unavailable, the development of a Cost Scaling Feature Factor will focus on how these scale with features such as part complexity, part mass, and fiber volume fraction. Indirect labor and utility costs are unchanged, varying only with production rate. Production rate will affect cost per part and scales with complexity, part mass, and fiber volume fraction. As dedicated tooling, capital, and direct labor resource costs scale with features, so:  
\[\text{Resource Cost}\ =\ f[\text{Part Features}\ \times\ \text{Tooling, Capital, Direct Labor}] \tag{4}\]  
A Cost Scaling Feature Factor is defined as:  
\[\text{Cost Scaling Feature Factor,}\ F=1/\Big{(}1-V_{f}\Big{)}^{x}\ \Big{(}1- \overline{C}\Big{)}^{y}\Big{(}1-\overline{M}\Big{)}^{z} \tag{5}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tooling Cost** & **Capital Cost** & **Annual Production Rate** \\ \hline \(\epsilon\)20,000 & \(\epsilon\)227,500 & 300 approx. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data for Reference Standard: 10 m spar cap analogue [29]. Figure 3: Spar cap mass with blade length [31]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Resource** & **Cost** \\ \hline Tooling cost of one mold tool & \(\epsilon\)240,000–\(\epsilon\)292,000 \\ Capital Cost for one mold tool & \(\epsilon\)1,750,000–\(\epsilon\)2,200,000 \\ Direct Labor & \(\epsilon\)23/hour \\ Indirect Labor per year & \(\epsilon\)600,600 \\ Utilities, electricity per year & \(\epsilon\)428,640 \\ Cost of unidirectional carbon fiber & \(\epsilon\)31/kg \\ Cost of epoxy resin & \(\epsilon\)3/kg \\ Cost of UD E-glass fiber & \(\epsilon\)3/kg \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calibration Standard: 35 m spar cap baseline calibration standard [29,30]. where \(Vf\) = volume fraction of fiber, \(\overline{C}\) = Complexity Factor,\(\overline{M}\) = Mass Factor. x, y, and z are Cost Factor Indices. To simplify the analysis, \(Vf\) is assumed to be 56% for 35 to 75 m, so will not vary. Complexity Factor \(\overline{C}\) is the ratio of part complexity \(n\) to maximum possible part complexity \(N\):  
\[\overline{C}=\text{ Part Complexity/Maximum Part Complexity}=\ n/N \tag{6}\]  
The spar cap is a box spar with a constant cross-section with no holes or corners. Complexity is defined as the number of unidirectional (UD) fiber plies inserted into the spar cap mold tool prior to vacuum infusion. Minimum and maximum complexity is the minimum and maximum number of plies, respectively, required for the part to meet service specification. Maximum complexity is the number of plies above which manufacturing cost becomes too expensive. Due to confidentiality issues, spar cap manufacturers were unable to supply detailed information on the number and distribution of plies in the spar cap, so the minimum and maximum number of plies are unknown. For this analysis, an average complexity of 0.5 is chosen halfway between minimum complexity, which approaches zero, and maximum complexity, which approaches 1. Therefore, the expression for Complexity Factor is:  
\[\overline{C}=\text{ Number of UD Plies/Maximum number of UD Plies} \tag{7}\]  
In the Feature Factor expression, as complexity increases, \(\overline{C}\) approaches 1, \(1-\overline{C}\) decreases, and the Cost Scaling Feature Factor increases. Mass Factor \(\overline{M}\) is defined as the ratio of spar cap mass \(m\) to the maximum mass \(M\) of the spar cap that can be cost-effectively produced:  
\[\overline{M}=\text{ Mass of molded part/Maximum mass that can be molded}=\ m/M \tag{8}\]  
A value of 10,000 kg for a 100% carbon fiber 100 m spar cap was conservatively chosen as the upper mass limit for \(M\) above which manufacturing is assumed to be prohibitively expensive using present resin infusion technology [29].