# 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
Index \(x\) was initially assigned a constant value of 1.5 while Factor Indices \(y\) and \(z\) were each assigned a value of 0.1. Values of \(y\) and \(z\) were varied until Equation (13) was satisfied for \(m\) = 500 kg (Table 4). With three known values of \(x\), \(y\) and \(z\), Capital Cost was estimated from Equations (13) and (15) for Spar Cap blade lengths ranging from 40 to 75 m for a maximum molding mass \(M\) = 10,000 kg (Figure 6). \[F=1/\left(1-V_{f}\right)^{1.5}\left(1-\overline{C}\right)^{1,2452}\left(1- \overline{M}\right)^{1} \tag{15}\]  
Labor cost is either a Direct Cost or Indirect Cost. Direct Labor costs are associated with the number and size of manufactured spar caps while Indirect Labor costs, such as Management and Administration, are assumed to be independent of spar cap size and number. The Direct Labor Cost for a 35 m blade spar cap was estimated as shown in Table 6.  
Example: Mold Preparation took 0.5 h with four operatives, as denoted by the number 4. At a Direct Labor rate of 30 euros per hour, the total cost is \(0.5\times 4\times 30=60\) euros. Similarly, Laminate Layup took fours hours with six operatives, so the cost is \(4\times 30\times 6=720\) euros. At an exhange rate of \(\varepsilon\)0.91/1 euro, the direct labor cost is \(\varepsilon\)1584 for a 35 m spar cap. Direct Labor cost is assumed to vary only with spar cap mass and was estimated for each spar cap, 35 to 75 m, using the 35 m \(\varepsilon\)1584 Spar Cap Direct Labor cost as a baseline. \[\text{Spar Cap Direct Labor}_{i}=35\text{m spar cap cost}\times\text{mass of Spar Cap}_{i}/\text{mass of 35m Cap} \tag{16}\]  
where spar cap Direct Labor Cost\(i\) is the cost of a spar cap longer than 35 m (Figures 4 and 7). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Hours** & **Labor** & **Total Cost (Euros)** \\ \hline Mold Preparation & 0.5 & 4 & 60 \\ Fabric Layup & 4 & 6 & 720 \\ Root studs & 5 & 2 & 300 \\ Vacuum bag & 0.5 & 4 & 60 \\ Infusion & 1.5 & 6 & 270 \\ Cure time & 5 & 1 & 150 \\ Consumable removal & 0.5 & 4 & 60 \\ Demold & 1 & 4 & 120 \\ Total & 18 & & 1740 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Direct Labor Cost for a single 35 m blade length spar cap [29,30]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Floor Space** & **Square Meters (m\({}^{2}\))** \\ \hline Warehouse and Administration & 1000 \\ Spars & 4000 \\ Total & 5000 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Floor space area. Production rate will decrease as fiber volume fraction, complexity, and mass increases. The Reference Standard has a production rate of 300 parts per year [29], which is the maximum possible production rate based on 18-h manufacturing time for one Standard, two 8-h shifts per day over seven days in a 48-week year. A period of 18 h per Standard is assumed to be the same for GFRP and CFRP. As for Tooling and Capital Cost, the same mathematical iterative technique was used to derive Cost Factor Indices \(x\), \(y\) and \(z\) that satisfied Equation (8) for \(m\) = 500 kg (35 m spar cap mass) and \(M\) = 10,000 kg. Unlike Tooling and Capital, the value of \(x\) for Volume Fraction was less than \(y\) and \(z\). Index \(x\) was initially given a constant value of 0.01, while Factor Indices \(y\) and \(z\) were assigned values of 0.006 and 0.2, respectively. Compared to the Reference Standard production rate, the actual production rate is:  
Actual Production Rate = Production rate of Standard \(\times\) Cost Scaling Feature Factor\({}^{-1}\)  
\[n_{r}=300\Big{(}1-V_{f}\Big{)}^{x}\Big{(}1-\overline{C}\Big{)}^{y}\Big{(}1- \overline{M}\Big{)}^{z} \tag{17}\]  
With three known values of \(x\), \(y\) and \(z\), and a maximum production rate of 285 parts per year [29] for the 35 m spar cap Calibration Standard with \(m\) = 500 kg, the production rate was estimated from Equation (17) for spar cap lengths 35 to 75 m for a maximum molding mass M = 10,000 kg:  
\[285=300\Big{(}1-V_{f}\Big{)}^{0.01}\Big{(}1-\overline{C}\Big{)}^{0.005}\Big{(}1 -\overline{M}\Big{)}^{0.1} \tag{18}\]