Overview

MAE 4272 is a lab-based class intended to enage students to actively design, build, and analyze fluid-thermal systems, linking the fluid-mechanical and thermodynamic/heat-transfer components of the Cornell Mechanical and Aerospace Engineering core curriculum.

For this class' final project, students (in teams of 3 to 4) were tasked with designing the blades of a small-scale wind turbine according to a small set of mechanical and environmental constraints. We did this to demonstrate the application of the fluid-thermal analytical techniques learned in class to an open-ended design project.

Project Constraints

Key constraints we designed around included:

• Blade span $\le 6~\text{in}$, root compatible with a $1~\text{in}$ hub, and speed $\le 3000~\text{RPM}$ for safe operation
• Resin 3D-printed blades (grey resin) and a required factor of safety ($\text{FOS} = 1.5$)
• Wind tunnel operating conditions characterized using a Weibull wind-speed distribution, with mean wind speed $4.782~\text{m/s}$ and $\pm 1.052~\text{m/s}$ standard deviation

Design process

1) Modeling approach

We combined:

• $1\text{-D}$ momentum theory (axial induction factor / Betz-limit framework)
• Blade Element Momentum (BEM) theory to connect flow conditions and airfoil performance to a spanwise blade geometry (chord and twist)

We targeted a tip-speed ratio ($\text{TSR} = 6$) as a high-efficiency operating point, then swept candidate operating points around that target.

2) Airfoil choice

We selected NACA 66(1)-212, motivated by:

• Similarity to airfoils already proven reliable in the lab (NACA 4412 / 0012)
• A slightly higher lift-to-drag ratio near our expected operating angles of attack

3) Optimization loop (geometry selection)

A MATLAB script searched over rotor speed ($\Omega$) and angle of attack ($\alpha$) to maximize predicted power:

• Discretized the blade into $40$ radial stations
• Swept $\alpha$ from $6^\circ$ to $12^\circ$
• Used low-Re XFOIL polar data for $C_L(\alpha)$ and $C_D(\alpha)$
• Computed spanwise inflow angle and set twist via $\beta(r) = \phi(r) - \alpha$
• Computed an optimal chord distribution based on Betz-Glauert and integrated tangential force → torque, then power $P = \Omega T$, selecting the best case

4) Structural check + CAD

We ran a simplified bending-stress estimate along the blade radius to check structural margin under expected conditions, then moved into manufacturing with appropriate caution about modeling simplifications.

The final blade geometry was lofted in Fusion 360 using interpolated NACA 66(1)-212 sections with the optimized chord and twist profiles.

Testing summary

Test method (wind tunnel)

We tested across multiple wind tunnel fan settings to capture performance outside a single “design point”:

• Zeroed the pressure transducer, then increased fan speed until the turbine began spinning (below $\sim 3~\text{Hz}$ it did not spin)
• At each fan speed, incremented the torque brake voltage by $0.4~\text{V}$, waited for steady RPM, recorded data, and continued until the rotor stalled (interpreted as reaching max power) or the brake hit its voltage limit

Data products (what we analyzed)

We generated power curves at $4~\text{Hz}$, $6~\text{Hz}$, $8~\text{Hz}$, and $10~\text{Hz}$, corresponding to wind speeds of $2.18~\text{m/s}$, $3.17~\text{m/s}$, $4.33~\text{m/s}$, and $5.394~\text{m/s}$.

Key outcomes reported:

• At $4~\text{Hz}$ and $6~\text{Hz}$, the turbine stalled before reaching the $10~\text{V}$ brake limit (so max power could be identified in those trials)
• At $8~\text{Hz}$ and $10~\text{Hz}$, the turbine did not stall before hitting the brake limit, indicating additional power capability beyond the test hardware limit
• With a $9.6~\text{V}$ brake max setting, the $8~\text{Hz}$ and $10~\text{Hz}$ trials produced $0.73~\text{W}$ at $1126~\text{RPM}$ and $1.4~\text{W}$ at $2213~\text{RPM}$, respectively
• The maximum torque ($0.0062~\text{N}\cdot\text{m}$) occurred near the wind speed closest to the optimizer’s design point, supporting the modeling/optimization approach
• The most efficient reported case was the $8~\text{Hz}$ ($4.33~\text{m/s}$) condition, with an example efficiency calculation yielding $C_P \approx 21%$

What we’d improve next

Proposed next iteration ideas:

• Retune tower height to push anti-resonance near peak-power RPM
• Use a higher-torque brake and improve hub–blade tolerancing
• Refine CAD loft resolution and smooth hub/tip transitions to reduce parasitic drag

My contribution:

I worked primarily on the Matlab optimization pipeline.