Wind Tunnel Drag Study — Flap Deflection

This page documents a wake survey experiment in ERAU’s subsonic wind tunnel, where I measured how drag on a NACA 4412 wing changes across five flap deflection angles, computed drag coefficients via momentum-deficit integration, and propagated measurement uncertainty to 95% confidence.

Project Overview

Control surfaces such as flaps are central to every phase of flight — increasing lift during takeoff and approach while simultaneously raising drag. Understanding this tradeoff experimentally, not just analytically, is essential for validating aerodynamic models. In this study, we used ERAU’s open-loop subsonic wind tunnel and a servo-actuated NACA 4412 wing model to directly measure how drag evolves as flap angle is swept from fully retracted to fully deflected. Wake survey methods — where the velocity deficit behind the airfoil is integrated to infer drag — provided a classic, non-contact drag measurement technique rooted in the momentum theorem.

• Measure wake velocity profiles behind a NACA 4412 2D wing at flap deflections of 0°, 15°, 25°, 35°, and 50°
• Apply momentum-deficit integration to compute drag force and drag coefficient at each configuration
• Compare the minimum-drag (flap retracted) and maximum-drag (full flap) conditions quantitatively
• Quantify measurement uncertainty at 95% confidence through full error propagation of velocity and density contributions
• Identify and account for setup irregularities that introduced additional experimental uncertainty

Experimental Setup

Testing was conducted in ERAU’s open-loop subsonic wind tunnel. The transparent-walled test section allowed direct observation of the instrumentation throughout each run. Two pitot-static probes were deployed simultaneously: a stationary probe to record freestream conditions and a motorized traverse probe to sweep through the wake region behind the wing. Pressure readings were fed to analog and digital manometers and captured by the data acquisition system.

The flap deflection system was custom-built: a servo microcontroller (ServoCity) interfaced with servos embedded in the wing allowed precise, repeatable angular positioning between test runs. A DC power supply regulated voltage to the servo system. Ambient conditions were logged before each sweep, enabling accurate air density calculation at each test condition:

• Ambient temperature T_amb = 294.15 K
• Ambient pressure P_amb = 102,268.94 Pa

The data acquisition pipeline ran a MATLAB script on the DAQ computer to log pressure data from the analog-to-digital converter (ADC) in real time, automatically step the traverse probe through programmed height increments, and export processed velocity profiles for post-processing.

The NACA 4412 wing was mounted to a force balance spanning the test section at a fixed angle of attack. During installation, the wing’s structural attachment failed at the initially commanded angle, requiring the model to be re-secured using electrical tape, with wingtip friction against the tunnel walls providing additional lateral support.

Wake Survey Method & Drag Calculation

Drag was inferred from the momentum deficit in the wake rather than from a direct force measurement. According to the momentum theorem, the drag per unit span D′ is proportional to the velocity deficit integrated across the wake height:

D′ = ρ_∞ ∫ U_w(U_∞ − U_w) dy

where U_∞ is the undisturbed freestream velocity and U_w is the local velocity in the wake. Numerical integration used MATLAB’s trapezoidal method over the traverse probe sweep. Drag coefficient was then derived as:

C_d = D′ / (½ ρ U_∞² c)

Uncertainty in drag was propagated from three independent sources using the sum-of-squares method at 95% confidence:

• Uncertainty in wake velocity U_w
• Uncertainty in freestream velocity U_∞ — itself depending on instrument resolution (δP_atm = 16.93 Pa, δT_atm = 0.278 K) and statistical spread in the dynamic pressure signal across N samples
• Uncertainty in air density ρ_∞

Results & Discussion

Wake velocity profiles across all five flap configurations are overlaid in Figure 5. At low deflection angles the wake velocity deficit is narrow and shallow, centered near height y = 0.32 m. As flap angle increases to 50°, the deficit broadens noticeably — the wake extends further in the transverse direction, indicating greater momentum extraction by the wing and, by consequence, higher drag. This widening is the visual signature of increased pressure drag driven by flow separation behind the deflected flap surface.

The drag coefficient C_d versus flap deflection is plotted in Figure 6 with 95% confidence error bars. The trend is predominantly increasing — C_d rises from 0.200 at 0° to 0.220 at 50° — consistent with the expected growth in pressure drag from enhanced flow separation. A small dip to C_d = 0.191 at 25° breaks the otherwise monotonic trend. This anomaly could reflect minor flow reattachment at that intermediate angle, measurement scatter from the mounting instability, or a combination of both. At higher Reynolds numbers or with a more rigidly mounted model, finer angle increments would be needed to resolve whether this dip is physically real or experimental artifact.

Drag Force Summary

Flap Deflection	Drag (N)	Uncertainty (N)	Cd
0° (Flap Retracted)	1.8824	± 0.0443	0.200
15°	1.9636	± 0.0493	0.205
25°	1.8328	± 0.0426	0.191
35°	1.9277	± 0.0482	0.199
50° (Full Flap)	2.2000	± 0.0587	0.220

Drag uncertainty grew with deflection angle, reaching a maximum of ±0.059 N at 50° — roughly 2.7% of the measured drag value. This indicates the repeatability of the wake survey method was maintained across all test conditions despite the structural instability of the mount.

Key Takeaways