Lab 03: Lift and Drag on Airfoils

Lab Overview

• Course: AE 315 – Experimental Aerodynamics, Section 04 (Robert Bryan) | March 28, 2025
• Objective: Measure the surface pressure distribution and wake profile of a NACA 4412 airfoil at multiple angles of attack, extract lift, drag, and moment coefficients, and compare against panel code (potential flow) predictions.
• Model: NACA 4412 airfoil, c = 6-inch chord, instrumented with 18 static pressure taps (10 upper surface, 8 lower surface)
• Test speed: 15 m/s; angles of attack: −3°, 0°, 3°, 6°, 9°, 12°
• Ambient conditions: T = 22°C (295.15 K), P = 30.1 inHg (101,930.3 Pa), ρ = 1.203 kg/m³

Procedure & Methodology

The tunnel was set to 15 m/s and the airfoil adjusted to each angle of attack from −3° to 12° in 3° increments. At each angle, the traversing pitot-static tube swept 76 height positions behind the airfoil to capture the wake velocity profile, while the 18 static pressure ports sampled the airfoil surface pressure simultaneously.

Pressure readings (in inH₂O) were converted to Pa and normalized by dynamic pressure to obtain the pressure coefficient C_p = (P_diff + q_inf) / q_inf. The lift coefficient was computed by integrating the pressure difference between lower and upper surfaces: C_l = (1/c) ∫ (C_p_lower − C_p_upper) dx. The drag coefficient was derived from the wake momentum deficit: C_d = (2/U∞²c) ∫ U_w(U∞ − U_w) dy. Moment coefficients about the leading edge and quarter chord were obtained from weighted pressure integrals. All results were compared to panel code (potential flow) predictions loaded from PanelCode.mat.

Results & Analysis

• Cl increased linearly with angle of attack, but remained below the panel code prediction due to viscous effects (skin friction, flow rotation).
• Cd increased with AoA; the drag polar was bowl-shaped rather than fishhook-shaped, partly attributable to elevated drag at −3° (likely measurement error or a larger-than-intended negative AoA).
• C_m,LE became progressively more negative with increasing AoA, indicating a growing nose-down pitching moment as lift built up.
• C_m,c/4 remained near −0.09 to −0.10, consistent with the theoretical near-constant aerodynamic center behavior; closely tracked panel code predictions.
• The lift-to-drag ratio peaked at approximately 9° AoA, after which increased wake drag reduced efficiency.
• Zero-lift angle of attack: −3.31° (extrapolated from experimental Cl vs α curve).

Moment Coefficients & L/D

• C_m,LE decreased from −0.10 at −3° to −0.40 at 12°, consistently above (less negative than) the theoretical potential flow values — attributable to real-fluid viscous effects reducing the actual pitching moment.
• C_m,c/4 fluctuated near −0.09, close to but slightly above the theoretical line, confirming the quarter-chord as near the aerodynamic center for this airfoil.
• Peak CL/CD ≈ 62 at 9° AoA (experimental); potential flow predicted a peak near 85 at 6°.

MATLAB Code

Wake traverse and surface pressure data were loaded from .mat and .csv files, converted, and integrated to produce aerodynamic coefficients. Below is a representative excerpt; the full script is AE315_LAB3_Code.m.

% Wake velocity from traversing pitot-static data
Velocity = sqrt(2 * dp / rho0);

% Freestream: average outside the wake bounds
freestream(i) = mean([Velocity(i,1:LowBnd(i)), Velocity(i,UppBnd(i):end)]);

% Drag from momentum deficit
D(i) = rho0 * trapz(z_matrix(i, LowBnd(i):UppBnd(i)), ...
  Velocity(i, LowBnd(i):UppBnd(i)) .* ...
  (freestream(i) - Velocity(i, LowBnd(i):UppBnd(i))));

% Pressure coefficient from 18 surface taps
q         = 0.5 * rho0 * freestream(i)^2;
Cp(i, :)  = (p_mean(i, :) ./ q) + 1;

% Lift from Cp integration (lower minus upper surface)
Cl(i) = trapz(lower_x_val, Cp_lower(i,:)) - trapz(upper_x_val, Cp_upper(i,:));

% Zero-lift angle of attack
zero_lift_AoA = interp1(Cl, AoA_vals, 0, 'linear', 'extrap'); % = -3.31°