Lab 03: Lift and Drag on Airfoils

Experiment Overview

The NACA 4412 is a classic cambered airfoil used on general aviation aircraft. This lab measured its real aerodynamic performance across a range of angles of attack, then compared those measurements against ideal potential-flow predictions. The gap between theory and experiment directly quantifies the performance penalty of viscosity: the reason every real wing produces less lift and more drag than inviscid models predict — a trade-off designers must account for from the earliest stages of wing design.

Map the pressure distribution across 18 static taps on the NACA 4412 at angles of attack from −3° to 12°
Conduct a wake survey with a traversing pitot tube to compute drag from the momentum deficit downstream
Extract lift coefficient C_l, drag coefficient C_d, and moment coefficients C_m,LE and C_m,c/4
Determine the zero-lift angle of attack and identify the most aerodynamically efficient operating point

NACA 4412 airfoil diagram showing the 18 numbered pressure tap locations along upper and lower surfaces — Figure 1: NACA 4412 airfoil with 18 pressure tap locations along upper and lower surfaces

Equipment & Tools

ERAU open-circuit wind tunnel (15 m/s test speed)
NACA 4412 airfoil model, 6-inch chord, with 18 static pressure taps (10 upper, 8 lower)
Traversing pitot-static wake probe (76 height positions)
Differential pressure transducers and data acquisition system
Panel code reference data (PanelCode.mat) for potential-flow comparison
MATLAB/Simulink for data processing and aerodynamic coefficient integration

Approach & Key Equations

At 15 m/s, the 18 surface pressure taps sampled the pressure distribution simultaneously at each angle of attack while a traversing probe swept 76 heights through the downstream wake. Lift was obtained by integrating the pressure difference between the lower and upper surfaces along the chord:

C_l = (1/c) ∫_LE^TE (C_p,lower − C_p,upper) dx

Drag was derived from the wake momentum deficit — a method that captures viscous drag directly from the velocity profile downstream and requires no physical force sensor. Pitching moments about both the leading edge and quarter-chord were integrated from the same pressure data, and all results were compared against panel code (potential flow) predictions.

Wake velocity profiles at six angles of attack from -3 to 12 degrees — Figure 2: Wake velocity profiles at six angles of attack from −3° to 12°

Pressure coefficient distributions along the NACA 4412 chord at all angles of attack, experimental vs panel code — Figure 3: C_p distributions along the NACA 4412 chord — experimental vs panel code

Key Results

C_l increased linearly with angle of attack but remained consistently below the potential-flow prediction — quantifying the lift penalty from viscous skin friction in a real flow.
C_m,LE became progressively more negative with angle of attack (stronger nose-down pitching moment), while C_m,c/4 stayed approximately constant near −0.09, confirming the quarter-chord as the aerodynamic center for this airfoil.
Zero-lift angle of attack = −3.31°, extrapolated from the experimental C_l vs α curve — consistent with theory for a positively cambered airfoil.
Peak L/D ratio occurred near 9° AoA, identifying the most aerodynamically efficient operating point for the NACA 4412 at this Reynolds number.
The drag polar was bowl-shaped rather than the ideal fishhook shape, partly attributable to elevated drag at −3° from a larger-than-intended setup angle.

Lift coefficient vs angle of attack – experimental compared to theoretical potential flow — Figure 4: Lift coefficient vs angle of attack for NACA 4412

Drag coefficient vs angle of attack – experimental compared to potential flow — Figure 5: Drag coefficient vs angle of attack for NACA 4412

Drag polar – Cd vs Cl showing the aerodynamic efficiency envelope of the NACA 4412 — Figure 6: Drag polar — C_d vs C_l for the NACA 4412

MATLAB Code

Surface pressure and wake traverse data were integrated to extract aerodynamic coefficients. The zero-lift angle was found by linear interpolation of the C_l–α curve through zero lift.

% Lift coefficient from pressure integration (lower - upper)
Cl(i) = trapz(lower_x, Cp_lower(i,:)) - trapz(upper_x, Cp_upper(i,:));

% Drag from wake momentum deficit
D(i)  = rho * trapz(z(i,:), Vel(i,:) .* (V_inf - Vel(i,:)));
Cd(i) = D(i) / (0.5 * rho * V_inf^2 * chord);

% Zero-lift angle of attack
alpha_0 = interp1(Cl, AoA_vals, 0, 'linear', 'extrap');  % = -3.31°

Valuable Takeaways

Viscosity costs lift and adds drag — quantifiably. Plotting both experimental and theoretical C_l curves makes this performance penalty tangible, not just a textbook abstraction.
The drag polar is one of the most information-rich plots in aerodynamics. Its shape encodes efficiency at every operating point, and reading it fluently is essential for wing design, glider optimization, and aircraft performance analysis.
The wake momentum method is a powerful, hardware-independent drag measurement technique used in academic and industrial wind tunnel testing, including at NASA Langley and major airframe manufacturers.
Gained end-to-end experience: raw pressure tap data → C_p distributions → integrated aerodynamic coefficients → validated polar curves — the same workflow used in real aerodynamic development programs.

Figure 7: Pitching moment coefficient about the leading edge vs angle of attack

Pitching moment coefficient about the quarter-chord vs angle of attack – confirming aerodynamic center — Figure 8: Pitching moment coefficient about the quarter-chord — confirming aerodynamic center

Lift-to-drag ratio vs angle of attack – peak efficiency near 9 degrees AoA — Figure 9: Lift-to-drag ratio vs angle of attack — peak efficiency near 9°

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