Lab 04: Forces and Moments on a Canard Delta Wing

Experiment Overview

Delta wing and canard configurations appear on high-performance aircraft like the Eurofighter and Saab Gripen because they sustain lift at extreme angles of attack through leading-edge vortex lift — a mechanism conventional airfoils cannot exploit. This lab used the ERAU Micaplex closed-circuit wind tunnel’s six-component force balance to measure the complete aerodynamic load set on a canard-delta model across a wide operating envelope, giving direct exposure to how professional wind tunnel testing is conducted.

Measure all six aerodynamic loads: lift, drag, side force, and pitching, rolling, and yawing moments
Apply aerodynamic tares using the image–invert method to remove structural interference from force balance readings
Compare performance at two Reynolds numbers and two yaw angles across angles of attack from −4° to 34°
Build a drag polar and identify the best C_L/C_D operating point for each test condition

Equipment & Tools

ERAU Micaplex closed-circuit wind tunnel (75 fps and 100 fps test speeds)
Canard-delta wing model (S_w = 242.01 in², b_w = 24.5 in, c_w = 9.88 in)
WAFBC six-component external force balance (sting-mounted)
Aerodynamic tare hardware: image and invert mounting configurations
MATLAB for tare correction, coefficient computation, and polar plotting

Approach & Key Equations

The model was tested at four conditions — 75 fps and 100 fps, at 0° and 10° yaw — while angle of attack swept from −4° to 34° in 2° steps. Raw balance outputs were corrected using the image-invert tare procedure, then non-dimensionalized by dynamic pressure q and reference area S_w:

C_L = Lift / (q·S_w) C_D = Drag / (q·S_w) C_m = Pitch / (q·S_w·c_w)

A quadratic curve fit to the drag polar (C_D = C_D0 + K·C_L²) extracted the parasitic drag and induced drag factor K for each condition. Reynolds numbers were computed from the “Reynolds Number per ft” channel in the raw tunnel data.

Lift force vs angle of attack across four test conditions – two speeds and two yaw angles — Figure 1: Lift force vs angle of attack — two speeds and two yaw angles

Figure 2: Drag force vs angle of attack across four test conditions

Side force vs angle of attack – nonzero side force at 10-degree yaw across the full AoA range — Figure 3: Side force vs angle of attack — nonzero at 10° yaw

Pitching moment vs angle of attack for all four test conditions — Figure 4: Pitching moment vs angle of attack

Rolling moment vs angle of attack – roll response increases sharply above 20 degrees AoA — Figure 5: Rolling moment vs angle of attack — increases sharply above 20°

Yawing moment vs angle of attack for all four test conditions — Figure 6: Yawing moment vs angle of attack

Key Results

C_L increased nearly linearly up to ~25°, then gradually rolled off — the signature of vortex lift breakdown on a delta wing rather than the abrupt stall of a conventional airfoil.
Higher Reynolds number (100 fps) produced marginally higher C_L and lower C_D, confirming that better flow attachment at higher Re improves overall efficiency.
10° yaw had negligible effect on lift but measurably increased side force and yawing moment — important considerations for directional stability analysis.
Best C_L/C_D = 4.21 at 12° AoA (75 fps, 0° yaw). Higher yaw and higher Re both reduced the peak efficiency ratio.

Speed	Yaw	Best C_L/C_D	AoA
75 fps	0°	4.21	12°
100 fps	0°	3.77	12°
75 fps	10°	3.19	12°
100 fps	10°	2.67	12°

Lift coefficient vs angle of attack across four test conditions — Figure 7: Lift coefficient vs angle of attack

Drag coefficient vs angle of attack across four test conditions — Figure 8: Drag coefficient vs angle of attack

Drag polar – CL vs CD showing performance envelope for all test conditions — Figure 9: Drag polar — C_L vs C_D for all test conditions

Valuable Takeaways

Delta wings don’t stall abruptly — they tolerate high angles of attack gracefully. The gradual vortex lift roll-off above 25° is why delta configurations appear on fighters and supersonic aircraft that must operate across extreme flight regimes.
Tare corrections are essential for accurate force balance data. Without the image-invert method, structural interference from the mount hardware would contaminate every measurement — a fundamental discipline in professional wind tunnel testing.
The drag polar compresses all performance information into a single curve. Reading it to extract C_D0, K, and the best-glide point is a core skill for aircraft sizing, mission analysis, and performance optimization.
Gained direct experience operating a closed-circuit facility, applying multi-variable test matrix design, and analyzing six-degree-of-freedom aerodynamic datasets — skills directly applicable to industry wind tunnel programs.

Lift-to-drag ratio vs angle of attack – peak efficiency at 12 degrees AoA — Figure 10: Lift-to-drag ratio vs angle of attack — peak at 12°

Figure 11: Pitching moment coefficient vs angle of attack

Side force coefficient vs angle of attack – effect of 10-degree yaw clearly visible — Figure 12: Side force coefficient vs angle of attack — 10° yaw effect visible

Rolling moment coefficient vs angle of attack – roll divergence above 24 degrees at yaw 10 degrees — Figure 13: Rolling moment coefficient — divergence above 24° at 10° yaw

Figure 14: Yawing moment coefficient vs angle of attack

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