Aerospace & Aeronautical Engineering / Aerodynamic Drag Polar
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LABORATORY 04 · AEROSPACE & AERONAUTICAL ENGINEERING

Direct Force Balance Measurements and Aerodynamic Drag Polars

Measure lift and drag forces simultaneously on a wing model using an external 3-component strain-gauge balance to determine parasite drag coefficient C_D0 and induced drag factor k. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.

AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS

Your virtual aerospace engineering laboratory.

TOTAL DRAG COEFFICIENT C_D—
FLIGHT & TEST CELL TELEMETRY

Ready to sample with C_L^2 = 0.36 dimensionless.

0.36 dimensionless
Wing span b: 600 mm

Adjust C_L^2, then execute aerospace trial.

Aeronautical telemetry and flight states are evaluated rigorously using 64-bit IEEE 754 precision. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity aerodynamic modeling.

Aeronautical assumptions and boundary condition limits

Parabolic polar relationship C_D = C_D0 + k * C_L^2 is valid strictly for attached flow prior to the stall boundary. The linear regression of C_D against C_L^2 yields an induced drag factor k = 0.0450 and parasite drag C_D0 = 0.0180 with R^2 > 0.999999.

Aeronautical apparatus & wind tunnel sensors.

Subsonic Wind Tunnel Test Section

Provides controlled airflow at V_inf = 30 m/s with flow angularity < 0.1 degrees.

External 3-Component Strain-Gauge Balance

Measures aerodynamic normal force, axial force, and pitching moment via calibrated Wheatstone bridges.

Finite Wing Model (AR = 6.0)

NACA 0012 rectangular wing planform with span b = 600 mm and chord c = 100 mm.

Automated Angle-of-Attack Actuator

Pitches wing model through precision stepper motor from -4 to +16 degrees with optical encoder.

Dynamic Pressure Pitot-Static Sensor

Continuously records reference dynamic pressure q_inf to normalize forces into non-dimensional coefficients.

Balance Signal Conditioning Chassis

Amplifies strain gauge microvolt signals with 24-bit delta-sigma converters and digital filtering.

FOLLOW THE METHOD

A reason behind every step.

Measure lift and drag forces simultaneously on a wing model using an external 3-component strain-gauge balance to determine parasite drag coefficient C_D0 and induced drag factor k. Standardized parameter settings: 0.04, 0.16, 0.36, 0.64, 0.81, 1.0 dimensionless.

01

Tare Weight and Balance Calibration

Execute zero-flow weight tare across all balance load cells to eliminate gravity tare moments across the pitch range.

02

Wind Tunnel Velocity Baseline

Start the wind tunnel and bring test-section speed to V_inf = 30 m/s, stabilizing dynamic pressure at q_inf = 551 Pa.

03

Zero-Lift Alignment Verification

Set angle of attack to alpha = 0 deg and confirm that measured lift on the symmetric wing is zero within balance tolerance.

04

Systematic Drag Polar Sweep

Step the model through angles of attack corresponding to C_L^2 = 0.04, 0.16, 0.36, 0.64, 0.81, and 1.00.

05

Force Resolution to Wind Axes

Resolve measured normal and axial balance forces into wind-axis lift L and drag D using measured pitch angles.

06

Drag Polar Plotting and Regression

Plot C_D versus C_L^2, perform linear regression to determine parasite drag C_D0 and induced drag factor k, and compute (L/D)_max.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into aerodynamic insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Aerodynamic Drag Polar mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
C_D = C_{D0} + k C_L^2 \implies C_D = m \cdot (C_L^2) + b
#Lift Coefficient Squared C_L^2 (dimensionless)Total Drag Coefficient C_D (dimensionless)Lift Coefficient Squared C_L^2Total Drag Coefficient C_DRemove

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CHECK YOUR UNDERSTANDING

Explain what the aerodynamic metrics mean.

In the standard parabolic drag polar C_D = C_D0 + k * C_L^2, what does the vertical intercept represent?

At the flight condition for maximum lift-to-drag ratio (L/D)_max in steady level flight, how do parasite drag and induced drag compare?

For a wing with aspect ratio AR = 6.0 and Oswald efficiency e = 0.85, what is the theoretical induced drag factor k = 1 / (pi * e * AR)?

If an aircraft doubles its lift coefficient C_L during a steady turn, by what factor does its induced drag coefficient increase?