Aerodynamic and physical foundations of Wake Survey Profile Drag.
Direct mechanical balance measurements of drag are frequently contaminated by model support strut interference and wingtip end-effects. To measure section profile drag c_d (the sum of skin friction and form drag) with unmatched precision, aerodynamicists utilize the wake survey momentum deficit method. When an airfoil generates drag, viscous shear within its boundary layers creates a downstream velocity deficit—a wake where total pressure P_0w is substantially lower than the free-stream total pressure P_0_inf. Applying the momentum theorem to a fixed control volume enclosing the airfoil reveals that the net profile drag per unit span equals the total momentum deficit convected downstream across the wake. B. M. Jones formulated an exact integral relating the section drag coefficient c_d to total and static pressure measurements across the wake: c_d = 2 * int [sqrt(q_w / q_inf) * (1 - sqrt(q_w / q_inf))] d(y/c). In this laboratory experiment, a multi-tube total-pressure wake rake is positioned one chord downstream of the trailing edge of an airfoil model. By recording total pressure profiles across the viscous wake deficit for various angles of attack, students perform numerical quadrature of the Jones integral to extract the profile drag polar, observing how viscous wake widening correlates with boundary layer thickening and trailing-edge separation.
Viva voce questions & analytical theory
Why is the wake survey method superior to external balance measurements for airfoil section drag?
The wake survey method measures section profile drag c_d directly from fluid momentum deficit without being contaminated by balance tare, model mounting strut drag, or test section sidewall friction.
How does the Jones formula account for static pressure recovery in the wake?
B. M. Jones assumed that each wake streamline expands isentropically from the survey plane to downstream infinity where static pressure equals P_inf. This relates the measured wake total pressure P_0w directly to the asymptotic velocity deficit.
What happens to the width and depth of the wake profile as angle of attack increases?
As angle of attack increases, the adverse pressure gradient on the upper surface thickens the boundary layer, causing the wake profile to broaden significantly and deepen, which dramatically increases the integrated drag coefficient c_d.
What is the difference between profile drag, skin friction drag, and form drag?
Profile drag is the sum of skin friction drag (viscous tangential shear forces on the surface) and form drag (pressure drag resulting from boundary layer displacement and flow separation). Both appear as momentum deficits in the wake.
Why must the wake rake be placed at least 0.7 to 1.0 chord downstream of the trailing edge?
Placing the rake 0.7 to 1.0 chord downstream allows static pressure across the wake to recover nearly to the ambient free-stream static pressure, minimizing errors from the Betz static pressure correction.
Can the wake survey method measure induced drag?
No. The wake survey measures only the profile drag (viscous momentum deficit). Induced drag resides in the kinetic energy of the swirling trailing vortex pair outside the viscous wake core.
Experimental precautions and wind tunnel safety
- Ensure the wake rake span covers the entire viscous wake so that outer probes record 100% of free-stream total pressure.
- Account for static pressure recovery in the near wake by incorporating the Betz static pressure correction if surveying x < 1.0c.
- Verify all rake total pressure tubes are purged and free from dust or aerosol contamination prior to testing.
- Avoid surveying deep post-stall separated wakes where massive reverse flow invalidates the unidirectional Jones equation.
Theoretical assumptions & flow limits
- The Jones formula assumes static pressure across the wake survey plane has recovered to ambient free-stream static pressure.
- Turbulent mixing and wake unsteadiness introduce slight RMS pressure fluctuations requiring low-pass digital filtering.
- Valid strictly for two-dimensional airfoil sections; does not capture three-dimensional induced drag or tip vortex energy.
- Probe spatial resolution (2 mm tube spacing) introduces minor discretization errors across steep shear gradients.