Aerospace & Aeronautical Engineering / Transonic Drag Divergence
FREE TO EXPLORE
LABORATORY 17 · AEROSPACE & AERONAUTICAL ENGINEERING

Transonic Critical Mach Number and Wave Drag Divergence

Detect critical Mach number M_crit where local sonic flow is first reached and measure the drag divergence Mach number M_dd and cubic wave drag rise. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.

AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS

Your virtual aerospace engineering laboratory.

WAVE DRAG INCREMENT DELTA C_D,WAVE—
FLIGHT & TEST CELL TELEMETRY

Ready to sample with dM^3 = 0.002 dimensionless.

0.002 dimensionless
Airfoil profile: NASA SC(2)-0714

Adjust dM^3, 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

Transonic wall interference corrections require complex slotted-wall porosity models. Linear regression of transonic wave drag against (M - M_crit)^3 yields a scaling constant k_w = 25.000 with R^2 > 0.999999.

Aeronautical apparatus & wind tunnel sensors.

Transonic Wind Tunnel with Slotted Test Section

Test section with longitudinal wall slots to eliminate acoustic choking and shock wave reflections.

NASA Supercritical Airfoil Model SC(2)-0714

Precision airfoil model featuring a flat upper surface, aft camber, and high critical Mach number.

Multi-Component Transonic Internal Strain Balance

Measures drag force with 0.01 N precision across extreme dynamic pressure ranges.

Surface Dynamic Pressure Transducer Array

Detects the exact chordwise position and strength of the standing upper-surface shock wave.

Continuous Mach Number Control Servo

Adjusts wind tunnel plenum suction to smoothly ramp Mach number with 0.001 precision.

High-Speed Shadowgraph Visualizer

Captures optical shadowgraph images of shock-boundary layer interaction and wake buffeting.

FOLLOW THE METHOD

A reason behind every step.

Detect critical Mach number M_crit where local sonic flow is first reached and measure the drag divergence Mach number M_dd and cubic wave drag rise. Standardized parameter settings: 0.0005, 0.001, 0.002, 0.0035, 0.0055, 0.008 dimensionless.

01

Slotted Wall Plenum Preparation

Set slotted wall ventilation porosity to 6% and verify plenum chamber auxiliary suction pump operation.

02

Subcritical Baseline Calibration

Run tunnel at M_inf = 0.65 (well below M_crit), recording baseline subcritical parasite and induced drag C_D,subcrit.

03

Critical Mach Identification

Gradually increase Mach number until surface pressure taps record local sonic speed (C_p = C_p,crit), logging M_crit = 0.720.

04

Transonic Mach Stepping

Step free-stream Mach through values corresponding to (M_inf - M_crit)^3 = 0.0005, 0.0010, 0.0020, 0.0035, 0.0055, and 0.0080.

05

Wave Drag Isolation

Measure total drag C_D at each Mach number and subtract baseline subcritical drag to isolate wave drag Delta C_D,wave = C_D - C_D,subcrit.

06

Wave Drag Cubic Regression

Plot Delta C_D,wave versus (M_inf - M_crit)^3, perform linear regression to determine scaling constant k_w, and pinpoint drag divergence M_dd.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into aerodynamic insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Transonic Drag Divergence mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
\Delta C_{D,\text{wave}} = k_w (M_\infty - M_{\text{crit}})^3 \implies \Delta C_{D,\text{wave}} = m \cdot (\Delta M^3) + b
#Mach Increment Cubed (M - M_crit)^3 (dimensionless)Wave Drag Increment Delta C_D,wave (dimensionless)Transonic Mach Increment Cubed (M_inf - M_crit)^3Transonic Wave Drag Increment Delta C_D,waveRemove

No readings yet. Execute an aerodynamic trial and record it.

Calculate it yourself.

CHECK YOUR UNDERSTANDING

Explain what the aerodynamic metrics mean.

What is the standard aerodynamic definition of the drag divergence Mach number M_dd?

What key geometric feature distinguishes a supercritical airfoil from a conventional NACA airfoil?

What is the Whitcomb Area Rule used for in aircraft design?

In the cubic wave drag model Delta C_D,wave = k_w * (M - M_crit)^3, what happens to wave drag when flying below M_crit?