Aerospace & Aeronautical Engineering / Normal Shock Wave Relations
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LABORATORY 12 · AEROSPACE & AERONAUTICAL ENGINEERING

Normal Shock Wave Pressure and Total Pressure Loss in Supersonic Ducts

Measure static pressure jump P_2 / P_1 and total pressure ratio P_02 / P_01 across a stationary normal shock wave in a supersonic duct as upstream Mach M_1 varies. Explore interactive wind tunnel simulation, flight dynamics, and aerospace engineering telemetry.

AERODYNAMICS · PROPULSION · FLIGHT DYNAMICS

Your virtual aerospace engineering laboratory.

PRESSURE JUMP RATIO—
FLIGHT & TEST CELL TELEMETRY

Ready to sample with M_1^2 - 1 = 1.5 dimensionless.

1.5 dimensionless
Test gas: Air (gamma = 1.400)

Adjust M_1^2 - 1, 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

Shock-wave boundary layer interaction (SWBLI) creates a lambda-foot near duct walls that slightly smears the idealized 1D jump. Linear regression of the pressure jump ratio against (M_1^2 - 1) yields a slope of 1.1667 matching the Rankine-Hugoniot relation with R^2 > 0.999999.

Aeronautical apparatus & wind tunnel sensors.

Supersonic Wind Tunnel Test Section

Continuously variable supersonic duct operating from Mach M = 1.2 to 2.5.

Variable Back-Pressure Exit Throttle Valve

Regulates downstream back-pressure to position a stable normal shock wave in the test section.

Multi-Channel Fast-Response Pressure Scanner

Samples wall static pressures upstream and downstream of the shock wave at 1 kHz.

Supersonic Pitot-Static Total Pressure Rake

Measures total pressure upstream P_01 and downstream P_02 across the shock discontinuity.

High-Speed Schlieren Imaging Camera

Captures optical shadowgraph and Schlieren images of the normal shock wave thickness and location.

Digital Environmental DAQ Computer

Logs stagnation conditions and computes experimental Rankine-Hugoniot pressure ratios.

FOLLOW THE METHOD

A reason behind every step.

Measure static pressure jump P_2 / P_1 and total pressure ratio P_02 / P_01 across a stationary normal shock wave in a supersonic duct as upstream Mach M_1 varies. Standardized parameter settings: 0.8, 1.25, 1.89, 2.61, 3.41, 4.29 dimensionless.

01

Supersonic Flow Stabilization

Start the supersonic wind tunnel, establishing stable supersonic flow at nominal Mach M_1 = 1.34 in the test section.

02

Normal Shock Wave Positioning

Gradually close the downstream throttle valve until Schlieren optics confirm a stationary normal shock centered over tap station 12.

03

Upstream and Downstream Pressure Acquisition

Record upstream static pressure P_1, downstream static pressure P_2, and stagnation pressures P_01 and P_02.

04

Systematic Mach Number Stepping

Adjust the supersonic nozzle block to step upstream Mach M_1 through values corresponding to (M_1^2 - 1) = 0.80, 1.25, 1.89, 2.61, 3.41, and 4.29.

05

Rankine-Hugoniot Jump Calculation

Compute static pressure jump ratio (P_2/P_1 - 1) and total pressure ratio P_02 / P_01 at each Mach operating point.

06

Rankine-Hugoniot Linear Regression

Plot (P_2/P_1 - 1) versus (M_1^2 - 1), perform linear regression to determine slope 2*gamma/(gamma+1), and verify gamma = 1.4 for air.

YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into aerodynamic insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Normal Shock Wave Relations mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
\left(\frac{P_2}{P_1} - 1\right) = \frac{2\gamma}{\gamma + 1} (M_1^2 - 1) \implies \Delta P_{\text{ratio}} = m \cdot (M_1^2 - 1) + b
#Upstream Mach Parameter (dimensionless)Pressure Jump Ratio (dimensionless)Mach Factor (M_1^2 - 1)Static Pressure Jump Ratio (P_2/P_1 - 1)Remove

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 theoretical value of the Rankine-Hugoniot slope 2*gamma/(gamma+1) for air (gamma = 1.4)?

What is the flow speed immediately downstream of a normal shock wave?

What happens to the total temperature T_0 across an adiabatic stationary normal shock wave?

Why does total stagnation pressure P_0 decrease across a normal shock wave?