Oblique Shock Calculator
Calculate fluid flow properties across oblique shock waves in supersonic flow
Calculate Oblique Shock Properties
Must be supersonic (M₁ > 1)
Angle between shock wave and flow direction
Default: 1.4 (air at standard conditions)
Oblique Shock Results
Upstream
Angles
Property Ratios
Downstream
Oblique Shock Relations: Based on conservation of mass, momentum, and energy
Key equations: θ-β-M relation, Rankine-Hugoniot relations
Applications: Supersonic aircraft design, wind tunnel testing, aerospace engineering
Shock Wave Analysis
Example Calculation
Supersonic Aircraft Intake
Given:
• Upstream Mach number: M₁ = 5.0
• Wave angle: β = 20°
• Specific heat ratio: γ = 1.4
Results
• Turn angle: θ = 10.66°
• Pressure ratio: p₂/p₁ = 3.245
• Density ratio: ρ₂/ρ₁ = 2.214
• Temperature ratio: T₂/T₁ = 1.465
• Downstream Mach: M₂ = 3.467
Shock Wave Types
Normal Shock
Perpendicular to flow direction
Maximum pressure rise
Oblique Shock
Inclined to flow direction
Flow deflection occurs
Detached Shock
Curved shock ahead of blunt body
Mixed normal-oblique character
Applications
Supersonic aircraft intake design
Spacecraft re-entry analysis
Wind tunnel testing
Supersonic nozzle design
Explosion blast analysis
Ballistics and projectiles
Understanding Oblique Shock Waves
What is an Oblique Shock Wave?
An oblique shock wave is an abrupt discontinuity in supersonic flow that is inclined at an angle to the flow direction. Unlike normal shocks, oblique shocks deflect the flow while compressing it, making them essential for supersonic aircraft design and aerospace applications.
Formation and Characteristics
- •Forms when supersonic flow encounters a wedge or ramp
- •Thickness is approximately 200 nanometers
- •Causes abrupt changes in pressure, density, and temperature
- •Flow remains supersonic in most cases
Key Equations
Pressure Ratio:
p₂/p₁ = [2γM₁²sin²β - (γ-1)]/(γ+1)
Density Ratio:
ρ₂/ρ₁ = (γ+1)M₁²sin²β/[2+(γ-1)M₁²sin²β]
Temperature Ratio:
T₂/T₁ = (p₂/p₁)/(ρ₂/ρ₁)
Variables: M₁ = upstream Mach number, β = wave angle, γ = specific heat ratio, θ = turn angle
Engineering Applications
Aircraft Design
Supersonic intakes use oblique shocks to slow air before entering engines
Wind Tunnels
Testing supersonic flows and measuring shock wave properties
Spacecraft
Re-entry vehicle design and heat shield analysis
Important Considerations
Strong vs Weak Shocks
Two solutions exist for given M₁ and θ
Shock Detachment
Large deflection angles cause curved detached shocks
Entropy Increase
All shock waves increase entropy and decrease stagnation pressure