What Is the Oblique Shock Angle & Deflection (Theta-Beta-M) Calculator?
Oblique shocks occur when supersonic flow encounters a concave corner or wedge, compressing the fluid across an angled shock front.
How Does the Oblique Shock Angle & Deflection (Theta-Beta-M) Calculator Work?
Resolves incoming velocity into normal and tangential components; normal component experiences normal shock jump equations.
Oblique Shock Angle & Deflection (Theta-Beta-M) Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
an( heta) = 2 cot(eta) rac{M_1^2 sin^2(eta) - 1}{M_1^2 (gamma + cos(2eta)) + 2}
Classical theta-beta-M relation coupling flow turning angle theta with shock wave angle beta.
How to Use the Oblique Shock Angle & Deflection (Theta-Beta-M) Calculator
- Input incoming freestream Mach M1, wedge turning angle theta in degrees, and gas gamma.
Step-by-Step Example Calculation
Supersonic Aircraft Air Intake Ramp
Input Values:
upstreamMach:2.5
deflectionAngleDeg:15
specificHeatRatio:1.4
Worked Steps: Weak oblique shock wave angle beta = 36.9°, downstream Mach M2 = 1.87 with 2.47x static pressure rise.
Understanding Your Result
Yields the shock wave angle beta, normal Mach component, downstream Mach number, and static pressure ratio.
Factors That Affect the Result
- Higher Mach numbers produce shallower shock angles; increasing turning angle steepens the wave until detachment.
When Should You Use This Calculator?
- Design of supersonic aircraft inlets, wedge diffusers, and supersonic projectile noses.
Assumptions & Limitations
- Applies to 2D planar wedge flows under continuum non-reacting perfect gas conditions.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard compressible fluid dynamics exact solution.