Calculator Inputs
Example Data Table
| M1 | θ (deg) | γ | Weak β (deg) | Strong β (deg) | Weak M2 | Strong M2 | Weak P2/P1 | Strong P2/P1 |
|---|---|---|---|---|---|---|---|---|
| 2.50 | 15.00 | 1.40 | 36.9449 | 83.0673 | 1.8735 | 0.5549 | 2.4675 | 7.0188 |
Formula Used
1) Mach angle: μ = sin-1(1 / M1)
2) Theta-beta-Mach relation: tan(θ) = 2 cot(β) [(M12 sin2(β) - 1) / (M12(γ + cos(2β)) + 2)]
3) Upstream normal Mach number: M1n = M1 sin(β)
4) Pressure ratio: P2/P1 = 1 + [2γ / (γ + 1)](M1n2 - 1)
5) Density ratio: ρ2/ρ1 = [(γ + 1) M1n2] / [(γ - 1) M1n2 + 2]
6) Temperature ratio: T2/T1 = (P2/P1) / (ρ2/ρ1)
7) Downstream normal Mach number: M2n2 = [1 + ((γ - 1)/2) M1n2] / [γ M1n2 - ((γ - 1)/2)]
8) Downstream Mach number: M2 = M2n / sin(β - θ)
9) Total pressure ratio: P02/P01 = (P2/P1) [(1 + ((γ - 1)/2) M22) / (1 + ((γ - 1)/2) M12)]γ/(γ - 1)
The calculator numerically searches the theta-beta curve, identifies the weak and strong branches, and checks whether the entered deflection remains below the attached-shock limit.
How to Use This Calculator
- Enter the upstream Mach number above 1.
- Provide the flow deflection angle in degrees.
- Set the specific heat ratio for the gas.
- Optionally enter upstream pressure, temperature, and density.
- Press
Calculate Shock Angleto solve both branches. - Review the branch table, absolute outputs, and curve plot.
- Use the CSV or PDF buttons to export results.
FAQs
1) What does this calculator solve?
It solves the oblique shock angle for a given upstream Mach number, wedge turning angle, and specific heat ratio. It also reports weak and strong branch properties, compression ratios, and downstream Mach number.
2) Why are there two shock angles?
An attached oblique shock can satisfy the theta-beta relation at two shock angles. The weak branch usually appears in external aerodynamics, while the strong branch produces stronger compression and often subsonic downstream flow.
3) What happens when the entered angle is too large?
If the wedge deflection exceeds the maximum attached turning angle, the solution becomes a detached bow shock. This calculator warns you when the input is beyond the attached-shock limit.
4) Does the calculator assume a perfect gas?
Yes. It uses standard calorically perfect gas relations with a constant specific heat ratio. That is the usual engineering assumption for introductory and many intermediate compressible-flow calculations.
5) Can I use custom gas properties?
Yes. Change the specific heat ratio to match your gas model. Air often uses 1.4, but other gases and temperature ranges may require different values.
6) Are the absolute pressure and temperature outputs required?
No. The main solution is based on ratios. Absolute outputs are included only to help you convert ratios into practical engineering values when upstream pressure, temperature, and density are available.
7) What does the plot show?
The plot shows the full theta-beta curve for the entered Mach number and specific heat ratio. It highlights the weak branch, strong branch, and the maximum attached turning point.
8) When is the weak solution usually preferred?
The weak solution is commonly observed because it gives a smaller shock angle and less severe compression, leaving the downstream flow at a higher Mach number than the strong branch.