Computed Moving Shock Results
Results use a one-dimensional ideal-gas moving normal shock model.
| Metric | Value | Units |
|---|
Moving Shock Calculator
Enter upstream state values and the shock speed in the lab frame.
Example Data Table
These sample cases show how changing shock speed and upstream velocity affects downstream states.
| Case | p₁ (kPa) | T₁ (K) | V₁ (m/s) | Wₛ (m/s) | M₁,r | p₂ (kPa) | T₂ (K) | ρ₂ (kg/m³) | V₂ (m/s) |
|---|---|---|---|---|---|---|---|---|---|
| Case A | 101.325 | 300.00 | 0.00 | 600.00 | 1.7280 | 336.100 | 443.565 | 2.6397 | 332.554 |
| Case B | 101.325 | 300.00 | 80.00 | 700.00 | 1.7856 | 360.024 | 456.257 | 2.7489 | 434.622 |
| Case C | 150.000 | 320.00 | 30.00 | 850.00 | 2.2866 | 890.019 | 619.062 | 5.0085 | 582.644 |
Formula Used
This calculator uses moving normal shock relations for an ideal gas. The shock speed and upstream velocity are converted into a shock-frame relative velocity first.
a₁ = √(γRT₁)
w₁ = Wₛ − V₁
M₁,r = w₁ / a₁
p₂ / p₁ = 1 + [2γ / (γ + 1)] (M₁,r² − 1)
ρ₂ / ρ₁ = [(γ + 1)M₁,r²] / [(γ − 1)M₁,r² + 2]
T₂ / T₁ = (p₂ / p₁) / (ρ₂ / ρ₁)
w₂ = w₁ / (ρ₂ / ρ₁)
V₂ = Wₛ − w₂
M₂,r² = [1 + ((γ − 1)/2)M₁,r²] / [γM₁,r² − ((γ − 1)/2)]
Δs = cₚ ln(T₂/T₁) − R ln(p₂/p₁)
The method assumes a one-dimensional normal shock, no area change, and ideal-gas behavior.
How to Use This Calculator
- Enter the upstream pressure in kilopascals.
- Enter the upstream temperature in kelvin.
- Provide the upstream gas velocity in the lab frame.
- Enter the shock speed in the same direction convention.
- Keep γ and R for your gas, or change them.
- Click the calculate button to show the result block.
- Review ratios, downstream properties, and the chart.
- Export the current result as CSV or PDF.
Frequently Asked Questions
1. What does this moving shock calculator estimate?
It estimates shock-frame and lab-frame properties across a moving normal shock. Outputs include pressure, density, temperature, velocity, Mach numbers, total pressure ratio, and entropy change.
2. Why is the relative upstream Mach number important?
A compressive shock requires supersonic approach in the shock frame. If the relative Mach number is one or lower, the entered case does not form a normal shock under these assumptions.
3. What is the difference between lab frame and shock frame?
The lab frame measures gas motion against a fixed observer. The shock frame moves with the shock. Shock relations are applied in the shock frame first, then converted back.
4. Which assumptions are built into the model?
The model assumes one-dimensional flow, an ideal gas, a normal shock, and no friction or area change across the wave. Oblique shocks and chemical effects are excluded.
5. Why can downstream lab velocity increase?
The shock slows the gas in the shock frame, not always in the lab frame. If the shock itself moves quickly, converting back to the lab frame can produce a higher downstream velocity.
6. What does the total pressure ratio show?
It shows how much stagnation pressure remains after the shock. Values below one indicate irreversible losses caused by shock compression and entropy generation.
7. Can this page analyze oblique or detached shocks?
No. This page is limited to moving normal shocks. Oblique cases need flow deflection geometry, normal components, and additional relations beyond this simplified setup.
8. Which inputs influence results the most?
Shock speed and upstream velocity strongly change the relative Mach number. Pressure and temperature shape density and sound speed, while γ and R define gas response.