Critical Mach Number Calculator

Critical Mach Number:

\[ M_{cr} = \frac{1}{\cos \Lambda} - \frac{t/c}{\cos^2 \Lambda} - \frac{C_{L}}{10 \cos^3 \Lambda} \]

Wing Sweep Angle (Λ):

degrees

Thickness-to-Chord Ratio (t/c):

(dimensionless)

Lift Coefficient (C_L):

(dimensionless)

Critical Mach Number (M_cr):

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1. What is Critical Mach Number?

The Critical Mach Number (M_cr) is the freestream Mach number at which the airflow over an aircraft first reaches Mach 1 at some point on the airframe. This marks the onset of transonic effects and is a crucial parameter in aircraft design.

2. How Does the Calculator Work?

The calculator uses the following equation:

\[ M_{cr} = \frac{1}{\cos \Lambda} - \frac{t/c}{\cos^2 \Lambda} - \frac{C_{L}}{10 \cos^3 \Lambda} \]

Where:

\( \Lambda \) — Wing sweep angle (degrees)
\( t/c \) — Thickness-to-chord ratio (dimensionless)
\( C_{L} \) — Lift coefficient (dimensionless)

Explanation: The equation accounts for the effects of wing sweep, airfoil thickness, and lift coefficient on the onset of transonic flow.

3. Importance of M_cr Calculation

Details: Knowing the critical Mach number helps aircraft designers optimize airfoil shape and wing sweep to delay the onset of shock waves and associated drag rise.

4. Using the Calculator

Tips: Enter wing sweep angle in degrees (0-90), thickness-to-chord ratio (typically 0.08-0.15 for transonic aircraft), and lift coefficient (typically 0.2-0.6 for cruise conditions).

5. Frequently Asked Questions (FAQ)

Q1: Why is M_cr important in aircraft design?
A: It determines the speed at which drag begins to increase rapidly due to shock wave formation, affecting fuel efficiency and performance.

Q2: How can I increase the critical Mach number?
A: By increasing wing sweep, reducing airfoil thickness, or decreasing lift coefficient (reducing angle of attack).

Q3: What's the difference between M_cr and M_dd?
A: M_cr is when local flow first reaches Mach 1, while M_dd (drag divergence Mach number) is when drag increases significantly.

Q4: How accurate is this calculation?
A: It provides a good estimate but wind tunnel testing or CFD is needed for precise values on complex aircraft geometries.

Q5: What are typical M_cr values for commercial jets?
A: Modern airliners typically have M_cr around 0.75-0.85, allowing efficient cruise at Mach 0.78-0.86.