Reynolds Number
Ratio of inertial to viscous forces; characterises airflow over an airfoil.
Formula
Variables
Example
Model aircraft fly at low Reynolds numbers, so their airflow behaves quite unlike a full-size jet’s.
How it works
The Reynolds number compares the tendency of moving air to keep going because of its momentum with the tendency of the air to resist relative motion through internal friction. In the formula, density, speed, and a characteristic length increase the importance of inertial effects, while dynamic viscosity reduces it. For an airfoil, using the chord length gives a useful measure of how the flow will behave across the wing section, helping predict whether the boundary layer will be more likely to stay smooth or become turbulent.
When to use it
Use this when analysing aerodynamic similarity, estimating boundary-layer behaviour, or comparing how the same wing section performs at different speeds, sizes, altitudes, or fluids. It is especially useful in wind-tunnel testing, aircraft design, and scaling results from model aircraft to full-size vehicles.
Worked example, step by step
Given: density ρ = 0.91 kg/m^3, velocity v = 68 m/s, chord length L = 1.8 m, dynamic viscosity μ = 1.7 × 10^-5 Pa·s Step 1: Substitute into the Reynolds number formula: Re = (ρvL)/μ = (0.91 × 68 × 1.8) / (1.7 × 10^-5) Step 2: Multiply the numerator: 0.91 × 68 × 1.8 = 111.384 Step 3: Divide by the viscosity: Re = 111.384 / (1.7 × 10^-5) Step 4: Compute the result: Re ≈ 6.55 × 10^6 Final answer: Re ≈ 6.6 × 10^6 (dimensionless)
Common mistakes to avoid
- Using kinematic viscosity ν instead of dynamic viscosity μ without changing the formula
- Choosing the wrong length scale, such as wingspan instead of chord length for an airfoil problem
- Forgetting that Reynolds number is dimensionless and should not have units
Did You Know?
Insects, model planes, and airliners fly in vastly different Reynolds-number regimes, so their wings differ wildly.
Share this formula
More in Aviation & Aeronautics
View allTrue Airspeed (rule of thumb)
BasicQuick estimate: true airspeed increases about 2% per 1000 ft of altitude above indicated airspeed.
Ground Speed
BasicGround speed is true airspeed adjusted for the headwind/tailwind component.
Flight Time
BasicTime en route equals distance divided by ground speed.
Fuel Required
BasicTotal fuel needed is the fuel-burn rate multiplied by flight time.
Rate of Climb
BasicVertical speed is the altitude gained per unit time (ft per minute).
3-Degree Descent Rate
BasicOn a standard 3° glide path, required descent rate (fpm) is roughly ground speed (kt) times 5.