Free Fall Air Resistance
Calculate free fall with air resistance using mass, height, gravity, and drag coefficient k. Get terminal velocity, time of fall, impact speed, and drag force with interactive physics charts.
About This Calculator
The Free Fall with Air Resistance Calculator computes the motion of an object falling under gravity while experiencing aerodynamic drag. Unlike ideal free fall where only gravity acts, real-world falling objects — from skydivers to raindrops — encounter air resistance that opposes their motion. This calculator uses the standard drag force equation F = kv² to model the non-linear effects of air resistance.
The calculation solves the differential equation of motion m·dv/dt = mg − kv² analytically. The terminal velocity vt = √(mg/k) represents the speed at which drag balances gravity. The time to fall a given height is computed from the position equation y(t) = (vt²/g)·ln(cosh(g·t/vt)). The velocity vs time and position vs time charts show the complete trajectory, illustrating how the object accelerates rapidly at first then asymptotically approaches terminal velocity.
Regional Notes
International (SI): Use mass in kg, height in meters, gravity = 9.80665 m/s². Default k = 0.24 kg/m for a typical skydiver.
United States (imperial): Enter mass in kg (convert lb ÷ 2.205), height in meters (convert ft ÷ 3.281), or switch gravity to 32.174 ft/s² and interpret results accordingly.
United Kingdom: Follow SI conventions. Gravity = 9.80665 m/s² on Earth. Adjust k for regional air density (UK standard ≈ 1.225 kg/m³ at 15°C).
Frequently Asked Questions
What is free fall with air resistance?
Free fall with air resistance accounts for drag force opposing gravity. Unlike ideal free fall where only gravity acts, real falling objects experience air drag proportional to velocity squared, reducing acceleration until terminal velocity is reached.
How does air resistance affect falling objects?
Air resistance slows the acceleration of falling objects. Initially objects accelerate at g = 9.81 m/s², but as speed increases, drag force grows until it balances gravity, resulting in constant terminal velocity.
What is terminal velocity and how is it calculated?
Terminal velocity is the constant speed reached when drag force equals gravitational force. It is calculated as vt = sqrt(mg/k), where m is mass, g is gravity, and k is the air resistance coefficient.
How is the drag coefficient k determined?
The air resistance coefficient k = ρAC/2, where ρ is air density (typically 1.225 kg/m³ at 15°C), A is cross-sectional area, and C is the dimensionless drag coefficient (e.g., 0.47 for a sphere, 1.0 for a skydiver horizontal). A typical k value for a skydiver is 0.24 kg/m.
What is the difference between maximum velocity and terminal velocity?
Terminal velocity is the theoretical steady speed an object would reach after falling long enough. Maximum velocity is the actual speed achieved at impact. If the fall is high enough, maximum velocity equals terminal velocity. For shorter falls, maximum velocity is lower.
How does a parachute change air resistance during free fall?
A parachute drastically increases the cross-sectional area A and drag coefficient C, which increases k. This reduces terminal velocity from about 55 m/s (200 km/h) to roughly 5-7 m/s (18-25 km/h), enabling a safe landing.
Does altitude affect air resistance in free fall?
Yes, air density decreases with altitude, reducing the drag coefficient k. At higher altitudes, air resistance is lower, resulting in higher terminal velocity. This is why skydivers fall faster at high altitudes before denser air slows them down.
Is this calculator suitable for engineering and physics students?
Yes, it is designed for physics students, engineers, and anyone studying kinematics. The velocity vs time and position vs time charts help visualize how drag affects free fall dynamics step by step.