Table of Contents
What Is Terminal Velocity?
Terminal velocity is the maximum speed a falling object reaches when the drag force equals its weight. At this point, the net force is zero and acceleration ceases. The object continues to fall at a constant velocity. Every object falling through a fluid (air, water, etc.) will eventually reach terminal velocity if it falls long enough.
A skydiver in a belly-down position reaches terminal velocity of about 195 km/h (120 mph) after roughly 12 seconds of free fall, covering about 450 meters. In a head-down position, terminal velocity increases to about 290 km/h (180 mph) due to the smaller cross-sectional area.
Terminal Velocity Formula
where m is mass, g is gravitational acceleration (9.81 m/s²), ρ is fluid density, Cd is drag coefficient, and A is cross-sectional area.
Terminal Velocities of Objects
| Object | Terminal Velocity | Cd |
|---|---|---|
| Skydiver (belly-down) | ~195 km/h | 1.0 |
| Skydiver (head-down) | ~290 km/h | 0.7 |
| Baseball | ~150 km/h | 0.3 |
| Golf ball | ~110 km/h | 0.25 |
| Raindrop (4mm) | ~30 km/h | 0.45 |
Factors Affecting Terminal Velocity
- Mass: Heavier objects have higher terminal velocities (Vt proportional to sqrt of mass).
- Shape: Streamlined shapes (low Cd) fall faster than blunt shapes.
- Area: Larger cross-sections increase drag and reduce terminal velocity (parachute principle).
- Altitude: Air density decreases with altitude, increasing terminal velocity at high elevations.
Frequently Asked Questions
How long does it take to reach terminal velocity?
A skydiver reaches about 99% of terminal velocity in roughly 15 seconds, after falling about 500 meters. The approach is asymptotic - the object never truly reaches exactly terminal velocity but gets arbitrarily close. The time constant depends on the ratio of mass to drag parameters.
Does terminal velocity change with altitude?
Yes. Air density decreases with altitude. At 10,000 meters, air density is about 0.41 kg/m3 (vs 1.225 at sea level), so terminal velocity is about 73% higher. This is why Felix Baumgartner reached over 1,300 km/h during his stratospheric jump.
Can terminal velocity exceed the speed of sound?
In principle, yes. If an object is heavy enough and the air is thin enough (high altitude), terminal velocity can exceed the speed of sound (~343 m/s at sea level). Baumgartner broke the sound barrier during free fall from 39 km altitude in 2012.