Terminal velocity (or limiting velocity) is the constant speed reached by an object falling through a fluid (air, water) when the resistance force of the fluid exactly balances the weight of the object. The acceleration then becomes zero and the motion becomes uniform.
Discover FizziQ
How to measure it in class
With the FizziQ app, it is possible to study the establishment of terminal velocity.
Steps:
- Film the fall of a light object (ping-pong ball, folded paper sheet, coffee filter)
- Use video tracking to measure successive positions
- Plot the velocity-time graph
- Observe the initial acceleration then the plateau (terminal velocity)
- Compare different objects (shape, mass) and observe the differences in v_t
- Measure v_t and verify the force balance
Scientific activities on this topic
- Fall with friction: https://www.fizziq.org/en/activities/ballistics-and-air-resistance/
- Comparison of different shapes
- Modeling air resistance
Learn more
Establishment of terminal velocity:
- At the beginning of the fall, v is approximately 0, so friction is weak
- The object accelerates under the effect of weight
- The more v increases, the more friction increases
- When mg = f_friction, acceleration becomes zero
- Velocity remains constant: this is terminal velocity
Friction model:
For moderate velocities: f = k x v (viscous friction) For high velocities: f = k x v^2 (turbulent friction)
Typical values:
| Object | Terminal velocity |
|---|---|
| Raindrop | 8 m/s |
| Ping-pong ball | 10 m/s |
| Skydiver (spread position) | 55 m/s |
| Skydiver (ball position) | 90 m/s |
| Open parachute | 5 m/s |
Formula
At terminal velocity, forces balance:
mg = f_friction
Turbulent model (v^2): f = (1/2) x rho x C_x x S x v^2
Therefore: v_t = sqrt(2mg / (rho x C_x x S))
where:
- v_t: terminal velocity (m/s)
- m: mass (kg)
- g: acceleration due to gravity (m/s^2)
- rho: fluid density (kg/m^3)
- C_x: drag coefficient (dimensionless)
- S: effective cross-section (m^2)
Application examples
- A skydiver reaches 200 km/h in vertical position, less than 20 km/h with open parachute
- Raindrops do not reach dangerous speeds thanks to their low mass
- Spores and pollen can remain suspended (very low v_t)
- Felix Baumgartner reached 1357 km/h in the stratosphere (very thin air)
FAQ
Q: Why do large objects fall faster than small ones? A: Mass increases faster than surface area (as r^3 vs r^2). The ratio mg/S increases, so v_t increases.
Q: How do you measure v_t with FizziQ? A: Film a sufficiently long fall. On the v(t) graph, v_t is the constant value reached after the acceleration phase.
Q: Does terminal velocity exist in a vacuum? A: No, without fluid there is no friction. The object accelerates indefinitely (or until reaching relativistic velocities).
Q: Why can a skydiver adjust their speed? A: By changing their position (effective surface area S), they modify friction and therefore their terminal velocity.
Related concepts
Free fall - Friction - Air resistance - Force balance - Uniform motion - Acceleration