From: veritasium
Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium through which it is falling prevents further acceleration [00:05:05]. This occurs when the force of gravity pulling an object down is equal to the force of air resistance pushing it up [00:05:10]. Every object has its own terminal velocity, which is the maximum speed it will reach in free fall through still air [00:06:01].
Factors Affecting Terminal Velocity
The terminal velocity of an object is influenced by several factors:
- Weight: Heavier objects generally have higher terminal velocities [00:06:28].
- Air Resistance: The force of air resistance is proportional to the object’s speed squared [00:05:33] and directly proportional to the density of the air it is moving through [00:07:45].
- Cross-sectional Area: A larger cross-sectional area leads to greater drag [00:09:54].
- Shape/Drag Coefficient: The overall shape of an object determines how smoothly air flows around it, which is captured by a dimensionless number called the Drag Coefficient [00:15:38]. A lower drag coefficient indicates less resistance.
Objects and Their Terminal Velocities
Hammer vs. Feather
The classic experiment of dropping a hammer and a feather illustrates the significant role of air resistance:
- On the Moon: In the near vacuum of the Moon’s surface, both objects accelerate at the same rate due to the Moon’s gravity and hit the ground at the same time [00:04:37].
- On Earth: On Earth, the hammer lands much earlier than the feather [00:04:51]. The feather quickly reaches its terminal velocity and moves at a constant speed, while the hammer continues to accelerate [00:05:00]. Despite its faster speed, the hammer experiences a greater force of air resistance than the feather, but its much greater weight makes this drag negligible in comparison [00:05:30].
Pennies
The common myth about a penny dropped from the Empire State Building being deadly is incorrect due to air resistance [00:04:23].
- A penny weighs approximately 2.5 grams [00:00:39].
- Without air resistance, a penny dropped from the Empire State Building’s 443-meter height would reach over 300 kilometers per hour [00:00:45].
- However, pennies reach their terminal velocity after falling only about 15 meters [00:10:15].
- Their maximum terminal velocity is around 80 kilometers per hour (50 miles per hour) [00:10:05].
- At this speed, a falling penny delivers only about 0.2 Joules of kinetic energy [00:20:21].
- Pennies also flutter and tumble as they fall, exhibiting two different terminal velocities as they oscillate between falling on their face and on their edge [00:11:10].
- Dropping pennies from a helicopter showed they would sting but not be fatal [00:03:06].
People and Objects in a Wind Tunnel
Experiments in a vertical wind tunnel demonstrate how different objects behave based on their weight-to-drag ratio:
- Identical Balls with Different Weights: Two balls of the same size and shape, but one heavier due to added water, experience the same air resistance. The heavier ball has a higher terminal velocity and requires a higher wind speed to float [00:06:24].
- Person vs. Lacrosse Ball: Despite vastly different sizes, shapes, and weights, a person and a lacrosse ball can have the same terminal velocity [00:06:44]. This is because the ratio of their weight to air resistance is the same, allowing them to float together in the tunnel [00:06:56].
Felix Baumgartner (Stratosphere Jump)
Felix Baumgartner’s 2012 jump from 39 kilometers above sea level showcased the effect of air density on terminal velocity:
- In the thin air of the stratosphere, Baumgartner reached a terminal velocity over 1300 kilometers per hour (over 800 miles per hour) after just 40 seconds of free fall, becoming the first person to break the sound barrier without a vehicle [00:07:21].
- The air at that altitude is 60 times less dense than at sea level [00:07:49].
- As he fell into thicker atmosphere, his terminal velocity decreased, slowing to 200 kilometers per hour by 2.5 kilometers above sea level [00:07:54].
Raindrops vs. Hailstones
The terminal velocities of raindrops and hailstones differ significantly:
- Raindrops: Through the thicker air of the troposphere, raindrops (0.5 to 4 mm in diameter) have a low terminal velocity of just 25 kilometers per hour (15.5 miles per hour) [00:08:10]. They are generally spherical but flatter on the bottom [00:08:50]. If too large, they break into smaller droplets [00:09:02]. A raindrop delivers about 0.002 Joules of kinetic energy [00:20:17].
- Hailstones: Hail can reach terminal velocities of over 200 kilometers per hour (124 miles per hour), about 10 times that of rain [00:09:29]. While ice is slightly less dense than liquid water, hail can grow much larger, up to 20 centimeters in diameter [00:09:41]. Since drag scales with radius squared and weight scales with radius cubed, larger hailstones have higher terminal velocities and carry more kinetic energy [00:09:54]. A large hailstone can deliver over 80 Joules of kinetic energy [00:20:24].
Ballpoint Pens
Similar to pennies, the myth of falling ballpoint pens being lethal from a skyscraper is largely unfounded [00:13:30].
- Plastic pens weigh about twice as much as a penny and have a smaller cross-sectional area [00:13:44].
- However, they still have too much drag relative to their weight to achieve a high terminal velocity [00:15:31].
- Tests with ballistics gel dummies showed they did not penetrate or cause significant damage [00:14:04].
Bullets
Bullets are designed for low drag, but their behavior in free fall is counter-intuitive:
- Modern bullet shapes have a drag coefficient between 0.1 and 0.3, significantly lower than a sphere’s 0.5 [00:16:16].
- If dropped from a skyscraper, a bullet would tumble and likely fall on its side, experiencing far more air resistance [00:16:33].
- A bullet fired straight up will slow down, stop at its peak (up to 3 km high), and then fall back down [00:17:02]. It tumbles on the way down and is much slower than its launch speed upon impact [00:17:21].
- If a bullet is not fired completely vertically, it maintains horizontal velocity and spin from the gun barrel, keeping it pointed forwards. This allows it to speed up to a significant fraction of its launch speed, making celebratory gunfire dangerous [00:17:37].
Fléchettes and Lazy Dogs
These were military kinetic projectiles designed to be dropped from aircraft:
- Fléchettes: Small metal darts, up to 15 cm long, with feathers to ensure straight fall [00:18:21]. They were cheap, didn’t require explosives, and could pierce helmets, causing nasty injuries [00:18:48]. Some were reported to pass through a rider and his horse [00:19:00].
- Lazy Dogs: Similar but heftier weapons used in the Korean and Vietnam wars [00:19:16]. While their kinetic energy might not be enough to fracture a skull, their ability to apply a large force to a small area made them dangerous [00:20:40].
Lethality of Falling Objects
The energy required to fracture a human skull is around 68 Joules [00:20:07].
- Raindrop: 0.002 Joules [00:20:17].
- Penny: 0.2 Joules [00:20:21].
- Baseball / Large Hailstone: More than 80 Joules, enough to crack a skull [00:20:24].
- Measuring Tape: In 2014, a man was killed by a falling measuring tape from 50 stories up [00:20:31].
Objects that weigh a few grams and are not aerodynamic, like pennies and plastic pens, are not fatal [00:20:53]. However, objects weighing more than a few hundred grams traveling at their terminal velocity are likely to be deadly [00:20:58]. Falling objects cause nearly 700 American deaths annually, ranging from loose tiles and bricks to construction tools, rocks, branches, and icicles [00:19:37].