I’m not a physics guy, but with all the discussion around the disaster in Oklahoma recently it had me pondering a terminal velocity question. From what I understand, any object with mass would possess a terminal velocity.
Since air has mass, what would be the terminal velocity of air? Specifically, how fast can a tornado/hurricane/natural disaster hurl air before it reaches a terminal velocity?
—Question submitted by Josh from Canada
The term terminal velocity has to do with an object moving through a fluid such
as air, water, honey, etc. Imagine, for example, taking a small steel ball and dropping
it from the top of the Empire State Building. There will be a force on the ball due
to the Earth’s gravity which will cause it to accelerate downward.
But there’s also some air resistance, which is a force due to the air having to flow around the ball as it falls. This force of air resistance acts opposite the direction of gravity (upward).
Experimentally, we find this resistive force is proportional to the square of the ball’s speed, so the faster the ball falls, the greater the force of air resistance, which decreases
the ball’s acceleration. Eventually the upward resistive force becomes large enough
that it balances the downward gravitational force, and the ball stops accelerating—it
just continues to fall downward, at a constant speed called the terminal velocity.
Image Credit: Proskydiving
This phenomenon is familiar to sky divers.
When a sky diver jumps out of an airplane,
he begins to accelerate toward the ground, but will eventually reach a terminal
velocity (in the “spread eagle” position) of around 100 miles per hour due to air resistance.
The terminal velocity depends on the sky diver’s cross-sectional area, so if he
sees another sky diver below him who is in trouble, he can put himself in a vertical position
(presenting a small area to the wind), which increases his terminal velocity and
allows him to catch up to and rescue the other sky diver.
Deploying a parachute greatly
increases the sky diver’s cross-sectional area and results in a small terminal velocity
(maybe 15 miles per hour or so), allowing him to land safely.
The same thing happens with rain drops. If it weren’t for air resistance slowing
them down, rain drops would hit the Earth with a lethal speed of several hundred miles
per hour, and every rain storm would be like a shower of bullets. Luckily, as rain drops
fall through the air, the air resistance causes them to stop accelerating when they reach
a gentler terminal velocity of around 15 miles per hour.
Thicker fluids result in smaller terminal velocities than thinner fluids like air. For
example, if you drop a steel ball in honey, the large resistive force will balance the
gravitational force very quickly, and the ball will fall through the honey with a very
slow terminal velocity.
Since the terminal velocity is the velocity of a body moving through a fluid, it
makes no sense to talk about the terminal velocity of the fluid itself (such as air). From
a point of view of simple physics, there’s no clear theoretical upper limit to the speed
at which air can move, other than the speed of light. In the real world, meteorological
conditions on the Earth govern how fast winds can be. The fastest winds on Earth are
those found in tornadoes, and have been measured in excess of 300 miles per hour.
David G. Simpson
NASA Goddard Space Flight Center