The Difference Between Terminal Velocity and Free Fall

Sky divers

Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. She has taught science courses at the high school, college, and graduate levels.

Terminal velocity and free fall are two related concepts that tend to get confusing because they depend on whether or not a body is in empty space or in a fluid (e.g., an atmosphere or even water). Take a look at the definitions and equations of the terms, how they are related, and how fast a body falls in free fall or at terminal velocity under different conditions.

Terminal Velocity Definition

Terminal velocity is defined as the highest velocity that can be achieved by an object that is falling through a fluid, such as air or water. When terminal velocity is reached, the downward force of gravity is equal to the sum of the object’s buoyancy and the drag force. An object at terminal velocity has zero net acceleration.

Terminal Velocity Equation

There are two particularly useful equations for finding terminal velocity. The first is for terminal velocity without taking into account buoyancy:

  • Vt is the terminal velocity
  • m is the mass of the object that is falling
  • g is acceleration due to gravity
  • Cd is the drag coefficient
  • ρ is the density of the fluid through which the object is falling
  • A is the cross-sectional area projected by the object

In liquids, in particular, it’s important to account for the buoyancy of the object. Archimedes’ principle is used to account for the displacement of volume (V) by the mass. The equation then becomes:

Free Fall Definition

The everyday use of the term “free fall” is not the same as the scientific definition. In common usage, a skydiver is considered to be in free fall upon achieving terminal velocity without a parachute. In actuality, the weight of the skydiver is supported by a cushion of air.

Freefall is defined either according to Newtonian (classical) physics or in terms of general relativity. In classical mechanics, free fall describes the motion of a body when the only force acting upon it is gravity. The direction of the movement (up, down, etc.) is unimportant. If the gravitational field is uniform, it acts equally on all parts of the body, making it “weightless” or experiencing “0 g”. Although it might seem strange, an object can be in free fall even when moving upward or at the top of its motion. A skydiver jumping from outside the atmosphere (like a HALO jump) very nearly achieves true terminal velocity and free fall.

In general, as long as air resistance is negligible with respect to an object’s weight, it can achieve free fall. Examples include:

  • A spacecraft in space without a propulsion system engaged
  • An object thrown upward
  • An object dropped from a drop tower or into a drop tube
  • A person jumping up

In contrast, objects not in free fall include:

  • A flying bird
  • A flying aircraft (because the wings provide lift)
  • Using a parachute (because it counters gravity with drag and in some cases may provide lift)
  • A skydiver not using a parachute (because the drag force equals his weight at terminal velocity)

In general relativity, free fall is defined as the movement of a body along a geodesic, with gravity described as space-time curvature.

Free Fall Equation

If an object is falling toward the surface of a planet and the force of gravity is much greater than the force of air resistance or else its velocity is much less than terminal velocity, the vertical velocity of free fall may be approximated as:

  • vt is the vertical velocity in meters per second
  • v is the initial velocity (m/s)
  • g is the acceleration due to gravity (about 9.81 m/s 2 near Earth)
  • t is the elapsed time (s)
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How Fast Is Terminal Velocity? How Far Do You Fall?

Because terminal velocity depends on drag and an object’s cross-section, there is no one speed for terminal velocity. In general, a person falling through the air on Earth reaches terminal velocity after about 12 seconds, which covers about 450 meters or 1500 feet.

A skydiver in the belly-to-earth position reaches a terminal velocity of about 195 km/hr (54 m/s or 121 mph). If the skydiver pulls in his arms and legs, his cross-section is decreased, increasing terminal velocity to about 320 km/hr (90 m/s or just under 200 mph). This is about the same as the terminal velocity achieved by a peregrine falcon diving for prey or for a bullet falling down after having been dropped or fired upward. The world record terminal velocity was set by Felix Baumgartner, who jumped from 39,000 meters and reached a terminal velocity of 1,341 km/hr (834 mph).

Distance and Time to Reach Terminal Velocity While Skydiving

Falling At Terminal Velocity

Skydiving is an adrenaline pumping and fun activity specifically due to the awesome feeling of falling at terminal velocity through the air. As people often lose perspective for distances and time when skydiving, the question arises what distance and time are needed to reach terminal velocity.

A typical skydiver on a belly-to-earth position will reach terminal velocity at a speed of approximately 120 mph (193 km/h) after 12 seconds of freefall and a fallen distance of 1,500 feet (450m). Skydivers can also attain higher speed and distance depending on the following four factors.

The Four Factors That Determine The Terminal Velocity (And How To Manipulate Them)

How The Jump Height Defines Terminal Velocity For Skydivers

The first important factor is jumping altitude. In theory, it should hold true that the higher the jumping altitude is, the longer the freefall and the higher the terminal velocity will be.

In practice, however, normal skydives are not likely to recognize this effect.

For example, the normal skydiving altitude for beginners is between 10,000-15,000 feet which will allow the jumper between 30-60 seconds of free fall. The skydiver is expected to reach a terminal velocity of 127.893 mp/h (206 km/h) after 12 seconds and a fallen distance of 1,500ft (450 m).

In comparison, experienced divers can go as high as 16,000 feet without oxygen support and would be able to enjoy at least 70 seconds of freefall. Despite the higher jumping altitude, they would only reach a terminal velocity of 127.894 mp/h which will not feel any different to 127.893 mp/h.

If skydivers want to reach higher speeds, they can either change their body position or they can increase their jump height tremendously by performing a so-called HALO jump.

A HALO jump classifies a jump with an altitude above 30,000 feet. This is so high that the skydiver will require special equipment for breathing and navigating.

Skydivers reach a higher terminal velocity during a HALO jump not only because of a longer free fall but also because of less air resistance. Air resistance is the force that works contrary to the gravitational pull of the earth i.e. it limits the terminal velocity skydivers can reach. (I will explain this relationship in more detail later in this post.)

Because air density decreases with increasing altitude skydivers will face less air resistance when jumping from 30,000 ft than from 10,000 ft. As a result, they will accelerate faster and to a higher terminal velocity. However, skydivers really need to increase their height by huge distances in order to recognize an effect.

On 24 October 2014, at the age of 57, Google’s Senior Vice President Alan Eustace set a new exit altitude record of 135,898ft (41,422 m) above Roswell, New Mexico, USA. As normal planes do not fly this high, he reached the desired altitude with the help of a helium-filled balloon.

Once he reached his desired altitude, he detached himself and fell to the earth at a speed of 808 mp/h (1,300km/h). The increased jump height together with less air resistance helped him to accelerate to this speed and to achieve the highest and longest free fall in human history (4 minutes and 27 seconds).

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If you want to achieve higher terminal velocity you “just” need to jump from a much higher altitude! If you are interested in knowing more about the biggest altitude that humans can jump from (including whether we can jump from space), check this post.

How The Jumpers Weight Impacts How Fast You Can Fall

The overall weight of the skydiver (i.e. weight of the jumper + skydiving equipment) also increases the maximum achievable terminal velocity.

The average skydiving equipment weighs 55 pounds (25 kg). If the skydiver weighs 175 pounds (80 kg), his overall weight will be 230 pounds (105 kg). As a result, he will be able to achieve a terminal velocity of 147 mp/h (235 km/h) after 13-14 seconds of free fall and after a fallen distance 1,700ft (540 m).

In contrast, a skydiver who weighs 220 pounds (100 kg) will be able to reach a terminal velocity of 160 mp/h.

In order to leverage this effect, small skydivers sometimes choose to wear weight belts that will increase their speed. More specifically, during formation jump, it is really important that the skydivers fall at the same speed – otherwise, it would be nearly impossible to grab each other and to stabilize the formation during the fall. As a result, skydivers need to wear weight belts in order to have the same weight.

In competitions like speed skydiving, the jumper’s weight will also matter since the goal is to achieve and maintain the highest possible terminal velocity over a given distance.

Most skydiving centers in the US set their weight limit at 240 pounds for solo jumps and at 220 – 250 pounds for tandem jumps. If you are overweight and want to perform a tandem jump, I have written a post that explains the weight limits and presents ways to jump even if you exceed those limits. You can find the post here.

How You Can Play Around With Your Falling Position To Be Faster

The third factor that defines the terminal velocity of skydivers is their position in the air. If skydivers fly in a head-down or feet-down position they have much less air resistance than in a belly-to-earth position.

The different positions can result in a speed difference of up to 40 mp/h (65 km/h).

If you are beginner, you need to start with a stable belly-to-earth position and slowly experiment with movements in the air. Once you have performed enough jumps, you can move to the feet-down position and finally to the head-down position. It is important to progress slowly here as any mistake can result in a wrong parachute deployment.

In competitions and formation jumps, skydivers often fly in a vertical position because it is essential to track through the air.

For example, on 31 July 2015, 164 skydivers broke the head down world record in Illinois. They fell at a speed between 190-240 mph and formed a vertical head down formation in the shape of a giant flower at a jump height of 19,700 feet.

Why You Should Choose Good Weather Condition To Jump

Last but not least: weather conditions. Depending on the weather conditions, skydivers will again face a different air density and air resistance. Hotter air for example is less dense than cold air. Therefore, skydivers cut through hot air more easily and reach a higher terminal velocity.

In addition, skydivers can avoid jumping in areas of ascending wind. Ascending wind does not only slow you down but is quite unpredictable and therefore dangerous.

You can achieve a higher terminal velocity if you jump during warm weather. However, this effect is probably too small to be noticed.

The Underlying Physical Forces of Terminal Velocity

If you are interested in understanding why the four factors determine the terminal velocity, I explained the physical mechanisms below.

Air drag – sometimes called air resistance, it is a force acting upon the opposite of a solid object. When there’s air resistance, heavy objects will have a higher terminal velocity than light objects. When a skydiver jumps from an airplane there is no air drag force yet. He will continue to accelerate to higher speeds until he encounters an amount of air resistance that is equal to his weight.

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Gravity – is the universal force that attracts objects to each other (i.e. to the center of the earth). The downward force of gravity remains constant regardless of the velocity at which the object is moving but increases with increases proximity. As the skydiver speeds up and comes close to the earth, he will experience a larger force of gravity that pulls him down and makes him fall faster.

Air Drag Force = Force Of Gravity
When the air drag force is equal to the force of gravity, the object reaches zero acceleration and falls into terminal velocity.

For skydivers, achieving a state of zero acceleration does not feel like falling but actually floating or even flying through the air. It is one of the feelings that skydivers enjoy most besides the breathtaking and majestic view.

What Is The Terminal Velocity On A Skydive Tandem Jump

During tandem jumps, we need to take into account the combined weight of the jumper and the instructor since each skydiving company has different weight limits. For example, a 165 lbs (75 kg) jumper with an instructor of the same weight at a jump altitude of 10,000ft will reach a terminal velocity of 170 mph.

If the same jumper jumped with an instructor that weighs 209 lbs (95 kg), he would achieve a speed of 270 mph and would experience a free fall of between 30-60 seconds.

If you perform a tandem jump, you will be much faster than during a solo jump due to the increased weight.

What Is The Highest Recorded Falling Speed Of A Human?

On 14 October 2012, at the age of 43, Austrian daredevil Felix Baumgartner broke the World’s record by becoming the first skydiver to reach a supersonic speed of 843.6 mph (1,357.6 km/h) and by becoming the first human to break the sound barrier (768 mph; 1,235.98 km/h;) in freefall.

He was able to achieve a speed much higher than the normal terminal velocity of a skydiver due to the much higher height and because of less air resistance at the exit altitude of 127,852ft (38,969.4 m).

This jump is not something that will be easily repeated. The Red Bull Stratos Project took five years of preparation including developing new equipment, finding the best jumping spot and training physically for the extreme conditions of the jump.

During this jump, Felix Baumgartner smashed eight world records in a span of three hours. His free fall lasted for about 4 minutes and 20 seconds and the whole journey took 9 minutes and 9 seconds.

Enjoy your free fall!

Hi, I’m Kai. The first time I jumped out of an airplane and experienced free fall was one of the most amazing moments of my life. For me, skydiving does not only stand for freedom and independence but being present in the moment and being respectful to others and oneself. Now I want to share what I’ve learned with you.

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ABOUT ME

Hi, I’m Kai. The first time I jumped out of an airplane and experienced free fall was one of the most amazing moments of my life. For me, skydiving does not only stand for freedom and independence but being present in the moment and being respectful to others and oneself. Now I want to share what I’ve learned with you.

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