Skydivers have been jumping out of balloons and planes for over 200 years and no one has ever exceeded the speed of sound (about 340 m/s) while falling towards the Earth.

Why is this? One might think that since you can fall through the sky for miles your speed would continue to increase. Although this would be true in a vacumn, on Earth the air around us produces a drag force that opposes the gravitational forces. The drag force will increase as your velocity increases. As a result, you will reach a velocity where the total force acting on you is zero. From that point onwards, your velocity will be constant. This is known as terminal velocity.

For a person falling through the air the terminal velocity is typically around 55 m/s (125 m.p.h.). The greatest velocity ever achieved during a parachute jump was by Joseph Kittinger, who achieved an estimated velocity of 274 m/s (614 m.p.h.) when leaping from a balloon that was at 103,300 feet. He was able to achieve this high velocity since air is very thin at that great altitude (and it is also very cold!). Very few people jump from such an extreme altitude.

Terminal Velocity

Let us bring this discussion of terminal velocity to the real world. Can you think of many examples of terminal velocity that you can see in the classroom? One very simple one is the fall of a coffee filter through the air. When you drop one, does it seem to move at a rather constant velocity? Or, does it keep moving faster and faster as it heads toward the ground? How do the leaves fall off trees? Does their velocity increase as they fall, or do they just "float" toward the ground (at a constant velocity).

When you release the coffee filter it must accelerate at some point in the fall, since when you first let go of the coffee filter it has no velocity but very soon after its release it will have a velocity. Since acceleration is the change in velocity, the coffee filter has accelerated. But after a second or so, the coffee filter will be falling at a constant velocity (there will be no further change in velocity). This means that the acceleration has dropped to zero.

What about more massive objects, such as bricks, people, and desks? Massive items will reach a terminal velocity as well, but at a higher speed after a longer fall.

Freefall Lab

Let us try to use the Freefall Lab to study terminal velocity with a simple simulation you can do in your home or classroom. You will need four pennies and a balloon. To start, place all four pennies inside the balloon. Do not inflate or tie the balloon. The mass of each penny is about 2.5 grams, and the balloon is probably less than 1 gram. The total mass should be around 10 grams. The radius of the non-inflated balloon is rather small (we can use a value of 1 cm for the radius). Drop the non-inflated balloon to the ground from a height of 2 meters (about six and a half feet).

How long did the balloon take to reach the ground? Did it seem to slow down or reach a terminal velocity (a constant velocity) as it dropped? Now go ahead and leave the four pennies in the balloon, but inflate the balloon. Measure the radius of the inflated balloon. Go ahead and drop the balloon from the same 2 meter height. Did it take the balloon longer to reach the ground? Did the balloon reach a terminal velocity?

With some basic laboratory equipment you could measure the time required for the fall, the position of the balloon as a function of time, etc., but in this case we will use the Freefall Gizmo. After setting the mass toballoon. The graph of position, velocity, and acceleration are shown in Figure 1. Each graph provides a wealth of information.

Looking at the graph of velocity you can see that the velocity continues to increase in a relatively linear fashion throughout the entire fall. The acceleration (which is the change in the velocity) is almost a constant value during the fall. It is apparent that the non-inflated balloon has not reached a terminal velocity.

Now go ahead and change the radius to represent the inflated balloon (in this case we use a value of 10 cm or 0.10 m). The balloon may have a slightly greater mass when filled with air (remember that each cubic meter of air has a mass of about 1.2 kg!). Release the ball in the simulation. Do you notice a significant difference in the graphical results? Did the object take longer to reach the ground? Did the acceleration reach zero? Was the velocity constant at any time?

When looking at the velocity vs. time graph in Figure 2 you can see that the velocity increased in a linear fashion after the release of the ball but after a short time began to flatten out and did not change for the remainder of the fall. The time the balloon reached terminal velocity is indicated in the graph.

Continued Investigations

Did the simulation match your observations? How does this relate to trying to break the sound barrier with a high altitude jump? With the non-inflated balloon, would it reach a terminal velocity if you dropped it from a higher initial height? Feel free to adjust the other parameters in the simulation to see how they influence the plots of velocity vs. time. Remember that an object will not fall to the ground if its density (mass per unit volume) is less than that of air (or the medium that the object is passing through).

In-Depth Information

Speed of a Skydiver
"No wind whistles or billows my clothing. I have absolutely no sensation of the increasing speed with which I fall. [The clouds] rushed up so chillingly that I had to remind myself they were vapor and not solid."

Current News

Terminal Velocity
"Strapped to a chair, constricted by a $3 million suit specially designed and built for the highest leap ever attempted, the aeronaut heads for the top of a 130,000-foot virtual diving platform. At that altitude, the balloon can go no higher, so he gets ready to cut loose and take a belly flop plunge. "