Tracking Parachute-like Motion and Measuring the Terminal Velocity

Drag (or air resistance) is a type of friction, acting on moving object.

Here I suggest a simple experiment that shows how under the influence of the drag force, objects reach a constant velocity, and that this terminal velocity depends on the magnitude of the drag.

I used a "natural parachute" - Dandelion, Ragworts and Silybum's seeds, and TRACKER- the free video analysis tool.

Some seeds with pappus.

Tracker (download and install here. Or use online version here. I preferer the installed version).

Camera (A phone camera may also be suitable, instructions below), solid background, ruler.

Scissors.

Drag is the friction that act between an object and a fluid (air of liquid), and is opposite to the motion.

Unlike dry friction, which is almost independent of velocity, the drag force is proportional to the velocity for low-speed flow.

Parachute is a nice example:

• At the very first moment, its velocity is zero, therefor the drag is zero too, and the acceleration is g (free fall acceleration).
• Immediately afterwards, the velocity is already larger than zero and the drag increases with it.
• The acceleration is therefore now smaller than g, but the velocity continues to increase, and with it the drag, and acceleration continues to decrease.

So, like in a negative feedback loop, the velocity increases while the acceleration decreases. The process will end when the drag will be equal to the weight, and the acceleration will be zero. From this moment the parachutes keeps moving at a constant "terminal velocity".

Pappus is structure that appear in some kinds of flowers, that function as a wind-dispersal mechanism for the seeds.

The pappus may be composed of bristles or awns and function as a "parachute" which enables the seed to slow down its fall and to be carried by the wind.

Tracker is a free software that enable easy video analysis for use in physics education.

The "video analysis" that Tracker offer means tracking the motions of objects in videos, to obtain their 2-D position-time data and associated physical quantities such as velocity, acceleration, momentum and energy.

Using the Tracker, the movement of an object (or some objects) can tracked from the movie file, frame by frame.

The simplest way to use Tracker is by paying attention to how the movie is being taken:

• Try to place the camera stably and parallel to the plane of motion, so that the distance between the camera and the object is more or less constant.
• Try to use a solid background in a contrasting color to the object, to facilitate the identification of the object in each frame.
• You should add a "reference object" in the plane of motion that is a known size (a ruler can fit :-).
• If possible, use a high-sensitivity camera that will allow you to take pictures with a short exposure (long exposure of moving objects may "smears" the image).
• If your camera allows high frame rate shooting, you will have more data points on the timeline.

I captured several videos of a falling seed with its pappus.

I have tried some frame rates, some seeds type, three different cameras and white/black backgrounds. Actually, all conditions works more or less, so the experiment is easy to repeat, you just need to make sure the camera is stable and add a reference bar to the frame.

The embedded video shows one example of the tracking process.

The velocity of the seed grew as expected from the explanation in step1- velocity increases while acceleration decreases, till it reaches a constant speed.

If we go back to the "negative feedback loop" (step 1): What do we expect to happen if we reduce the drag?

The acceleration decrease to zero when the drag equal the weight, but if the drag increases slower, the velocity will reach a higher value before the acceleration is reset. e.g, we expect to get again a terminal velocity, but higher than the previous terminal velocity.

In order to check this hypothesis, I took the same exact seed and cut some of its pappi.

It now has pappus in a smaller radius so its friction with the air (drag) is smaller.

And the result, in the attached graphs: same functional behavior, but with higher terminal velocity.

For the "full pappus" case, I measured terminal velocity of about 0.13-0.14m/sec.

For the "half pappus" case, I measured terminal velocity of about 0.23 m/sec.

The required step now is to remove the parachute completely and try to measure a free fall, so I tried....

In this case I was able to follow the seeds for a shorter distance, because the fall became so fast that the image was "smeared". But it is certainly possible to see that the graph of high as a function of time is a parabola, that indicates a constant acceleration.

It is possible to fit the data within the Tracker itself and get the "free fall" acceleration from the parabola equation. As you can guess, the fall was not really "free" and I got different values for different kind of seed (some of then tended to roll over while falling, some where bigger and some were harder to detect), the values of accelerations That I extracted from the data varies between 6 to 9.4 m/s^2.

For the attached example, the acceleration value measured was 8.8 m/s^2. Not so bad for a home measurement done using a flower seed and a simple camera.

For all the measurements above, I used a constant mass. i.e. - in each set of measurements I used the same exact seed and only changed its "parachute".

But the terminal velocity also depends on the mass (try to figure it out from step 1...).

You may try to change the mass too (for example, cut part of the seed, or stick a piece of plasticine on it)