Three Phases of Sky Diving
INQ-250PH: The Way Things Work
24 February 2014
Lydia Delamatta, Kristen Emrich, Samantha Garst, Casey Miller
I. Purpose of Project
The purpose of this project is to construct a number of experiments that will determine
the three phases of motion of a skydiver (e.g. freefall, terminal speed, and motion with a
parachute). To measure the phase of free falling, we propose a series of trials where we vary the
height from which we drop an object. During this we will keep measurements of height and time.
During the next phase, we will measure and analyze a series of trials that will have objects reach
the point of terminal velocity. We propose that a continuation of the first experiment will ensure
that we will reach a certain height that when the object is dropped, it will finally reach a terminal
speed at a specific time. For the final phase (motion with a parachute) we will be measuring the
effect of the surface area of the parachute. By varying the size of the parachute, and dropping an
attached object from a predetermined height, we will record the time it takes for the object to hit
the floor.
II. Description of Investigation
Overall, knowing our goal for the project, it is also important to better understand the
background for this experiment. We are learning about the three phases of a skydiver. The Free
falling stage is where we can observe how the forces of gravity acts on the velocity of a falling
object. The second phase, terminal speed (velocity reaches its highest value and remains
constant), is the phase that illustrates the correlation between balanced forces of gravity and air.
And finally, the third phase is observing motion with a parachute, which breaks the speed of
gravity, and makes the force pulling up (air) a bit greater, thus slowing the skydiver down.
Phase One: Free Fall
During Phase 1, in order to measure free fall, we decided to measure the velocity of a
constant object affected by differing heights. Our four different heights were 0.5m, 1.0m, 1.5m,
and 1.75m. Our constant object was a creation of a small metal ball taped to the top of a
shredded parmesan cheese container. This object would be consistent throughout the three
phases and be easily attached to the parachute to minimize any uncertainty when it came to our
data. For example, if we had used a different object throughout the three phases, we might have
had to debate whether a change in mass would affect our additional results. To measure the
position, time, and velocity of the object as it fell we placed a motion sensor atop the
predetermined height and measured the path of the ball downwards. All data was recorded by the
software DataLogger in the lab. We hypothesize that with a greater height, the object will have a
greater average velocity.
Phase Two: Terminal Speed
During Phase Two, we sought to mimic the first phase, by measuring the velocity of the
object as it moved downward. Our four different heights were again, 0.5m, 1.0m, 1.5m, and
1.75m. At first, our object remained constant. However, we soon found that we could not drop
the object from a height high enough to mirror the process of terminal velocity. Although we
could have found a way to increase the height, we understood that we would then not be able to
accurately use the motion sensors. Therefore, instead of differing the height, we decided to be
innovative with our object. For the object to reach a constant velocity, we had to add a piece of
cardboard under our object (laying horizontally affixed to the bottom). This was in the hope that
by increasing the surface area of the object, we would be able to measure terminal speed from a
lower height. We hypothesize that with the addition of a greater surface area, we will be able to
reach terminal velocity.
Phase Three: Drag Force
Our third and final phase was seeking to measure drag force. Therefore, in order to do so,
we dropped three differently sized parachutes at the same height of 5.18 meters (17 feet) and
measured the time it took to hit the ground. We built a series of parachutes out of nylon sports
cloth by assembling 12 equilateral triangles with tape. On the inside of the parachute, we affixed
popsicle sticks to the outside of the hexagon shape so that our parachute would maintain that
shape throughout the fall and take full advantage of the surface area. We varied the sides of the
triangles for the three parachutes with 0.15 m, 0.20 m, and 0.25 m, respectively. The surface area
for each hexagon was: (small) 0.0584 m2, (medium) 0.102 m2, and (large) 0.1623 m2. To the
outer triangles, attached to the border of the hexagon, we attached string to a rubber band that we
could stretch to fit around our object. We hypothesize that with a greater surface area, the object
will have a longer time to impact than with a smaller surface area.
III. Data and Graphs
Phase One: Free Fall
During Free Fall we wanted to test how objects fall when the only focus is position and
time. We took the average of all of our
trial runs to create a position vs. time
graph for our object at height one meter.
You can see that we added a
trend line to determine what the slope of
the line is. Since the slope is 0.1437 we
know that the velocity vs. time graph will display a horizontal line with velocity at 0.1437m/s.
The last conclusion we can draw from this graph is that acceleration is 0m/s2 since velocity is
constant and has no slope.
The next two graphs will represent the Position-Time graph for our object at height 1.5m
and height 1.75m. After each graph is a short sentence describing velocity and acceleration for
the respective graph.
The slope for this graph is m=0.1781. Then the Velocity-Time graph will be a horizontal
line at Velocity equal to 0.1781m/s.
The acceleration is m/s2 since the
velocity-time graph has no slope.
Here we see a slope of 0.3675
which gives us a constant velocity
represented by a horizontal line at
velocity equal to 0.3675m/s. The
acceleration would again be 0m/s2
since there is no slope on the
velocity-time graph.
From phase 1 we can conclude that as
height increases the slope of the
position-time line will increase as well giving us a greater average velocity.
Phase Two: Terminal Speed
An object will reach terminal speed when the velocity plateaus due to the drag force
equaling the force of gravity. We increased the surface area of our object so that the drag force
would increase by attaching a piece of cardboard. We hoped to determine if the object could
reach terminal velocity.
Below are the graphs
of the data that we collected.
While we found that our
object of 43.7g did reach
terminal velocity when
dropped from a height of 1m, 1.5m and 1.75m. As we analyzed our data we determined a few
things. First, our variant was
height and since our object
reached terminal velocity at 1
meter, there was no additional
information that we could
gather from increasing our
height. Instead, we should have
intentionally varied the mass of the object to determine the differences that mass makes on
reaching terminal velocity. We
did, inadvertently do this with
our height of 1.5m and 1.75 m
(graphs on next page).
We conducted these experiments on
different days and our object had been
altered by adding significant amounts
of glue and tape. The graphs reflect
that when the mass is greater, terminal
velocity is reached later than an object
with a smaller mass (assuming all other factors are equal).
We also concluded that the
slope of the first portion of the
velocity-time graph should be the same
for an object where the only variation
is the height from which it was
dropped. However, this was not the
case in our study. The slope of the first
portion of the graph at 1 meter is 0.4812 while the slope of the velocity -time graph at 1.5 meters
is 1.2397.
After coming to these conclusions
we would have changed the following:
(1) Varied mass of object keeping
surface area the same instead of height
(2) Conducted more runs for each object
to find a more accurate average
Phase Three: Drag Force
We wanted to see how surface area impacts drag force and speed of an object falling so
we built three parachutes and dropped them from a height of 5.18 meters. Below is a table of our
results. There were two
trial runs from each
parachute that we
determined were outliers
because they hit the wall
or flipped over. However,
the data including and
excluding the outliers remain pretty consistent. The trend that we noticed is that an object
attached to a smaller parachute takes less time to reach the ground due to the smaller surface
area. As the parachute size increased, the surface area, increased, and as a result the time that it
took to reach the ground decreased. The masses of the parachutes varied slightly but didn’t seem
to alter our finding significantly. Had we been measuring drag force on the parachute, this would
have been more of a consideration but since Fdrag = Fgravity and since Fgravity = mg the smaller
parachute (with less mass) would mean that the drag force would not need to be as high as it
would for our largest parachute.
IV. Conclusions of Phases/Discussion of Results (Sam)
During the first testing phase, we were measuring both height, position, and time as we
dropped a ball. After testing, we concluded that with a greater height, the higher the slope of the
position-time graph would be. In simple terms, we understand that a taller height will correlate
with a higher average velocity. What is important, however, is not to assume that the object is
falling at a faster rate. The constant velocity tells us that the acceleration of the object is zero. In
the act of free fall, a person’s acceleration will decrease until it reaches zero. Therefore, in this
phase, we are slowly approaching the terminal velocity.
In our second phase, we came to two conclusions: (1) when the mass of the object is
greater, it takes it much longer to reach terminal velocity, with the assumption (2) that with a
greater surface area, the object will be able to reach a slower terminal velocity. This conclusion
is based on the facts of air resistance and surface area—as the surface area of a falling object
increases, so does the air resistance (drag force). This increase in air resistance will allow the
object to reach a terminal speed faster (disproving the first conclusion). When we inadvertently
did not have the cardboard, the sensor was not capable, and our height not great enough, to
measure terminal velocity.
Our last phase conclusions mirrored our second phase in many aspects. Testing the effect
of surface area on time of impact was very successful. As we would predict, as the surface area
of the parachute increased, the time of impact increased as well. This is also due to the increase
in air resistance which would correlate with and effect on drag force. The outliers of our data
proved to be somewhat unimportant.
V. Overall Conclusion
During the course of the project, our group gained insight into the factors that apply to a
skydiver. Through the series of experiments and trials performed, we were able to observe the
effects of freefall, terminal speed, and drag force. Our analysis successfully measured these
desired factors with the help of our equipment. The trials raised awareness of the outside forces
of gravity and air and how they apply to the trajectory of a skydiver before and after using his or
her parachute. During our parachute trials, we changed the surface area of the parachute while
keeping the mass of the object dropping constant. By changing the surface area of our
parachutes, we were able to defend the notion that the larger the surface area the object being
dropped had, the slower the velocity was during the object’s descend.
There are errors that occurred over the course of our experiment that need to be
addressed. When working with the motion sensor, there were times when we did not get an
accurate reading due to the motion sensor failing to recognize our falling object. The increase in
the volume of our parachute was also a factor of error. When observing a skydiver’s parachute
during its descent, the volume of the parachute is completely inflated. This shape was not
replicated due to the difference in material and design of our parachutes. Even though our
parachutes consistently used the same material, we still could not fully replicate a real life
scenario without authentic parachute materials. Another factor of error that we came across was
the trajectory of the parachute drop. During the course of our experiments we were unsuccessful
in replicating the same straight-down drop for each run. By analyzing the differences among
each trial, we were able to minimize the outliers that appeared. Determining the terminal velocity
for our experiment gave us a great deal of difficulty. In the course of each trial, a stopwatch was
used to determine the amount of time it took for the parachute to reach the ground. This caused
an error because we could not measure when velocity became constant. The data we collected
helped us find many of our objectives for this experiment, but terminal velocity during our
parachute drop was difficult to accurately show. This was due to the insufficient levels of
resources. If these errors could be minimized we would find that the experiment, and our data,
would be more precise.