Investigation of vertical height variation in the flight of Mentos – diet Coke bottle rockets
Brandon G. Daniels
New Jersey Institute of Technology, Newark, Department of Physics
323 Dr Martin Luther King Jr Blvd, Newark, NJ, USA 07102
email address: bgd5@njit.edu
The initial volume of diet Coke present during the launch of Mentos-diet Coke bottle rockets was
varied while the number of Mentos was kept constant to observe the effect of the peak height of
the bottle rocket flight. The experiment found that there is an optimal initial volume of diet Coke
(and consequently an optimal weight for the rocket) to achieve the peak height of a bottle rocket
flight regardless of the number of Mentos. This optimal initial volume is suggested to be 1.5 liters
of diet Coke.
I. Introduction
As referenced by Science Buddies on the Scientific American website, diet Coke and Mentos
experiments are ubiquitous across the internet, but the interaction between the two substances still
holds notable parameters to explore (Science Buddies 2012). The interaction is not a chemical,
but a physical reaction in which the Mentos allow dissolved carbon dioxide gas to rapidly break
their bonds with water and escape the soda (Science Buddies 2012). When this process is kept
seal in a bottle, the pressure builds, and sudden release in this pressure can result in a myriad of
effects, one being a bottle rocket.
The point of this experiment is to explore one of the two key elements in the physical reaction:
the diet Coke. The carbon dioxide in the diet Coke detaches from the water molecules because
because the Mentos have nucleation sites, microscopic pits that aid in the dissolving of bubbles
(Richter 2010). Research such as that done by Jered Richter and his team has investigated the
effect more Mentos (and thus more nucleation sites) has on the reaction. However, explorations
into the effect that more soda or less soda has on the reaction is lacking. This experiment seeks to
investigate the effect the amount of dissolved carbon dioxide has on the over reaction and its
output thrust.
II. Theory
Research done by Richter in accordance with Houlberg, Kam, and West highlights the
correlation between the amount of Mentos and the height of a Mentos-Diet Coke geyser (see
Figure 1). This is essentially a Mentos-Diet Coke bottle rocket that has yet be flipped upside
down. They argue the height of the geyser varies as a root function with respect to the number of
Mentos implemented. This suggests there is a finite amount of “physical effect” adding Mentos to
the concoction will bring about.
FIG. 1. (Color Online) Line Graph of Height of a Mentos-Diet Coke Geyser along with A
Quadratic Trend Line and the Accompanying Trend Line Equation (Richter et al., 2010).
Going beyond that group’s research, this experiment seeks to explore the relation of the initial
volume of diet Coke to the height of Mentos-diet Coke bottle rocket flight (which is comparable to
Mentos-diet coke geysers). The hypothesis for this experiment is that the volume of diet Coke in
the bottle has a more noteworthy effect on the height of a bottle rocket than the number of mentos
used. This is hypothesized to be true due to it’s role as the primary source of weight which the
rocket must overcome to achieve flight.
III. Experimental Procedure
Fifteen bottles of diet Coke were acquired and one empty diet Coke bottle was emptied, cut in
half, and used as a launcher (a method to flip the bottles, allowing for the mouth of the bottles to
be upside down but not touching the ground). This was done so that no other pressure would be
contributing to the rockets’ launch success or failure other than the internal pressure inside the
bottle. Next, original mint Mentos were punctured using a thumbtack and strung onto paper clips
to be holistically delivered to the soda. These Mentos payloads had their paperclip stuck into a
cork, and this cork was wrapped in paper towel strips and replaced the bottles’ caps as the primary
agent keeping the bottles pressurized (see Figure 2). Paper towel strips were initially used to
thicken the corks so that they could effectively seal the mouth of the bottles. Additionally, trial 9,
trial 10, and trial 11 out of the total of 16 trials utilized the original soda cap as the pressure
stabilization method instead of the cork. The amount of Mentos used was varied from 5 to 7 in the
progress of optimizing the launch. Periodically, the temperature was taken to assess any outside
variables.
FIG. 2. (Color Online) General Set-Up for Mentos-Diet Coke Bottle Rockets (Stenson).
Trials 12-14 used a cork wrapped in duct tape rather then paper towel strips for a more
effective seal on the bottle. These trials all used the same duct tape wrapped cork as well as only a
5 Mentos payload. In these trials, the amount of diet Coke in the bottle was varied by pouring int
out into a measuring cup and discarding the excess volume. These trials were the only successful
trials. In each, the diet Coke was reduced to the desired volume, the cork with the Mentos payload
was pressed tightly into opening of the bottle, and the launcher was placed on top. Then the whole
apparatus was flipped, shaken, and left to launch.
All 15 trials were filmed with a camera phone 1,113 meters away. The relevant trials (12-14)
were analyzed using trigonometry to find the peak height of the bottle rocket flight. For trial 12,
no horizontal movement occurred, thus using a man-powered inclinometer, it was found that the
top of the rocket traveled 7 degrees up relative to the camera. Using the definition of tangent, this
means the bottle reached a height of 1.367 meters.
Trials 13 and 14 had a launch which did not go straight upward, thus the distance to the
maximum height was more involved to calculate. The horizontal distance of the flights was
photographed on-site. For trial 13, the rocket traveled 6.307 m, and for trial 14, 6.678 m. The
horizontal deviation of each flight was measured using the footage and an inclinometer. Trial 13
had a 29 degree deviation. Trial 14 had a -25 degree deviation. Since the distance to the launcher
remained the same (1,113 m), the height of each flight was found using first the law of sines and
then the law of cosines to find the distance from the camera wherein each bottle reached it’s peak
(assuming it reached its vertical peak midway in its horizontal travel). The horizontal distance to
the peak height of trial 13 was 1.16735 m. The horizontal distance to the peak height of trial 14
was 1.26668 m. Then the inclinometer was used again to find how high the rocket had risen, and
plugging that into the definition of tangent, the peak heights for trials 13 and 14 were found. The
peak height of trial 13 was 6.7397 m. The peak height of trial 14 was 3.6321 m.
IV. Experimental Results
As shown in Figure 3, there is a correlation between the initial volume of diet Coke in the
bottle rocket and the peak height which the Mentos-diet Coke bottle rocket will reach. The
maximum volume of soda hypothetically available was 2 liters since the diet Coke bottles all
initially contained 2 liters. The experiment was done using smaller portions.
FIG. 3. (Color Online) Line Graph of Height of Mentos-Diet Coke Bottle Rocket Flights where
the Number of Mentos is Held Constant at Five Mentos.
All trials reflected in the graph occurred at 30 degrees Fahrenheit. When the initial volume of
soda was 1.8 L, the peak height of flight was 1.367 m. When the initial volume was 1.5 L, the
peak height was 6.7397 m. This was the maximum height reached of all launches. When the
initial volume was 1.3 L, the peak height was 3.6321 m. When the initial volume of soda was 0.0
L, the peak height was 0.000 m. This was the minimum height reached of all launches. No
continuous polynomial could be used as a trend line for the graph. Only a piece-wise function
could operate as a trend line.
V. Discussion
Since the number of Mentos was held constant at five for each launch, and the same duct tapecovered cork was used in each trial, the only variable directly responsible for this variance in peak
height is the initial volume of soda. This suggests that there is some optimal initial volume of diet
Coke to reach a maximum bottle rocket flight height for any given number of Mentos. This
experiment suggests that optimal volume is 1.5 liters, but further research is needed. The last two
trials had horizontal deviation in their flight pattern.
Though this was accounted for using
trigonometry, there was +.1/-.1 error in the degree measurements made with the inclinometer.
Additionally, it could be argued that some of the thrust of the rocket going toward the horizontal
movement could have increased the vertical height if the launch was more optimized. Although,
the overall trend of the graph would arguably be the same. Additionally, the graph suggests there
is some threshold volume of initial soda that is necessary to achieve flight at all, but not enough
data was gathered to confirm this.
The majority of trials failed in the progress to optimize the launching process. The first 11
trials had a cork wrapped in a paper towel for a seal, and all failed to launch except for one. The
use of duct tape to thicken the cork seal was effective, but even then, the results could have varied
if a different cork was used. Overall, the biggest issue contributing to error was the difficulty in
crafting an experiment that was completely repeatable.
VI. Summary and Conclusion
In short, the investigation of vertical height variance in the flight of Mentos-diet Coke bottle
rockets yields that the initial volume of diet coke present at launch has a notable effect. This
experiment suggests there is an optimal volume of initial diet coke to achieve maximum height,
and that this volume is 1.5 L. This differs from research by Richter which suggested there was no
optimal number of Mentos to add to a Mentos-diet Coke bottle rocket after a certain number due
to its root function effects on flight height. This experiment also suggests there is a threshold
initial volume of soda needed to for the rocket to achieve flight at all, but further research is
needed.
References
Richter, Jered, Laura Houlberg, Dayna Kam, and Aubrey West, 2010, “Mentos and Coke,” TUHS
Physics, http://tuhsphysics.ttsd.k12.or.us/Research/IB10/RichHoulKamWest/index.htm
Science Buddies, “Spurting Science: Erupting Diet Coke with Mentos,” 2012, Scientific
American, https://www.scientificamerican.com/article/bring-science-home-coke-mentos/
Stenson, Gretchen. Pinterest. https://www.pinterest.com/pin/148689225173440297/