Rocket Lab Report
By: Tressa Parkes
Written for: Mr. Hendricks B4 Honors Physics Class
22 December 2016
Abstract
In this lab multiple different rockets were launched with different size engines, and the
results of the combinations were recorded. The main objective in the results was to find the final
height of a model rocket. This was done by a series of hypothesizing, creating, pursuing,
measuring, calculating, and analyzing. Within two and a half weeks the height of different
rockets with different engines was predicted, performed, and measured. The comparison of the
predictions of final height made and the results calculated are shown below.
Predicted Calculated
Rocket A B C A A B C A
Used Engine Engine Engine Engine Engine Engine Engine Engine
Red and 31.37m 77m 186m N/A N/A 85m 109m N/A
Silver
Red and 71.17m 117m 240m N/A N/A 125m 155m N/A
Yellow
Small N/A N/A N/A 33.65m N/A N/A N/A 97m
White
Introduction
The Rocket Lab was a series of smaller labs put together to become one two and a half
week long lab. The project was done in order to take everything learned within the first semester
of Mr. Hendricks Honors Physics class, and round it all off in a way that shows real world
application. In order to understand the rest of this report there are some phrases and concepts that
must be understood. These phrases and concepts include of kinematics, dynamics, impulse,
momentum, drag force, drag coefficient, the impulse momentum theorem, numerical iteration,
and different types of rocket engines. Kinematics is the study of motion while ignoring forces
and dynamics is the study of motion with forces. Impulse in terms of physics is the amount of
force acting on an object multiplied by the time. Momentum is the mass of an object multiplied
by the velocity of that object. Drag force, often called air resistance, is a force acting opposite to
the relative motion of any object. The drag coefficient is simply the number that represents this
drag force, or air resistance. Numerical iteration is a set of operations repeated in order to
determine an answer. It is needed in this lab, as in order to determine the final height of the
rocket with a math level a high schooler can understand, the values measured must be
continually put through different equations in order to get the final height. In terms of different
types of rocket engines, there are six that can be bought without needing special clearance. In
this lab four were used, 1/2A A, B, and, C engines. These letters represent the amount of
impulse of this rocket engine. The impulses of these engines are shown below.
A= 1.25
A= 2.5Ns
B= 5Ns
C= 10Ns
D= 20Ns
E= 40Ns
Rocket engines also have two numbers after them, these numbers represent the average thrust of
the engine and the delay time of the parachute. The impulse momentum theorem states that
F*t=p. F is defined as force, t is equal to time, and p is equal to the change of impulse. The
derivation of the Impulse momentum theorem is described below, and it begins with an equation
relating impulse, change of time, and force.
J= f*t
Because of Newton's second law, stating that F=ma, the value of F in the above equation can be
substituted for the value of ma.
J= ma*t
The next step can then be to realize that in this case acceleration is equal to the change of
velocity divided by the change of time because the definition of acceleration is v/t.
J= m(v/t)t
In the equation above there are two t values that cancel each other out resulting in the following
equation.
J= m(V)
Because the v is defined as vf-vi this
can be substituted into the equation.
J= m(vf-vi)
The next step is to distribute the value of m.
J= mvf-mvi
Now because the definition of p, momentum, equals mass times velocity (p=mv), the values of
mass multiplied by velocity are simply just momentum, or p.
J= pf-pi
The final step of this derivation is to note that pf-pi is the same thing as p.
J=p
Engine Thrust Analysis
Materials:
Calculator with CBL and DataMate
Candy box with a hole
Rocket Engine
Toy Car
Track
Digital Force Gauge
Experimental Procedure:
The goal of this experiment was to gather data about thrust as a function of time that will
be needed later on in this lab in order to predict how high the model rocket will travel. The
experiment was set up by taping the candy box, that would hold the engine, to a toy car and
placing it on the track. After that, a digital force gauge was placed on the track in order to
measure the force applied by the rocket engine. The toy car was taped to the candy box to make
sure that when the engine ignited, the rockets force would be applied to the gauge and not
backwards pushing it off the track. Because the track was at a slight angle, the rocket already
begun to push on the digital force gauge and thus had to be zeroed before recording any data.
The TI-84 calculator was connected to a calculator based laboratory (CBL) and the
program DataMate program was opened. Once in DataMate, the calculator was set up so that it
would perform tasks a certain way. First it was set to record data every 10th of a second, then so
that it would record 30 samples. The calculator was set to store the time data and the thrust
values in two different lists. In the first list, L1, time values were stored, and in the second list,
L2, the amount of force on the digital force gauge was measured and the calculator recorded that
data in its own list. The triggering was then set up based off of channel one on the CBL, and was
told to trigger when the force applied on the force gauge was decreasing. The trigger threshold
was set to be -2 newtons meaning that the program wouldn't start recording data till the force
applied on the gauge read -2N. This 2 is negative because the gauge reads pushing forces as
negative and pulling forces as positive, and the rocket engine is pushing against the gauge not
pulling on it.
Conducting the Experiment:
The experiment was conducted using the setup described above. From there a rocket
engine was placed in the whole of the candy box. A priming lead containing phosphorus on the
tip was placed inside the engine. Once this was attached to a battery the electrical current ignited
the phosphorus, which then lit the rocket engine. The calculator was attached to the digital force
gauge in order to measure the force applied to it.
Results:
To calculate the impulse of the rocket engine, the area under the curve, which
is equal to impulse, must be found. This is done by making rectangles underneath the curve
every .1 interval up to where it hits the curve. The areas of all rectangles are added up to create
an estimate of the rocket engine impulse. The impulse was calculated to be 8.2 Ns. In terms of
rocket engines, that would make this a C class engine as 5.0 Ns is B class and 10.0Ns is C class,
and since 8.2Ns is closer to 10, that makes this engine most likely to be a C class engine. The
different classes of engines are determined by how much impulse is given with each different
kind of rocket engine. The average thrust of this specific engine was calculated by adding
together all values the right hand side of the table above and dividing the sum by 24. The average
thrust of the engine turned out to be 4N. This makes the engine being tested a C4 model rocket
engine.
Drag Force (Air Resistance)
Materials:
Wind Tunnel
Model Rocket
Protractor
Experimental Procedure:
The goal of the drag force experiment was to find how much air resistance is acting on
the model rocket throughout its course of flight. This is done in order to find the drag coefficient
needed later in the lab in order to achieve the goal of being able to determine how high the rocket
will go. The drag coefficient is needed because without it our predictions would be seriously off.
The force of the air resistance on an object is proportional to the square of the velocity, FDrag =kv.
The constant in this equation is the drag coefficient, what is wanted at the end of this experiment.
The amount of air resistance depends not only on the size of the object, but the shape as well.
Objects with sharp corners catch more air on them and therefore have a harder time going against
that air, thus their drag coefficient is higher. Cars are now often made with smoothed curves
instead of sharp lines for this very reason. Smooth curves catch on less air, thus the car doesn't
have to push as hard against the air, getting a lower drag coefficient. With a lower drag
coefficient that car will also get better gas mileage due to the fact it doesn't have to push against
the wind as hard. The experiment was set up with a large wind tunnel with a model rocket inside.
The wind tunnel had a honeycomb structure on each side in order to get laminar flow, which is
essentially linear air flow. The model rocket was placed in the center of the wind tunnel hanging
from a string. When the wind tunnel was turned on, the air produced would push against the
model rocket. The wind produced in the wind tunnel represents the air that pushes against a
rocket once it is launched off the ground. The protractor taped to the outside of the wind tunnel
was then read from eye level to determine the angle at which the model rocket was pushed back
by the air.
Test 1: 30 degrees Test 2: 35 degrees Test 3: 30 degrees
Deriving an equation for the drag coefficient of a model rocket:
In order to be able to determine how high a
rocket will travel, the drag coefficient, kd needs
to be found. This is done by creating a free body
diagram of a rocket, or in this case a ping pong
ball inside a wind tunnel. The free body diagram
(figure 3) shows the three forces acting upon the
ping pong ball. These forces are T, mg, and Fd.
Because the T vector is funky (not in an
horizontal and vertical direction), it must be
broken up into its horizontal and vertical
components. This is shown in figure 3.
Figure 3
The next step is to use Newtons second law in order to get two equations of the forces on
the ping pong ball. One in the horizontal (x) direction, and one in the vertical (y) direction.
Fx = max
Fd - Tsin = max
Because the acceleration is 0, the max of the above equation becomes 0, and is therefore
canceled out of the equation.
Fd = Tsin
Now there is an equation that has two unknowns, and Fd. Because there are two
unknowns, two equations are needed. The second equation is derived from the vertical (y)
direction of the forces acting on the ping pong ball.
Fy = may
Tcos - mg = may
Once again the acceleration is 0, so may becomes 0, and is cancelled out of the equation.
Tcos - mg
Now that there are two equations and two unknowns, the problem is doable. The best
way to solve this is to use the substitution method. One way to do this is to solve the above
equation for T.
Tcos - mg / (cos)
T = mg / (cos)
There is now an equation that is solved for T, that can now be plugged into the x
direction equation.
Fd = mgsin / cos
Because sin/cos is equal to tan, the above equation can be simplified even more.
Fd = mgtan
In order to solve for Fd the results of the experiment performed must be used. In the
experiment it was found that the model rocket weighed 61g (.o61 kg), and the velocity (wind
speed of the tunnel) was 30 m/s, and the average angle measured was 32 degrees, the value of Fd
can be solved using the above equation and the experiment results.
Fd = .061(9.8)(tan32)
Fd = .074N
The second step of this lab, to calculate the drag coefficient, can now be performed due
to the derived equation solving for Fd. In order to find the drag coefficient (kd), the equation
shown below must be used.
Fd = kdv2
Due to the derivation of Fd = mgtan, allowing a value of Fd to be found, all the variables
needed to solve for kd can be found in a simple manner. First, the equation needs to be solved for
kd, the drag force.
kd = Fd / v2
The values determined during this experiment were then plugged into this equation to get
a final answer for what the drag coefficient of this model rocket is.
kd = .074 / 302
-4 2 2
Kd =
4*10 N*s /m
The other two rockets (red and silver, and small whites) drag coefficients were
calculated with educated guessing. Because the red and silver rocket couldn't fit into the wind
tunnel, itd drag coefficient couldn't be calculated with these materials, so educated guessing
came into play. Because a ping pong ball could fit into the wind tunnel and was about the same
circumference as the red and silver rocket, it was assumed their drag coefficients would be
similar. The estimated drag coefficient of the red and silver model rocket was 5*10-4. The small
white rocket was measured by assumption that because it was smaller than the red and yellow
rocket, its drag coefficient would be smaller as well. The estimation for the small white model
rockets drag force was 3*10-4.
Numerical Model
Materials:
Rocket height prediction spreadsheet
Calculator
Thrust analysis data
Experimental procedures:
The goal of this lab was to be able to predict how high a model rocket will go given its
mass and the amount of air resistance acting on it. This was most easily and effectively done
using an Excel spreadsheet that organizes and displays all data points, including the predicted
height for the model rocket and engine combination being used.
There are eleven columns in the rocket height prediction spreadsheet, time, thrust,
average thrust, drag force, average net force, average net impulse, initial velocity, final velocity,
average velocity, initial height, and final height. In each column the values were calculated
differently, often using previous values to determine them. Time was calculated using a constant
that had been predetermined a tenth of a second each data point. Thrust was determined by the
engine thrust analysis experiment, but the values being used were given from the manufacturer
due to inaccuracy in the experiment results. The average thrust was simply the number on the
model rocket engine following the letter. The drag force was determined using the wind tunnel
experiment and the average net force was determined taking the thrust from the previous tenth of
a second added to the current thrust of the model rocket divided by two. Average net impulse
was found by taking the average thrust and multiplying it by a tenth of a second. Initial velocity
was the final velocity of the previous tenth of a second and the final velocity was the average
force divided by the total mass of the rocket (including the engine) plus the initial velocity.
Average velocity was determined by taking the initial velocity added to the final velocity and
then divided by two. The initial height is simply the final height of the last tenth of a second.
And the final height, was determined by multiplying the average velocity by the change in time,
and then adding the final height of the previous tenth of a second. A free body diagram of the
rocket in flight is shown below.
Equations:
Average Thrust: (Thr1 + Thr2)/2
Average Net Force: (Thravg - mg - Fd)
Drag Force: (using previous Vf)
Average Net Impulse: Fnet*t
(Fd = Kd * V2)
Initial Velocity: (= last row's vf)
Final Velocity: (vi+Fnett/m)
Average Velocity: (vi + vf)/2
Initial Height: (= last row's hf)
Final Height: (hi+vavg*t)
Spreadsheet Results:
Red and Silver Model Rocket
(calculated using the spreadsheet)
Type of Rocket Engine: B6 Final Height: 77m
Mass (of rocket and engine): 0.083kg
Drag Coefficient: 5* 10-4
Type of Rocket Engine: C6 Final Height: 186m
Mass (of rocket and engine): 0.089kg
Drag Coefficient: 5* 10-4
Type of Rocket Engine: A8 Final Height: 31.37m
Mass (of rocket and engine): 0.080kg
Drag Coefficient: 5* 10-4
Red and Yellow Model Rocket
(calculated using the spreadsheet)
Type of Rocket Engine: B6 Final Height: 117m
Mass (of rocket and engine): 0.057kg
Drag Coefficient: 4*10-4
Type of Rocket Engine: C6 Final Height: 240m
Mass (of rocket and engine): 0.063kg
Drag Coefficient: 4*10-4
Type of Rocket Engine: A8 Final Height: 71.17m
Mass (of rocket and engine): 0.038
Drag Coefficient: 4*10-4
Small White Model Rocket
(calculated using the spreadsheet)
Type of Rocket Engine: 1/2A3 Final Height: 33.65m
Mass (of rocket and engine): 0.030
Drag Coefficient: 3* 10-4
The predicted final height can be found on the spreadsheet by looking at the final height
column and scrolling down until the highest value, or when the highlighted value is seen. When
0 is put into the spreadsheet for the drag coefficient, air resistance, the predicted maximum
height for a C6 engine in the red and yellow rocket, the predicted height becomes 937.56 meters
while with air resistance it is 240.44. The value is significantly larger ignoring air resistance, and
this shows that the value of air resistance should not be ignored as the results will be drastically
different than if air resistance was acknowledged, and in some situations these calculations could
cause large problems.
Conclusion
In conclusion, the model rockets and their engines that were closest to the predicted values were
the red and silver rocket engine with a B engine being a difference of 8 meters, and the red and
yellow with a B engine being a difference of 8 as well. The C engine for the red and silver rocket
had a difference of 77m in relation to predicted value and calculated value. The C engine for the
red and yellow rocket had a difference of 85m in relation to the predicted and calculated value.
And the small white rocket with a A engine, had a difference of 63m between the predicted
height and the measured height.
Predicted Calculated
Rocket A B C A A B C A
Used Engine Engine Engine Engine Engine Engine Engine Engine
Red and 31.37m 77m 186m N/A N/A 85m 109m N/A
Silver
Red and 71.17m 117m 240m N/A N/A 125m 155m N/A
Yellow
Small N/A N/A N/A 34m N/A N/A N/A 97m
White
There are many possible reasons for why the results of height were different than the
predicted height. A few, among many, of those possibilities include of slight curves when the
rocket was launched, wind, and the estimated guessing for the drag coefficients of the red and
silver and the small white rocket. Some ideas for avoiding these things, if possible, would be to
shoot the rockets on a not so windy day, and measure the drag coefficients for all rockets using a
wind tunnel big enough to fit them.
Reflection
Throughout this two and a half week span of the rocket project I have gained a better
understanding of the concepts studied in the first term of honors physics, and the confidence that
I am capable of doing these types of problems. The concepts of kinematics and dynamics and
impulse and momentum and drag forces and coefficients, things a year ago Id never even
imagine knowing have been even more vibrant than the first time learning them. The process of
learning something and then applying it to a real life situation, the exact goal of the rocket
project, puts you as a student into a position that everything you've learned has to be used and
understood, and if its not there is no way to perform the experiments let alone write about it. It
forces you to learn the concepts for yourself and how to portray them to different audiences in a
professional manner, something i never imagined gaining from a rocket lab. I encountered many
difficulties throughout the course of this project. I found myself not knowing how to get all the
information i needed from each experiment. I found that sometimes writing just wasn't enough to
remember the smallest details like a wire or wadding. To overcome this I would take pictures of
the experiments and then look back at them when writing my report. By doing this I was able to
write the numbers and data, write the math, do the calculations, and take pictures of nearly
anything else I may need. At the beginning I found the rocket project overwhelming. It was
experiment after experiment, and draft after draft. Looking back, I am now so grateful for this
experience. I learned not only the physics concepts, but I learned time management skills, new
ways of remembering things and sparking my memory, and I learned that teachers want you to
succeed, and will spend two and a half weeks of class and three days of their winter break just to
make sure each individual student understands the concepts. But perhaps the most important
lesson I learned from this lab was that I know these physics concepts, and I can for sure say I
now know them better than I have before.
