Rocket Lab
Sarah Robinson
Academy for Math, Engineering, and Science
Mr. Hendricks B3
Abstract
Three experiments were conducted in order to predict the final heights of a series of
rockets launched into the air. Then a fourth and final experiment was done where the rockets
were launched into the air. Here are the results of the predictions and the final results: The
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small white rocket with a 2 A3 engine was predicted to have a final height of 23 meters and the
actual result was a final height of 30 meters. The Red/Silver rocket with a C engine was
predicted to have a final height of 92 meters and the actual result was a final height of 450
meters. The Black/Red rocket with a C engine was predicted to have a final height of 72 meters
and the final result was a final height of 260 meters. The big white rocket with a C engine was
predicted to have a final height of 73 meters and the actual result was a final height of 190
meters. The Red/Yellow rocket with B engine was predicted to have a final height of 50 meters
and the actual result was a final height of 170 meters. The Red/Yellow rocket with a C engine
was predicted to have a final height of 97 meters and the actual result was a final height of 480
meters. Although the prediction for the small white rocket was close to the actual final height
when the rocket was launched, the heights for the other rockets were significantly different
from the predictions. This error was most likely due to the curvature of the rocket.
Introduction
The purpose of this project was to find out the final heights of rockets that were
launched with specific rocket engines. In this project, four steps were followed:
First Step: An experiment was conducted to measure the thrust of each ignited rocket engine.
A digital force gauge was used in conjunction with a graphing calculator to collect and record
the data.
Second Step: An experiment was conducted using a wind tunnel in order to calculate the drag
coefficients of a specific rocket.
Third Step: An Excel spreadsheet was used to predict the final height of the rockets with a
specific engine inside.
Fourth Step: Six rockets were launched into the air. The angles of the height of each launched
rocket were measured by three observers who were set up in an equidistant triangular pattern
from the launch pad. The final height of each launched rocket was calculated using these
measured angles.
The overall purpose of this project was to give the students a hands-on experience
involving all the skills and knowledge that was gained in the first half of the Physics class that
related to Kinematics, Dynamics, Momentum, and impulse. Kinematics is defined as the study
of motion. Dynamics can be defined as the study of how forces produce motion. Impulse is
defined as force multiplied by the time in contact with an object. Momentum is defined as mass
multiplied by velocity. Drag force can be solved for by multiplying the drag coefficient (K d) and
the velocity squared. Drag force can also be defined as the tangent of theta multiplied by mg
(mass multiplied by gravity). The drag coefficient is defined as Kd =
𝑡𝑎𝑛𝜃𝑚𝑔
𝑣2
. The impulse-
momentum theorem is J = Δp. This equates to impulse equals the change in momentum. This
∆𝑣
equation is derived from the equation J = Ft as follows: J = mat, J = m ∆𝑡 t , J = mΔv, J = m(vf –
vi), J = mvf – mvi, J = pf – pi, J = Δp.
There are many different types of rocket engines. To distinguish the rocket engines from
one another, each rocket engine has a designation code which contains a letter and a number.
A picture of a sample rocket engine with a designation code can be seen below. The letter
refers to the impulse of the rocket engine. Each of these impulses doubles as follows, starting
with the letter A: A = 2.5, B = 5, C = 10 etc. The number following the letter refers to the
average force in Newtons of each engine. Because the force of a rocket engine is not constant,
solving for equations which require a constant force would be impossible. To compensate for
this, and to allow calculations to be used in this project, Numerical Iteration was used.
Numerical Iteration is defined as the breaking up time increments into very small slices so that
the force for that specified time increment can be used as if it is constant.
Engine Thrust Analysis
What is the thrust versus time of a rocket engine?
In order to figure out the thrust of the engine, the letter code (which tells you the
impulse of the engine) of engine and its average force must be calculated. The letter code and
the average force equate to the type of rocket engine used. (I.E. A 8-7 The A is the letter code
and the 8 is the average force of the rocket engine.) To calculate the letter code, an experiment
must be done. The experiment was set up by attaching a digital force gauge to a track with duct
tape. Also attached to the track (a little further up it) was a duct tape loop, with another piece
of duct tape attached to the sticky side so the bottom of it would not be sticky. The purpose of
the loop was to hold the box and cart (as will be described later) in place so it wouldn’t hit
someone when the engine ignited. This duct tape loop did not affect the results of the
experiment at all. The rocket engine was duct taped into a long, thin box with a hole in the top
for the front of the engine to enter. This box was also duct taped to a .5 kilogram cart to enable
the engine to push it forward into the sensor. This was all connected to a calculator to record
the data we received from the experiment. Drawings of the experimental setup and a cross
section of the rocket engine can be seen below.
To utilize the calculator to obtain the proper information, a program called Easy Data
was used. The experiment was then fully set up as described above and below. The cart with
the box and the rocket engine attached to it was placed through the duct tape loop against the
digital force gauge, with the rocket engine facing away from the digital force gauge (see
illustration above). The set up of the experiment was done within the classroom, though the
actual engine was ignited outside. To ensure the cart and rocket engine combination would not
roll off of the track and onto the ground, the track was propped up on a piece of wood. As the
track was at a slight incline, this allowed the cart with the rocket engine attached to roll down
the track. This put pressure on the digital force gauge. In the Easy Data program, as it collects
data from the digital force gauge, a pulling motion is considered positive and a pushing motion
is considered negative. Because the force is a pushing force, all of the numbers obtained on the
calculator are negative. As a result of the pressure against the digital force gauge, the digital
force gauge had to be zeroed out as before the experiment began so as not to interfere with
the data that was collected during the experiment. In order to zero out the digital force gauge,
one has to go into set up in the Easy Data program and click zero. However, once zero was
clicked, the digital force gauge did not quite read zero. Despite this, the slight number was
statistically close enough to zero so it didn’t interfere with the data.
The calculator was set up, in order to enable it to collect and record the data from the
digital force gauge, and this provided the data for our experiment. The Easy Data program was
set to collect and record the data it received every two one-hundredths of a second. It was set
to collect 10 seconds of data and 200 samples. To avoid human error in calculating time, the
calculator was set up to use triggering. This program will trigger the data to begin recording
data once a certain threshold was met. The threshold in this case was -1 Newton of force. The
Newton’s number is negative because it was a force pushing against the digital force gauge,
rather than a pulling force that would have generated a positive force. The program is set up to
record data every two one-hundredths of a second, and then erase the data it just collected as
the program records the next set of data. To avoid losing important data, a 10% pre-storage
limit was set. This means that the calculator program would collect and then store the data it
received for 10% of the time limit set before the threshold was met. This ensured that no
important data was lost as before the experiment began, as the program stored and recorded
any data received.
The entire setup, which included the track, cart, and rocket engine, was taken outside.
The track was set up like it had been in the classroom, with it resting at a slight angle on top of
a small wedge of wood. The rocket engine was attached to a box, which was duct taped to the
cart. The cart with the box attached to it was then set inside the non-sticky duct tape loop on
the track so that the front of the cart (the opposite end from the rocket engine) was resting
against the digital force gauge. In order to safely ignite rocket from a safe distance away, a
phosphorus igniter was placed inside the rocket engine with the end sticking out. The
phosphorous igniter was hooked up to a battery via long wires which connected the battery
and igniter ends. Alligator clips were attached to the igniter ends of the wires.
After a countdown of five seconds, the battery was turned on, which fed electricity
through the wires to the igniter ends. This electric current traveled up the end rods and ignited
the phosphorus tip, which in turn ignited the rocket engine. The rocket engine burned for only a
few seconds. A small column of flame shot out the end for most of that time, then there was a
slight pop and puff as the engine put out pressure. If the engine had been attached to an actual
rocket, this pressure would have sent the nose cone flying off, and released a parachute which
would have slowed the descent of the rocket. Photographs of the execution of the experiment
described in this report, including the set up of the experiment are shown below. A drawing of
the set up is also in this space. A link to the video of the execution of the experiment is also
included below the photographs. (All the photographs and videos come from classmates)
http://youtu.be/zCROPm7Gl8s
Once the rocket engine burned out, the complete experimental set up was carried back
inside to the classroom. The collected data was then examined. Looking in the list area of the
calculator, the time was recorded in column L1 and the force was recorded in column L2. There
was about .3 seconds of pre-storage of data. The rocket burned out at about 1.3 seconds from
when the experiment began. A table and a graph of the data collected from the calculator are
shown below. In order to make it easier to graph the data, the absolute values of the numbers
were used.
Time (s)
0
.1
.2
.3
.4
.5
.6
.7
.8
.9
1.0
1.1
1.2
1.3
Force (N)
0
0
0
-.4
-5.02
-10.14
-5.24
-3.82
-3.55
-3.90
-3.94
-3.99
-1.421
-.02
The letter code and average force, which indicated which type of rocket engine was
used, was then calculated. The letter code was calculated by calculating the area under the
curve, using the absolute values of the collected data, and using midpoint rectangles on the
graph. A drawing of the way this was done can be seen below the actual calculations. The
addition of the approximate force measurements multiplied by the time measurements (.1
seconds each) (both obtained by the graph) is as follows: .04 + .3 + .76 + .76 + .41 + .35 + .36 +
.37 + .38 + .26 + .06 = 4.05 Newton-seconds. The area under the curve of a force as a function of
time graph is the impulse. The letter code of the engine also refers to the impulse. The resulting
number is lower than the next closest value for which the impulse should be calculated because
of human error and due to the fact that the numbers for the force were eyeballed rather than
using calculus to determine them. With this in mind, the actual impulse of the engine can be set
at 5 Newton-seconds. The letter code corresponding to the output of 5 Newton-seconds is B.
With this result, it can be concluded that the rocket engine used in the experiment is a B
engine.
To help determine the type of rocket engine used in the experiment, the average force
of the rocket was calculated. This was done adding the absolute values of the force
measurements (as seen in the table above) and dividing the total number by the number of
values calculated. The absolute values of the force measurements were used in order to make
the final number of the average force positive. That average force calculation is as follows: .4 +
5.02 + 10.14 + 5.24 + 3.82 + 3.55 + 3.90 + 3.94 + 3.99 + 1.421 + .02 = 41.441. The resulting
number was then divided by 11 to get the average force. The calculated result was 3.76, which
rounding for significant figures, is 4. It can be concluded from the calculations above that the
engine used in the experiment is a B – 4 engine.
The thrust of the engine is calculated by dividing the impulse of the engine as defined by
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the letter code divided by the average force. This calculation is as follows: 4 which equals 1.25
Newtons. This is the thrust of the engine.
In conclusion, the thrust of the engine as obtained by the outline above is 1.25 Newtons.
The time that rocket engine was burning was 1.3 seconds (as seen in the table).
Drag Force Analysis (Air Resistance)
What is the drag force coefficient on a rocket flying through the air?
This experiment was conducted in order to determine the drag force coefficient of a
specific rocket flying through the air. In order to solve for the drag force coefficient, it is first
necessary to derive the equation for the drag force. The equation for drag force is F d = Kdv2
where Kd represents the drag force coefficient. The mother equation of Fd = Kdv2 is Fd is
proportional to v2. The ‘is proportional to’ was changed to an equal sign, and a constant was
added to balance the equation. The chosen consonant was K. Using Fd = Kdv2, the velocity could
be used in conjunction with the derived drag force equation to work backwards to find the drag
force coefficient. The picture below is used to illustrate the values required in deriving the
equation for drag force. To derive the drag force equation, apply Newton’s Second law: ΣF x =
max. max will equal zero because there is no acceleration. Next, the ΣFx is broken down into its
proper values, using the x direction values obtained from the picture. ΣFx = Tsinθ – Fd. Add Fd to
both sides to get Fd = Tsinθ. This is one equation with two unknowns (T and Fd), so this does not
work. This requires another equation. Again, Newton’s Second Law is applied: ΣF y = may . The
may is again zero, because there is no acceleration. The ΣFy is broken down into its proper
values, as shown by all the y direction values obtained from the picture. ΣFy = Tcosθ – mg. Add
mg to both sides so the equation is Tcosθ = mg. Next, divide by cosθ so T is by itself. The final
𝑚𝑔
equation is T = 𝑐𝑜𝑠𝜃. Since the value for T can now be calculated, it can be plugged into the Fd =
Tsinθ which now can be solved. The final equation that will be used to figure out the values
𝑚𝑔
that need to be obtained during the experiment is: Fd = 𝑐𝑜𝑠𝜃 sinθ. Using a trigonometry identity,
this can be reduced to Fd = tanθmg. All of the numbers on the right side of this equation can be
solved for in the experiment.
Now that it has been shown what values to look for in the experiment, the experiment
could begin. A rocket, hanging by a string, was placed inside a wind tunnel. A protractor was
placed inside the wind tunnel behind the rocket, in order to show the angle at which the rocket
would be flying when the wind tunnel was turned on. A picture showing the set up of the wind
tunnel is below. Inside the wind tunnel at either end of the glass case where the rocket is
located, is a honeycomb structure used to direct the flow of air in order to make it less
turbulent as the rocket flies through the wind tunnel. A picture of this structure is also included
below. Drawings of both the wind tunnel and the honeycomb are included below the
photographs.
The wind tunnel was then turned on. The wind tunnel works by shooting air out of the
back of itself; as the wind tunnel is not a vacuum, air comes flowing into the wind tunnel. This
air is what sends the rocket, attached to a string, flying backwards and which allows the air
resistance of said rocket to be measured. As the wind tunnel pulled air in, the rocket was
pushed backwards at an angle of approximately 27°, as measured by the protractor. The exact
angle of the rocket’s position was very difficult to precisely measure because some turbulence
made the rocket bounce slightly, despite the honeycomb being in place. The speed of the air,
𝑚
which is equivalent to the velocity of the rocket, was measured to be 15 𝑠 . The mass of the
rocket inside the wind tunnel was 61 grams. This measurement of the mass needed to be
converted to standard physics units, or kilograms. This conversion was done as follows: 61 g
1 𝑘𝑔
(1000 𝑔) which equates to .061 kilograms. Although the mass of the rocket to be shot off later in
this experiment is slightly larger than the one described above, it would not fit into the wind
tunnel, so a slightly smaller rocket was used during this experiment.
In order to solve for the drag force coefficient, that variable had to be isolated in the
F
equation Fd = Kdv2. To do so, divide the equation by v2. This results in: Kd = 𝑣d2 . The equation for
Fd is Fd = tanθmg. When these values are applied, it results in the full equation of:
Kd =
𝑡𝑎𝑛𝜃𝑚𝑔
v2
. v = 15
𝑚
𝑠
. When one plugs the resultant values, the result is Kd =
𝑡𝑎𝑛27(.061)(9.8)
152
which equals Kd = .00135. There should not be three significant figures in this answer, since the
angle was unable to be calculated very accurately due to the turbulence. Thus, the true drag
coefficient of the rocket is .001.
In conclusion, this experiment showed that the drag force coefficient of the rocket is
.001. This result will be used later to help calculate the exact drag force on the real rocket.
Numerical Model of the Predicted Flight
What is the maximum height reached by a specific rocket with an A, B, and C engine,
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and another, smaller rocket with a 2 A engine?
To calculate the maximum height of a rocket, an Excel spreadsheet was used and can be
seen below this paragraph; a description of the formulas and calculations used in this
spreadsheet is given. The spreadsheet was filled out with reference to the Red/Yellow rocket
with a C6 engine. The mass of the Red/Yellow rocket is 39 grams. The mass of the C6 engine is
24 grams. This makes the total mass of the rocket and engine 63 grams. However, in order to
put the mass number into the spreadsheet, the value must be in kilograms. The conversion
1 𝑘𝑔
from grams to kilograms is as follows: 63 g (1000 𝑔) = .063 kg. This number was then put into the
spreadsheet. The drag coefficient (Kd) of the Red/Yellow rocket is .002.
Average
Drag
Force
Thrust
Average
Net
Impulse
Initial
Final
Average
Initial
Final
Final
(using
prior vf)
Average
Net
Force
Velocity
Velocity
Velocity
Height
Height
Time
0.00
0.01
-0.62
-0.06
1.87
0.88
1.37
97.16
97.30
3.8
0.00
0.00
-0.62
-0.06
0.88
-0.10
0.39
97.30
97.33
3.9
0.00
0.00
-0.62
-0.06
-0.10
-1.08
-0.59
97.33
97.27
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The spreadsheet was set up and solved for in the manner shown in the following
paragraph. The thrust was previously calculated and those values appear in the spreadsheet.
The next column in the spreadsheet is the Average Thrust. This is calculated by adding the two
thrust values for two tenths of a second and then dividing that total by 2; the equation is:
(Thr1+Thr2)/2. The next column in the spreadsheet is drag force. This is calculated by using the
previous row’s vf, and the equation is: Fd = kdv2. The next column is Average Net Force. This is
calculated by using this equation: Thravg - mg – Fd. The equation is broken down this way: the
average thrust (Thravg) is the value that was calculated in the second column mentioned above.
mg refers to the mass of the rocket and engine multiplied by the value of g (gravity) or 9.8. F d
represents the drag force as previously calculated and recorded in the Drag Force Column. The
next column in the spreadsheet is Average Net Impulse, which is calculated by the equation:
Fnet∙Δt. The net force (Fnet ) is the number that was previously calculated and recorded in the
column with the same name. Δt is the amount of time between samples. The next column is
Initial Velocity. The initial velocity value is previous row’s final velocity. The next column is Final
Velocity. This is calculated using the equation: vi+FnetΔt/m. The net force (Fnet ) was previously
calculated, as was the change in time. The m is the mass of the rocket and the engine
combined. The next column is Average Velocity. This is calculated by: (vi + vf)/2, or velocity
initial plus velocity final, divided by 2.
The final column of Final Height can now be calculated. There are two different
equations that can be used to calculate this value: hi+vavgΔt or D = RT (distance equals rate
times time), however, D = RT can only be used if the average velocity is constant, which is not
the case in this experiment. hi+vavgΔt is another equation that can be used to calculate the final
height. In order to use it for this experiment, it is being assumed that the velocity for a specific
instant is indeed constant. This assumption is called Numerical Iteration. hi+vavgΔt uses the
initial height (or the previous row’s final height) plus the average velocity as previously
constituted times the change in time between samples.
The maximum height value for the rocket can be seen using the spreadsheet by scrolling
down while looking at the final heights. The highest number in this column before the numbers
start to move downwards is the maximum height. On the section of the spreadsheet seen
above, the maximum height is highlighted. Using the Red/Yellow rocket, the values for the
maximum height of the rocket are based on each of the three engine sizes, A8, B6, and C6, and
can be calculated by using the spreadsheet. The drag coefficient for the rocket in all three cases
is .002. The A8 engine has a mass of 15 grams. The B6 engine has a mass of 18 grams. The C6
engine has a mass of 24 grams. The total mass of the rocket and the A8 engine is calculated at
54 g. As it needs to be put into kilograms so it can be applied to the spreadsheet, the
1 𝑘𝑔
conversion is as follows: 54 g (1000 𝑔) = .054 kg. The mass of the rocket and the B6 engine is
1 𝑘𝑔
calculated at 57 g. This is put into kilograms by the conversion that follows: 57 g (1000 𝑔) = .057
kg. The mass of the rocket and the C6 engine in is calculated at 63. This is put into kilograms by
1 𝑘𝑔
the conversion that follows: 63 g (1000 𝑔) = .063 kg. The thrust values that were plugged into
the spreadsheet were as previously obtained. Using these values, the maximum height for the
Red/Yellow rocket with the A8 engine is 30 meters. The maximum height for the Red/Yellow
rocket with the B6 engine is 50 meters. The maximum height for the Red/Yellow rocket with
the C6 engine is 97 meters.
This process of entering the values into the Excel spreadsheet as described above was
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repeated for the A3 engine. The drag coefficient for the small white rocket is .001. The mass
2
1
of the small white rocket is 23 grams. The mass of the 2 A3 engine is 7 grams. The total mass of
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the small white rocket with the 2 A3 engine is 30 grams. The conversion to put it into kilograms
1 𝑘𝑔
so it can be entered into the spreadsheet follows: 30 g (1000 𝑔) = .030 kg. The thrust values for
this rocket and engine were previously calculated. After plugging in the numbers into the
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spreadsheet, the maximum height for the small white rocket with a 2 A3 engine is 23 meters.
It is important to consider air resistance when working with rockets. If the air resistance
is ignored, the numbers become very skewed. For example, if all the same numbers as
previously shown for the C6 engine in a Red/Yellow rocket are applied to the spreadsheet, but
the drag coefficient is put at zero (which would result if one did not include air resistance), the
maximum height that would be calculated would be substantially higher. The original maximum
height WITH air resistance is 97 meters, but with NO air resistance, the maximum height that
would be calculated is 937 meters. These two numbers are not even comparable to one
another. They are so different. Air resistance in using rockets cannot be ignored, or else the
data received in the experiment will be very false and misleading.
In conclusion, the maximum height for a Red/Yellow rocket with an A8 engine is 30
meters. The maximum height for a Red/Yellow rocket with a B6 engine is 50 meters. The
maximum height for a Red/Yellow rocket with a C6 engine is 97 meters. The maximum height
for a small white rocket with a
1
2
A3 engine is 23 meters.
Actual Flight Results
What is the final height of rockets when they are launched with specific engine?
This experiment was set up in a similar manner as that of the thrust measurement lab.
The rocket was selected and the specific rocket engine was placed inside of it, with a plug to
hold the rocket engine into the rocket. All six of the rockets that were launched used the same
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version of a C6 engine, except the small white rocket that used a 2A3 engine, and the
Red/Yellow rocket which was shot off first with a B6 six engine and a second time with a C6
engine. The alligator clips were attached to the ends of the phosphorous lighter, ensuring that
the clips did not touch each other, after the phosphorous lighter was inserted into the engine
end of the rocket (as can be seen in the first picture below). The nose cone of the rocket was
removed (as can be seen in the second picture below) to insert a bit of fire retardant wadding
into the rocket. This was done to prevent the parachute from burning. The rocket was then
placed on the launch pad in the manner seen in the third picture. A drawing of the
experimental set up also follows.
Before the experiment began, the class decided that it would be necessary to have more
than one person measuring the angle of the rocket as it flew, so that if the rocket curved at all
in its flight no angle of the rocket’s flight would be missed. It was decided that three people
would be measuring angles. This is because if only one person measured the angles, they would
only get one set of angles from one side. Most rockets curve in their flight path as they rarely go
straight up when they are ignited, thus, a second person would be needed to counteract the
measurement of the angles from the first person, which would be wrong due to the curving.
However, if just two people measured angles there would likely be an error if the rocket curved
to either side, throwing off the angle calculations. Adding a third person measuring angles
would create a triangle which would ensure accuracy in measuring the rocket’s angles. The
three people measuring the angles were placed 50 meters away from the launch pad of the
rockets. This was measured by a running distance ruler (which can be seen in the second
picture) used by Alex. The angles were measured by a protractor with a string and a washer
attached hanging down which can be seen in the second diagram. The three people measuring
the rocket’s angles were Isaac, Trevor, and Kolton. The measurers held the protractors up and
raised the end of it with the rocket’s ascent. The final angle that was measured and recorded
for each of them was calculated by looking at the angle on the protractor where the washer
and string ended up hanging once the rocked reached its final height and subtracting that
number from 90. This subtraction was necessary because the protractor is set to begin
measuring at 90 degrees, rather than 0 degrees.
After setting up the experiment, and getting the people measuring the angles into place,
the rockets were then launched one at a time. A picture of one of the rockets flying through the
air after the parachute deployed can be seen here:
A runner was sent to pick up the fallen rocket once it had completed its descent and hit
the ground. The angles obtained by Isaac, Trevor, and Kolton (Their names were shortened
from Isaac, Trevor, and Kolton to I, T, and K, respectively for efficiency) were recorded for each
rocket. The three angles captured for each rocket are as follows:
Small white rocket: I = 30°, T = 34°, K = 25°. Red/Silver rocket: I = 87°, T = 89°, K = 75°.
Black/Red rocket: I = 88°, T = flier (a flier indicates that the measurement of the rocket’s angle
was over 90 degrees, and thus was not easily measurable. The flier values will not be counted in
this experiment and when the average is taken later, the number will be divided by 2 instead of
3), K = 70°. Big white rocket: I = 75°, T = 75°, K = flier. Red/Yellow rocket with B6 engine: I =
78°, T = 77°, K = 65°. Red/Yellow rocket with C6 engine: I = flier, T = 88°, K = 80°.
The final height was calculated by finding the tangent of the angle and multiplying that
by the distance away from the launch pad, then adding that full calculation the height of the
person measuring the angle of the rocket. This formula was found by using the illustration
representing the experiment below. The numbers in this illustration and the following
explanation are merely sample numbers, not actual data, so as to explain the process of getting
the equation used later to calculate the true heights of the launched rockets’ flights. To
calculate the opposite side of the triangle, which represents the height of the rockets, the
𝑥
numbers can be set up in a proportion as follows: tan(55) = 70 𝑚𝑒𝑡𝑒𝑟𝑠. Tangent is used because
the adjacent side to the angle is known, while the opposite side to the angle is the unknown
that is being solved for. In order to get the x by itself, and therefore find the final height that
the rocket went, one must multiply both sides by 70. Thus, the final equation to find the final
height is: x = 70 tan 55 + 1.5 meters. To clarify, the height of the rocket equals the distance
away from the launch pad times the tangent of the angle found plus the height of the person,
which in this sample is 1.5 meters. It is required to add the height of the person measuring the
angle of the rockets because the sightline for the people and accordingly, where the data
begins recording at eye level, is off of the ground; ground level would be zero. Since the person
measuring the angle has height that is not zero, the number must be included in the
calculations. In the final calculations, the average height of three people was 1.7 meters. Thus,
this is the number that will be used as the height of the person in the real equation below.
In order to complete the true calculations, only one angle of measurement for the
rocket’s flight can be used, therefore it is necessary to obtain the average of all three, or in the
cases where there was a flier, two, of the angles. It must be the average to avoid corrupting the
data, otherwise the data would not account for the curvature of the path of the rocket. The
averages were calculated as follows with all the numbers in degrees:
Small white rocket: 30 + 34 + 25 = 89. 89 divided by 3 equals 29.67°. Red/Silver rocket: 87 + 89
+ 75 = 251. 251 divided by 3 equals 83.67°. Black/Red rocket: 88 + 70 = 158. 158 divided by 2
equals 79°. Big white rocket: 75 + 75 = 150. 150 divided by 2 equals 75°. Red/Yellow rocket
with B6 engine: 78 + 75 + 65 = 220. 220 divided by 3 equals 73.33°. Red/Yellow rocket with C6
engine: 88 + 80 = 168. 168 divided by 2 equals 84°.
The final height of each of the rockets was calculated by using the predetermined
formula as described previously in this report. Using this formula, the final heights of each of
the rockets were calculated as follows:
Small white rocket: (50tan(29.67))+1.7 = 30.18. The result was rounded for significant figures
resulting in the final height of the rocket being 30 meters. Red/Silver rocket: (50tan(83.67))+1.7
= 452.4. The result was rounded for significant figures, resulting in the final height of the rocket
being 450 meters. Black/Red rocket: (50tan(79))+1.7 = 258.9. The result was rounded for
significant figures, resulting in the final height of the rocket being 260 meters. Big white rocket:
(50tan(75))+1.7 = 188.3. The result was rounded for significant figures, resulting in the final
height of the rocket being 190 meters. Red/Yellow rocket with B6 engine: (50tan(73.33))+1.7 =
168.67. The result was rounded for significant figures, resulting in the final height of the rocket
being 170 meters. Red/Yellow rocket with C6 engine: (50tan(84))+1.7 = 477.4. The result was
rounded for significant figures, resulting in the final height of the rocket being 480 meters.
In conclusion, this experiment was conducted in order to calculate the final heights of
launched rockets. The results for this experiment for each rocket launched are as follows: Small
white rocket: 30 meters. Red/Silver rocket: 450 meters. Black/Red rocket: 260 meters. Big
white rocket: 190 meters. Red/Yellow rocket with B6 engine: 170 meters. Red/Yellow rocket
with C6 engine: 480 meters.
Conclusion
The predicted final heights of the rockets before they were launched and the calculated
final heights after the rockets were launched are compared as follows:
1
The small white rocket with a A3 engine was predicted to have a final height of
2
23 meters, whereas the final height of the launched rocket was calculated as 30
meters.
The Red/Silver rocket with a C engine was predicted to have a final height of 92
meters, whereas the final height of the launched rocket was calculated as 450
meters.
The Black/Red rocket with a C engine was predicted to have a final height of 72
meters, whereas the final height of the launched rocket was calculated as 260
meters.
The Big White rocket with a C engine was predicted to have a final height of 73
meters, whereas the final height of the launched rocket was calculated as 190
meters.
The Red/Yellow rocket with B6 engine was predicted to have a final height of 50
meters, whereas the final height of the launched rocket was calculated as 170
meters.
The Red/Yellow rocket with a C6 engine was predicted to have a final height of
97 meters, whereas the final height of the launched rocket was calculated as 480
meters.
The actual results of the experiment do not match the predicted values, although the
predicted final height and the calculated final height for the small white rocket were fairly close
at 23 meters (predicted) and 30 meters (actual calculated height). For the rest of this project’s
data, there is a large discrepancy between the predicted final height data as compared to the
actual calculated final height data. There are several reasons why there might be such a large
difference between the predicted and actual final heights.
The skewed results are most likely due to the fact that rockets did not go straight
upwards once they were ignited and launched into the air; they curved one way or the other.
The curve of the rocket’s path might be due to a slight moving or bending or the launch pad.
This can be compensated for by using a sturdier launch pad. Another reason that rockets curve
in their flight path is because of the wind’s effect; although, on the day this experiment was
done, there was no significant wind. It is not possible to compensate for the wind’s effect on
the rocket, so if there is any wind at all, the results obtained could be off. As launched rockets
often have curved flight paths, it is necessary to measure the angles of the rocket’s path. Data
can be skewed because of the differences in the three people measuring the angles. The angles
that person one measured could be much higher or much lower than those of people two and
three. This affects the average angle, which affects the final height of the rocket. This average
angle affects the height because it is bigger, so a 1° or 2° difference can dramatically change the
actual height calculation. As an example, the reason that the small white rocket result was
relatively closer to the predicted height was because the angle and the height were relatively
low, resulting in less of a discrepancy when the average angle was off by a few degrees. Finally,
an additional reason that the results might be skewed is that when the rocket curves in its
flight, it lessens the distance between the rocket and some of the people measuring the angles,
while increasing it for others. This would make the results inaccurate because in this
experiment, the distance between all the people measuring the angles was set at 50 meters for
each rocket launched, rather than moving the distance of where the people measuring the
angles stood to a shorter or greater distance to make it more accurate.
The best way to compensate for the curving of the rocket is to use an altimeter. The
altimeter would sit inside the nose cone of the rocket when it is launched and it would measure
the exact final height of the rocket with great precision, by measuring the air pressure around
the rocket.
Reflection
I really liked this rocket project. I thought it was a lot of fun. I have gained a better
understanding of physics through this project. I have grown to love physics and find it fun. I like
that rather than just sitting in the classroom and talking about the math and science of physics,
we actually did a real world problem that brought the theories and principles of math and
physics to life. I feel this made applying the mathematics and science to the problem a lot
easier and more fun, since I was actual able to see the results of what I did, and not just what
the book wants me to regurgitate as the correct answer. I have learned how important it is to
have correct and precise measurements. If your measurements are off when you do the
experiment by just a degree or two, all the results of the experiment will be inaccurate. We ran
into this problem when we measured the angles of the heights of the rockets in the final
experiment. Even with the protractors and using three people to measure the angles, all our
measurements were off because we weren’t able to account for the curving of the rocket.
Though we now know the way to fix these measurements, which is to use an altimeter to
measure the actual final height, Mr. Hendricks would not allow us to use the corrective
instruments to do so. I think this was a good way to show us the importance of accurate
measurements. This project was difficult because of the time to write up each of the reports on
top of actually doing the lab in class. However, once I just got started on writing each section, it
went rather quickly. I tried my hardest to do each of the sections the day we did the lab, though
sometimes part of it had to be completed the next day. This also helped with the timing and
made it so I was not stressing at ten o’clock the night before to get it done. Consequently, I was
able to put a lot of thought and effort into each of the sections. While we did each of the labs, I
took very detailed notes. This helped me greatly when I wrote up each of the reports because I
had all the information I needed right in front of me; all I had to do was write it up. Taking
thorough notes also made it easier for me to understand what was going on in each of the labs.
If I didn’t quite understand what was going on in a particular moment, I could reread my notes
and understand what was happening very quickly. I am glad that an extra weekend was given to
the class to complete this project. I could have completed it by the original due date, but I feel
that the final project would have been more rushed. This might have resulted in me (or
someone else) missing something or not understanding something important, and perhaps
would not have ended up with as good of a report otherwise. This would have greatly increased
my stress level! I suggest that this might be a good thing to do for the students next year.
Providing even just a few more days to complete the project has helped my current class and
would really help the future students do a bit better job overall, I believe. All-in-all, I thought
this project was really fun and allowed us as students to more easily see the application of the
math and science that we use in the classroom in the real world.