Austin Cantwell
Thomas Fuller
Robert Weidner
Andrew West
Team 8
Engineering 112-533
Rocket Project Report
2
Table of Contents
Cover Page…………………………………………………………………………………..Page 1
Description of Project and Problem Statement …………………………………………….Page 3
Description of the as-built rocket with appropriate drawings………………………………Page 3
Operating procedures for the rocket………………………………………………………..Page 7
Description of safety measures taken……………………………………………………….Page 8
Expenses………………………………………………………………….…………………Page 8
Description of results from the computer simulation………………………………………Page 8
Comparison of computer simulation to experimental results......………………………….Page 18
Assumptions and experimental errors……………………………………………………..Page 22
Reflections………………………………………………………………………………….Page 23
Appendix A………………………………………………………………………………...Page 24
Appendix B…………………………...……………………………………………………Page 30
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1. Brief description of the project and problem statement
As a group, we had to design two separate water rockets. One rocket was built using the
parameters assigned to our group and the second was built according to what we believed would
provide the optimal setting for the largest maximum height. We wrote a program in order to
simulate the flight of a water rocket which we then used to find the optimal nozzle size and
whether or not a launch tube was beneficial or not for the second water rocket. Following the
launch of our rockets, we then compared our rockets performance to the computer simulation we
programmed.
2. Description of the as-built rocket with appropriate drawings
Bottle top
(neck cut off)
Tape
Polyester
fiberfill
Breathing holes for
altimeter (10 holes
using #49 drill bit)
Altimeter
Silicone glue
Silicone glue
2 in
Three fins,
120o apart
2 in
vw
5 in
4
Pressure
gauge
Quick
connect
Figure 2 Detail of Launch System
Safety
release
Schrader valves
(10)
5
Dt
Lt = 11.0 in
0.837 in
.0 in
0.250 in
.0 in
Figure 3 Detail of Launch Tube
6
Fdrag
descent
Fgravity
ascent
vrocket
mpayload
Positive
direction
s
mrocket
mair
mwater
Aprojected
vwater
Fthrust
Figure 4 Mathematical terms used to model the rocket.
mtotal
7
The rocket was constructed using 2 liter bottles, foam presentation board, and a silicon
based glue. The fins of the rocket were cut into a shape we thought would best keep the rocket
straight in flight. Assembly of the rocket is shown in Figure 1; the fins are glued to the end near
the nozzle. Each fin was approximately 120° from each other, giving an even amount of space
between them shown in Figure 4. One of the bottles is cut and glued in place to form the nose
cone of the rocket, where the altimeter is placed (showed in Figure 4 as mpayload).
The neck of the bottle acts as the nozzle of the rocket; no nozzles were glued into the
rockets. This was because the program showed that the best results would come from the rocket
without an inserted nozzle. A launch tube was used for both launches (Figure 3), the launch tube
fit directly in the neck of the rocket using an O-ring to keep an air tight seal. During the
pressurizing of the rocket a latch (Figure 2) is hooked to the bottle to keep it from launching
before it reaches the required pressure. The latch is then pulled off the rocket neck to launch.
3. Operating procedures for the rocket
Building the Rocket
1. We cut the top off of a two liter bottle and then fit it to the bottom of another two liter
bottle using silicon glue.
2. Then we cut the neck off of the top of the attached bottle.
3. Next we filled the chamber created between the two bottles with pillow stuffing.
4. Then holes were drilled into the chamber so that air pressure could change and the
altimeter could function.
5. Fins were traced onto a piece of poster board.
6. Fins were cut out of the poster board using a craft knife.
7. The bottle was sanded where the fins were to be attached.
8. Silicon glue was used to attach the fins.
(We did not use a nozzle.)
Launch Procedure
1.
2.
3.
4.
5.
The altimeter was placed into the chamber filled with pillow stuffing.
The top of the rocket was covered with a piece of tape.
The rocket was filled with water to the desired fill factor.
The launch tube was inserted into the rocket and a snug fit was made with the o-ring.
The bottom of the launch tube was screwed into the launch pad.
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6. The rocket was pressurized to 100psig using bike pumps.
7. The string attached to the launch pad was pulled to release the rocket.
4. Description of safety measures taken
While fabricating we used special care to use a sharp blade and cut away from ourselves while
using craft knives. We also took special care while building the rocket to not hit ourselves while
drilling holes. When launching we made sure to wear safety goggles to protect our eyes from any
potential shrapnel in the case of the rocket bursting. We also stood a safe distance away from the
launch pad while other groups were launching. We were always attentive whenever other groups
were pressurizing and launching their rockets so that if we needed to move we would be ready to
get out of the path of the rocket.
5. Expenses
Expendable Supplies
Two 2-L Pepsi bottles
Foam core board, 3/16-in thick
Polyester fiberfill
Paper towels
RTV silicone adhesive
Duct tape
Total:
$1.99 * 2 = $3.98
$3.49
$5.38
$0.97
$9.97
$4.99
$28.78
6. Description of Results from the computer simulation
The Rocket initially starts on the launch pad with a .505 inch diameter nozzle, fill fraction of .4,
11 inch launch tube and 100 psig. The rocket ways 70.06 g and has a payload of 6.6 grams.
When the rocket is released, it begins Phase one. Phase 1 is at time 0 and the rocket is moving up
the launch tube. No water is lost at this time, but the rocket is gaining momentum. Once the
rocket leaves the launch tube water becomes the propellant as it is ejected from the nozzle. Phase
2 is when the greatest acceleration is reached because of the high force of thrust and combination
of loss of water mass. Phase 3 begins when the rocket has ejected all of the water and pressurized
air becomes the propellant. During Phase 3 the rocket continues to accelerate, but at a slower
rate. At the end of Phase 3 the rocket reaches its maximum velocity and loses thrust; becoming a
glider. Phase 4 is split into 2 sections. The first part of Phase 4 is while the rocket still continues
on a positive trajectory because of momentum but is rapidly decelerating due to friction and
gravitational forces. The second part of Phase 4 initiates when the rocket has reached its
maximum height and begins to accelerate back to the ground in free fall.
*The red vertical line indicates the end of Phase 2 and beginning of Phase 3 (0.301 Seconds)
*The black vertical line indicates the end of Phase 3 and beginning of Phase 4 (0.376 Seconds)
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Figure 5: Pair vs. Time
The Pair Decreases moderately during Phase 2 because it is expanding and is the driving force for
pushing the water out of the nozzle. As the air expands, it rapidly cools and dissipates heat into
the surroundings as seen in Figure 6 which is very similar to Figure 5. The loss of water can be
seen in Figure 11. When Pair enters Phase 3 the air expansion is extremely rapid because air is
less dense than water and exits the rocket faster. During Phase 4 the pressure is constant and
equal to the ambient pressure.
Figure 6: Temp vs. Time
The rapid cooling of air can be attributed to the expanding gas as the pressure drops as seen in
Figure 5. Temperature drops occur in Phase 2 when air pushes the water from the nozzle and
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more rapidly during Phase 3 when air is being expelled. Although the expanding gas does cool, it
is not reasonable for it to approach below freezing temperatures. The temperature stays constant
once the rocket enters Phase 4 because the expansion of gas has ended.
Figure 7: Fthrust vs. Time
The rocket thrust is greater at the instant Phase 2 begins. The high thrust is because air is under
the greatest pressure (Figure 5) and water is leaving the rocket at the highest rate (Figure 11) The
opposite and equal reaction of the exiting water at maximum velocity provides the maximum
thrust. During Phase 3 the thrust decreases because the exciting air has less mass than water and
does not provide as much propulsion. During Phase 4 the rocket is in glide flight and has no
thrust and begins to slow down (Figure 15) and the acceleration is due to the constant force of
gravity (Figure 8).
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Figure 8: Fgravity vs. Time
The force of gravity is directly proportional to the mass. Therefore the force of gravity on the
rocket decreases as it loses water mass (Figure 11) during Phase 2 and air mass (Figure 12)
during Phase 3. After the propellants are consumed, Phase 4, the mass of the rocket and force of
gravity on the rocket are constant.
Figure 9: Fdrag vs. Time
The force of drag is proportional to the drag coefficient, air density, and projected area which are
all constants, but it is also exponential of velocity. During phase 2 and 3 the rocket is
accelerating (Figure 14) and the so is the drag force. Once thrust is zero (Figure 7) the rocket
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velocity decreases to zero (Figure 15) and there will be no drag. When the rocket accelerates
back to the ground, the drag will increase again.
Figure 10: Fnet vs. Time
Fnet is the combination of Fthrust (Figure 7), Fgravity (Figure 8), and Fdrag (Figure 9). Fnet is used to
represent all of the forces acting on the rocket during flight. The acceleration of the rocket
(Figure 14) is then able to be calculated as a ration of Fnet over mtotal.
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Figure 11: mwater vs. Time
During phase 2, water is the rapidly being pushed out of the rocket by the expanding air (Figure
5) and provides huge amounts of thrust (Figure 7). The rapid expulsion of water is represented
by the extreme negative slope of the mass of water in the graph above. Since water is the
heaviest component of the rocket, the mtotal graphs (Figure 13) also has a large negative slope.
During phase 3 and 4 there is no remaining water the therefore the mass is constant at 0
Figure 12: mair vs. Time
During Phase 2 the air in the rocket ix expanding, but does not leave the rocket, so the mass is
constant. When the water is completely expelled the rocket enters Phase 3 and pressurized air
leaves the rocket and causes a decrease in air mass. The exciting air still causes the rocket to
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accelerate (Figure 14) but not as quickly as water. The mair does not reach 0 because there is still
air in the rocket at ambient density that has mass.
Figure 13: mtotal vs. Time
The mtotal is the addition of mwater (Figure 11), mair (Figure 12), and constant masses mrocket and
mpayload. The greatest loss of mass is the water during Phase 2 and to a much lesser extent, mair
during Phase 3. The mtotal is constant to mrocket and mpayload during Phase 4.
Figure 14: arocket vs. Time
The acceleration of the rocket is computed as the ratio of Fnet (Figure 10) divided by mtotal
(Figure 13). The greatest acceleration is during Phase 2 because of the high thrust (Figure 7), but
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still continues to accelerate through Phase 3 as air is expelled. The rocket decelerates once all
propellant is consumed and it approaches the climax. The rocket then becomes zero when the
maximum height is obtained and then the constant acceleration of gravity overtakes the rocket
through the remained or phase 4.
Figure 15: vrocket vs. Time
Velocity is incrementally changed by arocket (Figure 14) as a factor of minute time intervals. From
the graph it is easy to see that the rocket’s velocity increases greatly through the Fthrust (Figure 7)
of water and air during Phase 2 and 3, but begins to slow down in the vertical direction then
accelerate in the negative direction.
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Figure 16: x vs. Time
The height vs. Time graph provides and overall picture of the rockets height trajectory compiled
from all of the calculations. The main source of data is from the vrocket (Figure 15) because height
is dependent on the velocity multiplied the minute increments of time. The effects of the
acceleration from the thrust of water and air can be seen in the beginning of flight and the
momentum carries the rocket through a trajectory only affected by the force of gravity and
frictional forces of drag.
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Figure 17: Forces vs. Time
Figure 17 is a combination of the all of the Forces in order to see how they are combined
together to calculate the net force. The height plot is provided to see the effects of the net force to
propel the rocket skyward.
Figure 18: Forces and Acceleration Vs. Time
Figure 18 relates the total Force to the rate of acceleration and the rate of velocity. The velocity
slowly decreases for flight in the positive direction once the force of thrust ends and the
acceleration ends.
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7. Comparison of Simulation to experimental results
Data with Launch Tube:
Figure 19:
Figure 20:
19
Figure 21:
Without Launch Tube:
Figure 22:
20
Figure 23:
Figure 24:
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Comparisons with Launch Tube
The max heights of the launches generated by the simulation (shown in Figure 19)
indicate that the 0.842 nozzle with a fill fraction from 0.2 to 0.3 would have the highest point.
The data collected from the class launches is very similar, showing that the 0.842 nozzle and a
0.4 fill fraction flew the highest.
The time it takes for the rockets to reach their maximum height increased as the fill
fractions increased in the simulation, shown in Figure 20. The same results are on each nozzle
nice. Data from the class launches is not very consistent but from the launches that seem to be
creditable, the data agrees with the simulation. The data shows an increase in the amount of time
it takes for the rocket to reach its max height as the fill fractions are increased.
Time of impact with the ground increased as the rockets fill fractions increased in the
simulation, shown in Figure 21. From the class data the largest impact times are with the rockets
with the greatest fill fractions. This shows that the data agrees with the simulations, the greater
the fill fractions of the rockets the higher total times they had.
Comparisons without Launch Tube
The rocket from the simulation that reaches the highest point had a 0.225 nozzle with a
fill fraction from 0.2 to 0.3, found in Figure 22. Data from the class launches disagrees with the
simulation; the data shows the rockets that had a nozzle 0.842 with a 0.5 fill fraction and the
nozzle 0.63 with a 0.4 fill fraction reach a much higher point.
Without the launch tubes, the time to reach the maximum heights still increased as the fill
fractions increased which can be seen in Figure 23. The data from the class didn’t contain many
times for this section, from the times that were recorded it can be seen that they agree with the
simulation. The higher fill fractioned rockets took longer to reach their maximum heights. The
nozzle sizes didn’t affect these results overall.
The data from the simulation shown in Figure 24 indicates that the total in air time of the
rockets increased with the increase in the fill fractions. From the data that was collected from the
class, it shows that the simulation was accurate. The rockets total time till impact was larger
when they had a greater fill fraction.
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8. Assumptions and experimental errors
In the first phase of the computer program it is assumed that water does not come out of the
rocket while it is traveling up the launch tube. This is not completely true though because some
water escaped the rocket during this part of the launch. This error would lead to the excel
program estimating a height higher than the actual launch. In phase two of the rocket flight we
assumed that no air escaped from the rocket while the water was escaping and this is highly
unlikely. In all of the phases it was assumed that there was no force due to wind and there was
clearly a wind blowing. This will obviously alter the flight path of the rocket and could increase
drag force which would decrease the height of the flight. The program was also not a perfect
mathematical model. Even though it was close a few things were not perfect such as the
temperature calculation which could lead to a false estimation. One potential experimental error
was in filing the rocket with water because we used a scale to measure out the water and then
poured it into the bottle. There is possible human error in operating and reading the scale as well
as the fact that some of the water was lost while pouring into the rocket. Also the drag created
by the fins was not accounted for in the program. This drag led to a lower flight than estimated in
the program. Another source of possible error was in pumping up the rocket. It was hard to tell
when the rocket was exactly at 100 psig so it is likely that the rocket was launched with slightly
more or slightly less pressure, which would affect the height of the launch. The fabrication and
insertion of the nozzles could have led to errors for many of the teams. If the nozzle was not
inserted perfectly straight or if the nozzle was manufactured in a way such that it was not flat it
could lead to erratic flight path and likely would lead to a substandard rocket performance. The
altimeters were the main source of error in this experiment. They were clearly not functioning in
a realistic manner because some rockets that went around 30 feet in the air and then crashed into
the ground were said to have gone 300 feet in the air by the altimeter. It is clear that the
altimeters did not accurately measure the height of the flights. This could be due to the way that
holes were drilled in the chambers or the altimeters may have been malfunctioning.
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Reflections
This project encompassed numerous skills we have acquired in engineering class in the
last two semesters. During the programming portion of the project, we implemented much of the
physics we had learned over the previous year. We had to use our VBA programming skills in
order to write a program that could simulate the flight of our water rocket and then be able to
analyze the results effectively in a comprehensive report. Our knowledge of units was essential
as we had to convert all units into SI units before we could even begin analyzing data. Possibly
the biggest skill we had implemented throughout the project was teamwork. This project was too
complicated to not have full participation by each member of the team. If we could do this
project over again, we would have made sure the fins we attached firmly to the side of the liter
bottle and take care in attaching them so that they were equally spaced. We felt like the fins
played a big part in the flight of the water rocket. Overall however, this project went relatively
smoothly and we don’t believe there should be many improvements made other than using more
sophisticated altimeters. The project didn’t cost much and it was quite impressive compare to the
project we did in ENGR 111 so I believe it would be wise to continue the project.
24
Appendix A
Option Explicit
Sub Rocket()
'Team #8
'Density
Dim densatm, densair, denswater As Double
denswater = Cells(24, 4)
'Pressure
Dim patm, pair As Double
patm = Cells(23, 4)
pair = Cells(13, 4)
'Mass
Dim minit, mmair, mair, mwater, mtotal, mrocket, mpayload As Double
mmair = Cells(21, 4)
mrocket = Cells(12, 4)
mpayload = Cells(11, 4)
'Constants
Dim r, temp, tempinit, tempamb, g, cd, cnozzle, y, cair As Double
r = Cells(26, 4)
tempamb = Cells(25, 4)
g = Cells(19, 4)
cd = Cells(14, 4)
cnozzle = Cells(15, 4)
y = Cells(22, 4)
cair = Cells(20, 4)
'Volume
Dim volinit, volair, volbottle As Double
volbottle = Cells(6, 4)
'Velocity
Dim velrocket, velwater As Double
'Force
Dim fthrust, fgravity, fdrag, fnet As Double
'Area
Dim anozzle, aprojected As Double
anozzle = Cells(9, 4)
aprojected = Cells(10, 4)
'Rate
Dim mratewater, mrateair As Double
'Time
Dim time, deltatime As Double
deltatime = Cells(3, 4)
'other
Dim f, lt, x, arocket, count1, count2 As Double 'f=fill fraction; time=time since rocket left launch
pad; x=vertical distance
f = Cells(7, 4)
25
lt = Cells(17, 4)
temp = tempamb
densatm = (mmair * patm) / (r * tempamb)
densair = (mmair * pair) / (r * tempamb)
volair = (1 - f) * volbottle
mair = densair * volair
mwater = f * volbottle * denswater
mtotal = mrocket + mpayload + mwater + mair
time = 0
x=0
velrocket = 0
volinit = (1 - f) * volbottle
tempinit = tempamb
'Phase 1 Calculations
velrocket = ((2 * ((pair - patm) * anozzle - mtotal * g) * lt) / mtotal) ^ (1 / 2)
x = lt
velwater = 0
fthrust = (pair - patm) * anozzle
fgravity = mtotal * g
fdrag = (1 / 2) * cd * densatm * aprojected * (velrocket) ^ 2
fnet = fthrust - fgravity - fdrag
arocket = fnet / mtotal
'Display Data
Cells(34, 1) = time
Cells(34, 2) = pair
Cells(34, 3) = temp
Cells(34, 4) = fthrust
Cells(34, 5) = fgravity
Cells(34, 6) = fdrag
Cells(34, 7) = fnet
Cells(34, 8) = mwater
Cells(34, 9) = mair
Cells(34, 10) = mtotal
Cells(34, 11) = arocket
Cells(34, 12) = velrocket
Cells(34, 13) = x
'Phase 2 Calculations
count1 = 0
count2 = 0
Do While mwater > 0
26
volair = volbottle - (mwater / denswater)
temp = tempinit * ((volinit / volair) ^ (y - 1))
pair = (mair * r * temp) / (mmair * volair)
mratewater = cnozzle * anozzle * ((2 * denswater * (pair - patm)) ^ (1 / 2))
mwater = mwater - (mratewater * deltatime)
mtotal = mrocket + mpayload + mwater + mair
velwater = cnozzle * ((2 * (pair - patm) / denswater) ^ (1 / 2))
fthrust = mratewater * velwater
fgravity = mtotal * g
fdrag = (1 / 2) * cd * densatm * aprojected * ((velrocket) ^ 2)
fnet = fthrust - fgravity - fdrag
arocket = fnet / mtotal
velrocket = velrocket + (arocket * deltatime)
x = x + (velrocket * deltatime)
time = time + deltatime
'Display Data
count1 = count1 + 1
If count1 = 10 Then
count2 = count2 + 1
count1 = 0
Cells(34 + count2, 1) = time
Cells(34 + count2, 2) = pair
Cells(34 + count2, 3) = temp
Cells(34 + count2, 4) = fthrust
Cells(34 + count2, 5) = fgravity
Cells(34 + count2, 6) = fdrag
Cells(34 + count2, 7) = fnet
Cells(34 + count2, 8) = mwater
Cells(34 + count2, 9) = mair
Cells(34 + count2, 10) = mtotal
Cells(34 + count2, 11) = arocket
Cells(34 + count2, 12) = velrocket
Cells(34 + count2, 13) = x
End If
Loop
'End Phase 2 Calculations
'Phase 3 Calculations
tempinit = temp
minit = mair
Do While pair > patm
mwater = 0
27
volair = volbottle - (mwater / denswater)
temp = tempinit * ((mair / minit) ^ (y - 1))
pair = (mair * r * temp) / (mmair * volair)
densair = (mmair * pair) / (r * temp)
mrateair = cnozzle * anozzle * ((y * (2 / (y + 1)) ^ ((y + 1) / (y - 1)) * densair * pair) ^ (1 / 2))
mair = mair - (mrateair * deltatime)
mtotal = mrocket + mpayload + mwater + mair
fthrust = mrateair * cair
fgravity = mtotal * g
fdrag = (1 / 2) * cd * densatm * aprojected * ((velrocket) ^ 2)
fnet = fthrust - fgravity - fdrag
arocket = fnet / mtotal
velrocket = velrocket + (arocket * deltatime)
x = x + (velrocket * deltatime)
time = time + deltatime
'Display Data
count1 = count1 + 1
If count1 = 10 Then
count2 = count2 + 1
count1 = 0
Cells(34 + count2, 1) = time
Cells(34 + count2, 2) = pair
Cells(34 + count2, 3) = temp
Cells(34 + count2, 4) = fthrust
Cells(34 + count2, 5) = fgravity
Cells(34 + count2, 6) = fdrag
Cells(34 + count2, 7) = fnet
Cells(34 + count2, 8) = mwater
Cells(34 + count2, 9) = mair
Cells(34 + count2, 10) = mtotal
Cells(34 + count2, 11) = arocket
Cells(34 + count2, 12) = velrocket
Cells(34 + count2, 13) = x
End If
Debug.Print "mtotal, mair, mwater, mrocket, mpayload, mmair, minit"; mtotal, mair, mwater,
mrocket, mpayload, mmair, minit
Loop
'End Phase 3 Calculations
'Phase 4 Calculations
Do While x > 0
'Still going up: Ascent
If velrocket > 0 Then
28
mwater = 0
volair = volbottle - (mwater / denswater)
pair = patm
temp = tempinit * ((mair / minit) ^ (y - 1))
densair = (mmair * pair) / (r * temp)
mair = densair * volair
mtotal = mrocket + mpayload + mwater + mair
fthrust = 0
fgravity = mtotal * g
fdrag = (1 / 2) * cd * densatm * aprojected * ((velrocket) ^ 2)
fnet = fthrust - fgravity - fdrag
arocket = fnet / mtotal
velrocket = velrocket + (arocket * deltatime)
x = x + (velrocket * deltatime)
time = time + deltatime
'Rocket Descending
Else
mwater = 0
volair = volbottle - (mwater / denswater)
pair = patm
temp = tempinit * ((mair / minit) ^ (y - 1))
densair = (mmair * pair) / (r * temp)
mair = densair * volair
mtotal = mrocket + mpayload + mwater + mair
fthrust = 0
fgravity = mtotal * g
fdrag = (1 / 2) * cd * densatm * aprojected * ((velrocket) ^ 2)
fnet = fdrag - fgravity
arocket = fnet / mtotal
velrocket = velrocket + (arocket * deltatime)
x = x + (velrocket * deltatime)
time = time + deltatime
End If
'Display Data
count1 = count1 + 1
If count1 = 10 Then
count2 = count2 + 1
count1 = 0
Cells(34 + count2, 1) = time
Cells(34 + count2, 2) = pair
Cells(34 + count2, 3) = temp
Cells(34 + count2, 4) = fthrust
Cells(34 + count2, 5) = fgravity
29
Cells(34 + count2, 6) = fdrag
Cells(34 + count2, 7) = fnet
Cells(34 + count2, 8) = mwater
Cells(34 + count2, 9) = mair
Cells(34 + count2, 10) = mtotal
Cells(34 + count2, 11) = arocket
Cells(34 + count2, 12) = velrocket
Cells(34 + count2, 13) = x
End If
Loop
'End Phase 4 Calculations
End Sub
30
Appendix B
31
32