A Study to Determine the Significance of Frictional Drag on Rocket Flight.

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Feb 22, 2014 (3 years and 6 months ago)

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A Study to
Determine

the Significance

of
Frictional Drag

on
Rocket Flight.


Natasha Selvey

Jed Clinger

Alyssa Vincent
-
Hill

Physics / per. 3 / 2005
-
2006



Abstract

Viscous drag is the frictional force determined by the surface of a rocket that acts
against
its upward motion.
This study measured the maximum height achieved
by a small model rocket launched with different coverings with various (though
unknown)
frictional coefficients
.
These d
ifferent frictional surfaces
were

tested to
determine the significanc
e of frictional drag on the flight of the rocket.
The
e
xperimental resea
rch shows that friction does have

a notable impact on the
maximum height that the rockets fly
; when tested as a controlled variable, friction
greatly impeded the model rocket’s maximum

flight height.


Introduction


Th
e goal of this study is to determine the significance of frictional drag on model rockets. D
uring
the modern space age, much of the experimentation that has been used to develop real rockets and
missiles has been conducted

using small models of larger rockets. These small rockets allow scientists to
measure the scaled effects of thrust, lift, propulsion, air resistance, drag and gravitational resistance on
rockets in a safer
less expensive

environment. Many of the discoveri
es that have been made on models
have been successfully translated to a bigger scale with larger rockets
, and have been used in the research
and development necessary for real rockets.


The basic forces and principles at work during rocket flight are the
same basic physical principles
studied in entry
-
level physics class; gravity, thrust, energy, velocities, friction and drag are all involved in
rocket flight.
Eric Burgess, Fellow and Assistant Secretary of the British Interplanetary Society, Honorary
Memb
er of the Pacific Rocket Society, elaborates further;


“We recollect that from the simple idea of units the next step is to the
consideration of matter when it is in motion or when a force is applied to
matter. A force is defined as that which changes the

motion of a body. It
is needed to move a body from a rest position or to stop a mass that is
already moving. Momentum, on the other hand, is the product of mass
and velocity, so that force can be described as the rate of change of
momentum. Velocity descr
ibes the rate at which an object is moving
and can be found from the distance traveled divided by the time taken
traveling that distance.” (Burgess, 1952)



These principles can be controlled to control the flight of the rocket; Burgess continues: “A very

important relationship exists between force, mass, and acceleration. The force in pounds is found to be
equal to the weight in pounds multiplied by the acceleration in feet per second per second. The greater the
force applied, the greater the acceleration

sustained. Acceleration thus becomes controllable by variation of
the propulsive force, the thrust of the rocket.” (Burgess, 1952)



Propulsion is broadly defined as the changing motion of a body. George P. Sutton,
Associate Division Leader at the Lawren
ce Livermore National Laboratory, explains; “
Propulsion
in a broad
sense is the act of changing the motion of a body. Propulsion mechanisms provide a force that moves
bodies that are initially at rest, changes a velocity, or overcomes retarding forces when

a body is propelled
through a medium. Jet propulsion is a means of locomotion whereby a reaction is imparted to a device by
the momentum of ejected matter.” (Sutton, 1986) Rocket engines create this propulsive force via the
combustion reactions (the chemi
cal reactions create heat and pressure) which drives the rocket upward.


Rockets are merely chambers in which fuel is burned to create pressure which powers upward
motion. Burgess
explains basic rocket design in his book, “Rocket Propulsion”;
“The simples
t rocket [thus]
consists of a chamber in which a fuel can be burned… Burning takes place, a heat releasing or exothermic
chemical reaction takes occurs and the molecules of the gases produced by the combustion dash hither and
thither at high velocities. A
specially designed exhaust nozzle changes this random molecular motion to a
stream of gas which issues from the mouth of the rocket at a very high speed.” (Burgess 1952)
Rocket
propulsion systems (also known as rocket engines) are propulsion devices that p
roduce thrust by ejecting
matter originally in the rocket; this ejected material is called propellant. (Sutton, 1986) Sutton details the
types of solid propellants used in rockets; “The term
solid propellant
has several connotations, including a)
the rubbe
ry or plastic
-
like mixture of oxidizer, fuel and other ingredients that have been processed and
constitute the finished product, b) the processed but uncured product, c) a single ingredient, such as the fuel
or oxidizer.” (Sutton, 1986)
Propulsion engines
produce gases that create pressure to force the rocket
upwards;
“In the
combustion chamber
of the chemical rocket a reaction takes place between fuel and the
oxidizer. The main combustion products are gases which are heated by the chemical energy released.

As
these hot gases are contained in a relatively small volume, the thermal expansion of the gases results in a
high pressure. These pressurized gases are expanded and accelerated by a nozzle, resulting in a reaction
force on the rocket vehicle.” (Cornelis
se,
Schöyer

and Wakker, 1979)



While the propellant produces the force pushing the rocket upward, friction and drag are forces that
act against the rocket during its ascent.
Sutton formally defines drag; “
The
drag
is the
aerodynamic force
in
a direction o
pposite to the flight path due to the resistance of the body in motion in a fluid.” (Sutton, 1986)
Burgess continues this analysis, detailing the exact force (friction and drag) that propulsion must counter to
carry the rocket upwards; “In an atmosphere th
e velocity of the rocket is limited due to the effects of air
resistance. A maximum velocity is reached, in vertical flight, when the propulsive force is exactly balanced
by the retarding forces of drag and gravity”

(Burgess, 1952)
Different kinds of drag
act on the ascending
rocket, depending on the build and design of the rocket, and the stage its at in flight.
Researchers J.W.
Corneslisse, H.F.R.
Schöyer
, and K.F. Wakker explain these distinctions in their book, Rocket Propulsion
and Spaceflight Dynamics
;


“The drag of a rocket vehicle can be split into the following components:
wave drag
,
due to the presence of shock waves and dependent on the
Mach number;
viscous drag
, due to friction;
induced drag
, due to the
generation of lift;
base drag
, due to the
wake behind the vehicle;
interference drag
, due to the interaction of various flow fields; and
roughness drag
, due to the surface roughness su
ch as rivets and
welds.”



Viscous drag
is the main component
[of drag]
at subsonic speeds. It
can be estimated b
y considering the
friction drag coefficient,
C
D
, for a
flat plate of equal length and equal
whetted area
as the rocket vehicle.
These coefficients are based on the whetted area as a reference area.
For most large rockets, one may assume the boundary layer
to be
turbulent. Transition from laminar to turbulent takes place around Re =
10^6 based on the body

length, so that for small vehicles, still a major
portion of the boundary layer may be laminar. Surface roughness may
cause a transition from laminar to tu
rbulent at lower Reynolds
numbers.” (
Cornelisse,
Schöyer

and Wakker, 1979)


Because the rockets experimented upon in this study are traveling at subsonic speeds, viscous drag is the
main drag component that the study will attempt to test for and measure.


The study aims to begin to quantify the effects of viscous drag on the flight speeds and distances
of model rockets. To test this, the rockets are to be tested in flight covered with different materials (fabric,
different types of sandpaper) and shot off

with the same type of engine each time. This will allow analysis of
the height and speeds of flight under different circumstances, and the variable (the drag) is controlled
because all of the other flight conditions are the same.


A great deal of resear
ch has already been done on rockets and rocket propulsion science. Many
basic physical laws pertaining to rockets and rocket propulsion have been discovered
. However, the exact
impacts of friction and drag are not known. This study aims to answer the quest
ion;
does friction significantly
impede the flight of a small model rocket?


We hypothesize that the different surfaces covering the rocket will have
an

insignificant to
negligible effect on the rocket’s flight, but we don’t believe that the friction will

significantly impair rocket flight
over the short distances that are traveled by model rockets.
We came to this conculsion through analysis of
the formula for drag force.


The basic equation for the calculation of the drag force is
D = C
D

ρ
V
2
.
D is drag

force; C
D

is the
coefficient of drag (which is constant, depending on the material covering the rocket and the rocket’s
shape). A stands for the reference area of the rocket (the cross
-
sectional area of the tube).
ρ

is the density
of the medium that the o
bject is moving through (air, in the rocket’s case). V stands for the velocity of the
rocket.


We believe that the impact of drag on the upward motion of the rocket will be negligible because of
the implications of the drag force formula. Because model ro
ckets don’t encompass very much force and
aren’t traveling very fast, the V^2 in the formula (which is the deciding formula for the strength of the drag
force) won’t be significantly large; therefore, we
hypothesize

that the impact of the drag force on the

flight of
the rocket won’t be significant either.


Materials

1 simple rocket kit or rocket

Rocket launcher

6 1/2A6 Estes rocket engines

2 A83 Estes rocket engines

Wadding paper

Fabric

Sandpaper
(
of

36d

grit
)

Sandpaper
(
of 220c grit)

Pencil/paper to
record d
ata

D
igital camera

(optional)

Stopwatch

Measuring

tape

Astrolabe

Scissors

Hot glue gun

Superglue

Masking tape

Ruler

M
atch

Methods

1.

Build rocket according to kit instructions (painting not necessary).

2.

Measure rocket's length (above the fins a
nd below the plastic nose cone) and circumference.

3.

Cut a piece of each
type

of sandpaper and fabric the width of the circumference and the length of the
rocket's length with a half
-
inch of overlap.

4.

Curl the papers and fabric into a tube and glue th
e edges together with hot glue to form a sturdy tube of
sandpaper or fabric.

5.

Cut a slit in one end of the paper/fabric tube that will allow the launch wire to move through the launch lug
unobstructed
.

6.

Mount of the launch lug of the rocket on the ma
tch to allow the launch wire to be clear of the
sandpaper

or fabric covers (so the covers do not impede motion).

7.

Find a large, clear, grassy field on a clear, still day (as little wind as possible).

8.
S
et up the rocket launcher and position the launch
er operator here.

9.

Measure 120ft away from the launch site and position the
astrolabe

operator at this point.

10.

Load 1/2A6 engine in naked rocket (no covers
) and prepare rocket for launch.

1
1
.

Countdown and launch rocket. Timer should record the time

the rocket took to reach its parachute
ejection point (this is the maximum height of its journey);
astrolabe

operator should record the angle that the
rocket's launch makes with his/her position at this point.

1
2
.

Record the launch observations.

1
3
.

Repe
a
t the launch process with the ½
A6 engines; 2 small sandpaper, 1 large sandpaper, 1 fabric, 1
more
with no cover
.

1
4
.

Launch the rocket
twice
with the
two
A83 engines: once with the large grain sandpaper taped onto the
outside of the
rocket,
and
once with

the
large

grain sandpaper cut up and stuffed in the rocket (this is to
control the weight variable in the experiment).

1
5
.

Record all data.

1
6
.

Use basic right
-
angle trigonometry to
analyze

the data and mathematically determine the height of the
rocket f
rom the measured angle.
Record

the
exact values and approximations of the

calculated data.




This study was performed at Adair Park on

the morning of

May 20
th
, 2006. The rocket used in the
experiment was Estes
Freedom
model (Kit #10024).



Data Presenta
tion and
Results


We used basic right
-
triangle trigonometry to find the maximum height that the rocket
traveled to by measuring the angle of sight with a astrolabe from a point 120ft away from the
launch point. Knowing this angle, and the ground distance,
we were able to co
nstruct the right
angle diagram above, and use this diagram, as well as the tangent trigonometric ratio (tanθ = side
opposite/side adjacent) to solve for the missing side (the y value) of the triangle


which also
happened to be the maximum height that the

rocket traveled.






Recorded experimental data:

(data is adjusted for significant digits)


Engine Type:
Estes ½ A6


Rocket Cover Type


Theta Value


Time (launch to

maximum height)


Distance (ground)


Height (exact)


Height
(approximate)
(ft)


Nake
d (1)



35


-


120ft


120tan35


89


Naked (2)



40


2.2
s


120ft


120tan40


105


Big Sandpaper (1)



20


3.4
s


120ft


120tan20


48


Small Sandpaper (1)



30


2.8
s


120ft


120tan30


74


Small Sandpaper (2)



31


2.1
s


120ft


120tan31


77


Fabric (1)



31


2.0
s


120ft


120tan31


77


Engine Type:
Estes A83


Rocket Cover Type


Theta Value


Time (launch to

maximum height)


Distance (ground)


Height (exact)


Height
(approximate)
(ft)


Big Sandpaper
-

outside



47


3.2s


120ft


120tan47


133


Big Sandp
aper
-

inside



69


3.4
s


120ft


120tan69


317




With the first set of engines we used to launch the rocket (1/2A6) we launched 6 trials using
different variables (rocket covers) that test our question. First, we launched the rocket “naked” without a
san
dpaper or fabric cover. It reached a height of 84

feet, which was far higher than the other trials when the
rocket wore a sandpaper or fabric cover. The only trial when the rocket traveled higher with the 1/2A6
engine was the second time we launched it wit
hout a
cover, and then it traveled 100

feet in the air.


The second time we launched the naked rocket, we found that it traveled faster than the rockets
with covers. The second naked trial took 2.2 seconds from liftoff to its peak in the air. When we laun
ched the
first trial of the rocket with the small sandpaper cover it was in the air for 2.8 seconds, and the first trial of the
big sandpaper cover yielded a time of 3.
4

seconds. Although

the fabric cover had a shorter time period
,

it
did not fly as high a
s the rocket without a cover, and the same applies to the second trial of the small
sandpaper cover.


Discussion

We can assume that the rockets with covers had more friction as they flew
, because the surfaces
of all of the covers were rougher than the smoo
th uncovered rocket.

The rocket with the fabric cover
performed nearly as well as the rocket with the small sandpaper cover. The fabric cover trial went 72

feet
into the air and in 2.0 seconds. The small sandpaper trials went 69 feet into the air in 2.8

se
conds and then
7
2 feet into the air in 2.1

seconds. The average for the two small sandpaper trials is 70

feet, and compared
to the fabric cover test of 72 feet, the two covers are quite close in their effect of drag on the rocket. The big
sandpaper trial s
howed that with a larger sandpaper cover, more drag is created, because it flew the longest
with the shortest height, 43

feet in 3.4

seconds.

To control for the effect of
the most extreme weight differences (with the heaviest sandpapers)
,

the
rocket with t
he
coarse

sandpaper cover was tested twice, with
the
coarse

sandpaper cover on the outside
once and then on the inside of the rocket. This assures no difference in weight, and explains if the weight
variable plays a large role in the results. We tested thi
s with a different engine, A83 which is more powerful,
and explains why the rocket flew considerably higher than our first six trials. Our results showed that with
the sandpaper cover on the outside the rocket flew 128

feet high in 3.2 seconds. But with th
e sandpaper on
the inside (same weight as when the cover is on t
he outside) the rocket flew 312

feet high in 3.4

seconds.
That is a height difference of 183

feet in 0.2 seconds.

Analysis of the drag equation proves the significance of the drag force actin
g on the rockets.
D =
C
D

ρ
V
2
.
For the rocket fired with the A83 engine, the drag force is the friction impeding the rocket’s
ascent. Because the same rocket weighing the same amount with the same engine flew
133

feet in 3.2
seconds cove
red with sandpaper,

and 317 feet in 3.4

seconds uncovered, we know that some force was
impeding the covered rocket’s motion. Knowing the formula, we can deduce the factor that prevented the
motion;


D is the impeding force.
The cross
-
sectional area is the same for both tria
ls (the same rocket was
used), and the
ρ

constant is also constant. The velocities were different between the two trials, but we know
that velocity is a product of initial acceleration, which was constant for both trials. Because F = ma, we know
that acceleration also equals F/m, and initial fo
rce and mass were the same for the experiment. Therefore,
an impeding force must exist


and looking back to our initial drag equation, we see that C
D
, the drag
coefficient, is the factor that we cannot account for. Knowing that the surfaces were significa
ntly different,
we can come to the conclusion that the drag coefficient was the deciding factor in the significantly different
data that was collected during the test.
However, t
here are
assumptions

with this question
.

Velocity is not
perfectly constant du
ring the rocket’s flight, although it is close; the rocket engine gives the rocket a burst of
thrust at the beginning of it’s flight, and then continues to burn
at a constant rate
until the rocket reaches its
maximum height at the top of its flight path.
M
ass is not
constant either; mass is lost as propellant is burned
during flight.





Analysis


This study asked whether or not it is possible to determine if friction has
a significant

effect on the
maximum height that a small rocket flies
. According to te
sts, friction
does

have a significant effect.
Comparing the height of the na
ked rocket tests (average of 92

ft) to the height of the large sandpaper cover
test with the 1/2A6 engine (43

ft), the naked rocket flew more than twice the height of the large san
dpaper
covers. The average speed for
the naked rocket tests was 36

ft/sec, and the speed for the large sandpaper
test was 12

ft/se
c. That is a difference of 23
ft/sec, which means the naked rocket flies considerably higher,
and
faster.

Because the fabric
cover yielded very close results to that of the small sandpaper covers, the two
can be considered t
o have the same drag coefficient.

By calculating the average heights of the

two naked
rocket tests (92

ft) and comparing that to the average of the fabric an
d small sandp
aper tests (71

ft) that
is a
height difference of 21

ft. The average spee
d for the naked rocket was 36

ft/sec, and the average speed for
the fabric and
small sandpaper covers was 30

ft/sec. This difference in speed
is much

closer.

From the d
ata collected, it can be concluded that this alteration of friction on the rocket does effect
the rocket
.

This study’s hypothesis predicted that friction would not have a significant effect on the height or
speed of the rocket. Data shows that
even a

small

difference in friction

greatly affects the flight of the rocket.
The smaller sandpaper and fabric slowed the rocket approximately 5.90 ft/sec in comparison to the rocket’s
flight without any friction.
T
he
coarse

sandpape
r covers slowed the rocket 12

ft/se
c in comparison to the
naked rocket’s flight.






Further Study



Although
the study

attempted to prevent
as many non
-
controlled

variables
as possible
,
several
problems occurred throughout the course of the study
. It was not anticipated that the rocket’s
parachute
would detach itself after two trials. So, in order to make due, it was reattached with masking tape. That did
not work and data collection was forced to continue with the rocket falling from the sky without a parachute
each trial. Luckily the roc
ket
fared

quite well and did not damage itself too badly until the last trials. But by
the end of the data collection the rocket was certainly in a different state from when the beginning

(for
instance, its sides were rougher due to slight crumpling of the

body tube). T
his slight damage to the rocket
may have altered the data.
Adding

masking tape to the rocket to prevent further damage between trials,
weight was added to the rocket. After a particularly bad fall using the A83 engine for the first time, the
top of
the rocket took some damage, which probably affected the amount of drag on the rocket. But this did not
completely take away the credibility of the data, because after the rocket’s damage, the rocket still
performed consistently with our data when f
lying naked, even
in its

less than desirable state.


To prevent this particular problem in the future, it would be advisable to bring
a repair kit
, to the
launching site in case of the parachute detaching itself. The rocket used in this experiment was be
lieved to
be ready for launching. But if this experiment were to be performed again, higher precautions would be
taken when building the rocket. If another group were to perform this experiment, they should take care to
use a strong white glue, and bring e
xtra glue when launching the rocket.


Another improvement to the study would be to increase the trials and use the same size engine for
each trial. This study had only six 1/2A6 engines due to money constraints and the two A83 engines were
produced from a

parent out of luck. It would be important to perform about 3 trials for each rocket cover as
well as the rocket without the cover. It would also yield better results if tests had been performed with the
cover on the inside and outside for each different c
over. The test with the
large

grain

sandpaper cover did
show drag, but for the sake of consistency, a next
-
time consideration would be more tests for each. This
study could not do this simply because of a lack of money to buy enough engines.


If
this expe
riment were to be repeated, several additional steps would be logical
. First, it would be
important to test a rocket using less drastic changes in friction. Instead of testing three variables (fabric,
small sandpaper, large sandpaper), a group should test
more rocket covers that will have a
less distinctly
different

effect on friction. This will enable more accurate conclusions to be made with the collected data.
Some examples of these less drastic friction covers could be comparing the naked rocket wit
h a
slightly
perforated rocket, o
r using covers like different fabrics, plastic bag material, paper, or different grades of
sandpaper.


Performing this test with larger rockets would make the difference in height due to drag more
pronounced and easier to meas
ure with a higher degree of accuracy. Many of the angle measurements
taken in this experiment may have been off by one or two degrees because of the difficulty in getting an
accurate measurement on an astrolabe in the time it takes for a rocket reach its p
eak of flight.


One factor that may have unbalanced the results is that the mass of the rockets depending on
which cover was used in each trial. More mass would result in a slower acceleration of the rocket when
acted on by the same force as acted on a roc
ket with less mass because Newton’s 2
nd

law, the net force
acting on an object equals the mass of the object multiplied by its acceleration.
This was addressed
by
launching the rocket with the coarser and heavier sandpaper once on the outside of the rocket
, and once on
the inside so that the weight of the rocket would be the same but the friction and drag would still be tested.
The results of this experiment stood consistence with our data gathered already and the rocket with the
sandpaper on the inside fle
w significantly higher even though the mass was the same.


Another factor that may have influenced our data is a phenomenon called trajectory dispersion; the
effects of the atmosphere and wind variables on the rocket’s flight. ‘Rocket Propulsion and Spacef
light
Dynamics’ explains;

“The presence of the Earth’s atmosphere will lead to aerodynamic
forces on the vehicle and in many cases one has to account for the
aerodynamic forces and moments to predict accurately the vehicle’s
trajectory and performances. B
ecause of the unpredictable
aerodynamic forces and moments the trajectory may deviate from the
normal trajectory. Such aerodynamic moments may by caused by
steady wind, wind
-
gusts, atmospheric turbulence, but also be fin
misalignment and production inaccur
acies. The deviation of the
trajectory of the rocket is known as
trajectory dispersion.
For guided
vehicles, the dispersion of the impact point, for instance, is minimized
by means of a special guidance system.” (p317)
(Cornelisse et al
, 1979
)



Although
the experiment was performed during the morning on a cool, clear day (
though there
were occasional gusts of wind
) there was no way to completely eliminate this variable. Therefore, the data
that was recorded by the
astrolabe

(that was used to create the right triangles which we analyzed to find the
maximum heights achieved by the rockets) cannot be exactly correct; if the wind blew the rocket off an
exactly straight course (which no doubt occurred, at least minimally) the roc
ket didn’t fly straight up, and the
triangle didn’t have an exact right angle (and therefore, the trigonometry wasn’t exactly accurate). However,
this variable was minimized, so the data is as correct as it could have been under the circumstances.


Conclu
sion


We have determined that the drag created by the external surface texture of model rockets does
have a significant impact on the flight speed and maximum height of the rocket’s flight. We drawn this
conclusion from two sets of collected data, and have

also verified this result with mathematical analysis.
This verdict follows our basic earlier beliefs about friction, and shows that friction and drag are significant
present forces even when the motion involved doesn’t encompass a great deal of force, spe
ed or distance.


L
iterature Cited

Hobbs, Marvin.
Fundamentals of Rockets, Missiles and Spacecraft.
John F. Rider Publisher, Inc, 1962


Sutton, George P.
Rocket Propulsion Elements; An Introduction to the Engineering of Rockets.
Wiley
-
Interstice Publicatio
n, 1986.


Burgess, Eric.
Rocket Propulsion (with an introduction to the idea of interplanetary travel).
Chapman and
Hall Ltd, 1952.


Cornelisse, J. W, Schöyer, H. F. R, Wakker, K. F.
Rocket Propulsion and Spaceflight Dynamics.
Pittman
Publishing Ltd, 197
9.