Model Rocket Drag Analysis
using a
Computerized Wind Tunnel
National Association of Rocketry
Research & Development Report
by
John S. DeMar
NAR 52094
2nd Place
NARAM-37
July 1995
Geneseo, NY
TABLE OF CONTENTS
Introduction
This NAR Research & Development report describes a series of experiments
using a computerized wind tunnel to determine the drag coefficients of
typical model rocket designs. The main goal of this report is to derive
a practical list of drag coefficients to improve the usefulness of existing
altitude prediction software. To verify the accuracy of the data, the predicted
altitudes are compared to actual tracked altitudes for a sample of the
models tested (TBD).
The drag measurements were made using a commercially available wind
tunnel intended for experimentation at the high school and undergraduate
college level. The design of this equipment is less sophisticated than
a wind tunnel found at a research facility, but is more accurate than the
typical home-made device. As shown in this report, the wind tunnel is tested
for accuracy and is found to be sufficient for the purposes of this report.
Several model rockets were built for each of six series of tests to
isolate the major effects on drag: frontal area, finish, nose shape, body
shape, fin cross-section, and launch lug. The resulting table of drag coefficients
represents most of the typical configurations, making it very useful in
many areas of model rocketry. Some applications are: optimizing parameters
for maximum altitude in a competition design; selecting an appropriate
motor for the model and field size; and verifying compliance within the
limit of an FAA waiver.
The methods used in this report may prove useful in studying other
research topics in the future. Some of these ideas are discussed further
in the last section.
1.0 Project Description
1.1 Background
Most serious rocket hobbyists are interested in predicting the apogee
of their model, either for design optimization, motor selection, FAA waiver
compliance, or just plain curiosity. In the past few years, the use of
altitude prediction software has become common place due to the reduced
prices of high performance personal computers. Many programs are available
commercially and in the public domain (through the on-line services and
the Internet).
An altitude prediction program requires the user to input physical
information about their rocket and motor selection. Most of the values
are easily measured (mass, frontal area) and the motor thrust curves are
based on NAR S&T data. But the drag coefficient (Cd) is more elusive.
Most programs require the user to give their 'best guess' for the Cd, and
only the most expensive commercial package will calculate the Cd based
on specific parameters and some general assumptions [Rogers, 1994].
For practical purposes, it is difficult or impossible to find measured
drag coefficient values for model rockets. In the Handbook of Model Rocketry
[Stine, 1984] some values are given for a simple model and there is a beginner's
level discussion on the causes of drag. Many 'old rocketeers' have their
own guidelines based on years of experience with various rocket designs.
However, even these values vary greatly from person to person. Another
generally accepted method is to track several flights of the same model
and work 'backwards' to determine the Cd by successive guesses in the software
simulation. This method works well but is not practical for most people.
An error in the drag coefficient will cause a considerable error in
the predicted altitude, especially for low-drag models (shown by varying
Cd in an altitude prediction program). Therefore, it would be a great improvement
to have a list of measured Cd's which represent many of the designs, materials,
and finishes used in model rocketry.
To measure the coefficient of drag, a model rocket (or plane or car)
is placed in a wind tunnel with a controlled air flow. Normally, this would
require access to a commercial or university research facility. Another
option would be to build a home-made wind tunnel -- useful for showing
general concepts but do not have the accuracy in air flow or instrumentation
needed for actual measurements.
For this report, the author was fortunate enough to borrow a Jetstream
500 'portable' wind tunnel (six feet long) from the manufacturer (Interactive
Instruments, East Glenville, NY). This device is intended for educational
purposes at the high-school and undergraduate level, and is calibrated
for drag and lift measurements of wing sections and model cars.
1.2 Test System
The following diagram shows the system used to measure the drag force
for each model tested. The Jetstream
wind tunnel is described in more detail in Appendix A. The wind tunnel
is computer controlled by both an internal microprocessor and an external
personal computer. The wind speed may be controlled from a front panel
and the drag may be measured on an LCD display, or a PC may be used to
communicate with the system using interactive software. Both methods were
used in this experiment with equal results.
![[Wind tunnel graphic]](tunnel.gif)
Each of the models in the test series were analyzed using the following
procedure:
![[Test Procedure]](testproc.gif)
Before the models were measured, the wind tunnel was tested for accuracy
and low-turbulence using the following method [Parks, 1995]:
![[Calibration Procedure]](sphere.gif)
The results of these validation tests proved to be within 10% of the
expected results for the Reynolds number of the test (~100,000) using a
3/4" polished steel sphere. For larger spheres, the results were much
higher than expected; this would indicate turbulent flow [Pope, 1966].
The tests of the actual models will have a Reynolds number of about 800,000,
which should be high enough for laminar flow (above 500,000) [Pope, 1966].
However, a somewhat higher Reynolds number of 1,500,000 is recommended
for serious research [Pope, 1966]. For practical purposes in model rocketry,
the flow will be turbulent before it passes the nosecone for most designs
[Stine, 1986] and, therefore, a less-than-perfect air stream should prove
adequate.
These calibration tests were much better when the intake of the wind
tunnel was isolated from the exhaust [per Pope, 1966]. The intake was position
inside the door of a large closed room, and the output was placed in another
room (the measurements were made in the hallway between them!).
1.3 Basis of Calculations
The drag force of an object in a non-turbulent air stream at sub-sonic
velocity is computed from the following formula [Puckett, 1959] [Pope,
1966]:
fd = (0.5)
v^2
Cd Ax
where:
fd is the drag force (newtons or kg-m/sec^2).
is the density
of air (kg/m^3).
v is the air velocity (m/sec).
Cd is the drag coefficient (no units).
Ax is the cross-sectional area (m^2).
Solving for Cd and substituting standard air density gives:
Cd = [ 2 fd ] / [ (1.29) v^2 Ax ]
where:
= 1.29 kg/m^3
at 25C at sea level.
For practical values in our measurements, converting units gives:
Cd = [ 2 (9.8) (10^-3) Fd ] / [ (1/3.6)^2 V^2 (10^-4)Ax ]
where:
1kg = 9.8N, and 1kg = 1000gms.
1m/sec = 3.6km/hr, and 1m2 = 104 sq.cm.
Simplifying, gives:
Cd = [ (1969) Fd ] / [ V^2 Ax ]
where: Fd is the drag force in grams,
V is the air velocity in km/hr,
Ax is the cross-sectional area in sq.cm. (ie: frontal area of body
and fins).
The drag measurements (Fd) were taken three times and averaged. This
was recommended by the wind tunnel designer due the way the load cell operates.
The average values for the drag force were entered into the data tables
in Section 2, and used to compute the Cd using the formula shown above.
1.4 Limitations & Assumptions
1.4.1 Wind Tunnel Velocity Limit
The main limitation of the experiment is due to the maximum velocity
of the wind tunnel (~120 km/hr). The average velocity of most model rockets
(mid- and high- impulse, too) is in the range of 200 to 600 km/hr. As long
as the velocity stays well below the speed sound (~1190 km/hr) the drag
coefficient remains relatively constant above a minimum airspeed. For bodies
the size of model rockets, the minimum airspeed for laminar flow is about
80 km/hr. Therefore, these experiments were run near the maximum velocity
of the wind tunnel, which is about 50% above the airspeed needed for laminar
flow.
1.4.2 Instrumentation Resolution
The instrumentation in the wind tunnel reads the drag force with a
resolution of about 0.5 gm (the analog to digital converter has 10-bits
of resolution with 500gm full scale). For small diameter models and very
low drag models (where drag forces are <10gm) these limitations will
cause a significant error (>5%). To minimize this problem, a moderate
body diameter was chosen for the tests. However, too large of a diameter
would cause airflow interference with the chamber walls, and the model
would be too long to fit in the 16" long test area. A BT-20 (~0.75"
dia.) tube, 8.5" long, was used as the standard body to meet these
criteria.
1.4.3 Verification Error
The prediction software and verification flights assume a straight
boost with little or no wind. Other factors, such as variations in actual
motor performance, will add to the error between predicted and actual altitudes.
The tracked flights will be acceptable if below 10% closure error using
the Geodesic method. Considering all of the practical variations in the
model, motor, launch angle, atmospheric conditions, etc., the derived Cd's
will be considered verified if the percent error between predicted and
actual altitude is less than 10%.
1.4.4 Subsonic Limit
This report is not concerned with trans-sonic or super-sonic effects
on drag. The derived table of drag coefficients should not be used for
velocities above 80% the speed of sound (950 km/hr or 260 m/sec).
1.4.5 Secondary Factors
The analysis of other dynamic factors are beyond the scope of this
report. For instance, the effects of dynamic stability can change the Cd
of a rocket as its angle of attack oscillates due to corrective forces.
Also, the base drag of the rocket is known to change when the motor is
operating. These two topics would be interesting research areas for future
R&D reports.
2.0 Measurement Series
The following six series of measurements were designed to isolate the
various effects on a model rocket's drag. Each section shows the design
of the model and the results of the tests.
Each model was tested at three airspeeds: 80, 100, and 120 km/hr. The
measurements are repeated with the model removed in order to subtract the
drag of the mounting apparatus. The resulting Cd's at the upper two airspeeds
should be lower to indicate laminar flow. If not, the flow is significantly
turbulent; this is not necessarily an error, but reveals the nature of
the air flow.
All models are designated by a model number; some models were retested
as part of another series if they have the desired characteristics. See
Appendix B for drawings of each model.
2.1 Calibration Sphere
The goal of this series is to verify that the airflow is predictable
for purpose of this experiment. Also, the derived Cd for the sphere is
easily compared to the standard value of ~0.5 at low Reynolds numbers and
~0.15 at Reynolds numbers above where laminar flow begins [Pope, 1966].
| Test Item |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 1.5" Smooth Sphere |
20.6 |
34.7 |
48 |
0.56 |
0.60 |
0.58 |
Reynolds number is not high enough for laminar flow. However, this
is close to standard for sphere, which validates the instrumentation.
2.2 Scalability
The goal of this series is to show that the Cd is not dependent on
the size of the model. Other factors were kept constant across the three
sizes (such as shape and finish).
| Model# - description |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 1 - BT-5, 7.3" long |
1 |
3.3 |
4 |
0.19 |
0.41 |
0.35 |
| 2 - BT-20, 10" long |
3.3 |
7.7 |
10 |
0.50 |
0.75 |
0.68 |
| 3 - BT-50, 13.3" long |
13.3 |
19.3 |
21.3 |
0.84 |
0.78 |
0.73 |
The BT-5 model is too small to read accurate forces. The BT-20 and
BT-50 are within 10%.
2.3 Surface Effects
The goal of this series is to show the effect on Cd due to the quality
of the model's finish. The first model has unfinished kraft tubing and
balsa fins; the second model has one coat of primer and one coat of Krylon
paint; and the third model has a filled, polished, and waxed lacquer finish.
| Model# - description |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 4 - unfinished |
6 |
9.7 |
11.3 |
0.92 |
0.95 |
0.77 |
| 2 - krylon |
3.3 |
7.7 |
10 |
0.50 |
0.75 |
0..68 |
| 5 - polished lacquer |
3.7 |
7.3 |
9 |
0.57 |
0.71 |
0.61 |
The surface finish shows a measureable effect.
2.4 Fin Effects
The goal of this series is two show the effect of fin shaping on a
model's Cd. The first model has square edged fins, the second has rounded
edges, and the third has tapered "airfoil" fins.
| Model# - description |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 6 - square edged fins |
|
|
|
|
|
|
| 2 - rounded edged fins |
|
|
|
|
|
|
| 7 - airfoiled fins |
|
|
|
|
|
|
The differences in forces were not measurable. A different test method
would need to be developed to test the fin shape effects.
2.5 Launch Lug Effects
The goal of this series is to test the effect of launch lugs on a model's
Cd. The first model has no lug (for tower launching), the second has a
1/8th inch inside diameter lug (2 inches long), and the third has two wire
loop lugs (one forward and one rear).
| Model# - description |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 2 - no launch lug |
3.3 |
7.7 |
10 |
0.50 |
0.75 |
0..68 |
| 8 - 1/8" x 2" lug |
6.3 |
9.7 |
13 |
0.96 |
0.95 |
0.88 |
| 9 - two wire loops |
5.3 |
9.3 |
11.7 |
0.81 |
0.91 |
0.80 |
The addition of a launch lug added 29% to the Cd and the wire loops
added 18%.
2.6 Nose Shape Series
The goal of this series is to compare the Cd's of the same model with
various nose cone shapes.
| Model# - description |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 2A - w/ elliptical 2:1 cone |
3.3 |
7.7 |
10 |
0.50 |
0.75 |
0..68 |
| 2B - w/ straight 3:1 cone |
5 |
10 |
11.7 |
0.77 |
0.98 |
0.80 |
| 2C - w/ parabolic 3:1 cone |
4.3 |
8.3 |
11 |
0.66 |
0.81 |
0.75 |
| 2D - w/ half sphere cone |
3.7 |
8 |
10 |
0.57 |
0.78 |
0.68 |
| 2E - w/ flat nose |
9.7 |
16.3 |
21.3 |
1.48 |
1.60 |
1.49 |
The flat nose was predictably the most draggy. The sphere and elliptical
had similar effects, and the straight conical nose was 18% higher. The
parabolic (Apogee PNC) was higher than expected.
2.7 Body Shape Series
The goal of this series is to show the effect of the shape of the model
on the Cd. Five typical rocket designs are measured and compared.
| Model# - description |
Fd(80) |
Fd(100) |
Fd(120) |
Cd(80) |
Cd(100) |
Cd(120) |
| 2 - straight body |
3.3 |
7.7 |
10 |
0.50 |
0.75 |
0..68 |
| 10 - 2:1 5% boattail |
2.3 |
5.7 |
7.7 |
0.35 |
0.58 |
0.52 |
| 11 - 20:1 40% (payloader) |
4 |
6.3 |
8.3 |
0.61 |
0.62 |
0.56 |
| 12 - 20:1 90 % (egglofter) |
10 |
14 |
18.3 |
0.43 |
0.38 |
0.35 |
| 12x - 6:1 30 % (egglofter) |
10 |
16.3 |
22.3 |
0.43 |
0.45 |
0.63 |
| 13 - 1:1.5 +transition |
6.3 |
9.7 |
11.3 |
0.96 |
0.95 |
0.77 |
The boattail reduces the Cd over 20%. A full tapered egglofter gives
the lowest drag. As expected, a positive transition increases the Cd.
3.0 Flight Prediction and Tracking
3.1 Verification Method
To complete the experiment, the derived Cd's were used to compute the
expected altitude using an altitude prediction program and compared to
actual tracked altitudes of the same models. The resulting errors are used
to determine the validity of the test system and the test methods.
3.2 Altitude Prediction Software
Three software programs were used to predict the maximum altitude of
each test model based on the Cd's derived from the wind tunnel measurements.
The three programs are: (1) Rogers Aerosciences ALT4 ($65), (2) Stephen
Roberson's Alticalc ($20), and (3) the author's software (not yet available).
Each of these programs use numerical integration methods to calculate
acceleration during discrete time steps and graph the altitude, velocity,
and acceleration for the whole flight period.
The predicted altitude was chosen at the point where ejection would
occur.
3.3 Motor Selection
The flight tests were done using Estes 1/2A3-2T's and 1/2A3-4T's, depending
on the estimated delay required for maximum apogee. When possible, multiple
flights were tracked using motors from the same pack and the altitudes
were averaged. All flights were tracked to ejection. [TBD]
A future improvement to the verification method would be to save one
motor from each pack and test it on a thrust stand. Then, take the resulting
thrust-time curve and use it in the simulation for predicted altitude.
3.4 Results
The Cd's for the 120 km/hr condition (highest velocity) were used for
the predicted altitudes. The altitudes were predicted with three different
programs: I) Rogers, II) Alticalc, and III) author's.
A few representative flights will be tracked at NARAM-37. (DID NOT
HAPPEN!)
NOTES:
Mass is in grams, area is in square centimeters, and altitude is in
meters.
2gms were added to the mass to allow for tracking powder and streamer.
| Model |
Cd |
Mass |
Area |
Est. I |
Est. II |
Est.III |
Est Avg |
Flight 1 |
Flight 2 |
Flight 3 |
Flt Avg |
%error |
| 1 |
xxx |
|
1.58 |
---- |
---- |
---- |
|
|
|
|
|
|
| 2A |
0.68 |
9 |
2.0 |
|
154 |
131 |
|
|
|
|
|
|
| 2B |
0.80 |
9.3 |
2.0 |
|
141 |
121 |
|
|
|
|
|
|
| 2C |
0.75 |
9.9 |
2.0 |
|
142 |
122 |
|
|
|
|
|
|
| 2D |
0.68 |
8.4 |
2.0 |
|
158 |
134 |
|
|
|
|
|
|
| 2E |
1.49 |
7.9 |
2.0 |
|
108 |
90 |
|
|
|
|
|
|
| 3 |
0.73 |
21.8 |
4.87 |
|
93 |
51 |
|
|
|
|
|
|
| 4 |
0.77 |
8.3 |
2.0 |
|
150 |
127 |
|
|
|
|
|
|
| 5 |
0.61 |
8.3 |
2.0 |
|
166 |
141 |
|
|
|
|
|
|
| 6 |
xxx |
9 |
2.0 |
---- |
---- |
---- |
|
|
|
|
|
|
| 7 |
xxx |
9 |
2.0 |
---- |
---- |
---- |
|
|
|
|
|
|
| 8 |
0.88 |
9.3 |
2.0 |
|
135 |
115 |
|
|
|
|
|
|
| 9 |
0.80 |
9.3 |
2.0 |
|
141 |
121 |
|
|
|
|
|
|
| 10 |
0.52 |
11.5 |
2.0 |
|
149 |
130 |
|
|
|
|
|
|
| 11 |
0.56 |
9 |
2.0 |
|
166 |
142 |
|
|
|
|
|
|
| 12 |
0.35 |
18 |
7.2 |
|
246 |
275 |
|
|
|
|
|
|
| 12x |
0.63 |
24 |
7.2 |
|
178 |
210 |
|
|
|
|
|
|
| 13 |
0.77 |
8.9 |
2.0 |
|
146 |
124 |
|
|
|
|
|
|
4.0 Conclusions
Using a small wind tunnel to measure model rocket drag has produced
significant information to help improve altitude prediction. Most of the
predicted altitudes (based on the derived Cd's) were within ___% of the
tracked flights. (TBD)
The experimental methods could be improved by increasing the airspeed
and reducing the turbulence of the wind tunnel. However, for most model
rocket designs, the current system appears to be adequate.
Future experiments with this system would be interesting and may produce
other useful results. Some areas of study would be:
- Investigating dynamic stability of a model rocket using a wind tunnel.
Gordon Mandell published both theoretical and experimental work on this
topic in the early 1970's using much less sophisticated technology. New
computer techniques and automated instrumentation would allow a wider range
of tests.
- Investigated the base drag of a model rocket using a wind tunnel. A
rocket is known to have drag effects from the jet exhaust while the motor
is burning propellant. However, little is known about this factor and it
is usually ignored in simulations. A high-pressure air jet could be routed
through the mounting strut and to the back of the model to simulate the
mass flow of a rocket motor [Parks, 1995].
Appendix A: Jetstream Wind Tunnel
Link to Jetstream Specifications: http://www.wsg.net/~ii/Jetspec.htm
Appendix B: Test Model Drawings and Measured Drag Coefficients
NOTES:
1) All models are finished with average smoothness, primed and sprayed
with Krylon, unless noted.
2) All models have no launch lug unless noted.
3) All dimensions are in inches. Dimension X is 0.75 unless noted.
Test Model Drawings (con't)
Bibliography
Pope, Alan, 1966, Low-Speed Wind Tunnel Testing, John Wiley &
Sons, New York.
Standard text describing theory, design, construction, calibration,
and measurement for professional sub-sonic wind tunnels.
Parks, Robert, June/July 1995, personal correspondences..
Described how to test the wind tunnel for accuracy for the purposes
of this experiment. Suggested using smooth spheres of various sizes over
a range of air speeds to test for laminar flow or turbulence in the test
area.
Puckett, Allen E., 1959, Guided Missile Engineering, McGraw-Hill,
New York, NY..
Section 2: Aerodynamics of Guided Missiles. Used for drag computation
at subsonic air speeds and its limitations.
Stine, G. Harry, 1983, Handbook of Model Rocketry, Prentice Hall,
New York, NY..
Reference for typical range of drag coefficient values for a model
rocket.
Tilley, Donald E., 1976, University Physics, Cummings Publishing,
Menlo Park, CA..
Used as general reference for units conversions and constants.
(c)1996, John S. DeMar
(Interactive Instruments links added
2/21/97)