The Relationship between Super-Roc Length and Drag Coefficient:
Rocksim Erroneously Suggests That Size Matters
Jay G. Calvert
NAR 71767
C Division
Objectives
The primary objective of this study is to use a series of test flights to determine the
relationship between the length of a rocket and its coefficient of drag (CD). This
information is particularly useful when developing a winning strategy in the Super-Roc
Altitude (SRA) family of events in NAR competition. The scoring of SRA involves
multiplying the length of the model (which must fall within a defined range that increases
with motor impulse) by the altitude achieved. It is a matter of some debate among
experienced competitors whether the preferred approach is “long and low”, “short and
high”, or somewhere in between.
A secondary objective of this study is to compare the empirical results obtained above
with predictions made by the popular commercial software package Rocksim (Apogee
Components). Can Rocksim accurately predict a winning SRA strategy?
Approach
In Phase I of this study, the actual effect of rocket length on peak altitude was determined
empirically through a series of test flights. Five different lengths, ranging from 48 inches
to 120 inches, were flown three times each. A single vehicle was used for all 15 flights,
meaning that the forward and aft sections (containing all functions required for flight)
were held constant and length was increased in 18-inch increments by adding a piece of
BT50 airframe and a coupler to the middle of the rocket. Peak altitude was measured by
a miniAlt/WD altimeter (Perfectflite) housed in a padded and vented payload
compartment. The small size of this unit and associated battery allow it to fit easily into a
BT50 tube, and the relatively light weight (about an ounce, including battery) allow for a
fairly close approximation of the weight of an actual BT50-based Super-Roc (which
would normally be flown without an altimeter). The motor of choice for all 15 flights
was the Estes D12, therefore these results are most directly applicable to the D-SRA
event (although I believe they are also predictive of other impulse SRA events). The
D12-7 was used for the 48, 66, and 84 inch lengths, while the D12-5 was used for the 102
and 120 inch rockets. This ensured that ejection of the parachute occurred after (but not
too long after) apogee. The flight characteristics of each launch, including any observed
anomalies, were documented.
In Phase II, the flights were modeled in Rocksim (Apogee Components). The shapes,
weights, and finishes of the rockets were duplicated as closely as possible. Launch
conditions (latitude, elevation, temperature) were set to mimic the average conditions
during the test flights. Launch angle and wind speed were set to zero to simulate vertical
flight profiles. The default setting for Rocksim is to dynamically calculate a CD value
during the simulated flight based on the shape and finish of the rocket and the airspeed.
The default CD calculations were used, and the predicted altitudes compared to the
measured altitudes from Phase I. Then, the dynamic CD function was turned off and the
simulations were rerun using various static CD values until the simulated peak altitudes
exactly matched the observed altitudes. The results are reported below.
Previous work
A Google search, and browsing of several NAR R&D report archives, failed to locate any
other studies that specifically dealt with the effects of rocket length on drag coefficient.
It is possible that such reports exist but are not readily available, or are not indexed in
such a way that they are easily found. To the best of my knowledge, this is the first
experimental evaluation of the subject.
My A-Division son Alex Calvert is submitting an R&D report in this year’s NARAM.
He used the same miniAlt/WD altimeter to measure the CD of rockets of various shapes,
including some that resemble super-rocs.
Equipment, Facilities, and Budget
Equipment: Data from the miniAlt/WD altimeter (Figure 1) was downloaded to a PC
running Windows XP Pro, using the Data Capture application and cable provided by
Perfectflite.
Figure 1. The Perfectflite miniAlt/WD altimeter.
The most recent version of Rocksim, version 8.0.0f5, was used on a PC running
Windows XP Pro. Latitude was set to 42˚, elevation to 900’ above sea level, and
temperature to 65˚ F. Launch angle was set to 0˚ and wind speed was set to 0 mph.
Standard Estes or equivalent components were used to construct the super-roc. The fins,
nose cone, and payload bulkhead were balsa wood. A 12” nylon parachute was used.
The aft 12” section of airframe (only) used heavy duty 24 mm tubing from LOC
Precision. This portion of the rocket houses the motor, fins, shock cord mount, and lower
launch lug. The sturdy tubing allowed the business end of the vehicle to withstand the
wear and tear of fifteen flights with no ill effects. Other tubes were unfinished (glassine
coated) Estes BT50. Rocksim diagrams of the five rockets lengths are shown in Figure 2.
Figure 2. Rocksim models of five length variants of the same super-roc design, as flown
in Phase I of this study.
Facilities: Test flights were conducted on two days, at two locations. Flights of the 48”
and 66” rockets were made on Sunday April 3, 2005 at a launch hosted by Tripoli
Michiana at Three Oaks, Michigan (elevation 646’ MSL). Flights of the 84”, 102”, and
120” rockets were made on Saturday April 9, 2005 at a launch hosted by the Jackson
Model Rocket Club at “Gumbert Field”, located north of Jackson, Michigan (elevation
937’ MSL). Club launch gear was used, including 3/16” launch rods four feet long.
Weather was similar on the two days, with mostly sunny skies, temperatures in the 60s,
and a light and variable breeze. There was little or no visible weather cocking observed
on any of the flights, and the effects of wind were therefore ignored in the Rocksim
simulations.
Budget:
Rocket components (dealer prices)
Altimeter and accessories
Engines (dealer prices)
Rocksim Upgrade (version 7 -> 8)
TOTAL
$12
$120
$32
$56
$220
Data and Results
Phase I: Fifteen successful test flights were made without any structural damage, motor
failures, recovery failures, altimeter failures, or significantly non-vertical launches.
There was no need to repeat any flights. Peak altitude was determined after each flight as
a series of audible beeps. In addition, a full flight profile was downloaded from the
altimeter at the end of each day (Figure 3). The altimeter data from the 15 flights is
shown in Table 1, and the means (+/- one standard deviation) are plotted in Figure 4.
Table 1. Raw data from Phase I test flights.
Flight
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Length
(in)
48
48
48
66
66
66
84
84
84
102
102
102
120
120
120
Length
(cm)
121.92
121.92
121.92
167.64
167.64
167.64
213.36
213.36
213.36
259.08
259.08
259.08
304.8
304.8
304.8
Weight
(g)
108
108
108
128
128
128
148
148
148
168
168
168
188
188
188
Motor
D12-7
D12-7
D12-7
D12-7
D12-7
D12-7
D12-7
D12-7
D12-7
D12-5
D12-5
D12-5
D12-5
D12-5
D12-5
Altitude
(ft)
920
940
999
821
802
871
628
688
629
589
500
530
451
491
432
Altitude
(m)
280
287
304
250
244
265
191
210
192
180
152
162
137
150
132
Comments
Good
Good
Good
Good
Good
Good
Good
Good
Good
Good, some flexing
Good, some flexing
Good, some flexing
Good, much flexing
Good, much flexing
Good, much flexing
Figure 3. Representative data capture sets from two of the 15 flights.
Measured Altitudes (Phase I)
350
Altitude (meters)
300
250
200
150
100
50
0
0
20
40
60
80
100
120
140
Rocket Length (inches)
Mean Altitude +/- SD
Figure 4. Observed peak altitude means and standard deviations.
If this had been a D-SRA contest, the scores would have been calculated as shown in
Table 2 below (length in cm x altitude in meters). Also, the backtracked CD values are
shown. The increase in CD is quite dramatic, with values exceeding 3 for the longest
super-roc. Interestingly, the SRA scores are almost identical within the range of legal DSRA entry lengths (from 150 cm to 300 cm).
Table 2. Mean Altitudes, SRA Scores, and Backtracked CD values.
Rocket Length
Mean Altitude
SRA Score
(in/cm)
(meters)
48/122
290
35,415
66/168
253
42,478
84/213
198
42,162
102/259
164
42,616
120/305
140
42,550
Calculated CD
(from Rocksim)
1.31
1.43
2.08
2.68
3.22
Phase II. In order to determine whether Rocksim can accurately predict super-roc
performance, the dynamic CD calculation routine (the default) was enabled again and
tested with the same five simulated rockets. The predicted altitudes (and therefore SRA
scores) differed from the empirical data from Phase I. The results are shown in Table 3.
Table 3. Predicted altitudes and SRA scores using the Rocksim default CD routine.
Rocket Length
Mean Altitude
SRA Score
(in/cm)
(meters)
48/122
266
32,482
66/168
225
37,684
84/213
193
41,136
102/259
167
43,295
120/305
146
44,479
Conclusions and Future Work
Examination of Table 2 indicates that, with the possible exception of the extreme low end
of the D-SRA length range, there is no significant difference in SRA score between short,
medium, and long super-rocs. Specifically, rockets in the 66 – 120 inch (168 – 305 cm)
range all give scores that are between 42,162 and 42,616. This represents only a 1%
spread and is well within expected performance variation due to “random” effects such as
motor impulse heterogeneity and wind gusts. Put another way, the empirical data says
there is no “winning strategy” in terms of choosing a short, medium, or long model from
among the permitted range of lengths in the D-SRA event. Apparently the “Founding
Fathers of Super-Roc” knew what they were doing when choosing a scoring algorithm
and setting length windows. Even after many years of experience, there is no consensus
among serious competitors as to whether winning super-roc models should be at the high,
medium, or low end of the length spectrum.
In contrast, the most recent version of Rocksim (8.0.0f5) failed to accurately reflect realworld performance. Table 3 shows an ever-increasing predicted SRA score as one
increases rocket length from below the minimum to above the maximum for D-SRA. A
competitor that relied only on Rocksim to design a super-roc would mistakenly believe
that longer is always better, and would risk structural failure (crimping) in order to use a
maximum length rocket for every flight.
Rocksim underestimates the performance of the shorter rockets and overestimates the
performance of the longer ones (compare Tables 2 and 3). Presumably, the dynamic CD
calculation algorithms are assigning too high a value to the base (48”) rocket, but
assigning too low an incremental penalty for each additional length of BT50 tubing
inserted in the middle of the rocket. One possible cause for underestimating the CD of
the longer models may be a failure to take into account additional drag due to flexing of
the rocket during boost. I observed visible bowing and flexing of the 102” super-roc,
which became more dramatic in the full-length 120” model. Refinements to the Rocksim
program may improve its accuracy in future releases.
The data generated in this report are specific to the D impulse SRA event, but are
probably applicable to many if not all impulse categories. As the impulse increases, so
does the diameter of the corresponding motor and therefore the width of a minimumdiameter rocket. Simultaneously, the SRA rules incrementally increase the minimum and
maximum super-roc lengths. As a result, the overall shape (aspect ratio) remains more or
less constant over a range of impulses. This year’s NARAM features B-SRA. Under the
assumption that the data generated in this report is also valid in the B impulse range, I
intend to fly a relatively short super-roc first (unless low clouds present a tracking
problem). The shorter rocket will be easier to handle and less subject to crimping in
flight, yet should give a score that is equivalent to a much longer super-roc. Once a valid
score is recorded, I will follow up with a longer model for my second flight and attempt
to confirm my hypothesis that the SRA scores will be very similar.
This study focuses on super-rocs with a single diameter (that of the engine). A common
strategy is to build a model that transitions to a smaller diameter at the forward end. This
has the advantage of maintaining the length advantage while reducing the weight and
drag penalties associated with long lengths of relatively large diameter tubing. The
effects of configurations of this type on CD and SRA score would make for an interesting
series of future R&D reports.
The Relationship between Super-Roc Length and Drag Coefficient:
Rocksim Erroneously Suggests That Size Matters
Jay G. Calvert
NAR 71767
C Division
Summary
The effect of super-roc length on drag coefficient, peak altitude, and super-roc altitude
event scoring was determined empirically (Phase I) in a series of test flights and
compared to Rocksim simulations of the same models (Phase II). In Phase I, a D impulse
super-roc equipped with a very small altimeter was flown in five different length
configurations ranging from 48” to 120” (three flights in each configuration). The data
shows a clear decrease in altitude with increased length, due to weight of the added
airframe tube and increased drag. After adjusting for increased weight, the coefficient of
drag (CD) was backtracked from the altitude data using Rocksim. CDs ranged from 1.31
for the shorter model up to 3.22 for the longest super-roc. The SRA scores (length times
altitude) were remarkably constant over the entire range of allowed lengths, suggesting
that there is no “best length” in this event. When the same rockets were carefully
modeled in Rocksim, the predicted altitudes varied considerably from the observations.
Rocksim underestimated the performance of the shorter rockets and overestimated the
performance of the longer ones. As a result, Rocksim mistakenly indicates that a
maximum length super-roc will have significant advantage over a medium or short superroc in the same impulse category.