--- /dev/null
+
+\chapter{Comparison with experimental data}
+\label{chap-experimental}
+
+In order to validate the results produced by the software, several
+test flights were made and compared to the results simulated by the
+software. In addition to the software produced, the same simulations
+were performed in the current {\it de facto} standard model rocket simulator
+RockSim~\cite{rocksim}. The software used was the free demonstration
+version of RockSim version 8.0.1f9. This is the latest demo version
+of the software available at the time of writing. The RockSim site
+states that the demo version is totally equivalent to the normal
+version except that it can only be used a limited time and it does not
+simulate the rocket's descent after apogee.
+
+Comparisons were performed using both a typical model rocket design,
+presented in Section~\ref{sec-comparison-small}, and a large hybrid
+rocket, Section~\ref{sec-comparison-large}. A small model with
+canted fins was also constructed and flown to test the roll
+simulation, presented in Section~\ref{sec-comparison-roll}. Finally
+in Section~\ref{sec-comparison-windtunnel} some of the the aerodynamic
+properties calculated by the software are compared to actual
+measurements performed in a wind tunnel.
+
+
+
+
+\section{Comparison with a small model rocket}
+\label{sec-comparison-small}
+
+For purposes of gathering experimental flight data, a small model
+rocket representing the size and characteristics of a typical model
+rocket was constructed and flown in various configurations. The
+rocket model was 56~cm long with a body diameter of 29~mm. The nose
+cone was a 10~cm long tangent ogive, and the fins simple trapezoidal
+fins. The entire rocket was painted using an airbrush but not
+finished otherwise and the fin profiles were left rectangular, so as
+to represent a typical non-competition model rocket. The velocity of
+the rocket remained below 0.2~Mach during the entire flight.
+
+In the payload section of the rocket was included an Alt15K/WD Rev2
+altimeter from PerfectFlite~\cite{perfectflite}. The altimeter
+measures the altitude of the rocket based on atmospheric pressure
+changes ten times per second. The manufacturer states the accuracy of
+the altimeter to be $\pm (0.25\% + \rm 0.6~m)$. The altimeter logs
+the flight data, which can later be retrieved to a computer for
+further analysis.
+
+Four holes, each 1~mm in diameter were drilled evenly around the
+payload body to allow the ambient air pressure to reach the pressure
+sensor, as per the manufacturer's instructions. The rocket was
+launched from a 1~m high tower launcher, which removed the need for
+any launch lugs. Figure~\ref{fig-rocket-picture} presents a
+picture of the test rocket and the tower launcher.
+
+
+\begin{figure}
+\centering
+\parbox{75mm}{\centering % width 7.4cm
+\epsfig{file=figures/pix/rocket-tower,height=11cm} \\ (a)}
+\hspace{10mm}
+\parbox{35mm}{\centering % width 3.4cm
+\epsfig{file=figures/pix/rocket-closeup,height=11cm} \\ (b)}
+%
+\caption{The test rocket awaiting launch on the tower launcher (a) and
+ a close-up of its ventilation holes (b).}
+\label{fig-rocket-picture}
+\end{figure}
+
+
+A design of the same rocket was created in both OpenRocket and
+RockSim. During construction of the rocket each component was
+individually weighed and the weight of the corresponding component
+was overridden in the software for maximum accuracy. Finally, the
+mass and CG position of the entire rocket was overridden with measured
+values.
+
+One aspect of the rocket that could not be measured was the average
+surface roughness. In the OpenRocket design the ``regular paint''
+finish was selected, which corresponds to an average surface roughness
+of 60~\textmu m. From the available options of ``polished'',
+``gloss'', ``matt'' and ``unfinished'' in RockSim, the ``matt'' option
+was estimated to best describe the rocket; the corresponding
+average surface roughness is unknown.
+
+The rocket was flown using motors manufactured by WECO Feuerwerk
+(previously Sachsen Feuerwerk)~\cite{weco-feuerwerk}, which correspond
+largely to the motors produced by Estes~\cite{estes}. The only source
+available for the thrust curves of Sachsen Feuerwerk motors was a
+German rocketry store~\cite{sf-thrustcurves}, the original source of
+the measurements are unknown. The thrust curve for the C6-3 motor is
+quite similar to the corresponding Estes motor, and has a total impulse
+of 7.5~Ns. However, the thrust curve for the B4-4 motor yields a
+total impulse of 5.3~Ns, which would make it a C-class motor, while
+the corresponding Estes motor has an impulse of only 4.3~Ns. Both
+OpenRocket and RockSim simulated the flight of the rocket using the
+SF B4-4 motor over 60\% higher than the apogee of the experimental
+results. It is likely that the thrust curve of the SF B4-4 is wrong,
+and therefore the Estes B4-4 motor was used in the simulations in its
+stead.
+
+
+\begin{table}
+\caption{Apogee altitude of simulated and experimental flights with
+ B4-4 and C6-3 motors.}
+\label{tab-flight-results}
+\begin{center}
+\begin{tabular}{ccccc}
+ & \multicolumn{2}{c}{B4-4} & \multicolumn{2}{c}{C6-3} \\
+\hline
+Experimental~~~~ & 64.0 m & & 151.5 m & \\
+OpenRocket~~~~ & 74.4 m & +16\% & 161.4 m & +7\% \\
+RockSim~~~~ & 79.1 m & +24\% & 180.1 m & +19\% \\
+\hline
+\end{tabular}
+\end{center}
+\end{table}
+
+
+Figure~\ref{fig-flight-B4} shows the experimental and simulated
+results for the flight using a B4-4 motor (simulations using an Estes
+motor) and figure~\ref{fig-flight-C6} using a C6-3 motor. The RockSim
+simulations are truncated at apogee due to limitations of the
+demonstration version of the software. A summary of the apogee
+altitudes is presented in Table~\ref{tab-flight-results}.
+
+Both simulations produce a bit too optimistic results. OpenRocket
+yielded altitudes 16\% and 7\% too high for the B4-4 and C6-3 motors,
+respectively, while RockSim had errors of 24\% and 19\%. The C6-3
+flight is considered to be more accurate due to the ambiguity of the
+B4-4 thrust curve.
+%
+Another feature that can be seen from the graphs is that the estimated
+descent speed of the rocket is quite close to the actual descent
+speed. The error in the descent speeds are 7\% and 13\% respectively.
+
+
+\begin{figure}[p]
+\centering
+\epsfig{file=figures/experimental/flight-B4-4,width=12cm}
+\caption{Experimental and simulated flight using a B4-4 motor.}
+\label{fig-flight-B4}
+\end{figure}
+
+\begin{figure}[p]
+\centering
+\epsfig{file=figures/experimental/flight-C6-3,width=12cm}
+\caption{Experimental and simulated flight using a C6-3 motor.}
+\label{fig-flight-C6}
+\end{figure}
+
+
+% B4-4 C6-3
+%Exp 64.0 151.5
+%OR 74.4 +10.4 +16% 161.4 +9.9 +7%
+%RS 79.1 +15.1 +24% 180.1 +28.6 +19%
+
+
+The rocket was also launched with a launch lug 24~mm long and 5~mm in
+diameter attached first to its mid-body and then next to its fins to
+test the effect of a launch lug on the aerodynamic drag. The apogee
+altitudes of the tests were 147.2~m and 149.0~m, which correspond to
+an altitude reduction of 2--3\%. The OpenRocket simulation with such
+a launch lug yielded results approximately 1.3\% less than without the
+launch lug.
+
+
+
+
+\section{Comparison with a hybrid rocket}
+\label{sec-comparison-large}
+
+The second comparison is with the Haisunäätä hybrid
+rocket~\cite{haisunaata-launch}, which was launched in September 2008.
+The rocket is a HyperLOC 835 model, with a length of 198~cm and a body
+diameter of 10.2~cm. The nose cone is a tangent ogive with a length
+of 34~cm, and the kit includes three approximately trapezoidal fins.
+
+The flight computer on board was a miniAlt/WD altimeter by
+PerfectFlite~\cite{perfectflite}, with a stated accuracy of
+$\pm0.5\%$. The flight computer calculates the altitude 20 times per
+second based on the atmospheric pressure and stores the data into
+memory for later analysis.
+
+The rocket was modeled as accurately as possible with both OpenRocket
+and RockSim, but the mass and CG of each component was computed by the
+software. Finally, the mass of the entire rocket excluding the motor
+was overridden by the measured mass of the rocket. The surface
+roughness was estimated as the same as for the small rocket,
+60~\textmu m in OpenRocket and ``matt'' for RockSim.
+
+Figure~\ref{fig-flight-haisunaata} presents the true flight profile
+and that of the simulations. Both OpenRocket and RockSim estimate a
+too low apogee altitude, with an error of 16\% and 12\%,
+respectively. As in the case of the small rocket model, RockSim
+produces an estimate 5--10\% higher than OpenRocket. It remains
+unclear which software is more accurate in its estimates.
+
+% Experimental 965m
+% OpenRocket 814m
+% RockSim 853m
+
+
+One error factor also affecting this comparison is the use of a hybrid
+rocket motor. As noted in Section~\ref{sec-motors}, the vapor
+pressure of the nitrous oxide is highly dependent on temperature,
+which affects the thrust of the motor. This may cause some variation
+in the thrust between true flight and motor tests.
+
+\begin{figure}[p]
+\centering
+\epsfig{file=figures/experimental/flight-haisunaata,width=12cm}
+\caption{Experimental and simulated flight of a hybrid rocket.}
+\label{fig-flight-haisunaata}
+\end{figure}
+
+\begin{figure}[p]
+\centering
+\epsfig{file=figures/experimental/flight-roll-rate,width=12cm}
+\caption{Experimental and simulated roll rate results using a C6-3
+ motor.}
+\label{fig-flight-roll}
+\end{figure}
+
+
+
+\section{Comparison with a rolling rocket}
+\label{sec-comparison-roll}
+
+In order to test the rolling moment computation, a second
+configuration of the small model rocket, described in
+Section~\ref{sec-comparison-small}, was built with canted fins. The
+design was identical to the previous one, but each fin was canted by
+an angle of $5^\circ$. In addition, the payload section contained a
+magnetometer logger, built by Antti~J. Niskanen, that measured the
+roll rate of the rocket. The logger used two Honeywell HMC1051
+magnetometer sensors to measure the Earth's magnetic field and store
+the values at a rate of 100~Hz for later analysis. The rocket was
+launched from the tower launcher using a Sachsen Feuerwerk C6-3
+motor. Further test flights were not possible since the lower rocket
+part was destroyed by a catastrophic motor failure on the second
+launch.
+
+After the flight, a spectrogram of the magnetometer data was generated
+by dividing the data into largely overlapping segments of 0.4~seconds each,
+windowed by a Hamming window, and computing the Fourier transform of
+these segments. For each segment the frequency with the largest power
+density was chosen as the roll frequency at the midpoint of the
+segment in time. The resulting roll frequency as a function of time
+is plotted in Figure~\ref{fig-flight-roll} with the corresponding
+simulated roll frequency.
+
+
+The simulated roll rate differs significantly from the experimental
+roll rate. During the flight the rocket peaked at a roll rate of 16
+revolutions per second, while the simulation has only about half of
+this. The reason for the discrepancy is unknown and would need more
+data to analyze. However, after the test flight it was noticed that
+the cardboard fins of the test rocket were slightly curved, which may
+have a significant effect on the roll rate. A more precise test rocket
+with more rigid and straight fins would be needed for a more
+definitive comparison. Still, even at a cant angle of $7^\circ$ the
+simulation produces a roll rate of only 12~r/s.
+
+Even so, it is believed that including roll in the simulation allows
+users to realistically analyze the effect of roll stabilization for
+example in windy conditions.
+
+
+\section{Comparison with wind tunnel data}
+\label{sec-comparison-windtunnel}
+
+
+Finally, the simulated results were compared with experimental wind
+tunnel data. The model that was analyzed by J.~Ferris in the
+transonic region~\cite{experimental-transonic} and by C.~Babb and
+D.~Fuller in the supersonic region~\cite{experimental-supersonic} is
+representative of the Arcas Robin meteorological rocket that has been
+used in high-altitude research activities. The model is 104.1~cm long
+with a body diameter of 5.72~cm. It includes a 27~cm long tangent
+ogive nose cone and a 4.6~cm long conical boattail at the rear end,
+which reduces the diameter to 3.7~cm. The rocket includes four
+trapezoidal fins, the profiles of which are double-wedges. For
+details of the configuration, refer to~\cite{experimental-transonic}.
+
+The design was replicated in OpenRocket as closely as possible,
+given the current limitations of the software. The most notable
+difference is that an airfoil profile was selected for the fins
+instead of the double-wedge that is not supported by OpenRocket. The
+aerodynamical properties were computed at the same Mach and Reynolds
+numbers as the experimental data.
+
+
+\begin{figure}[t]
+\centering
+\epsfig{file=figures/experimental/ca-vs-mach,width=11cm}
+\caption{Experimental and simulated axial drag coefficient as a
+ function of Mach number.}
+\label{fig-experimental-CA}
+\end{figure}
+
+The most important variables affecting the altitude reached by a
+rocket are the drag coefficient and CP location. The experimental and
+simulated axial drag coefficient at zero angle-of-attack is presented
+in Figure~\ref{fig-experimental-CA}. The general shape of the
+simulated drag coefficient follows the experimental results. However,
+a few aspects of the rocket break the assumptions made in the
+computation methods. First, the boattail at the end of the rocket
+reduces the drag by guiding the air into the void left behind it,
+while the simulation software only takes into account the reduction of
+base area. Second, the airfoil shape of the fins affects the drag
+characteristic especially in the transonic region, where it produces
+the slight reduction peak. Finally, at higher supersonic speeds the
+simulation produces less reliable results as expected, producing a too
+high drag coefficient. Overall, however, the drag coefficient matches
+the experimental results with reasonable accuracy, and the results of
+actual test flights shown in Sections~\ref{sec-comparison-small} and
+\ref{sec-comparison-large} give credence to the drag coefficient
+estimation.
+
+
+\begin{figure}
+\centering
+\epsfig{file=figures/experimental/cp-vs-mach,width=12cm} \\
+(a) \\
+\epsfig{file=figures/experimental/cna-vs-mach,width=12cm} \\
+(b)
+\caption{Experimental and simulated center of pressure location (a)
+ and normal force coefficient derivative (b) as a function of Mach
+ number.}
+\label{fig-experimental-CP-CNa}
+\end{figure}
+
+The CP location as a function of Mach number and the normal force
+coefficient derivative \CNa\ are presented in
+Figure~\ref{fig-experimental-CP-CNa}. The 3\% error margins in the
+transonic region were added due to difficulty in estimating the normal
+force and pitch moment coefficient derivatives from the printed
+graphs; in the supersonic region the CP location was provided
+directly. At subsonic speeds the CP location matches the experimental
+results to within a few percent. At higher supersonic speeds the
+estimate is too pessimistic, and due to the interpolation this is
+visible also in the transonic region. However, the CP location is
+quite reasonable up to about Mach~1.5.
+
+The simulated normal force coefficient derivative is notably lower
+than the experimental values. The reason for this is unknown, since
+in his thesis Barrowman obtained results accurate to about 6\%. The
+effect of the lower normal force coefficient on a flight simulation is
+that the rocket corrects its orientation slightly slower than in
+reality. The effect on the flight altitude is considered to be small
+for typical stable rockets.
+
projects / debian / openrocket / blobdiff