\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.