X-Git-Url: https://git.gag.com/?a=blobdiff_plain;f=core%2Fdoc%2Ftechdoc%2Fchapter-experimental.tex;fp=core%2Fdoc%2Ftechdoc%2Fchapter-experimental.tex;h=eecb07f82ef2fbd24187d42083c9fae719ede098;hb=84094f3e8b4e8d27310532c092ec9738156417d3;hp=0000000000000000000000000000000000000000;hpb=fc3d9fa48747ea14f7d77e573df16386c9fdf89e;p=debian%2Fopenrocket diff --git a/core/doc/techdoc/chapter-experimental.tex b/core/doc/techdoc/chapter-experimental.tex new file mode 100644 index 00000000..eecb07f8 --- /dev/null +++ b/core/doc/techdoc/chapter-experimental.tex @@ -0,0 +1,353 @@ + +\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. +