**E178: Assignment 8** |[home](../index.md.html)|[syllabus](../syllabus.md.html)|[assignments](../assignments.md.html)|[labs](../labs.md.html)|[final project](../finalproject.md.html)|[flight data](../FlightData.md.html)|[getting certified](../RocketryCertification.md.html)| # Analysis of First Set of Flight Data If you successfully completed your first set of flights, you will analyze the flight data from your first set of flights. If you were unsuccessful in your first set of flights, you will analyze the two flights of the prototype Class Adventurer rocket from [10 June 2022](../FlightData.md.html#flightdatafiles/madcowadventurer). It made four flights between 9 June 2022 and 11 June 2022. You will get to analyze the other two for Assignment 9. Your data collection may differ from the standard for the Class Adventurer. Your analysis should be appropriate for the data you collected. If you use the existing Class Adventurer data, the data you should present are: ## Acceleration, velocity, and altitude data. Display as much as you can from the accelerometer data, the velocity data, and the altitude data from the Large Teensy data files, the Featherweight Raven Data files, the GPS files, and Open Rocket or Rocksim simulations of your flights or the two 10 June flights. An OpenRocket model for the Adventurer is [here](../SimModels/ClassAdventurer.ork). Be sure to indicate regions of interest, such as supersonic/subsonic transitions, burnout, descent rates under drogue and main parachutes, etc. ## Axial rotation angle during ascent. Both the rate gyro data and the magnetometer data can be used to calculate the axial rotation angle from liftoff to apogee. You can either plot the angle versus time for each of the sensors separately, or do data fusion to combine them. A reasonable start for data fusion is in [KalmanFilterExample](../PDF/KalmanFilterExample.pdf). ## Average $C_D$ The post-boost portion of the rocket flights can be used to look at $C_D$, as explained in [$C_D$ From Post-Boost Flight Data](../PDF/CDfromPostBoost.pdf), the average $C_D$ can be determined by a plot of $-\frac{2m}{A_p\rho}(a+g)$ versus $v^2$ or a plot of $-\frac{2m}{A_p\rho}a$ versus $v^2$. Include a 95% confidence intervals on the value of $C_D$. There are refreshers on statistics [here](https://drive.google.com/file/d/1_T4TviLt9oUw6PXEDxpSGv6yuUdPVigi/view?usp=sharing) and [here](https://www.youtube.com/playlist?list=PLDA3QBjykWVxDiGsN1Xpm2ynGekSvEC9E). ## $C_D$ as a Function of Velocity If your accelerometers are good enough, you can actually calculate the $C_D$ as a function of velocity. As explained in [$C_D$ From Post-Boost Flight Data](../PDF/CDfromPostBoost.pdf), \begin{equation} C_D=-\frac{2m}{A_p\rho}\frac{(a+g)}{v^2} \end{equation} and you can then plot $C_D$ versus $v$. ## Thrust Curve With either your average $C_D$ or your $C_D$ as a function of velocity, you are able to calculate the thrust curve for your motor from the accelerometer data. As explained in [Thrust Curve from Acceleration and Velocity Flight Data](../PDF/ThrustCurveFromFlightData.pdf) you can calculate the thrust from an iterative solution of \begin{equation} T=m(a+g)+\frac{1}{2}C_DA_p\rho v^2 \end{equation} and \begin{equation} m(t)=m_0+\frac{1}{v_e} \int_{t_0}^{t} Tdt \end{equation} Plot the thrust curves for both flights and compare with the Thrustcurve.org curve. ## Temperature vs Altitude There are two thermistors on opposite sides of the rocket. They tend to show different temperatures before liftoff, when one thermistor is in the shade and the other is in the sun. Plot the temperature versus altitude from apogee to landing as both a function of time and of altitude and see how close the slope comes to the standard lapse rate. Also plot the temperature versus velocity from liftoff until just before apogee and explain the resultant curve as best you can. # Available Software There is a MATLAB .m file that combines data from the Teensy Data Logger with Open Rocket data and GPS data. It is called [ScanTeensyDataLoggerGPSRotTempAdventurer](../MATLABModels/ScanTeensyDataLoggerGPSRotTempAdventurer.m). The default values are for the J825R Adventurer flight on 9 June 2023. You will need to edit things to correspond to the data you are processing. # Deliverables Your deliverable is a section in your Final Report describing your process and results. If you are analyzing the Class Adventurer you must include: 1. The acceleration, velocity, and altitude plots and analysis. 2. The axial rotation plots and analysis. 3. The average $C_D$ plots and analysis. 4. The plots of $C_D$ vs. $v$ and analysis. Pay special attention for trans- and supersonic regions. 5. Plots of the calculated thrust curves for the motor with the thrust curves from ThrustCurve.org overlain. Comment on the comparison between the nominal and the actual thrust curves. 6. The plots of temperature vs. time and temperature vs. altitude. If you have time, Include a plot of temperature vs. velocity and comment on its significance.