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## Contents1 Doppler Shift Theory2 Hardware3 Software4 Experiment #14.1 "Sounding" Rocket4.2 Test Results4.2.1 Flight waterfall spectrogram4.2.2 Launch phases4.2.3 Recovery phases4.2.4 Data post-processing5 Experiment #25.1 ERROR CorrectionDoppler Shift Theory

(I have to update the theory bit as it's not entirely correct. In fact relativistic effects have to be taken into account in a manner  very much similar to accounting for the Doppler shift in light)

The Doppler shifted frequency is given by the following formula:

frx = fo (1 - Vs,r/c),

Vs,r=Vs-Vr,

df =-fo*Vs,r/c,

where:

* fo, Hz - the transmitted frequency
* frx, Hz - the frequency of the wave arriving at the receiver
* Vs,r=Vs-Vr, m/s - the speed of the transmitter Vs (source) relative to the receiver moving with the speed Vr. (Vs,r is positive when                                 the transmitter and receiver move away from each other)
* c, m/s - the speed of the wave (approx. 342 m/s for sonic waves travelling in air at 20 deg. C)
* df, Hz - the Doppler frequency shift.

Description of a more sophisticated variant of the Doppler tracking system for a model rocket can be found  in the Chuck McConaghy's article here.

## Hardware

Simple Piezo Buzzer CR34M is used to generate sine audio tone.

Specification:
• Resonant frequency:2kHz ±500Hz
• Operating voltage:3 to 15Vdc
• Current at 12V DC:10mA
• Sound output at 30cm:90dB typical (12Vdc)
• Size:30mm dia., 22mm high 46mm across mounting ears
• Mass: 7g

The buzzer is powered  by  a single 12V A23 battery. The battery mass is 7g

Sound is recorded by  either  a mobile smart phone or a video camera

## Software

A shareware  audio frequency analyser program, Spectrum Lab, designed by DL4YHF is used to analyse measurements. The analyser can be downloaded from: http://www.qsl.net/dl4yhf/spectra1.html

The program useful feature – spectrum waterfall display where both intensity and frequency are shown in the time domain.

## Experiment #1

### "Sounding" Rocket

A simple one stage model rocket, Doppler-1, was designed to carry  the buzzer and the battery.

The buzzer is covered by a aerodynamically shaped fairing to prevent airstream from entering the buzzer resonator.

### Test Results

The rocket was launched twice on B6-4 motors. Results of the second test are presented in the following sub-sections.

Due to a failure the parachute didn’t eject resulting in a very rapid descent at about 11 m/s

Both video and audio recording were performed.

#### Flight waterfall spectrogram

Very good correlation between the motor trust curve and the measured spectrum

#### Data post-processing

Further analysis of the velocity curves can produce altitude data, or more generally, distance data.This is accomplished by integrating the data with a simple Microsoft Excel spreadsheet.

Due to motor noise during the launch it is not possible to measure speed during the acceleration phase. Altitude corresponding to the max speed calculated as Vmax*Tmax/2.

## Experiment #2

To test practicalities of the Sound Ranging technique we set up a simple experiment. Its details are described in the video below.

#### ERROR Correction

After completing the above video a systematic error was identified. Correcting data accordingly provided significantly better  results.

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