Student 1, Student 2, Student 3, Student 4Section 3 Team 2

E80: Experimental Engineering Rocket launches on 4/19 and 4/26 Lucerne Valley dry lake bed Rockets had various sizes, sensors, and

motors Take data, analyze it, and compare it to

theoretical models we developed

Photo courtesy of Professor Cardenas

Configure and verify RDASConfigure and verify video telemetryConnect jumpers for vibration sensorsPhysical launch preparationsLaunchRecover data

Inertial Measurement Unit mounted on a large and small rocket Accelerations Angular velocities

IMU calibrated with a turntable apparatusEuler method and rotation used to find

global variables

Experimental and Theoretical Results IMU DataIMU Data

Flight ModelFlight Model

RockSimRockSim

Vertical Position Horizontal Position

Both RDAS and IMU have pressure sensors

Mounted on a medium rocketPressure sensors calibrated with a

pressure chamberAltitude can be calculated from pressure

RDAS pressure

IMUpressure

RDAS altitude

IMU altitude

Flight Model

RockSim

RDAS

IMU

RockSim Flight Model RDAS Data Analysis

IMU Data Analysis

Apogee (m) 262.76 290.75 191.23 208.20

Time (s) 7.89 8.2052 7.045 7.8

Sources RockSim and Flight Model

RockSim and RDAS

RockSim and IMU

Flight Model and RDAS

Flight Model and IMU

RDAS and IMU

% difference in apogee

10.11 31.51 23.17 41.30 33.09 8.50

Apogees from data consistently lower than predicted apogees from the flight model and RockSim

Calibration errorLaunch angleDynamic wind vs. static wind

Theoretical resonant frequencies, obtained by modeling the rocket as a hollow tube with free-free boundary conditions.

f1 = 165 Hz, f2 = 456 Hz, f3 = 893 Hz.

Expected peaks after folding = 35 Hz, 56 Hz and 93 Hz.

€

fn =ωn2π

=(β nL)2

2π

EIzρAL4

E = Young’s modulus, Iz = second moment of the beam, A = cross sectional area of the beam ρ = densityßn= a property dependent on boundary conditions

Resonant peaks also determined by taking data with the DAQ, to get rid of folding.

DAQ data can only be obtained for half of the rocket. Resonant peak obtained for half-rocket and extended onto

the full rocket. Assumed only parameter changing is length.

First resonant frequency at 178 Hz, which should appear at 22 Hz after folding.

€

f full =Lhalf

2

L full2 fhalf

Large vibration Strain gages along the body of the large

vibration rocket Strain gages measure changes in length

The magnitudes of the length changes can be used to determine characteristic vibration

Large vibration Strain gages along the body of the large

vibration rocket Strain gages measure changes in length

The magnitudes of the length changes can be used to determine characteristic vibration

Obtain raw data from the RDAS. Split up raw data according to events.

Takeoff, ejection charge and deployment, landing.

Perform FFT on each output channel. Assume the sensor closest to the motor is the

input for take off. Obtain FRF by taking the ratio of the output and

the input for the first event of the rocket. Determine resonance frequencies.

77 Hz

51 Hz46 Hz

f=77 Hz

0

100

200

300

400

500

600

0 20 40 60 80 100 120

Position (cm)

Relative Amplitude

f = 46 Hz

0

10

20

30

40

50

60

0 20 40 60 80 100 120

Position (cm)

Relative Amplitude

f = 51 Hz

0

50

100

150

200

250

0 20 40 60 80 100 120

Position (cm)

Relative Amplitude

Theoretical Predictions:

• Hollow beam model - 165 Hz

• DAQ experimental prediction - 178 Hz

Experimental Value - 154 Hz

Difference - 7%

Theoretical Predictions:

• Hollow beam model - 456 Hz

Experimental Value - 451 Hz

Difference - 1%

Theoretical Predictions:

• Hollow beam model - 893 Hz

Experimental Value - 877 Hz

Difference - 2%

Experimental vibration data matched theoretical model fairly closely

Data from large IMU rocket fit with flight model and RockSim shapes, but differed in altitude

RDAS and IMU data from temperature and pressure rocket agreed with each other, but fit neither of the theoretical models

Change sampling rate of RDAS (200 Hz is too low)

Use low-pass filters to block out unwanted noise

Have more than 6 channels collecting data

Have Global Positioning System onboard rocket for confirmation

Experimental ResultsA: x-positionB: y-positionC: z-position

Theoretical PredictionsA: z-position

(Rocksim)

Recovery charge did not ignite

Fatal flat spinDamage to the

RDAS

The natural frequency of a hollow tube is given by:

€

fn =ωn2π

=(β nL)2

2π

EIzρAL4

E = Young’s modulus, Iz = second moment of the beam, A = cross sectional area of the beam ρ = densityßnL= a property dependent on boundary conditions independent of length.

€

fhalf =(β nL)2

2π

EIzρA

1

Lhalf2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

f full =(β nL)2

2π

EIzρA

1

L full2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

k k

€

fhalff full

=L full

2

Lhalf2

€

f full =Lhalf

2

L full2 fhalf

€

⇒