MAGE McNeese Acceleration due to Gravity Experiment

TEAM MEMBERS:

 Mukesh Wagle  Ramji Neupane  Shankar Thapa  Rajesh Wagle  Sagar Kharel (Team Leader)

THE MISSION OBJECTIVE

 Measurement of the change of acceleration due to gravity (g) with respect to altitude (h).

SCIENTIFIC DESIGN

 Acceleration due to Earth’s gravity (g) is the acceleration that acts on all objects that fall within the Earth's gravitational field.  It is inversely proportional to the square of the radius of the earth.

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CALCULATING ACCELERATION DUE TO GRAVITY

Newton's second law of motion relates Force (F), mass of an object (m) and acceleration (a) of an object as: F=ma. For force generated by an object of mass m, falling towards the Earth, the relation becomes:

F=mg

where, g is the acceleration due to Earth’s gravity.

When it comes to gravitational force ‘F’ between two objects of masses m1 and m2, Newton’s Law of gravitation states: where, G is the universal gravitational constant (6.67x10

11 Nm 2 kg -2 )

 We can set the two equations 1 and 2 to get the following relation where, m and m m e 1 refer to the mass of an object falling towards the Earth , is the mass of the earth g is an acceleration due to Gravity, and r is the distance between the object and the Earth.  Solving for g, we get: 3

  Universal gravitational constant (G) and mass of the earth are constants. Thus, we notice that the acceleration due to gravity will change only with an object's distance from the earth and is inversely proportional to the square of the distance, as given by:   Acceleration due to gravity at Palestine, TX and Lake Charles, LA at 31 degree latitude is 9.7974 m/s 2

ACCELERATION DUE TO GRAVITY AT HEIGHT R E + H  At a distance of d = r e + h from the center of the earth (height of h from the Earth’s surface), the acceleration due to gravity is:  5  Dividing eq. 5 by eq. 3, we get , Expanding by binomial theorem and neglecting higher powers of h/r e , 

PENDULUM METHOD

 Time period of oscillation of pendulum is given by:  T = 2 ∏ *√ (l/g) where, l is the length of the pendulum and g is acceleration due to gravity.

 So, g = 4 where, w ∏ 2 *f 2 *l = w 2 *l is the angular frequency

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DATA ACQUISITION AND ANALYSIS

We will collect data at a sampling frequency of 10 Hz.  We will calculate the Power Spectral Density (PSD) for every 10 minutes of data.

 The highest, low frequency peak (around 1.5 Hz) is the resonance frequency of our pendulum (that is length and g dependent)  Because our precision will increase with the time of observation, with stretches of 10 minutes of data, we can get a 0.0017 Hz resolution and have enough data points over the flight.

 This frequency resolution corresponds to an error of 0.1 % in our measurement of g (in ideal situations)

VOLTAGE VS. TIME

POWER SPECTRAL DENSITY

Resonance Frequency Of Pendulum About 1.5 Hz

ACCELERATION DUE TO GRAVITY VS. ALTITUDE Expected Upper Limit 1 s Lower Limit 1 s The expected change in g at 30 km is about 1 % Quite small ! We think we can measure this.

PAYLOAD DESIGN

 Acceleration due to gravity is to be calculated using the pendulum method.  The design of the payload has been divided into subcategories to provide the necessary attention and research for each area.  These subcategories include system, thermal, mechanical, electrical, and software design.

SYSTEM DESIGN

 System components: spring blades (high pass mechanical filter), copper coil, super-magnet, Basic Stamp and batteries are arranged for stable and safe design of the payload.  This design sequence of relaying and converting information promoted the most robust and relatively accurate results.

THERMAL DESIGN

 The payload will be flying in the location of Palestine, Texas and will ascend to an altitude of approximately 30km. Through the different altitudes we expect a minimum temperature of -60 o C and a maximum temperature of about 80 o C.

 We will be using sponge foams and fiber glass wool which will act as passive insulation to our electrical equipments inside the box.

 We will also have a ceramic heater with the basic stamp to keep the components at reasonable temperature.

MECHANICAL DESIGN

 We focused on creating a payload of a low weight, high thermal stability, and a suitable degree impact resistance.

 The box concept is simply a rectangular payload.  We used foam core as the principle material of the payload.

 The only component that we were able not to reduce too much in weight was the coil because we needed a bigger coil to get good readings of induced voltage from our experiment.

WI

A. B.  A. Primary experimental setup with a magnet and coil  B. Current experimental model for the payload to be launched  It relays on passively inducing a current through the motion of the magnet due to the shaking of the box

VALUE OF G (IN THE LAB) WITH DIFFERENT PENDULUM LENGTH (3 MINUTES DATA SETS)

WEIGHT BUDGET OF THE PAYLOAD

(WE ARE A FLYING ELEPHANT, OUR AT LEAST WE ASPIRE TO BE)  BalloonSat (Basic Stamp Kit) 70 g Battery, spring blades 45g Inter and Outer Module 160 g Mesh, Frame, standoffs 125 g Copper Coil Total 1500 g 1900 g  The payload is in compliance with FAA (Federal Aviation Administration) that the payload needs to be less than 131kg/m 2 .

ours being 88.9 kg/m 2

SOFTWARE DESIGN

 Basic Stamp editor and Matlab software are used in the project.

 Our payload will take voltage readings from the coil and will store it in BalloonSat. There will be controlled reading of voltage from the payload with specific sampling frequency (10 Hz). This data will be gathered after the flight.

ELECTRICAL AND SYSTEM DESIGN

  We will be using magnet-coil setup in our experiment. A magnet placed within a circular coil will provide some signals upon motion due to external movement.

Battery Magnet and Coil => Input pin =>  Analog to Digital Converter (ADC) => EEPROM

BASIC STAMP EDITOR

DATA ACQUISITION AND ANALYSIS PLAN

 The readings will be retrieved from the EEPROM using PBASIC language in a Basic Stamp editor.  Analysis of the readings and calculations of g as a function of altitude, error analysis and data display will be done using Matlab.

TESTS DONE

 Measured values of v with GLX, used to calibrate our Basic Stamp output  Mechanical tests (very robust design)  Temperature tests (tested in low temperature freezer, -80 C)  Software tested over time equivalent to flight time

PROJECT MANAGEMENT

    First Semester Spent in planning and training Second semester started with LVDT (Linear Variable Differential Transformer) experimental planning Planning was modified to Capacitor Method (active power) and eventually to Pendulum method (passive power), which turned out to be the successful one.

The coil used for test purpose at the beginning of payload design resulted to be the main component for the payload.

GANTT CHART

THANKS

 Dr. Giovanni Santostasi  Dr. T. Gregory Guzik  Dr. John P. Wefel  NASA facility, Palestine, TX