Reference / Paper · 2009
Peak of Flight #246: Educator's Plan - Build a Mechanical Accelerometer
Apogee Components' Peak of Flight newsletter, issue 246 (2009-10-20).
- peak-of-flight
- apogee-components
- model-rocketry
Reference / Paper · 2009
Apogee Components' Peak of Flight newsletter, issue 246 (2009-10-20).
Apogee Components' Peak of Flight newsletter, issue 246 (2009-10-20).
Feature Article: Educator’s Plan: Build An Accelerometer Cover Photo: Starlight Rocketry’s Sparrow glider rocket kit. To get one today, visit: www.apogeerockets.com/Starlight_Sparrow.asp Apogee Components, Inc. — Your Source For Rocket Supplies That Will Take You To The “Peak-of-Flight” 3355 Fillmore Ridge Heights Colorado Springs, Colorado 80907-9024 USA www.ApogeeRockets.com e-mail: [email protected] ISSUE 246 OCTOBER 20, 2009 Geeeeeeee! What an awesome ACCELERATION! Written By Pierre Boivin Editor’s Note: Pierre Boivin is an educator living in Quebec, Canada. His native language is French, so please bear this in mind as you read this English edition of his curriculum. We left this mostly untouched so you can get a taste of the international flair of this article. As space educator, I frequently read the Apogee Components literature. With the Model Rocket Propulsion (www.ApogeeRockets.com/mod_rocket_propulsion_ bk.asp) publication, a companion comes freely, Activities for Model Rocket Propulsion. On the second page, Tim wrote “Measuring acceleration is hard to do”. Hmmm! It is hard to believe, because I have measured acceleration for many years….. so easily. Let me show you! AMROC company commercialized the onboard accelerometer in 1969. Stine in the 4th edition of his Handbook of model Rocketry presents the instrument. Essentially, it was a The first of these onboard actriangle lead mass, on celerometers for measuring the maximum acceleration was a compression spring, built and perfected by Lindsay scratching a scribe Audin, of Hillside, New Jersey, paper inside the instruin the early 1960s. Stine (1976) ment as a recorder. Kranich introduced in 1995 a model with a rubber band and a centering ring as the recorder. An accelerometer is used to measure how fast a rocket changes its speed in the vertical direction. Our accelerometer uses a lead weight suspended by a rubber band to sense changes in the rocket motion. It is a modified Kranich concept. It is a mechanical (Inertial-mass) accelerometer; mono axial (vertical); exclusively for positive acceleration; ranging from +1 g to +25 g. Material and Design The list of material is quite simple and easily available: 10 cm of Airframe Tube 18/18 (Apogee Cat No 10086) (BT-20); DO NOT use a blue motor mount (Estes), it’s too weak! 2 centering rings 13-18 (Apogee Cat No 13028) (BT20); 2 cm of an empty motor case 18 mm; 1 screw eye small size; 1 fishing sinker size (20 g); 1 micro torch (Micro-jet® from Solder-It®) using disposable lighter; 1 paper clip; 4 to 6 orthodontics rubber bands (Apogee Cat No 24002) and many spares; Wood glue, of course; X-acto® and calliper. Building the Accelerometer Glue a centering ring (support) at one end of the body tube section. Let it dry. Drill a tiny hole (the diameter of the paper clip) through the diameter of the glued centering ring. Cut a 4 cm x 50 mm slot lengthwise on the body tube section at the opposite end of the centering ring. Cut a 2 cm section of the 18 mm empty motor case. Put this section on a dish plate. With the micro torch melt the fishing sinker (please take adequate precautions melting the lead...) inside the section of the motor case. In a minute, screw the screw eye at the center of the melted lead. Let it cool. This is your inertial mass. Hang your rubber band(s) to the screw eye. Introduce this setup inside the tube; Introduce a straight section of paper clip throughout the hole at side of the tube, throughout the rubber band, and Continued on page 3 About this Newsletter Newsletter Staff You can subscribe to receive this e-zine FREE at the Apogee Components web site (www.ApogeeRockets.com), or by sending an e-mail to: [email protected] with “SUBSCRIBE” as the subject line of the message. Page 2 You will learn to build your own accelerometer for pennies. Tim loves that too. This is so simple that everyone can build their own, launch it and calculate his rocket peak acceleration. ISSUE 246 Writer: Tim Van Milligan Layout / Cover Artist: Tim Van Milligan Proofreader: Michelle Mason OCTOBER 20, 2009 Continued from page 2 Build an Accelerometer Payload through the hole at the opposite side of the tube! Understand!? OK Introduce an Indicator-centering ring by the bottom of the tube, close, very close, to the bottom of the Inertialmass. A mechanical positive accelerometer & mono-axial. Glue a centering ring (stopper) at bottom of the body tube section. Let it dry. You are ready. Calibrating the accelerometer (finding the spring constant – K) Assumption: We assume the rubber band stretch is linear (a constant amount for each increase in weight/g force). Protocol As shown in Figure 3, measure and note the length of the rubber band at rest ( l ). Hang 50 g on the rubber band, simulating acceleration. Measure and note the length of the rubber band under tension and the force (in Newtons) on the dynamometer (L). Hang 100 g on the rubber band. Measure and note the length of the rubber band under tension (L). Continued on page 4 • Reusable Rocket Motors Save Money • Holds Aerotech’s Reload Propellant • Sizes: 24mm To 98mm Diameter • Power Range: E Through N • Cases For Any Project • Rouse-Tech Quality • Affordable! www.ApogeeRockets.com High-Power Reload Casings www.ApogeeRockets.com/Rouse-Tech_Monster_Motors.asp ISSUE 246 OCTOBER 20, 2009 Page 3 Continued from page 3 Build an Accelerometer Payload length (independent variable) vs force (dependent variable). Measure and note the length of the rubber band at rest ( l ). Support Force Scale Hang 200 g on the rubber band. Measure and note the length of the rubber band under tension and the force (in Newtons) on the dynamometer (L). Measure and note the length of the rubber band at rest ( l ). Hang 500 g on the rubber band. Measure and note the length of the rubber band under tension and the force (in Newtons) on the dynamometer (L). Variable mass Measure and note the length of the rubber band at rest ( l ). Compute the spring constant - K. It is EXCLUSIVE to EACH rubber band or set of rubber bands or spring. Table 1: Collect data on the So, do it with every one. length of the rubber band with different weights attached. The spring constant is demonstrated by the following equation: If F = m * a then F = k * length and M * a = k * length; so K = (m * a) / length. But, it’s easier to get K graphically by the slope of the curve. Using the accelerometer Newton’s first law of motion Yes, I know … one more time; but it’s so fundamental. And so on, up to 1,000 g (1 Figure 3: Calibrating the Kg). accelerometer (finding Fill up the table and graph the spring constant - K). A body in motion will stay in motion and a body at rest will stay at rest unless an external force acts upon it. As our rocket is launched and accelerates, a mass at rest wants to stay at rest. The rocket accelerates upright Continued on page 5 Roam In Our Forest of Over 170 Different Types • Unique and exotic kits from over 20 different manufacturers • Skill Levels range from “easy” to “fiendish” • Sizes from 1/4A motor to level-2-high-power • We build & fly them to find out what they’re like, saving you grief • More new ones arriving all the time • Educational bulk packs available too www.ApogeeRockets.com/All_rocket_kits.asp Page 4 ISSUE 246 OCTOBER 20, 2009 www.ApogeeRockets.com Looking For A Fun Rocket Kit? Continued from page 4 Build an Accelerometer Payload or Quest Zenith II® are fine. from this Inertial-mass stretching a rubber band or a spring (an extension spring). As the rubber band stretches a tension is developed which increases more and more by the accelerating rocket. The tension in the rubber band (or the extension spring) is proportional to the acceleration of the rocket and the Inertial-mass used. When the rubber band stretches during acceleration, the Inertial-mass pushes against the Indicator-ring. The Indicator-ring, pushed by the Inertial-mass, slides freely inside. As the acceleration decreases at burnout, the rubber band contracts and pulls the Inertial-mass back up to his original level. The Indicator-ring stays at the furthest level by the friction between the ring side and the inside of the accelerometer. With a metric calliper (or a ruler), measure the distance, in millimetres, between the pencil marks ( L & l ). The measuring is the difference between the TOP of the Indicator-ring at rest (on the launch pad) and the TOP of the Indicator-ring at the recovery. With the mass of the mass and the Force in the accelerometer you can get the acceleration! Experimentation You have a big, big choice for the loader: Quest Payloader One®, Sky Dynamo®, Quest Magnum Sport Loader® Protocol 1) Make a general mechanic verification of the accelerometer. 2) Check the free motion of the Inertial-mass. 3) Introduce the Indicator-ring in the bottom of the accelerometer. 4) Slide the Indicator-ring as close as possible under the Inertial-mass. 5) Make a pencil mark of the start position of the Indicator-ring with a sharp & dark pencil, easily spotted after the flight. Use the TOP of the Indicator-ring as a start position. Identify this mark as 1 g. ** This mark is a frequent source of mistakes. Make the mark very precisely, it’s the position (L) where every measurements will start, so …. 6) Introduce the accelerometer vertically in the payload section of the rocket. Use bubble wrap or Kleenex® to secure vertically the instrument if you are putting it inside a larger diameter rocket. Check the fitting of the nose cone. 7) After the flight, extract the accelerometer with care. DON’T move the Indicator-ring, mark its position. Use the TOP of the Indicator-ring. Continued on page 6 Model Rocket Design and Construction By Timothy S. Van Milligan New 3rd Edition Now Shipping! This new 328 page guidebook for serious rocket designers contains the most up-to-date information on creating unique and exciting models that really work. With 566 illustrations and 175 photos, it is the ultimate resource if you want to make rockets that will push the edge of the performance envelope. Because of the number of pictures, it is also a great gift to give to beginners to start them on their rocketry future. For more information, and to order this hefty book, visit the Apogee web site at: www.ApogeeRockets.com/design_book.asp Apogee Components 3355 Fillmore Ridge Heights Colorado Springs, Colorado 80907 USA telephone: 719-535-9335 website: www.ApogeeRockets.com ISSUE 246 OCTOBER 20, 2009 Page 5 Continued from page 5 Build an Accelerometer Payload g = a * 9.81 m/s2 g (gravity) is a unit of acceleration. It is based on terrestrial gravity (9.81 m/s2) as a unit, so: ** This mark is a frequent source of mistakes. Make the mark very precisely; it’s the position ( l ). 8) With a metric calliper (or a ruler), measure the distance, in millimetres, between the pencil marks ( L & l ). 1 g = 9.81 m/s2 9) Make a general mechanical verification of the accelerometer. 3 g = (9.81 m/s2) * 3 = 29.43 m/s2 Results 2 g = (9.81 m/s2) * 2 = 16.62 m/s2 And so on ...... Applications Newton’s second law of motion Yes, I know … one more time; but …. OK OK. A force is equal to the mass times the acceleration or F = m * a. As our rocket is launched and accelerates the force in the rubber band equals the acceleration of the rocket times the mass we used. So the mass is measured easily, and if we can measure the force in the rubber band, BINGO we get the third parameter, the acceleration. The friction force between Indicator-ring and the body tube is assumed to be zero. If F = m a, In 1969, AMROC designed many experiments for mechanical accelerometers. Let me summarize some of them. 1) The best way to connect and ignite a cluster of motors. An application of your mechanical accelerometer is to setup the best way to connect & ignite a cluster of motors. Many have tried but no one got a real and complete solution. So, knowing the maximum acceleration, you can assess if all motors were perfectly ignited. If the max acceleration doesn’t equal the total thrust /rocket’s weight, then motors weren’t ignited in synch. TADAAAAAA ! so F / m = a, then [ K * (L – l) ] – p / m = a 2) The thrust of the ejection charge. Example: K = rubber band slope = 3.92 N/m L = Length of rubber band at rest = 0.5 cm l = Length of rubber band on tension (cm) p = weight of inertial-mass = 0.196 N [ 3.92 * (0.5 – l) ] – 0.196 / 0.020 = acceleration and the number of gees is g = a * 9.81 The g’s unit is computed by the following equation: One more application of your mechanical accelerometer is the measuring of the thrust of the ejection charge. A lot of precautions should be taken: To prevent burning your launch pad, boost the level of the rocket by 15 cm; Tape tightly the rocket to the rod with electric tape at 2 places on the body tube; Take care for a free ejection; Continued on page 7 Your Cool Rocket Designs Look So Much Better In RockSim Version 9! Launch It. v9 www.RockSim.com Space Foundation certified as an excellent teaching aid. Page 6 For further information, call Apogee Components at: 719-535-9335. ISSUE 246 OCTOBER 20, 2009 Continued from page 6 Build an Accelerometer Payload Take care for a frictionless moving between the launch lug of the payload and the launch rod; Take care for a frictionless nose cone – body tube junction. your data represents a relation between variable x and variable y. A series of trials should be performed for the assessment of the precision level of your accelerometer. A mean (based on 10x trials, at least) with the standard deviation generates a fair approximation. 3) My rocket’s drag One more application of your mechanical accelerometer is the measuring of drag; so useful to the optimization of a rocket design. Use this equation to compute drag (D): D = P – (g * m) Check & re-check the perfect return to 0 of the rubber band at rest. So, NO residual constraints should be on the rubber band. Some low acceleration can generate imprecision relate to an imperfect return to 0 of the accelerometer. If your data is weird, re-check your assumptions: without spin, vertical flight, frictionless launch lug, ….. D = Drag (N) P = average thrust (N) g = number of g m = mass of rocket (g) Discussion When you analyze your own data, don’t forget the fact that it is an approximation. Figure 4 NEVER ASSUME ONE RESULT AS A FAIR AND ACCEPTABLE RESULT! With an elementary instrument like a home-brewed mechanical accelerometer, Now, a general call to everyone, let me know : How can this accelerometer be redesigned so it is more sensitive or more accurate? My email address is: [email protected]. References Newton I., Philosophiae Naturalis Principia MathematiContinued on page 8 Pratt Hobbies GO BOX Launch Controller Launch controller for mid-power rockets. Hooks right up to your car’s battery. No more dead AA batteries! Plenty of electricity to set off any type of rocket motor igniter. 24 foot cord, allows you to stand far back for launch safety. Audible continuity buzzer lets you know the circuit is armed and ready for launch. Flat-jaw alligator clips Only $39.99 P/N 7705 Brought to you by: (for easy hook-up of igniter.) www.ApogeeRockets.com/go-box_controller.asp ISSUE 246 OCTOBER 20, 2009 Page 7 Reader Questions and Answers Continued from page 7 Build an Accelerometer Payload Responses By Tim Van Milligan ca, London, 1686. AMROC, AMROC’S Accelerometer, Owner’s Technical Manual, 1969, Vol 1 No 7,10 pp. Stine H. G., Handbook of Model Rocketry, 1976, 4th edition, Follett Pub Co,p. 254. Just finished the Apogee Saturn 1B about two weeks ago. Took it for a walk and here is the pic! -- Bill Perretti VERY COOL!!! I love it. I’d say you did an excellent job on building the kit. Keep up the good work. Kranich J., Do-It-Yourself Accelerometer, Estes Educator News, 1995, Vol 21, p. 6-7. Van Milligan T., Measuring velocity and acceleration of rockets, Technical Publication # 10, 2000, 4 pp. About The Author: Pierre Boivin, of Quebec, Canada, is a former infectious diseases epidemiologist, microbiologist, economist & bioethician. He is currently retired, and has been a full time space educator (trained at the Canadian Space Agency) at the Quatre-vents High school for 8 years. Yes... We Have Engine Mounts Too. www.apogeerockets.com/motor_mount_kits.asp You get: (4) AT 29/13 (4) AT 41/18 (2) AT 56/18 (2) AT 66/18 (1) AC-56 (1) AC-66 Price: $22.72 You Save: $5.17 You get: (6) AT 13/18 (6) AT 18/18 (6) AT 24/18 (6) AT 33/18 Price: $26.00 From Estes, you would spend over $44.45! http://www.ApogeeRockets.com/body_tubes.asp Page 8 ISSUE 246 OCTOBER 20, 2009