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    Teaching physics with Angry Birds: exploring the kinematics and dynamics of the game

    View the table of contents for this issue, or go to the journal homepage for more

    2013 Phys. Educ. 48 431

    (http://iopscience.iop.org/0031-9120/48/4/431)

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    Teaching physics with AngryBirds: exploring the kinematicsand dynamics of the gameM Rodrigues1,2 and P Simeao Carvalho2,3

    1 Middle and High School Rodrigues de Freitas, Porto, Portugal2 IFIMUP, University of Porto, Rua do Campo Alegre s/n, 4169-007 Porto, Portugal3 Department of Physics and Astronomy, Faculty of Sciences, University of Porto,Rua do Campo Alegre s/n, 4169-007 Porto, Portugal

    E-mail: [email protected] and [email protected]

    AbstractIn this paper, we present classroom strategies for teaching kinematics atmiddle and high school levels, using Rovios famous game Angry Birds andthe video analyser software Tracker. We show how to take advantage of thisentertaining video game, by recording appropriate motions of birds thatstudents can explore by manipulating data, characterizing the red birdsmotion and fitting results to physical models. A dynamic approach is alsoaddressed to link gravitational force to projectile trajectories.

    Introduction

    Students motivation is now an important goal inteaching physics, and the use of video games inclasses usually increases students attention. Infact, video games are appreciated by all kinds ofstudents. Angry Birds is a very popular game fromRovio, categorised as a physics game becausethe motion algorithms are based on the kinematicsof projectiles [1]. We can use a video analyserto study the birds motion when launched by theplayer from the slingshot. To do so, we only needto record video clips from the game with a screenrecorder.

    Kinematics analysis of the game can bean excellent teaching strategy at all levels ofeducation, either as an introduction to a subject,or as an application of kinematics and dynamicsconcepts, from a problem-solving perspective.

    In this paper we show how to give a basickinematics treatment of the game with the help of

    video analysis and modelling software (Tracker),and outline strategies for teaching kinematics inschools.

    The gameAngry Birds is a game created initially for theApple iOS in 2009 [2] and later adapted forcomputers and games consoles. Today, there areseveral thematic editions. It is a dynamic strategygame, based on the laws of physics for projectilemotion, where the objective is to destroy theegg-thieving pigs, housed in their buildings, bythrowing the angry birds against them with thehelp of a gigantic slingshot.

    The screen recorderFraps is benchmarking freeware developed byBeepa [3] that indicates the number of framesper second displayed on the computer screen.

    0031-9120/13/040431+07$33.00 c 2013 IOP Publishing Ltd P H Y S I C S E D U C A T I O N 48 (4) 431

    http://iopscience.org/pedmailto:[email protected]:[email protected]

  • M Rodrigues and P Simeao Carvalho

    This program also allows image capture and videorecording of everything displayed on the screen.Here we use a version that captures video clips ofup to 30 s (which is enough for our purposes).

    The video analyserTrackerToday, thanks to the evolution of video analysersin different areas of physics, such as biomechan-ics and biophysics, there is much free analysersoftware for didactic purposes. This is in generaleasy and intuitive to use, and provides excellenttools for teaching kinematics in schools.

    We have used one of the best and mostpowerful freeware video analysersTracker. Thisopen source software is authored by Brown [4, 5]and was developed for the Open Source Physics(OSP) project [6]. Tracker is also a data modellingtool because it incorporates the Data Tool module,created by the same author.

    Tracker comes with a built-in manual, butwhenever students are not familiar with thissoftware we advise teachers to build simple,practical and appropriate guidelines for theactivity proposed.

    To make measurements with Tracker (or anyother video analyser), it is necessary to know thereal dimensions of at least one object in the videoclip to allow conversion of the image dimensions,initially given in pixels, to real dimensions.Trackers Calibration Tape tool sets the value of100 units (pixels) for a predetermined length bydefault (figure 1). When a new value is introducedto the calibration tool the software divides thatvalue by the number of pixels of the length, fixingthe correspondence between one pixel and thestandard input unit; for example, converting thevideo pixel lengths into metres or centimetres.

    When the video does not present any objectwith a known dimension, an arbitrary size canbe assigned to one of the objects shown in thevideo, or we can determine the real dimensionsof the game objects by making use of a simplesuppositionthe game takes place somewhere onEarth.

    Preparation of educational materialElaboration of videos

    The videos were recorded with Fraps, which wasset to record at 30 frames s1.

    Figure 1. The calibration tape appears with a defaultvalue of 100, for a standard length of 100 pixels.Reproduced with permission from Rovio EntertainmentLtd.

    It is desirable to launch the red bird in sucha way that it can hit the ground without collidingwith any obstacle, and also with the zoom set insuch a way that frame translational movementsand zooming of the image do not occur, keepingthe reference system of coordinates unchanged.Thus, visualization of the parabolic trajectory ofthe red bird is more evident (it is easily achievedat the first level of the game, as illustrated infigure 1). Note that for Fraps to capture 30 framesin each second effectively, it is necessary that thecomputer maths processor and video card are fastenough; otherwise repeated frames will appear inthe video.

    Teaching strategiesTeaching kinematics at middle school level

    Kinematics can be introduced at middle schoollevel by exploring Angry Birds.

    To begin with, students may choose aconvenient position for the reference axes, definea standard length and unit (e.g. the teacher maysuggest that the height of the slingshot be 5 m),and track the birds position with time to visualizethe trajectory. Students should be encouragedto change the referential origin, and with thisprocedure observe what happens to the valuesdisplayed on the data table, in particular theposition and speed values. They may also beencouraged to change the values and dimensionsof the calibration tape, and draw conclusionsabout the importance of defining a standard unitof length.

    The notion of stroboscopic images can beintroduced when interpreting the birds path, inwhich the spacing between successive positions

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  • Teaching physics with Angry Birds

    has a direct relationship with time (for constanttime intervals), allowing first contact with theconcepts of speed and velocity.

    These first video analysis procedures (cre-ating a referential, establishing a standard unitof length and tracing the path) represent aparticularly useful activity when students startstudying kinematics, because we can introduceand discuss the importance of fundamentalconcepts such as position, trajectory, movement,rest, etc in a practical and operational (hands on)way, making learning more effective. This kind ofactivity can be done: (1) at home as experimentalworkthe video and a guide can be provided onthe internet; or (2) collaboratively by students inthe classroom, if there are computers available forall of them (no more than two or three studentsper computer is strongly advised).

    For a more advanced level, after tracingthe path teachers can introduce graphs ofposition versus time, speed versus time andacceleration versus time by analysing andinterpreting Trackers graphs. Indeed, these canbe seen simultaneously as the trajectory of thebirds motion is drawn in Trackers main window(up to three can be viewed at the same time),promoting debate concerning well-known studentmisconceptions about their interpretation [79],namely the contradiction between the positiongraph and the trajectory of the body [10].

    There is also space for more traditional(although very useful) strategies, such as askingstudents to build graphs of speed and accelerationfrom data tables, either on paper or with acomputer application (e.g. Excel). It is quiteimportant to explain how to calculate the speedand acceleration (see figure 2), based on thebirds positions; this will help students to betterunderstand these concepts from a mathematicaland a conceptual point of view. They will haveto apply algorithms to calculate the average speedand acceleration, and establish the limits forwhich it is physically acceptable to consider theseaverage values as the instantaneous speed andacceleration of objects.

    Teachers can also introduce the conceptof composition of motions, exploring the twobasic types of motion discussed in the classroom(uniform rectilinear motion (urm) and uniformlyvaried rectilinear motion (uvrm)), and thecorresponding graphical representation.

    Figure 2. A data table, displayed at time intervals offive frames, obtained from the birds positions. Thespeed (v) at the instant 0.167 s, is obtained, for bothaxes, by subtracting the corresponding axis positions atthe instants immediately after (t = 0.333 s) and before(t = 0.000 s),and dividing the result by the time intervalbetween these two instants. The result is approximatelythe instantaneous speed of the bird. This calculationprocess is known as the Euler method [11].

    Teaching kinematics and dynamics at high schooland university levels

    At high school and university levels it is importantto maintain the procedures referred to for middleschool level, because it is always useful not toassume prior knowledge. However, at this higherlevel kinematic analysis can be more complexand implies a clear approach to the concept oftwo-dimensional movement, usually associatedwith the projectiles motion. This approach can befirst introduced through an exploration activity orby posing a problem, for example what kind ofmotion does the bird have when launched by theslingshot?.

    At this point teachers may decide tointroduce, or recall, the laws of motion for

    July 2013 P H Y S I C S E D U C A T I O N 433

  • M Rodrigues and P Simeao Carvalho

    Figure 3. The strobe effect for the positions, markedon the x and y axes, allows qualitative conclusions to bedrawn about the motion along each axis. The positionsare displayed at intervals of five frames. Reproducedwith permission from Rovio Entertainment Ltd.

    position and speed, for the two types ofmotion (urm and uvrm along the x andy axes, respectively), associating mathematicalexpressions with the physical equations ofkinematics, and giving an interpretation for thephysical quantities involved.

    The interpretation of the parabolic motionrequires a graphical analysis of the positionand speed with time, along the x and y axes.To help students analyse the two componentsof the motion, we suggest they should admitthe motion of two independent particles, eachparticle following the laws of motion for thebird in the corresponding axis. With Tracker it ispossible to create virtual models of particles withthe Model Builder module, plotting on the x andy axes the positions that obey the correspondingbirds laws of motion, as if they were shadows ofthe bird projected on the axes (figure 3).

    The dynamic approach to the movement ofthe bird comes from asserting that the parabolicshape of the trajectory must be related to theexistence of an external force acting on the bird(according to Newtons first law). The parabolicmotion gives two important dynamic indications:(1) there is a downward vertical acceleration,suggesting the existence of a force similar tothe gravitational and (2) the air resistance isnegligible. The use of the Data Tool moduleallows identification of the acceleration of thebird.

    One problem that can be given to students,in particular at university level, concerns thedimensions in the Angry Birds world. As alreadymentioned, there are no references in the gamethat allow us to know the real dimensions of

    Figure 4. Modelling on the graph y(t). The value ofthe second-order term (a), multiplied by two, givesthe vertical acceleration of 185.584 pixels per secondsquared (pixel s2).

    objects and birds. The only parameter that can bemeasured is time.

    To overcome this problem, we may considerthat the virtual world of Angry Birds is somewhereon Earth (after all it is a game created by humans).Therefore, a challenging problem can be put tothe students: determine the dimensions of thered bird, knowing that the launch occurs onEarth.

    In the following, we suggest two methodsto compute the dimensions of objects in AngryBirds, considering the standard gravitationalacceleration on Earth as 9.8 m s2.

    Method 1: fitting to the position graph data

    Using the default calibration tape (figure 1),students can use the graph y(t) by fittingparameters to a quadratic equation (figure 4). Atthis point they should know the physical meaningof all the parameters they need to fit, but theymust recognize that the acceleration value, set bythe coefficient of the quadratic term of the fittingequation, is given in pixels per second squared.

    Now students must realize that if the gametakes place somewhere on Earth, the gravitationalacceleration will be 9.8 m s2. So, there is adirectly proportional relationship between thevalue of the acceleration from the fit and thegravity on Earth that allows them to convertthe standard unit (pixel) into SI units (metres)

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  • Teaching physics with Angry Birds

    Figure 5. With the calibration tape in metres, thedimensions of the slingshot and of the red birdcan be measured using the tape tool. Their valuesare approximately 5.0 m and 1.1 m, respectively.Reproduced with permission from Rovio EntertainmentLtd.

    (see also [12]):

    185.584 standard units

    1 s2=

    9.8 m

    1 s2

    standard unit =9.8

    185.584= 0.0528 m.

    Therefore, each pixel in the video corre-sponds to about 5.3 cm. The estimated error formeasuring positions is about 2 pixels, so theuncertainty will be about 10.6 cm.

    Once the conversion factor from pixels tometres has been determined we only have toreplace the number marked on the calibration tapeby multiplying the number of pixels (100) by theconversion factor (in our case: 0.0528 100 =5.28 m). Students can now use the calibration tapetool from Tracker to measure the dimensions ofany object in the game (figure 5) in metres.

    This method is a simple and quick wayto solve the problem, but requires studentsto understand the functioning of Trackerscalibration process. It is based on mathematicalconsiderations concerning the motion along they axis, but does not involve any deep kinematicsknowledge.

    Method 2: analysis of speed graphs anddetermination of physical parameters

    With this method students can work analyticallywith the equations of motion in a substantiallymore elaborate way.

    Figure 6. The origin of the referential is set to coincidewith the initial position of the bird. Reproduced withpermission from Rovio Entertainment Ltd.

    Students are supposed to keep in mind thatthe gravitational acceleration in the game is thesame as on Earth (just like in method 1). Inthe vertical direction, the bird has a uniformlyvarying rectilinear motion due to gravitationalacceleration. Therefore, the vertical motion of thebird is described by expressions:

    y = y0 + v0yt (1/2)gt2 (1)

    vy = v0y gt. (2)

    Therefore, they only need to find y0 and v0yto obtain the equations for the motion in theirentirety.

    Teachers should encourage their students tolook for symmetries and invariants in the studyof physical phenomena, and realize that it isconvenient to choose the origin of the referentialso that the initial position is y0 = 0, at t = 0(figure 6).

    Students know that the bird must stop itsvertical ascent at a given instant (thmax), reachinga maximum height from which it begins to fall.At that instant, the vertical speed vy = 0. Note thattime is an invariant in this analysis, because it doesnot depend on the calibration of the video image.By symmetry, thmax is half of the flying time(considering the x axis parallel to the ground).

    They can find thmax by looking for the instantwhen the vertical position is maximum, eitherfrom the y(t) graph curve, or (more easily) fromthe data table, or even using data tool facilities(which provide the maximum value of y byselecting statistics in the menu bar).

    However, teachers should point out thatwith this procedure a considerable error maybe introduced, since it is not guaranteed thatthe frame corresponding to the instant when thebird reached its maximum height was captured

    July 2013 P H Y S I C S E D U C A T I O N 435

  • M Rodrigues and P Simeao Carvalho

    Figure 7. The graph vy(t). The instant thmax can bedetermined at vy = 0, using the fitting equation.

    during the recording. Obviously, the error willbe smaller for higher recording acquisition rates(frames s1). For example, if the game is recordedat a rate of three frames per second, the time erroris about 0.33 s, while if recording at 25 framesper second, the time error estimate decreases to0.04 s. In this work we recorded at a rate of 30frames per second (time error of about 0.033 s).

    Measuring thmax = (1.967 0.033) s fromthe data table, students can determine v0y bysolving, according to equation (2), the relation0 = v0y gthmax. Admitting g = 9.8 m s2, itgives v0y = (19.280.32) m s1. This procedureis very simple and the uncertainty is about 1.7%.

    Another, perhaps more sophisticated, way toobtain v0y is by using the graph vy(t) (figure 7).

    From the fitting parameters in figure 7,we compute as an average value thmax =361.646/184.898 = 1.956 s. The estimateduncertainty is about 1.3% (this can be calculatedwith Excel from the standard deviations of thelinear fit).

    Using equation (2) and g = 9.8 m s2,at thmax = 1.956 s we obtain v0y = (19.17 0.25) m s1. These results are very similar tothose reported above within the experimentalerror.

    Therefore, the expressions that quantify thebirds position and speed during the verticalmotion are:

    y = 19.17t 4.9t2 (m) (3)

    vy = 19.17 9.8t2 (m s1). (4)

    Figure 8. The calibration tape is placed vertically, be-tween the x axis and the marked position correspondingto the chosen instant. Reproduced with permission fromRovio Entertainment Ltd.

    DimensionsTo calibrate the dimensions of objects in thegame, students must choose the highest possiblelengths for the calibration tape, because thelarger the tape calibration, the lower the errorintroduced. Taking the frame when t = 1.967 sand using equation (3), they can calculate therespective marked position of the bird: y =18.75 m. This value must now be inserted into thecalibration tape (figure 8). Finally, students canuse the tape tool to measure the dimensions of theobjects in the game.

    Teachers can also ask students to completethe study of the birds motion, finding theequation of the horizontal movement, by deter-mining the horizontal initial speed with a similarprocedure. This is an easy task since the necessaryparameters (maximum range and flight time) areobtained from the graph vx(t).

    ConclusionsAngry Birds is a good example of how videogames can be used in physics classes for teachingand learning physics. In this paper we havereported how to explore kinematics and dynamics,within the subject of projectile motion, using thered angry bird; other physical concepts and laws(such as linear momentum or the conservationlaws) can be taught with other birds from thegame [1315].

    The game itself has also now been developedto higher stages, with gravity effects around plan-ets [16] and new features based on the successfulStar Wars films being introduced [17]. Thisgives more opportunities for exploring physics

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  • Teaching physics with Angry Birds

    in new contexts, teaching in richer environmentsand, undoubtedly, motivating students to usemultimedia tools for learning physics.

    AcknowledgmentsM Rodrigues and P Simeao Carvalho are gratefulto Fundacao para a Ciencia e a Tecnologiafor funding projects PTDC/QUI/69685/2006 andPTDC/CTM/099415/2008.

    Received 4 February 2013doi:10.1088/0031-9120/48/4/431

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    Marcelo Jose Rodrigues is a middleand high school teacher and a researcherat IFMUP. His research interests areinteractive educational materials, physicseducation and teaching training.

    Paulo Simeao Carvalho is an assistantprofessor at the Porto University Physicsand Astronomy Department. He is also aresearcher at IFIMUP. His researchinterests are liquid crystals, multimediacurricular materials, physics educationand teaching training (initial andcontinuous).

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    Teaching physics with Angry Birds: exploring the kinematics and dynamics of the gameIntroductionThe gameThe screen recorderThe video analyser---TrackerPreparation of educational materialElaboration of videos

    Teaching strategiesTeaching kinematics at middle school levelTeaching kinematics and dynamics at high school and university levelsMethod 1: fitting to the position graph dataMethod 2: analysis of speed graphs and determination of physical parameters

    DimensionsConclusionsAcknowledgmentsReferences