Friction in Line Rider

Is there friction in Line Rider? Does it function as physics would expect? To test this, I set up a simple track:


Basically, a slope with a flat part to start with and to end with. Let me show you something simple before further analysis:


This is the x-position vs. time for the line rider on the first horizontal portion of the track (before he or she goes down the incline). This shows the rider traveling at a constant speed of 0.71 m/s. If friction were present, the rider would slow down. If you do not believe me (and why should you?) try creating your own line rider track with a long horizontal section. The rider will not stop, but continue on at a constant speed.

Ok, so no friction on the horizontal line. This makes a little bit of gaming sense. Who would want a rider to stop in the middle of the track and be stuck? That wouldn’t be fun. But, is there friction on non-horizontal portions? To test this, I will use the work-energy principle.

Work – Energy
Here is a crash course in the work-energy theorem. Basically, the work done on an object changes its energy. (see, that wasn’t complicated). Where work is defined as:


Where F is the force acting on the object and delta r is displacement. Since these are both vector quantities, you can not simply multiply them. In this case the dot product (or scalar product) is used. If you don’t like that, you can use the following instead:


Where F and delta r are now the scalar magnitudes of the vectors and theta is the angle between F and delta r.

For the line rider track, there are only two forces (assuming no or negligible air resistance) acting on the line rider. There is gravitational force and there is the force the track exerts on the rider. The force the track exerts on the rider can be broken into a component perpendicular to the track (called the normal force) and a component parallel to the track – friction.

Below is a diagram (a free body diagram) representing the forces on the rider as he (or she) is going down the incline.


To calculate the work, all forces will need to be included. The work can be calculated one of following ways:


Where the thetas are for the angles between the displacement and each force.

For this case, I will calculate the work for each individual force. First, let us look at the work done by the normal force. The rider is moving down the incline, and the normal force is perpendicular to the incline, so work would be:


Now work done by friction:


Where there is a relationship between the friction force and the normal force (in this model). The harder two surfaces are pushed together, the greater the frictional force. This gives the following relationship between the magnitude of the normal force and the friction force:


Where ? is the coefficient of kinetic friction between the two surfaces (in this case the line rider and the track).

The goal is to calculate the ?, so an expression for the normal force is also needed. For this case, the line rider stays on the track. This means that his velocity perpendicular to the track is zero and stays at zero. If his perpendicular velocity stays zero, his (or her) acceleration must be zero perpendicular to the track (notice that the acceleration is zero because the velocity STAYS zero, not because the velocity is zero. MANY MANY MANY people mess that part up). Anyway, if the acceleration perpendicular to the track is zero, the forces perpendicular to the track must add up to zero (vector sum).

The normal force is already perpendicular to the track. The friction force is not, but the gravitational force has some component in the direction perpendicular to the track


Where the yellow vector represents the component of gravity in the direction perpendicular to the track. Since this creates a right-anlge triangle, the magnitude of this component will be
In this case, the magnitude of the gravitational force is mass of the object times the local gravitational field (approximately 9.8 Newtons per kg). This means that the work done by friction can be expressed as:


Where ?r is the distance along the track, ? is the angle of the incline of the track.

Finally, the work done by gravity. The angle between gravity and ?r is ?_c (90 degrees – ?).


Looking at the track, the slope is inclined at an angle ? and has a length of ?r. The expression ?r sin(?) is equivalent to the opposite side of the right triangle, in this case that is the change in height of the rider (?y), so the work done by gravity is:


I think we are finished with work. So, the total work done on the rider while going down the incline is:


That is great. But….Work. What is it good for?

So, I have talked about work. The work-energy relationship says that the work done on an object is its change in energy. In this case, the line rider will only have a change in translational kinetic energy. So


So the change in kinetic energy will be from the top of the incline to the bottom. Putting together from the total work:


Notice that the mass cancels (good because I never really knew that the mass was anyway)


In this expression, I can measure ?y, v_lower and v_upper. Solving this expression for ?:




The plan
So, I can measure the upper and lower velocities and I can measure ?y and ?x. From this I can calculate ?. After that, I will change the incline and see if ? changes (it shouldn’t change).

Measuring ?y and ?x


Using tracker video analysis, I found the coordinates (with respect to the red origin as shown) for the beginning and end of the incline. The beginning is at (4.77 m, -1.00 m) and the end of the track is at (15.29 m, -14.44 m). This gives a ?y = 13.44 meters. (a big hill for a 5 year old to go down) and ?x = 10.52 meters

Velocity at the bottom


This linear fit to the last part of the run shows a horizontal velocity of 13.22 m/s.

Velocity at the top

I previously stated the velocity at the top. It is 0.71 m/s

Calculating ?
So, plugging stuff in:


Notice that this is a unitless quantity (as it should be).

A different situation
Now, we can look at a different track with the same change in y, but different slope. The final velocity should be less because friction will be greater in magnitude AND exert over a larger distance. This will mean that friction will do more work and thus reduce the energy gained (friction is doing negative work). However, the coefficient of friction should be the same.

Here is a track with a different slope:


From this, the following position-time data is obtained.


In this graph, it can be seen that the speed at the top of the incline is 0.68 m/s This is slightly different than the 0.71 m/s from the last run and shows the error associated with the data collection (but that is a whole different page that I have not written).

Also, the final speed is 16.25 m/s (faster than before) – this is really important.

From the video, ?x and ?y can be obtained. The point at the top of the slope is (4.67, -0.99) and at the bottom it is (35.38, -13.86). This gives ?x = 30.71 m and ?y = -12.87 m.

Plugging in…


What? That is odd. A negative coefficient of friction? That would mean that friction is making it speed up. Suppose there were no friction at all. Then the work-energy equation would say:


Solving for the final velocity:


And plugging in the data from above:


This is slower than with friction. Maybe I need another test.

Another friction analysis

My favorite method for looking at friction is the measure the motion of an object sliding both up and down and inclined plane. Here is the line rider track I created to do that.


The up and down is important because on the way up the track, gravity is slowing the rider down and so is friction (because friction is in the opposite direction to the motion). On the way down, gravity pulls down the incline, but friction is acting in the opposite direction. The result is that the acceleration up and down the incline will be a little different (depending on the coefficient of friction).

Going up the incline


Here friction and the gravitational force are both pointing down the incline.

Going down the incline


Now they are “working against each other”. Going down the incline should have a smaller acceleration than going up.

Newton’s Second Law
Newton’s second law is what relates forces, mass and acceleration. It is most often written as:

- but this is bad way of writing it. A better way would be:

There are two main differences in these equations. The key difference is that the second version is a vector equation (relating vectors). The other difference is the inclusion of F_net. This says that it is the sum of all the forces that relates to the acceleration.

To make this analysis simpler, we can let one of the coordinate axes be parallel to the incline.


This will allow us to write the vector equation as the following two equations:

So the net force in the y direction (perpendicular to the incline) must be zero.

Going up the plane, the x-motion can be described by:


Where the friction force can be modeled by:


so, up the plane:


Solving for the acceleration (the mass cancels)


The only thing different going down the plane is the direction of the frictional force, so the acceleration would be:


The data
Here is a plot of the x-position (in the frame with the x-axis parallel to the incline) versus time


In this graph, I have fit a quadratic equation to the part with the rider going up the track and a different function for going down. If you recall the scale of the line rider experiment, I described how the acceleration can be found from a quadratic fit. In this case, the accelerations are

Up the incline: a_x = – 4.00m/s²

Down the incline: a_x = – 4.00 m/s²

This suggests that either the frictional force is too small to be measured, or there is no frictional force (since the acceleration is essentially the same on the way up and on the way down. Another possibility is that there is a frictional force, but it can not be seen because of excessive error in the data collection process. Even if my scale was off (from before), the acceleration should still be different on the way up and on the way down.

Comparing angle of incline to the acceleration
If there is no friction, the acceleration should be related to the angle of the incline. If you remove the frictional force from the previous equations, you get:


Solving for theta:

This gives us a calculated angle of the incline

? = 24.1 degrees.

Looking at the video, the measured angle of the incline is 35.1 degrees.

Evidence for friction
There is evidence of some type of frictional loss of energy. In this track, the rider goes up the incline, then down. He then goes back up another incline. Below is a plot of his y-postion (in the non-rotated frame of reference) versus time.


If there was no friction present, the rider would go back to the same height as before (conservation of energy). In this case, the rider lost some energy.

Conclusion
I am not sure how friction is implemented in line rider. When you play the game, the implementation seems plausible (it doesn’t look weird). It is possible that I am encountering significant errors due to the way the data is obtained. This could be errors introduced through dropped frames in the screen capture, different time rates or error in locating the rider in each frame.

I suspect that friction is implemented by just making the acceleration lower that what it should be for planes (but the same acceleration up and down the plane). I am very sure that there is zero friction on the horizontal surfaces.

There is no air resistance in line rider. Sorry to spoil the suspense.

To test for the presence of an air resistance force, a track was created that let the rider fall.


(note the markers on the side. These are used to keep track of how the origin is moving).

Below is the y position of the rider as a function of time:


In this situation, the rider falls about 100 meters. A quadratic line is fit to the data and an acceleration is obtained that is very similar to the previous case (where air resistance was assumed to be negligible). If there had been air resistance, this graph would have become more linear as the rider fell. Perhaps 100 meters is not far enough to fall, but in real life this should be far enough to detect the presence of an air resistance force. Or does it? Lets make a simple check.

Let’s assume the line rider is a sphere with a diameter of 0.75 meters (since his sled is 1 meter long, it is probably not as wide). When an object falls in the presence of an air resistance force, we can draw a diagram representing the forces (we like to call this a free body diagram).


This is a complicated situation to analyze because the air resistance force depends on the velocity (which depends on the forces acting on the line rider). Perhaps the easiest method to examine the motion of the rider (with air resistance) is using numerical methods. In a numerical solution, the problem will be broken into many small time intervals. During each time interval, the forces won’t change too much so we can assume they are constant. The only problem with this approach is that there will be many, many small problems to solve. To solve these many little problems, we could employ a 4th grader to do all these tedious calculations, or we could use a computer. I vote to use a computer as our labor force. Might as well use them now before they take over the world (you know, like in the movie Terminator or the Matrix).

Here is the basic recipe that will be used to look at the velocity of a falling object with air resistance:

**1./ Calculate the forces on the rider (this will be gravity and the air resistance force). The gravitational force near the surface of the Earth is simply proportional to the mass of the rider (more on this later). The air resistance force will be proportional to the cross sectional area of the rider as well as the velocity squared.**

**2./ Update the momentum using the momentum principle: (I will write it for just the y-direction so that it is a scalar equation)**


Where momentum (p) is:


**3./ Update the position. This can be accomplished by rearranging the expression for the y-velocity:**


Again, this assumes that the time interval is small

**4./ Rinse, add conditioner and repeat.**

I know this looks like it is cheating, but it works.

Air resistance force
For the magnitude of the air resistance force, we can use the following model


Where rho is the destiny (I am your density, I mean…your destiny) of the fluid (in this case, air has a density of approximately 1 kg/m³
A is the cross sectional area of the object
C is the drag coefficient. The drag coefficient for a sphere is 0.1
v is the magnitude of the velocity.
The direction of this force is in the opposite direction to the velocity.

For this comparison, A will be approximated as a rectangle 1 meter by 0.4 meters (I completely made that up – well, not the 1 meter)
The drag coefficient is more complicated to guess. According to the ultimate source of truth ([wikipedia](http://en.wikipedia.org/wiki/Drag_coefficient#Cd_in_other_shapes)), a smooth brick has a coefficient of 2.1. For this calculation, a coefficient of 1 was used.

The mass of the falling object is also required. According to that child growth chart, a 5 year old is about 19 kgs. Add the sled and the mass can be approximated as 24 kg (again, a made up number).

Here is the program to calculate the position as a function of time for both an object with air resistance and without. The program was written in python using the [VPython modules](http://www.vpython.org).

Here are the results:


Note that the numerical model without air resistance and the line rider data a little off. This is likely due to dropped frames in the movie of the line rider.

Another method to test for air resistance is to look at the horizontal motion. The line rider starts with some initial velocity in the horizontal direction. If there is no air resistance, this velocity should remain constant (because there are no forces acting in the horizontal direction). Below is a graph of the x-position from both the line rider data and the numerical model with air resistance.


It appears as though the line rider data shows a mostly constant horizontal velocity. There is a transition in horizontal velocity (from 0.73 m/s to 1.52 m/s) that occurs a little before 1 second. The only thing that I can think of that this would relate to is when the video transitions from showing the line rider moving to having the background move.

The point is: clearly the line rider data is more straight that curved like the numerical data.

I claim there is no air resistance in the line rider game. To further test this, one would need to let the rider fall for a much longer time, but I was too impatient to do that.

Kids, don’t try this at home! Ich hatte ja keine Ahnung, daß einen Videospiel-Charakter gibt, der anscheinend fast universell verhaßt ist. Und wenn, dann hätte ich Wetten auf Sherry aus Resident Evil 2 abgeschlossen. Für mich wäre die Existenz eines Adoring Fan gerade ein Grund, ein bestimmtes Spiel zu kaufen. Das witzigste an der Geschichte ist jedoch die kindliche Erklärung dafür (siehe Titel).

Ein einfaches Jump’n'Run mit Doppelsprung, ein paar Plattformen und tödlichen Spitzen wäre wohl kaum eine Erwähnung wert, wenn die Level wie in You Made It jedoch persistent sind, also nach Veränderungen auf dem Bildschirm das Ausgangsbild nicht gelöscht, sondern übermalt und zu Beginn jedes neunen Levels zu einem Rätsel, wo sich die aktuellen Plattformen befinden, wird, schon.

Second Death ist ein interessantes Kunst-Projekt, mit Hilfe dessen man seinen eigenen Second Life-Charakter töten, als löschen lassen kann: Man unterschreibt einen Vertrag, übergibt sein Passwort, macht ein Testament und wird irgendwann in der Zukunft von Gevatter Tod heimgesucht. Der Leichnam wird eingefroren und es wird einem ein riesiges Denkmal gesetzt. Wer das mit einer ernsthaften Absicht in Anspruch nimmt, sollte sich wohl wirklich eine richtiges Leben suchen.

Dann gibt es auch noch ein neues Doom II-Remix-Album von OC-Remix, das ist ganz hörenswert, stilecht und garnicht so sehr in eine Nische gerutscht.

Außerdem habe ich noch zwei äußerst ansehnliche Linerider-Videos aufgetan. Aber Vorsicht, darin ist schrecklicher Ami-Nu-Rock enthalten, unbedingt den Ton abschalten!

Linerider ist ein ziemlich simples aber spaßieges Internetspiel.

Es geht darum, eine möglichst spannende und große Bahn zu bauen,

dann drückt man einfach Play und

ein kleines lustiges Männchen mit einem Schlitten

rodelt deine selbst kreierten Bahn herab…oder halt herauf.

Um die Bahn zu bauen (zu zeichnen)

wählt man den Stift oder das Lineal und die Farbe :

BLAU, ROT oder GRÜN.

Die Farben!

Wenn ihr die Bahn blau zeichnet ist es einfach nur normale Strecke

mit normaler Geschwindigkeit.

Bei einer roten Strecke fährt das Männchen wesentlich schneller 

und kann so über lange Strecken auch bergauf fahren.

Die grüne Farbe (unsere Lieblingsfarbe) ist zum 

verfeinern der Bahn durch Hintergrundbilder

oder Motive wie z.B. Bäume, Häuser oder Flüsse.

Testet es einfach mal, wir hatten schon viele Stunden Spaß

und ihr werdet hoffentlich auch viel Spaß haben.

Euer Djunior und Euer Djack.

Um dia alguém me mostrou um joguinho muito interessante. Tratava-se de um jogo que você desenha a pista para um bonequinho de trenó andar… só isso, sem objetivos, missões, vidas, tiros, cogumelos, caixas [ ? ], princesas, nada! Só você, o boneco no trenó, um lápis e a tela branca.

Eu pessoalmente gastei muito tempo da minha vida nesse jogo, o maldito LineRider. É um jogo que eu realmente aconselho.

Ah é, o blog é sobre o Mario…. então olhem só o resultado da equação ócio+linerider+mario

B.

Welcome to my blog.

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Get your own ASCII art here.

A TV commercial for McDonald’s that features Line Rider. (via link]

VIEW

Multiple sources seem to indicate that a new Line Rider video is, indeed, an actual McDonald’s commercial. The video below is a 30-second cut of the commercial. There is also a 10-second version. References one, two, three, four..

Line Rider is a fairly well-known website flash drawing “game” where you can experiment with making lines with your mouse, and pressing play so that a little man on a sled can coast down, accelerate, do flips and tricks, and such on the lines you drew. Optionally, you can create unused lines that instead act as scenery details, like trees in the background or whatnot, whatever you can think of.

I’ve been a fan of these videos for some time now, my favorite being the impressive artwork of TechDawg, who actually has his own site for showcasing his efforts. I am not certain of the creator of the Line Rider track shown in the commercial, but I am doubtful it is TechDawg partly due to the fairly small amount of detail — practically a child’s drawing compared to TechDawg’s incredible complexity.

My favorite TechDawg Line Rider Movies..
Line Rider – Monumental™ A Line Rider Short by TechDawg
Line Rider – Transcendental™ by TechDawg
LineRider “TechDawg LABS (+)” A Line Rider Short by TechDawg

As well as trying to post a ‘game making tutorial’ each Friday, I’ll also try to find some idling curiosity for you to play with over the weekend.

First up is Line rider. Linerider is, well, linerider…

Draw a line (in your browser, on the Line Rider site) and set the sledger off… brilliantly compelling – but why is it such fun?

If you find yourself hooked, here are some Line Rider video tutorials.

I think you can make movies of your own line rides? If you can and do, why not post a link as a comment?

Just by the by, what principles from physics does the Line Rider “game” depend on? (and indeed, is Line Rider a game?!).

How are these “physical laws” represented in the Line Rider, and how do they affect the behaviour of the character within it?

He estado bastante ocupado con un proyecto bastante grande que espero que de frutos, se trata de una pagina web para anuncios de mi ciudad, no revelare tantos detalles porque hay quienes conocen mi blog que se podrían adelantar con la idea y robármela; pero de todos modos no me preocupan, nadie supera mis diseños (¬¬ solo un profesional, aunque ya me falta poco para superarlos xD [si lo sé estoy presumiendo demasiado jaja pero es la verdad])

Solo dire que uso un servicio de google.

Lo que me estaba enfureciendo era el [añada aquí su insulto] Internet Explorer, quería poner transparencias con PNG pero es una lata ponerlas en IE mientras que en Firefox se ven perfectas y como no quiero crear una versión para Firefox y otra para IE, tuve que quitar algunas cosas y sustituir las imágenes PNG por GIF para que al menos pudiera crear unos recuadros redondeados para el contenido.

Después me estuve todo el día decidiendo como se vería mejor el diseño, cambie como 5 veces el diseño del fondo que al final me decidí por un simple degradado azul a blanco, lo simple a veces es lo mejor.

Quedo bastante bien para mi parecer y eso que soy muy exigente si algo no queda bien lo vuelvo hacer, eso si tengo ganas xD, por eso a veces dejo trabajos sin concluir.

Otra cosa por contar… …pensando…

Hoy estuve horas y horas jugando con un simulador super adictivo, igual como lo fue para mi el linerider. Se llama Falling Sand Game, no hay puntuaciones, no hay enemigos, no hay vidas, ni un “game over”, creo que eso es lo que lo hace adictivo, al no poder perder xD. Consiste en dibujar un escenario donde puedes colocar diferentes sustancias y elementos como: agua, arena, sal, aceite, gas metano, cera. Con los que puedes interactuar experimentando con ellos y divertirte con las reacciones que producen en el escenario, bueno no sé como sea el efecto en otras personas pero a mi me tuvo pegado horas y horas sin aburrirme, ahora mismo logre despegarme de el para escribir algo en el blog.

Bueno, me despido, nos leemos luego.

PD: Si se preguntan por el titulo, es lo primero que se me ocurrió poner xD

Linerider es un juego que a pesar de su interfaz simple conseguirá engancharnos y estar buenos ratos delante del ordenador. El juego en cuestión consiste en dibujar un circuito por el que va a circular un personaje con un trineo. Este podrá hacer volteretas, ir marcha atrás, saltos, … Parece fácil peró ya vereis que dibujar un circuito con el ratón y que el trineo no se estrelle en un buen rato no és cosa fácil. Os dejo como ejemplo un par de circuitos espectaculares que se encuentran por la red.

Podeís jugar a el en este enlace

Suerte a todos

Yay! A new Segment on our site. Flash of the week. Flash Games, Flash Websites, and other Flash Stuff.

Cursor*10

Simple is innovative. Run up 16 stairs and get wished by a Happy New Year message. Burst the pyramids and you will need all 10 cursors to complete the level.

Thanks to WebWare

And here are the Runner ups.

2.Doof.com

3. Flash Earth

4.I am Legend
5. LineRider

They are great.

=I love this icon. This one too (+[_]::)

เพื่อนๆ เคยเล่นเกม Line Rider กันบ้างหรือเปล่าคะ? เกมที่ผู้เล่นจะต้องลากเส้น เพื่อให้นักขี่

เลื่อนน้ำแข็งที่อยู่ในเกมซิ่งไปตามเส้นทางที่โลดโผนโจนทะยานตามจินตนาการของเราค่ะ

ซึ่งมีผู้เล่นหลายคนทีเดียวที่สามารถวาดลายเส้นที่น่าตื่นเต้นท้าทายจนไม่น่าเชื่อว่า นักขับขี่

เลื่อนที่อยู่ในเกมจะผ่านไปได้ โดยโพสต์ไว้บน YouTube เพื่อนๆ ที่ไม่คุ้นเคยอาจจะลองค้น

ดูตัวอย่างวิดีโอได้ด้วยคีย์เวิร์ด Line Rider ค่ะ

มือใหม่ที่สนใจอยากลองเล่นเกม Line Rider ก็สามารถเข้าไปที่เว็บไซต์ linerider.com นะคะ

ล่าสุดมีข่าวออกมาว่า ช่วงปลายปี 2008 เจ้าเกม Line Rider จะเข้าไปซิ่งในเครื่องเล่นเกมชั้น

นำอย่าง Nintendo Wii และ DS อีกด้วยค่ะ…กราฟิก 3D ที่ดูสมจริง พร้อมเสียงประกอบที่น่าตื่น

เต้นเร้าใจ คงจะทำให้เกมนี้มีความสนุกมากยิ่งขึ้นอย่างแน่นอน ลองดูคลิปตัวอย่างข้างล่างนี้นะ

คะ เห็นแล้วอยากเล่นมากๆ เลยค่ะ

Fast paced XY track (all blue) with some hypnotical moves.