Physics Behind Tiny Wings

Tiny Wings

We will be exploring the physics behind tiny wings. This project will go into detail about looking at the projectile motion, momentum, forces and energies behind the tiny bird that flies through the sky. For those of you who do not know what tiny wings is, this intro will be helpful.  The video shows how the game is played on the iPod touch or iPhone. The following is a trailer of the game that will explain the point of the game and demonstrate how the bird flies; and you might also notice physics in action:

-- the website from which the video came from is: http://www.youtube.com/watch?v=VUnlE4cGgz0

And now we can look onto the different general categories of physics in the game...

Physics Behind Tiny Wings- Energy

Our Tiny Bird has quite a lot of energy on his way down the hill...
In order to look at all of the energy that is going on when the bird is moving on the planet Neptune, we have to take into consideration his mass, the gravity of Neptune, along with how high he is at certain times.  We also needed to know the velocity of the bird.  When we know what these variables are, we can plug them into Kinetic and Potential Energy of the tiny bird in order to find out the Total Energy that the bird has.  To find the height of the bird, we figured that one inch on the screen would equal two meters.

Tiny bird's mass is 2.5 kg

His velocity is 1.42 m/s

His height is 2 meters

The acceleration of gravity acting on him is 11.46 m/s^2 considering he is on Neptune

In order to know his energy we must first look at the different energies he possesses:

Due to the coefficient of friction, he has the force of friction acting upon him. He also has kinetic energy and potential energy. 

We then can see that our bird at the top of the hill has 103.1 J of energy. With how the energy is distributed looking at a bar chart of total energy below:

This graph shows just how much friction there is in this game. 

Physics Behind Tiny Wings- Forces

Our tiny bird is on planet Neptune...
 With Tiny bird being on planet Neptune, he has gravity pulling him down at 11.46 meters/seconds^2.  Because the gravity is considerably more than what it is on earth, the bird will go down faster, and have a tendency to start to come down faster when in the air.  We realized that when the tiny bird was on the ground, there was a normal force, force of gravity, and a force of friction that was  slowing him down. (down below is the coefficient of friction).  Here are two pictures of the bird.  One is while he is in mid-air, and the only force acting on the bird is gravity.  The second is when he is on the turf.  These two pictures show the two different forces that act on the tiny bird in this game.  


     FORCES
  Force Normal= mass*gravity
     the mass of the bird (2.5 kg) times the gravity (11.46 m/s^2) equals 28.65 Newtons.  This is the normal force of our bird.


  Force of Friction= Fnormal*coefficient of friction
     our normal force (28.65 Newtons) times the coefficient of friction (.9) equals 25.785 Newtons.   This is our force of friction on our tiny bird.


  To find the Force of our bird, we looked at p=mv (momentum).  our momentum is 3.55 kg*m/s, and so we know the impulse, F*t, is equal to this momentum.  By knowing that the time is 1.182 seconds (solved in the projectile motion post), we can find the Force by plugging in the numbers.  
        F(1.182)=3.55  ==>>  F=3.00 Newtons
  Now that we found the Force of the bird, we plugged the equation into F=ma, and found that the acceleration of the bird was 1.2 m/s^2.  (3.00 Newtons=2.5kg*a)

force uk= .9, we assumed the surface to be a turf like surface.
link to coefficient of friction  

Physics Behind Tiny Wings- Projectile Motion and Momentum

Our bird will be called tiny bird...

mass of tiny bird -- 2.5 kg

screen size is 2x3 inches

1 in= 2m 

The top of the hill is the start, or the zero point/ equilibrium 

Tiny Bird is on planet Neptune, so his acceleration will be 11.46 m/s^2

Equations to determine the projectile motion of tiny bird:

∆x= v_o t+1/2 at^2

v^(2 )= v_o^2+2ad

v_f= v_o+at

The top of the hill is about 2.125 meters from the ground. Our bird is about .75 meters above the top of the hill. 

The total distance in the y-direction is 2m. The total distance in the x-direction is 1.678m. The angle of the hill we measured to be about 50 degrees using a protractor on the screen. And the total distance we calculated tiny bird to have traveled was about 2.611 meters. 

By knowing the distances in the x and y directions, we could plug the information into the equations below. First we solved for the y-direction for it's initial velocity and the plugging that velocity into a second equation to find the time. After obtaining the time, we then put the time in to solve for the initial velocity in the x, then to continue to solve for the x-velocity. 

After going back and measuring the actual distance tiny bird is from the bottom of the hill, the actual distance is about 2.5 meters meaning he will make it to the bottom of the hill and not go to far and crash. The percent error in our calculations was about 4.3% which shows the game to be  fairly realistic. :)  

And now we must look at his momentum...

momentum= m*v=F*s

We will be using the mass * velocity to find his momentum 

tiny birds mass is the same as above and his velocity is 1.42 m/s^2 

Momentum is the same as impulse, or how much force at a second is behind an object. It's calculated by the change in velocity multiplied by the object's mass. The impulse of tiny bird was 3.55 N-s which means at that moment of him coming down the hill, he has 3.55 N-s of force. And now that we have the momentum, we can calculate his force using the change in time from above...

Physics Behind Tiny Wings -Wrap up of Tiny Wings

Conclusion of Tiny Wings

In this blog, we looked at the energy, projectile motion, forces, and momentum of how Tiny Wings works.  By using physics, we solved many equations involving distance, time, velocity and acceleration. And after doing this,  we were able to understand more about how the game worked and see how much physics is involved. In conclusion, we discovered the physics behind Tiny Wings!

Link to where the picture came from