Baseball

 

Believe it or not, a baseball is a projectile that is used by the scout to stun enemies. The stun time is determined by the distance the ball is shot from. 

 

It gets launched at a lightning speed of 3000 HU/s which is about 57.2 m/s (127 mph). This seems fairly accurate to the real world as one of the maximum exit speed was 122.3 mph. 

 

Distance

 

Again we can use kinematic to do a quick calculation for the max distance it can travel. 

 

Theta = 45 degrees

vix = viy = cos 45 * 57.2 m/s

viy = 30.0 m/s

vix = 30.0 m/s

 

Now to find the time

 

vf = 0 m/s

vi = 30.0 m/s

a = 15.24 m/s/s

 

t = vf - vi 

         a

t = 0 m/s - 30.0 m/s

                15.24

t = 1.97 s

 

1.97s x 2 = 3.94 s

 

Now we can find the distance which can be found using this:

 

dx = vix x t

dx = 30.0 m/s x 3.94s

dx = 118.2 m 

 

This distance also does seem reasonable since the farthest distance ever hit was 135 meters. But that is because the acceleration of the video game is more than the acceleration on earth. If the ball was hit on earth, it would go further than it is.

 

vf = 0 m/s

vi = 30.0 m/s

a = 9.8 m/s/s

 

t = vf - vi 

         a

t = 0 m/s - 30.0 m/s

              9.8 m/s/s

t = 3.06 seconds

 

3.06 s x 2 = 6.12 s

 

dx = vix x t

dx = 30.0 m/s x 6.12s

dx = 183.6

 

This would definitely break the world record. The distance in the game seems more reasonable not just because of the distance, but also the hand time of the baseball. Most home run hits; the hang time seems to be around 4 seconds, just like the hang time in the video game world. (http://www.hardballtimes.com/batted-balls-and-home-runs/) I believe game designers design this projectile to be as close to as real life. 

 

Energy and Forces

 

I will be finding the kinetic energy of the ball on impact.

We would first need to find the final velocity using kinematics equations

 

m =142.52 g = 0.1425 kg 

 

viy = 0 m/s

t = 3.06

a = 15.24

 

vfy = viy + at

vfy = 15.24 m/s/s x 3.06 s

vfy = 46.6 m/s

vix = vfx = 30.0 m/s

 

vf = sqrt (vfx ^2 + vfy^2)

vf = sqrt ( 30.0 m/s ^2 + 46.6 m/s ^2)

vf = sqrt (3071.56 m/s^2)

vf = 55.4 m/s

 

Now we can use the kinetic energy equation

Ek = 1/2 m v^2

Ek = 0.5 x 0.1425 kg x 55.4 m/s ^2

Ek = 218.7 J

 

Now to convert to PSI which we get only 0.407 PSI. How much force would that feel on your head? The surface area of the face is 0.037 m^2. This means that:

 

0.037 m^2 = 57.4 in^2

 

force = 57.4 in^2 x  0.407 lb /in^2

force = 23.4 lb

 

Getting hit with a baseball at that velocity is like putting 23.4 lb or 19.6 kg on your face.

 

In real life, baseballs can cause serious damage. However it may not always fracture the skull of the head. In fact, there is a very high chance that a baseball will not break or crack the skull. It would rather bruise and/or cause internal bleeding and etc.  Other parts of the body such as ribs, and the waist take less force to break and therefore have a higher risk of being fractured or broken. However, the chances of getting hit are pretty slim. (http://www.straightdope.com/columns/read/3045/can-a-hard-hit-baseball-crush-your-skull-revisited)

 

Arrows

Long Bow

 

Arrows are also another popular projectile used. They are also a very fast projectile at 1800 HU/s and 2600 HU/s when fully stretched. 

In m/s the arrow travels at 34.29 m/s to a maximum velocity of 49.53. In real life, it is actually slower than regular bows which can have speeds from 46 m/s -113 m/s (http://en.wikipedia.org/wiki/Compound_bow). Arrows are very powerful in the game, as they can one shot kill if hit in the head.

 

We shall determine the total energy of the arrow, which is just the kinetic energy plus gravitational energy. We will be calculating it on the max distance shot at the typical 45 degree angle since it gives the furthest distance. 

 

For uncharged shot

 

cos 45 =        vix     

                  34.3 m/s

 

vix = 24.3 m/s = viy

 

vfy = viy + at

t = 24.3 m/s

     15.24 m/s/s

t = 1.59 s 

total hang time = 1.59 s x 2 = 3.12 s 

 

dx = vi x t

dx = 24.3 m/s x 3.12 s

dx = 75.8 m

 

 

Although it may seem like the distance is very short, it is. However we also have to keep in mind that the velocities of the arrows when it was launched is also much slower than it is in real life. An average arrow can travel around 200 ft - 250 ft which is 183 m - 229 m. This is the distance for ancient bows which is what the weapon skin in Team Fortress 2 looks like. Nowadays arrows can travel much further over 1000 m in distance. 

 

 

Crossbow

 

The crossbow belongs is the medic's arsenal as his primary weapon. It has the ablility to heal teammates on contact and damage enemies.  The crossbow similar to the long bow launches arrows, however the string of the bow is parallel to the ground rather than vertical. In the game, this projectile goes at 2400 HU/s which is about 45.7 m/s. Crossbows also use a trigger to fire the arrows which for a long bow it is manual. Most modern day crossbow fires much faster than a bow and arrow.  The average speed of a modern crossbow is around 315 fps which is about 96 m/s, twice the speed in game. 

 

We can also again find the max distance of the crossbow bolt:

 

cos 45 =        vix     

                 45.7 m/s

 

vix = 32.3 m/s = viy

 

vfy = viy + at

t = 32.3 m/s

     15.24 m/s/s

t = 2.11 s 

total hang time = 2.11 s x 2 = 4.22 s 

 

dx = vi x t

dx = 32.3 m/s x 4.22 s

dx = 136 m

 

In real life, cross bows are not shot at a 45 degree angle. But if it were it could reach a distance of 603 m

 

cos 45 =        vix     

                 96 m/s

 

vix = 67.8 m/s = viy

 

vfy = viy + at

t = 67.8 m/s

     15.24 m/s/s

t = 4.45 s 

total hang time = 4,45 s x 2 = 8.9 s 

 

dx = vi x t

dx = 67.8m/s x 8.9 s

dx = 603 m