Rockets

 

The rocket launcher is the soldier's main weapon to use in combat. It can load up to 4 rockets at a time. Like all rockets, these also explode on contact. With the explosion, it creates a knockback effect on its opponents. The more contact made, the bigger the knockback effect becomes. Therefore, the soldier has the unique ability to use the knockback effect on them to launch them in the air. This is called a rocket jump. This technique can surprise many enemies and get to places other classes cannot. They are considered highly mobile because of this technique. 

 

Unlike all other projectiles, rockets behave much differently than all other projectiles in the game. This is mainly because gravity does not affect this projectile. This means if you shoot a rocket parallel to the ground, it will continue to keep going until it hits something. This would clearly mean that the rocket has infinite energy. Imagine shooting a rocket straight up in the sky. It would not fall back down and continue to go up forever. Clearly this part of the video game defies the laws of physics.

 

Another major difference is that the rocket does not accelerate throughout its 'journey'. Rather there is the initial velocity where is accelerates at the start just at around 200 milliseconds and from there on it stays on a constant velocity, never changing speed. This means the Fnet would be 0 since it is constant.  In the video, we can clearly see the smoke and fire from the combustion of the rocket yet it is still staying the same. This is one part of physics that does not make sense in the video game. The rocket should have been accelerating because as the rocket burns the fuel it gets lighter and so the inertia goes down and it should go fast. Another way you can look at it is that the fuel is what makes it accelerate, this means as long as there is smoke trials and the blast visible it is still burning and using energy and so it should be accelerating.  (If the rocket didn't already have infinite energy) 

 

From tracker, we can see that the rocket travels at a constant velocity. However, there is damage drop off, meaning the damage on enemies gets weaker the further the distance. This would only mean that the mass of the rocket launcher decreases over time as it burns fuels. But of course, seeing that the rocket has 'infinite' energy' the mass should be the same.

 

Force on the player

 

Now we will calculate the force a person feels when they launch a rocket. The rocket launcher is basically an RPG. The model PG-7VL war head resembles that projectile and weighs in at 2.6 kg. (http://en.wikipedia.org/wiki/RPG-7). The speed of the rocket launcher is around 1100 HU/s or 21 m/s taken from the wiki page (http://wiki.teamfortress.com/wiki/Projectile). We will assume for now the mass of the projectile to be 2.6 kg.

 

According to Newton’s 3rd: Every force has an opposite and equal force acting against it. This means if there is a force applied to propel the rocket right, then there must be a force pushing left. In the video game world, we can see this happen with the recoil animation. Recoil is just a fancy word for describing newton's third law

For recoil, energy is conserved between the rocket and the rocket launcher meaning the kinetic energies are the same as it follows the law of conservation of energy. We can use the equation W = FD to determine the force applied on the rocket. 

 

First we would need to find the change in kinetic energy. So we use the equation: Ek = 1/2 x m x v^2

 

v = 21 m/s

m = 2.6 kg

 

Ek = 1/2 x m x v^2

 

Ek = 1/2 x 2.6 kg x 21 m/s^2

 

Ek = 573.3 J =570 J

 

570 joules is quite a lot for kinetic energy. Getting hit with an object that has

a kinetic energy at around 500 J can be lethal, not the include the explosive

energy that it can release.

 

For the rocket itself, it changes Ek from 0 J to 570 J is less than a second

(As it reaches 21 m/s in around 200 milliseconds). From tracker we can

see that the rocket covers a distance of 2.569 m - 0.243 m = 2.526 m

This means that:

W = FD

570 J = F x 2.326 m

F = 245 N

 

To verify we can use the forces equation to also calculate the force of the force as it launches. From tracker we can see the rocket reach it velocity of 21 m/s in just 0.209 s

This means that the acceleration is:

vf = 21 m/s

vi = 0 m/s

t = 0.209s

a = vf - vi

           t

a =  21m/s - 0 m/s

            0.209 s

a = 100.47 m/s/s

 

We can use the force equation to determine the net force of the rocket which is just the force applied, because it is not subjected to gravity.

 

Fnet = ma

Fa = Fnet

Fa = ma

Fa = 2.6 kg x 100.47 m/s/s

Fa = 261.22 N = 261 N

 

This means the soldier would feel 261 N in the opposite direction which results in the rocket recoiling up. There is also an exhaust port at the back which also releases some of the energy. This would mean that the force on the soldier would actually be less. 

 

Percent Deviation

 

Percent deviation = 261 N -245 N = 6.13% deviation

                                            261 N

Why is it a bit off? Well from tracker we found that it takes just 2.326 m to accelerate to a speed of 21 m/s. We can use this kinematic equation:

 

vf = 21 m/s

vi = 0 m/s 

d = 2.326 m

vf^2 = vi^2 + 2ad

a = vf^2 - vi^2

           2d

a = 21 m/s ^2 - 0m/s ^2 

               2 x 2.326 m

a = 94.7 m/s

 

as you can see the acceleration is a bit off when you use this kinematics equation the acceleration is off, which is why the force applied is also a bit off 6% deviation is not bad and it shows the accuracy of tracker. 

 

Energy of Rocket

 

Using the data collected above, we will calculate the total energy of the rocket. There are actually only 2 main parts for its energy. Firstly there would not be any gravitational potential energy due to the fact that this projectile is not affected by gravity.  Therefore there is only the kinetic and the explosive potential energy of the rocket. We can find the explosive potential energy using sources and so we only need to find the kinetic energy of the rocket in game. We already know that the explosive potential energy is the total energy of the rocket at the start since there is no kinetic energy before the rocket is launched. 

 

For this calculation we will assume mass stays constant during its journey. 

 

The kinetic energy of the rocket in game would be 570 J (calculation above)

 

From the weight of the rocket, only 1.43 kg is what makes the rocket explode (95 % HMX and 5% wax)

HMX is the actual explosive material. This means that:

 

0.95 X 730 kg = 694 kg is actually explosive 

 

From the relative effectiveness factor (R.E. factor) (http://en.wikipedia.org/wiki/Relative_effectiveness_factor) It is said that 1 g of HMX releases 1.70 times more than 1 g of TNT. Since we know that 1 g of TNT releases 4.184 KJ, we can solve and find out the energy released in one PG-7VL war head.

 

Eexplosion = 694x 1.70 x 4.184 KJ/g

 

Eexplosion = 4936 = 49.3J of energy released, which is a lot of energy. 

 

This means the total energy in the system us 9,673,000 J + 992 J = 9,673,992 J total which is a lot and a lot of energy. One clip can hold 4 rockets; this would mean that there is 4 times that energy per clip that the soldier can release in a rocket.  This amount of energy per rocket is close to about 3 kilo-watt hours. (1/4 of energy used every day by Canadians) 

 

That is however the total energy of the rocket. If we were to try to find the total energy is transferred to an enemy itself, it would be about a half to 3 quarters of the energy. This is because the rocket has a blast radius that shoots out energy in all directions. This would mean only about half the energy actually hits the enemy. But due to the shape of the rocket, it actually can focus more energy on a single point. This would mean that an enemy would recieve more than half the energy of the rocket.