Pipes

Pipes are launched out of a grenade launcher. It is the demoman's primary weapon and is also explosive. Like the rocket, it can explode on enemy contact, but if it misses the target it does not explode but rather it rolls around on the floor and then explodes. There is a timed explosion that occurs. Since this is an explosive weapon, there is also a knockback affect that can push enemies away. Demomen can use this knockback effect to also be launched in the air. Other special property is has is that it explodes 2.3 seconds after launch regardless of where the projectile is (air or ground)

Maximum Distance

Pipes are affected by gravity and so they arc in the air. We can use projectile motion to determine how far, high, and how much energy is needed to launched a pipe bomb.

According to the wiki, the velocity of a pipe bomb is 1215 HU/s which is about 23.15 m/s

The optimal angle to launch for the furthest distance is to launch at 45 degrees, the midway point.

This means that vix = cos 45 X vi

vix = 0.7071 X 23.15 m/s

vix = 16.37 m/s

We can use this equation: viy = vfy + at to find the time when the pipe is halfway through the air.

This is allowed rather than using T.B.E.E since the vertical displacement is 0 m

a = 15.24 m/s/s

x = viy = 16.37 m/s

vfy = 0 m/s

16.37 m/s = 0 m/s + 15.24 m/s/s X t

t = 16.37 m/s

15.24 m/s/s
t = 1.074 s x 2 = 2.148

This means it will take 2.148 s for the projectile to hit the ground

For projectile motion we can find the furthest displacement using this: dx = vix X t

t = 2.148 s

vix = 16.37 m/s

dx = 16.37 m/s x 2.148 s

dx = 35.16 m

This means the furthest distance a pipe bomb can travel is 35.16m or 1846 HU.

Energy of Pipes

Unlike the energy of the rocket, we would need to take into effect the gravitational potential energy of the pipe. For calculation purposes we will set the launch angle at 45 degrees. Any angle would work, and the total energy of the system would still be the same since the pipe launcher uses the same amount of energy to launch the pipe regardless of the angle. We will also need to find the mas of a pipe grenade. This gun resembles the MGL (http://en.wikipedia.org/wiki/M32_MGL) (http://www.evike.com/product_info.php?products_id=33476) which the grenade has a mass of 0.5200 kg per pipe

Et = Eg + Ek + Eexplosion

We will disregard the energy released from the explosion since that can be found online.

At 45 degrees the max height the pipe can reach is: viy ^ 2 = vfy ^ 2 + 2 x a x dy

vfy = 0 m/s

viy = 16.37 m/s

a = 15.24 m/s/s

0 m ^ 2 = (16.37 m ^ 2) + 2 x 15.24 m/s/s x dy

dy = 268.0 (m/s)^2

2 x 15.24 m/s/s

dy = 8.793 m

We can now find the gravitational potential energy at the maximum height.

Eg = mgh

m = 0.52 kg

g = 15.24 m/s/s

h = 8.793 m

vix = 16.37 m/s

Eg = 0.5200 kg x 15.24 m/s/s x 8.793 m/s

Eg = 69.68 J

Ek = 1/ 2 x m x v^2

Ek = 0.52 kg x (16.37 ^2)

2

Ek = 69.68 J

This means that

Et = Ek + Eg + Eexplosion

Et = 69.68 J + 69.68 J + Eexplosion

Et = 139.36 J + Eexplosion

Now to find the potential energy of the explosion which is the same as the amount or energy released on explosion. I looked into the materials of a grenade and found that 180 g where explosive material composed of 'composition b'. On the R.E. factor which measures the TNT equivalent (http://en.wikipedia.org/wiki/Relative_effectiveness_factor) it is 1.35 for composition B. Since I know that 1 g of TNT releases 4.184 KJ, we can find out the total energy of this whole system.

Eexplosion = 180 g x 1.35 x 4.184 KJ/g

Eexplosion = 1016 KJ of energy = 1,016,000 J of energy.

This means that the total energy is 1,016,000 J + 139.36 J = 1,016,139.36 J of energy which is also a lot of energy. This would definitely be 100% fatal in reality. However, this also has a bit of controversy with physics. Pipe bombs, hardly have any damage drop off meaning it retains and does basically the same damage regardless the distance. As for a rocket, firstly it has more kinetic and explosive energy, but it does far less damage than a pipe bomb, the further the distance.

Stickies

Stickies are launched from what is called a sticky bomb launcher. It is the secondary weapon of the demoman. Just like the pipe bombs, they are explosive and are subjected to gravity which means it arcs in the air. However, the special property that this projectile has is that it sticks to any surface it comes in contact with (besides sticking onto enemies). The mass of a sticky bomb is unknown. We will take the mass of a sticky bomb in real-life (bomb made in World War 2) (http://en.wikipedia.org/wiki/Sticky_bomb) which has a mass of 1.0 kg. Unlike the pipe bombs, they do not detonate automatically; instead the player can decide whether to detonate. This enables players to set sticky traps around corners and in hiding spots to just wait for an enemy to pass by. On detonation, the sticky bomb creates an explosion that also creates a knock back effect just like rockets and pipe bombs. However, the player can self-detonate anytime. This enables players to easier jumps and control. This is what is called a sticky jump. A sticky jump has the capacity to jump further than a rocket jump.

Max Distance

We can again use kinemactics equation to find the max distance.

Theta = 45 degrees

vix = viy = cos 45 x 47.5 m/s

vix = viy = 33.6 m/s

vfy = viy + at

0 m/s = 33.6 m/s + 15.24 m/s x t

t = 2.2 s

total time = 2.2 s x 2 = 4.4 s

dx = vix x t

dx = 33.6 m/s x 4.4s

dx = 147.84 m

According to the internet the maximum a sticky can travel is 1600 HU which is about

Forces

When a stickybomb is shot and it lands on a surface such as the ground, it almost instanteously stops, meaning that it has a very high frictional force. The sticky loses all it momentum and you can notice that is barely slides along the surface. It just stops. Even when shot at an intial velocity of 17.5 m/s it takes less than 100 milliseconds for it to stop. For these calculations we will assume the sticky bomb hits the surface at the initail speed. Over time the speed changes as this projectile is subjected to gravity, so to keep it simple it will hit the surfaces at its intial velocity.

We can use Fnet = ma. The mass of the sticky bomb I will assume to be 1.0 kg since the sticky bomb launcher

as stated in the wiki, is a modified version of the grenade launcher.

This would give us an acceleration of:

a = vf - vi

t

a = 0 m/s - 17.5 m/s

0.042 s
a = 417 m/s

Fnet = ma

Fnet = 1.0 kg x 417 m/s

Fnet = 417 N

We can use Fnet = ma

The mass of the sticky bomb I will assume to be 1.0 kg since the sticky bomb launcher

as stated in the wiki, is a modified version of the grenade launcher.

Theta = 45 degrees

Fax = Fay

Fnet = Fa + Fg

417 N = Fa + 9.8 N

Fa = 407.2 N

Fax = Fay = cos 45 x 407 = 288 N

1)

Fnet = 417 N

Fax = Fn = 288 N

Fnet = Ff + Fg - Fa

Ff = 417 N - 9.8 N + 288 N

Ff = 695.2

Now we detemine the Mu

Ff = Fn x (Mu)

695.2 N N = 288 N x (Mu)

Mu = 3.35

3)

Fnet = 417 N

Fnet = (Fn + Fg) - Fa

417 N = Fn + 9.8 N - 407 N

Fn = 417 N + 407 N - 9.8 N

Fn = 814 N

For this example below, this is where the physics gets a little weird.

2)

Fnet = Ff = 417 N

We can find Mu which is the coefficent of friction.

Fg = Fn

Fg = 1.0 kg x 9.8 m/s

Fg = 9.8 N = Fn

Ff = Fn x (Mu)

417 N = 9.8 N x Mu

Mu = 42.5 = 43

This coefficent is very, very high. It is very extreme. The coeffecient of rubber on concrete is only 1. This friction is around 43 times more than that.

Compared to the other coefficent of 0.96 it is much off.

The next figure is a FBD of a sticky on the wall.

The Fnet = 0

This means that Fg = Ff, and Fn = Fa

Fg = mg = 1.0 kg x 9.8 m/s

Fg = 9.8 N = Ff

(Mu) = 43

Ff = Fn x 43

9.8 N = Fn x 43

Fn = 0.23 N = Fa

However if we were to use the Mu above at 3.35 we would get

Ff = Fn x 3.35