Motion

## Kinematics

Both position and velocity have 3 components, one per each of the orthogonal axes, namely, x, y and z.

### Position

There is an integer position with respect to the block on which a player is on top, and the player position, which is scaled at 0.5 per block and admits floating numbers. To convert from player position to block position, multiply the player position by 2, and floor it. That is:

P
b

=

⌊

2

P
p

⌋

{\displaystyle \displaystyle{P\_b = \left \lfloor 2P\_p \right\rfloor}}

where

P
b

{\displaystyle P\_b}

is block position and

P

p

{\displaystyle P\_{p}}

is player position. Such that when you have a negative number for a player position -0.3, in terms of block position it would be -1 and not 0.

### Time

1 unit of time in the game is 0.08 seconds. That is, every 25 units of time, 2 seconds pass.

### Velocity

The game keeps track of the player's velocity (i.e. time over distance) for x, y and z, using the unit of time mentioned above. To convert to distance per second, multiply it by 12.5 units per second; to convert to blocks per second, multiply it by 25 units per second.

## Gravity

The gravitational constant is perhaps equal to -1.8816 which is approximately equivalent to -47.04 blocks per second square. The maximum velocity in the y direction that one can attain is 5 distance per unit of time (i.e. 125 blocks per second), as can be observed when jumping to the void when the server is no longer updating.

## Locomotion

### Reaching the designated velocity

For each kind of locomotion there is a maximum velocity that the player can attain. For almost every transverse location, their maximum velocities are attained in three steps (except at least, locomotion in water that only has 1 step) that happen every 0.04 seconds of increments of the kind

(

8
7

)

(

1
2

)

n

{\displaystyle \left(\frac{8}{7}\right)\left(\frac{1}{2}\right)^n}

where n is the step number (and the steps are between 1 and 3): first, it increases by 4/7 the maximum velocity, second it increases by 2/7 the maximum velocity, and finally it increases by 1/7 the maximum velocity. (The same phenomenon is observed for friction but in reverse, by decreasing instead of increasing and without a fixed number of steps) Now, 1/7 the maximum velocity shall be named the "minimum unit of increment".

### Crouching

To crouch one has to press c and move in some direction. The maximum crouch velocity without carrying any weapon is 0.084 (1/5 that of sprinting and 30% that of walking) which is equivalent to 2.1 blocks per second. The minimum unit of increment for crouching is 0.012. Crouching has the specific property that if the player moves and doesn't jump, then the player cannot fall down in y unless the block below is deleted. (See: Invisible Wall of Crouching)

### Walking

To walk one merely has to move in some direction. The maximum walk velocity without carrying any weapon is is 0.28 which is equal to 7 blocks per second. The minimum unit of increment for walking is 0.04.

### Sprinting

To sprint one has to press shift and move in some direction. The maximum sprint velocity without carrying any weapon is 0.42 (five times that of crouching and 150% that of walking) which is equivalent to 10.5 blocks per second. The minimum unit of increment for sprinting is 0.06.

### Friction

If the player stops pressing a button to move, the velocity of the player divides by 2 every 0.04 seconds, until it reaches below 1e-6, at that moment, it becomes zero. That is, friction is modelled by exponential decay (but here expressed in terms of exponential growth using 1/2 instead of a negative exopnent and a 2), and as such, it has the following equation:

v
(
t
# )

{

v
i

(

1
2

)

⌊
t

/

0.04
s
⌋

if
v
≥

10

−
6

0
,

otherwise

{\displaystyle v(t) = \begin{cases}
 v\_i\left(\frac{1}{2}\right)^{\lfloor t/0.04s \rfloor} & \text{if } v\geq 10^{-6}\\
 0, & \text{otherwise}
\end{cases}}

where

v
i

{\displaystyle v\_i}

is the initial velocity at which it starts decaying, t is the duration of the decay so far, and

v
(
t
)

{\displaystyle v(t)}

is the velocity at time t.

### Weapon carry multiplier

Depending on which weapon you're carrying it will incur a multiplier cost on one's velocity

Weapons and their weapon carry multipliers
 Assault Rifle
 Light Sniper Rifle
 Gun

### In Water

When you move in water you'll move slower than you usually do. You'll move at 4/7 of that of walking on ground for locomotion in the transverse plane as maximum velocity as a result of there being only one step of increase when moving in water, instead of three (See: Reaching the designated velocity). Whereas for moving upwards and downwards happens at a constant speed of 0.08 in the y velocity component, that is 2 blocks per second (or 1 unit of distance per second), depending on whether the player is pressing space (moving up) or not (moving down).

### Jumping

In order to jump you have to press the space key. Jumping does not affect the velocity in the x and z components, it does, however, affect the velocity in the y component, having an initial velocity of 0.2748, that is, 6.87 blocks per second.

### Parachuting

*See:* Parachuting

One descends in a parachute at a constant velocity of 0.2, while motion in other directions is limited by a maximum of 0.28 speed, and its momentum is conserved while no key is pressed.

### Skydiving

*See:* Skydiving

When skydiving, one descends at a constant velocity of 0.4 to 0.8, which can be increased or decreased through the use of keys that go with or against the orientation of the player. Similarly as in parachuting the momentum is conserved and the limit is also 0.28 in speed for other directions.

## Ballistics

*See:* Ballistics

The bullet arrives immediately before its trace for blocks and players. The trace of the bullet takes between 0.433 to 0.466 seconds to travel 91 blocks. In other words, around 195.278 to 210.162 blocks per second (~200 blocks per second). The reason why it is possible to avoid a bullet is not so much that one avoids an individual bullet, but rather one avoids the trace of a round of bullets moving, one after the other, towards some direction, as the enemy moves the muzzle. (especially when using a light submachine gun)

A weapon can damage beyond draw distance.

### Jumping off from the block

A dropping jumps at a random direction and attains a distance of 0 to 1.5 blocks of distance away from the centre of the block (if it reaches a position at the same level where the jump began), and thereafter it slides for a small while before giving away to friction and stopping completely.

### Buoyancy

A dropping within the water will go upwards at half the speed a person would, that is, a speed of 0.04 units of distance per units of time (i.e. 1 block per second) and reach the surface, until it is such, so that when bobbing up, the water will cover just half of the dropping.

## Camera

Depending on the movements of the mouse, the player is able to move the camera and rotate it in the yaw and pitch axes, which have a range equal to (-π radians, π radians) and they both have a smallest increment of 2e-7. And when dying, the camera rotates so that it faces the source of death and it rotates also in the roll axis, depending on the absolute position of the source with respect to the player (like to the south or to the north, instead of back or front), the specifics of which remain mysterious.

1. ↑ It has been checked for crouching, walking, sprinting, and the exception of water, only.