Helpful Formulas

# What are the formulas we will be using?

## Speed:

For speed we only will really use one single formula most of the time. This would be the speed formula represented as S=D/T where S is speed D is the distance the object/entity traveled and T which represents the time in which they did it! Each variable that the speed formula includes has its own formula. T=D/S where T is the time it took the entity/object to travel D is the distance it traveled and S is the speed at which it did. and finally D=S\*T where D is the distance traveled S is the speed it was moving at and T is the time it took to do that. Other words for speed would be things like velocity which when applied to other formulas will be defined by speed and not actually involving advanced/classical mechanics.

## Attack Potency

When we are finding the energy release for a character there is a bunch of formulas that are needed and not one single formula is universally applied. When finding attack potency we need to find somethings volume. When we find volume we find mass. These are fundamental aspects of calculating attack potency. Sometimes when finding the total energy release you will not have to calculate the mass for an object because it will be done for you. For example when finding the energy release of moving a planet we already have the Mass of the earth calculated for us by dandy scientists. When calculating the energy needed for a crater or something of similar nature we need the volume for the shape that was created from the energy blast. This method would include figuring out what shape you are looking at and using the formula for that shape. Now not in every case will this lead straight into the j/cc value which is a basic multiplicative value after finding volume. You might have to find the mass of the object which includes multiplying the volume by the material its made out of. These processes do not take a bunch of work and we are going to lessen the load even more! (TLBW staff is just superior like that). So lets get it going!

## Basic Shape formulas

This is a cone a very simple shape. Cones consist of a circular shape at the base and a rectangular upriser giving its 3D form.

Volume Formula**: V = *π\*r^2\*h/3*** *(Where V is volume. r is the radius of the shape, h is the height of the shape)*

This is a cylinder a 3 dimensional shape that consists of a circular top and bottom. Another very simple shape to identify

Volume Formula: **V = *π\*r^2\*h*** *(Where V is volume r is the radius of the shape and h is the height of the shape)*

This figure is a sphere a very very basic shape with an even easier formula. its a 3 dimensional circle being the easiest way to describe it.

Volume Formula: **V= 4/3\**π\*r^3*** *(Where V is the volume and r is the radius)*

This a cube this is an interesting shape made up of exclusively squares. Very interesting figure to look at.

Volume Formula: **V = a^3** (Where A is the edge of the shape) This formula is very basic and will most likely not be used

when talking about destructive areas.

This is a rectangular prism aka (**Rectangular cuboid)** this is made up of 4 rectangles and 2 squares for its 3D shape.

Volume formula: V = L\*W\*H (Where L is length W is the width and H is the height) this is very common in things like buildings and non functional elongated blast holes.

## Other practical shape volume formulas

This shape is a sphere as a whole but the volume in specific is a spherical cap this shape is super common in terms of craters for explosions that didnt fully get a vertical shot down. This would result of a omnidirectional blast.

Volume Formula: V = **(1 / 6) \* π \* h (3 \* r^2 + h^2)** (Where V is the volume h is the height of the shape and r is the radius)

This is a shape known as a spherical wedge which is a fundamental aspect of a sphere which divides segments of the sphere into multiple vertical parts.

Volume Formula: V = **(θ/2π)(4/3)π\*R^2** (Where r is the radius of the figure) This shape isn't too common but here is

this anyway

This is what is known as a spherical sector where a cone shaped figure will be taken out a solid object from a carved manner.

Volume Formula: V = **(2/3)π\*R^2\*H** (Where R is the radius and H is the height)

## Other Non geometrical formulas

Distance of characters: Now the distance between two people is very important and will be needed for every speed calculation and even some AP ones. When looking at a panel like the one on the left pixel measurements can be used. But sometimes the angle doesn't allow for that like here. In this case you would do something called ang sizing. Now that whole process will be explained in other places once you understand that here is the formula.

**2atan(tan(35deg)\*(object size in pixels/panel height in pixels))**

Radians to degrees formula: **Radian measure × (180°/π)**

Continuation

 This will be the overview for GBE: When talking about planets we have something that is called gravitational binding energy. This to be exact is the amount of total energy release needed to destroy a planet without it reforming into its shape. Planets by nature will pull in on themselves due to the gravitational nature of celestial bodies.

Volume Formula: GBE = **3 \* G \* M^2 / (5\*R)** (Where G is the gravitational constant M is the mass of the object and R is its radius in meters)

Kinetic Energy: In physics, the **kinetic energy** of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. Kinetic energy isnt just used for simple things but rather anything that moves holds kinetic energy.

The Formula: 0.5\*M\*V^2 (where M is the mass of the object and V is the velocity or speed of it in m/s) Doing this process will show for the total energy released when this object is moving.

Gravitational Potential Energy: gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (converted into kinetic energy) when the objects fall towards each other. Gravitational potential energy increases when two objects are brought further apart. In other words as something is pulled to a higher altitude more energy will build and the amount of total energy built will be a result of the objects mass the height as well as the gravity that is pulling down on it. So a celestial object with higher gravitational constants will result in higher numbers.

The Formula: Ep = **M\**g\**h** (where Ep is gravitational potential energy in joules M is mass in kg G is the gravitational constant and H is how high it was lifted)