Calculations and Equations

Calculations are considered by the more math-inclined Spacebattlers to be the heart and soul of the Vs. forum.
It is a general policy of the debating forums that the real-world laws of math, physics, and logic apply to the fictional situations and universes we analyze unless explicitly stated to the contrary. (Many universes, for example, allow faster than light travel which we accept as a valid premise.)
In the debate forums, calculations generally take the form of the mathematical quantification of certain events seen or described on screen. For example, a character may describe a slug of a certain size traveling at a certain speed, and from that description we will calculate the kinetic energy of the slug. Alternatively, we may see a fireball arise from an explosion on screen, and by calculating the duration and breadth of the fireball, one can very generally estimate the size of the explosion that caused it. 
These calculations are often crucial in a debating setting.
It isn't really that hard to calculate basic firepower, yields, and etc by yourself. Here are a few equations for a quick result.
==Kinetic Energy==
Kinetic energy calculation is required to demonstrate the destructive potential of a projectile, usually solid, moving at a certain velocity.
The simplified equation that ignores relativistic projectiles(slower than 14%c is the general accepted figure for dividing 'relativistic' speeds and 'hypervelocity' speeds) is the following.
*Kinetic Energy = ½ x Mass of the projectile x velocity²
Please take note, the mass of the projectile MUST be measured in Kilograms , and the velocity MUST be measured in meter per second. The resulting Kinetic energy comes out in Joules. 
For example, a Halo MAC fires a 600-ton slug at 30,000 meters per second.
Put that into the equation, and we get
MAC energy = ½ x 544,200(kgs) x 30,000² = 489,780,000,000,000 Joules.
===Relativistic Kinetic Energy===
If you ever was interested in the theory of relativity, you might remember than a matter's mass increases as it gets closer to the speed of light. In this case, the above equation sadly does not work as it does not take into consideration the increased mass of the projectile.
The simplest equation for calculating the relativistic kinetic energy is the following.
*Kinetic Energy = ((1/sqrt(1-percentage out of the speed of light²))-1) x Original Mass of the projectile x Speed of light²
Note, the 'Percentage out of the speed of light' refers to how fast the projectile is going compared to the speed of light. A projectile moving at half light speed would be 0.5, where as three quarters lightspeed will be 0.75.
If you don't know what 'sqrt' is, it's this: √. If you're asking this, it's probably one of the buttons you never pressed on the calculator. 'sqrt(x)' refers the the number that, when squared, will result in the original number(aka the x).
For example, sqrt(4) = 2, and sqrt(9) = 3, sqrt(16) = 4, and so on.
===Sources for Kinetic energy/ballistics Calculations===
*Ballistics Calculations
==Heat Energy/ Directed Energy Weapons ==
A Directed Energy Weapon, such as a laser or plasma-based weapon, uses heat energy to directly damage a target. To determine the destructive capabilities of these weapons, kinetic energy calculations are inappropriate.
To calculate the energy emitted by a DEW, you must find a source that demonstrates the DEW in question melting or vaporizing an object. One may then, after determining the composition of the melted or vaporized object, determine the heat energy necessary to accomplish this feat.
There are 2 main equations in relation to heat energy. They are the following.
*Heat Energy = Specific Heat capacity of the target(Often abbreviated as the letter 'c') x Mass of the Target x The change in temperature of the Target.
*Heat Energy = Mass of the Target x Enthalpy of Vaporization or Fusion of the Target.
The Specific Heat Capacity has many forms of measurement, and the mass of the target must be changed according to what units you used to measure the Specific Heat Capacity. If the c is measured in Joules per Kilograms, then the mass must be measured in kgs. If the c is measured in Joules per pound/gram/whatever, then the mass should also be measured accordingly.
Also, all temperatures should either be measured in degrees Kelvin or degrees Centigrade .
The first equation can only be used if the target does not undergo a phase transition . If it does, that is where the second equation comes in.
The second equation must be used when the target was vaporized or melted, and it's results should be added to the first equation. For example, if a laser fired at a block of ice(at -10ºC with a mass of 1kg) completely vaporized it on Earth, the equation to determine the heat energy emitted by the DEW would be:
Energy of Laser = Specific Heat Capacity of ice x 1 x 10 + 1 x Enthaly of Fusion of ice + Specific Heat Capacity of Water x 1 x 100 + 1 x Enthalpy of vaporization of Water
==Matter-Energy transition==
The formula for energy released by mass-energy conversion is one of the most simple and iconic formulas in physics. Matter conversion calculations are relevant when considering total conversion to energy via antimatter annihilation, or other similar conditions,
The energy released is equal to the mass of the annihilated matter times the square of the speed of light, or
e=mc^2
where e is measured in joules, m is the mass in kilograms, and c is the speed of light, or 300,000,000 m/s.
This equation is a mathematical representation of the idea that matter and energy are the same thing in differing forms. Matter cannot be destroyed, but it can be converted to energy, and vice versa.
==TNT equivalent==
You will quickly notice if you've ever been to the Vs. Debates forum, that people, when stating energy of large quantities, express them as "blah-blah-blah peta/tera/giga/mega/kilotons". This may confuse you as to why people are using a measurement of weight to measure energy. This type of energy scale is only known as the TNT equivalent .
TNT equivalent is a method of quantifying the energy released in explosions. The ton (or tonne, i.e. metric ton, which is 1000kilograms) of TNT is a unit of energy equal to 4.184 gigajoules(4,184,000,000,000 Joules), which is approximately the amount of energy released in the detonation of one ton of TNT. The megaton of TNT is a unit of energy equal to 4.184 petajoules, or 4,184,000,000,000,000,000 joules.
One gram of TNT on this scale is equal to 1000 calories, or 1 kilocalorie. One calorie is approximately equal to 4.184 joules.
One kilogram of TNT is equal to 1000 grams of TNT.
One Ton of TNT is equal to 1000 kilograms of TNT.
Here is the scale for bigger amounts of energy. Take note, while such energy seems to be A LOT, most Sci-Fi verses have their firepower in such magnitudes it must be expressed in the TNT equivalent to avoid the page being full of zeros.
*1 kiloton = 1000 tons
*1 megaton = 1000 kilotons
*1 gigaton = 1000 megatons
*1 teraton = 1000 gigatons
*1 petaton = 1000 teratons
*1 exaton = 1000 petatons
*1 zettaton = 1000 exatons
*1 yottaton = 1000 zettatons
Most famous SF verses are in the mega~tera region.
For a simple conversion of Joules into tons of TNT, divide the results you got from the other equations above by 4,184,000,000.
===Sources on Nuclear detonation effects and etc.===
*Fireball size and blast radius of different yields calculator
*Nucler bomb effects calculator
Category:Calculations