Physics

Real World

The physics discussed in this section reflect the real world.

If you are looking for game mechanics, see the game mechanics category. The thruster mechanics and Gyroscope mechanics mechanics discuss the areas in which those components don't reflect real-world physics.

Work in Progress

This page will contain a series of physics lessons designed to teach the basics of real-world physics. As the box above says, there should also be references made wherever the game physics do not properly reflect what is written here.

For more information on this project, please contact DocTanner. You can also use the wiki forums or the comments at the bottom.

As with anything on a wiki, feel free to contribute! Improve existing sections, fill in missing sections, or add new ones. Empty sections should be marked with the {{Stub}} tag.

Mass and Inertia

"Inertial mass is a quantitative measure of an object's resistance to changes in velocity" — Wikipedia

Depending on the context, mass can refer to several things. For our purposes, though, we'll be discussing inertial mass. For other definitions of mass, see the Wikipedia link above.

On Earth, mass and weight are roughly equivalent terms: one kilogram of mass weighs one kilogram at 1G. (G being the unit symbol for "Gravity", a measure of {{#Force|force}} where 1G is equal to the force of gravity on earth.) However, while weight varies based on gravity, mass remains constant.

In space, the most accurate definition of mass is resistance to {{#Acceleration|acceleration}}. Essentially, the more mass an object has, the more force is needed to change it's velocity by some fixed amount. This property is called inertia.

"Inertia is the resistance of any physical object to any change in its motion (including a change in direction). In other words, it is the tendency of objects to keep moving in a straight line at constant linear velocity." — Wikipedia

As you can see, there's not much difference between the definitions of mass and inertia. In fact, you can think of mass as simply the measure of inertia. While this isn't entirely accurate in all contexts, it works well enough for the purposes of this discussion.

Mass is measured in grams (g) but equations in physics generally use kilograms (kg) as the base unit. As with all other SI units, "kilo" means one-thousand. So 1kg = 1000g. On earth, 1kg weights roughly 2.2lbs. However, it is important to remember that pounds are a measure of weight, not mass, and are not a useful measure in space.

Since we know from Newton's second law that the sum of all external forces, F, is equal to the mass multiplied by the acceleration, mass can be thought of as a proportionality constant between force and acceleration.

Velocity

"Velocity is the rate of change of the position of an object, equivalent to a specification of its speed and direction of motion, e.g. 60 km/h to the north." — Wikipedia

As Wikipedia's definition says, velocity is a vector that refers to an object's speed and direction. The magnitude (number) of the vector refers to the rate of change, or speed, while the sign refers to relative direction.

Velocity, relative to position on a line, is determined with the following formula:

$v={\frac {\Delta d}{t}}$
Where:
$v$	: Velocity (km/s)
$\Delta d$	: Change in position (km)
$t$	: Time (s)

Units

How we measure velocity depends on where we are and what we are measuring. In the US, we usually measure terrestrial objects such as cars in miles-per-hour (mph or m/h). In other countries, terrestrial objects are measured in kilometers-per-hour (kph or km/h). For faster objects, such as spacecraft, we usually measure in kilometers-per-seconds (km/s).

In all cases, velocity is measured as distance over time. Specifically, it is the distance the object will travel in the given amount of time. So a car travelling at 60mph will change its position by 60 miles in a one hour period.

In Space Engineers, all velocities are measured in meters-per-second.

Direction

If you are driving on the highway, your velocity might be 60mph. However, if you were backing into a parking space, you might be travelling at -5mph. This is because we tend to define a car's velocity in relation to the direction the car is facing.

Since velocity is a one-dimensional vector, it is sometimes useful to measure an objects movement using two separate velocities. For example, the speed of a plane is often measured as a combination of its linear speed (how fast it moves parallel to the ground) and its vertical speed (how fast it climbs or descends). So on take-off, a plane might have a linear velocity of 500mph while climbing at 100 feet-per-minute (fpm). The linear velocity determines how long it will take you to travel between airports on the ground while your vertical velocity determines how high you will be while travelling. While you could also measure its actual net velocity, this value isn't particularly useful in reference to objects on the ground.

For objects moving in three-dimensional space, it can even be useful to measure speed as three separate velocity vectors. This is a specific case, however, and somewhat beyond the needs of this page.

Combining multiple vectors

//missing: How to calculate results / interpret numbers. Pictures for clarification of the drawing process.

A vector contains two informations: a scalar (normal 1 dimensional number) and a direction. A scalar can be completely described by its value. The direction points somewhere without having a size. For example if you're running with 20km/h towards free beer the scalar would have the value of 20km/h while the direction would be towards the beer. Note that a vector only has a value and a direction. It does NOT have a positon. If you draw a coordinate system you can put it wherever you want as long as you keep its orientation and length. To draw a vector we can randomly choose a starting point. Now we look at the direction the vector is supposed to go and draw a straight line in that direction. Choose a scale (like 1cm on the paper equals the force of 100N). It must stay the same for all vectors within the same sheet. You now can calculate your vectors length. Cap the drawn line at that length.

So now we have multiple vectors, what do we do with them? First of we name them so we always now what vector we are dealing with. So the first vector becomes "vector a", the second "vector b" and so on. Second we will name the point a vector starts "base" and the point it ends "tip" just to make explaining easier. (Hint: It often is a good idea to put the base of one vector at (0,0) coordinates.) Now we have to figure out what kind of calculation we need to do. Thruster forces are normally added or substracted for example. We'll keep with those two operations, multiplikation and division with more than one vector is difficult if you didn't learn how to do it in school. If you need to multiply or divide with no more than one vector and one or more numbers you can take the length of your vector and treat it like any other number. The direction stays the same.

Addition: Vector a + vector b = vector c. Draw vector a on a coordinate system. Now take vector b and draw it in a way that the base of vector b is at the position of the tip of vector a. Then draw vector c, your result, from the base of vector a to the tip of vector b.

Substraction: Vector a - vector b = vector c. Draw the bases of vector a and b on the same point. Now draw vector c from the tip of vector b to the tip of vector a.

Acceleration

"Acceleration is the rate at which the velocity of a body changes with time." — Wikipedia

Just as velocity is a change in position over time, acceleration is a change in velocity over time. Like velocity, it is also a vector. The equation for acceleration is very similar to the equation for velocity:

$a={\frac {\Delta v}{t}}$
$\Delta v=v_{f}-f_{i}$
Where:
$a$	: Acceleration (km/s2)
$\Delta v$	: Change in velocity (km/s)
$t$	: Time (s)
$v_f$	: Final velocity (km/s)
$v_i$	: Initial velocity (km/s)

Units

Acceleration is always measured with the same time unit as the velocity it's based on. For example, if the object's velocity is measured in km/s, its acceleration would be measured in km/s².

Direction

The direction of acceleration is relative to the direction of the velocity. In laymans terms: if the velocity is increasing, the acceleration is positive; If the velocity is decreasing, the acceleration is negative.

For example, if your ship is travelling forwards, it's velocity is positive. So if you are speeding up, the acceleration is positive. If you are slowing down, the acceleration is negative. Similarly, if your ship is travelling backwards, the velocity is negative. So if you are speeding up, the acceleration is negative. If you are slowing down, the acceleration is positive.

If this sounds confusing, think about it this way: assume we're measuring velocity in km/s. So, acceleration is measured in km/s². Every second, you should be able to add your velocity and the acceleration together to get your new velocity. If you know you're speeding up, but adding your velocity and acceleration and velocity together results in a smaller velocity, then you've got one of your signs wrong. (Keep in mind that "smaller" refers to magnitude, not value. For example, -10km/s is smaller than -20km/s.)

Force

"A force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or a flexible object to deform, or both." — Wikipedia:Force

Force can be understood simply as a "push" or a "pull". So it can cause an object to speed up, slow down, change direction, or break.

$F = m*a$
Where:
$F$	: Force (N)
$m$	: Mass (kg)
$a$	: Acceleration (m/s2)

Torque

Note: Torque in Space Engineers, specifically that applied by  Gyroscopes does work according to the real-world physics described here. Research is on-going to determine the nature of in-game torque.

If a force can be thought of as the cause behind a linear acceleration, or deceleration, then a torque is simply the cause behind a rotational acceleration, or rotational deceleration. Simply put, a torque is a rotational force. It is measured in newton meters (Nm) or foot-pounds. Note that this is not newtons per meter. A torque can also be referred to as a moment, or the moment of a force about a point. Moments and torques share the same unit.

Mathematically, torque is defined as:

$T=F*r$
Where:
$T$	: Torque (Nm)
$F$	: Force (N)
$r$	: Distance between where the force acts, and the axis about which the object will rotate. (m)