Airship Movement

Mechanics ‣ General Mechanics ‣ Airship Movement

The forces that apply on an object in flight.

Airship movement is done and calculated, using physics and kinematics equations much like in reality. It involves thrust generated from the engines, being translated into acceleration - with subsequent velocity gain and distance traveled. The airship will also take into account the drag force which opposes the thrust, constructed from each ship’s unique drag coefficient and velocity. Finally, terminal velocity comes into effect with the help of thrust, and the opposing drag force.

Airship movement is influenced by numerous factors in different fields ranging from various component’s HP, the use of pilot stamina or even external sources such as the Phobos Mine Launcher or the Minotaur Heavy Cannon.

Overview

The forces that apply on the airship dictate its movement patterns and behavior. Here is a brief overview of how they interact with each other to make up the ship’s movement.

Thrust and Acceleration

In order to move, an airship has to acquire velocity, which derives from acceleration. For a ship to accelerate, it has to generate thrust. Thrust is generated from the engines of a ship, and translates into acceleration in consideration of the ship’s mass. The direction of the acceleration is then determined by the position of the engine relative to the center of mass of the ship.

${a ~ = ~ F ~ / ~ m}$

While:

$a$ is the acceleration of the ship contributed from the engine.

$F$ is the thrust generated by the engine.

$m$ is the mass of the ship.

Ship Type	Mass, (t)	Thrust, (N)	Lift Force, (N)
Goldfish	150	600,000	487,500
Junker	140	840,000	770,000
Squid	95	874,000	380,000
Galleon	320	1,024,000	800,000
Spire	210	945,000	787,500
Pyramidion	200	700,000	600,000
Mobula	175	787,500	1,312,500
Shrike	82.5	660,000	206,250
Magnate	200	800,000	600,000
Judgement	290	959,900	959,900
Stormbreaker	95	902,500	285,000
Corsair	250	1,250,000	1,000,000
Crusader	180	675,000	450,000

Velocity and Drag

As the ship accelerates, it acquires velocity. Velocity is what makes the ship move in a certain direction and cover distances, however, it also generates a drag force. The drag force(more commonly referred to as air resistance), is a force generated from the ship bumping into air particles as it builds speed - the larger the speed of the ship, the larger the drag force is. The drag force acts as a counterpart to thrust, working in the opposite direction to it and thus, effectively causing a reduction of acceleration. In addition to the drag force being influenced by the speed of the ship, it is also determined by the drag coefficient of the ship.

${F_d ~ = ~ \frac{1}{2} ~ C_d ~ v^2}$

While:

$F_d$ is the drag force of the ship.

$C_{d}$ is the drag coefficient of the ship.

$v$ is the speed of the ship.

Drag increasing with velocity also means that acceleration of ships is not constant and the velocity of the ship in uniform acceleration is determined by

$v(t) = \sqrt{ \frac{a}{\frac{1}{2}C_d}} \tanh(t\sqrt{ \frac{1}{2}aC_d) }$

Drag Coefficients

Drag coefficients, are constants that derive from the shape and surface area of the object in motion. They influence the drag force of the ship, and can be also calculated by using the acceleration and terminal velocity of the ship.

${C_d ~ = ~ 2 a ~ / ~ v_t^2}$

While:

$C_{d}$ is the drag coefficient of the ship.

$a$ is the acceleration of the ship.

$v_t$ is the terminal velocity of the ship.

Ship Type	Longitudinal Drag Coefficient	Angular Drag Coefficient	Vertical Drag Coefficient
Goldfish	0.0045	0.1327	0.0225
Junker	0.0133	0.1164	0.0561
Squid	0.0083	0.0736	0.0277
Galleon	0.0049	0.1873	0.0173
Spire	0.0115	0.0749	0.026
Pyramidion	0.0061	0.1322	0.0208
Mobula	0.0088	0.0509	0.0519
Shrike	0.0111	0.1065	0.0173
Magnate	0.0069	0.0356	0.0234
Judgement	0.0084	0.0378	0.0229
Stormbreaker	0.0186	0.0552	0.0234
Corsair	0.0082	0.1111	0.0356
Crusader	0.0083	0.1076	0.0195

Terminal Velocity

As the acceleration of the ship is translated into more speed, the drag force gets larger due to increased speed, and the sum of forces working on the ship decreases in result.

${F_{res} ~ = ~ F ~ - ~ F_d}$

While:

$F_{res}$ is the sum of forces on the ship.

$F$ is the thrust generated by the engines.

$F_d$ is the drag force of the ship.

At the point at which the thrust will be equal to the drag force, the sum of forces working on the ship will be equal to 0. Meaning, that the speed of the ship does not have any acceleration to draw more speed from, and the ship has reached a final speed - terminal velocity.

${v_t = \sqrt{2 a ~ / ~ C_d}}$

While:

$v_t$ is the terminal velocity of the ship.

$a$ is the acceleration of the ship.

$C_{d}$ is the drag coefficient of the ship.

Example

An example of the forces at play on a Goldfish as it starts to accelerate from rest, until it reaches terminal velocity:

Click on the picture for a larger display.

Component HP Effects

Output

Apart from the pilot's involvement in controlling the ship's thrust intensity and direction using the helm and throttle, the engine output and balloon lift force are determined by the engines and balloon HP. They are multiplied by the percentage of HP of the component and decrease linearly in accordance to it.

With less thrust generated when a component loses HP, the drag caused by speed over-powers the thrust generated by the engine, resulting in negative acceleration. Negative acceleration will cause speed to decrease over time, until terminal velocity is reached once more.

The component HP percentage multiplier for engine thrust and balloon lift outputs, is applied on top of any other possible modifiers that come from piloting equipment, enhancement tools or stamina usage.

An example of the terminal velocity of a Goldfish traveling at top speed, as it slowly begins to lose engine HP up until a fixed point in time, until it reaches terminal velocity once more:

Click on the picture for a larger display.

Drag

In addition to the balloon HP affecting the lift it generates, it also affects the longitudinal drag modifier of the ship in an exponential manner:

${F_{d_\ modifier} ~ = ~ 0.3 ~ (HP ~ / ~ 912)^2 ~ - ~ 0.3}$

While:

$F_{d\ modifier}$ is the longitudinal drag modifier.

$HP$ is the balloon HP.

An example of the terminal velocity of a Goldfish traveling at top speed, as it slowly begins to lose balloon HP up until a fixed point in time, until it reaches terminal velocity once more:

Click on the picture for a larger display.

Helm Tools Effects

Kerosene, used as a speed modifying helm tool.

The use of helm tools by the pilot, modifies the ship's movement and behavior in various ways. It offers a wide range of tools, from speed enhancing tools and tools for accelerated turning, to tools that allow sudden vertical maneuvers and tools that reduce sinking speed with a popped balloon - helm tools are essential for optimized control over a pilot's ship, and over the engagement.

Helm tools achieve their purpose by temporarily modifying the ship's stats. Whether it be increased thrust or lift generation like with Kerosene or the Hydrogen Canister, or with drag modifying tools like Moonshine, Phoenix Claw or Drogue Chute.

Pilot Stamina Effects

The use of stamina by the pilot, modifies the ship's movement and behavior across all fields. Pilot stamina is a regenerative way of temporarily enhancing ship movement, for up to 4 seconds at a time.

Stamina works by modifying the engine thrust, and balloon lift outputs, with addition of longitudinal, vertical and angular drag modifications. It is important to note, that pilot stamina modifies the longitudinal and vertical drag by decreasing them, while it modifies the angular drag by increasing it. Due to the extensive effects of pilot stamina, it is usually used as a multi-purpose tool, or as an emergency measure.

External Effects

AJunker being hit by a Minotaur Heavy Cannon, getting pushed by the hit.

Aside from the pilot and crew involvement, there are external sources that could affect how the ship behave and move. They range from bumping into terrain and being pushed by wind, to weapons such as the Phobos Mine Launcher and Minotaur Heavy Cannon firing at the ship.

The Phobos Mine Launcher alongside the Minotaur Heavy Cannon, apply thrust to the ship at the hit position at the moment of impact - resulting in pushing the ship with every shot fired.

It is possible to abuse pilot stamina or helm tools that increase angular drag, such as Kerosene or Moonshine, to minimize the implication of the push on the ship. Notably, it is also possible to use tools that decrease angular drag at the time of the hit, such as Phoenix Claw to amplify the result of the push.