Showing posts with label physics. Show all posts
Showing posts with label physics. Show all posts

Friday, February 26, 2010

Endless Blue - Week 09 - 3D Combat

Physics



Danger From All Sides

Despite the tranquil vista of oceans of the Endless Blue setting, Elqua is a very dangerous place to simply live.  Without solid boundaries to prevent the encroachment of other creatures, every cubic inch of the seas can hide a quick death in the jaws of a predator or by the passive defenses of prey.  To eat or be eaten is the basic law of nature, and on Elqua it is as true as anywhere.  Eventually, inevitably, sooner or later everything has to fight for its life.

The depth that combat takes place uses the table-top as an anchor point, just as if you were playing a game in any other setting.  However, being surrounded in other games only means having eight opponents ringed around you.  In the Endless Blue campaign setting, where a character’s buoyancy keeps him floating at a controllable depth in the water, becoming surrounded means twenty-six opponents boxing a victim in from all directions – eight around, nine above, and nine below.  With that many possible combatants, keeping track of three dimensional position on a two dimensional plane becomes problematic.

3D Combat: Grid Abstraction

To address this, each model will need a special die.  At first glace it would appear to be a twenty-sided die, closer inspection of the faces reveals two sequences of 0-9 in two colors.  In the case of the examples here, the two colors are light blue and dark blue.  Each face signifies how many “cubes” (the 3D equivalent to D20’s “squares”) above or below the table-top the creature floats.  The lighter blue numbers represent altitudes higher than the models on the table-top, and darker blue means lower depths.  Each cube roughly equals 5 cubic feet of space.  This means a die set to 2 is approximately 10 feet above the table top, and 5 means twenty-five feet below the table-top.  When a creature moves, simply add (for ascending upward) or subtract (for sinking downward) the number of cubes moved from the die.  Becoming parallel with other creatures on the table-top is considered 0 (of either color).

So this:
2D Combat: Mer flanked by 3 Ceph


...becomes this:

3D Combat: Mer flanked by 3 Ceph

Remember that ascending any number of cubes greater than the creature's Constitution score results in a check for the pull.  Should a creature risk letting its natural buoyancy pull it upward in combat, attackers are allowed an attack of opportunity.  If an attacker is located directly above a victim, the victim cannot use its natural buoyancy to pull it out of combat.

Obviously, when a creature has moved more than forty-five feet (9 cubes) away from the table top in either direction, the die can no longer track their distance from the table-top.  Use the same methods as if the creature had passed off the edge of the table-top.  Opponents at these distances rarely matter in immediate combat due to the severely truncated ranges that weapons and spells can travel in the medium of water.
Not all creatures fit easily into a single cube.  For a rough estimate, creatures Small or Medium will normally take up one cube.  Creatures of Tiny, Diminutive, and Fine sizes take up less than a single cube, and multiples of these creatures can occupy the same cube.  Since creatures these sizes have no reach, they must enter the cube a victim occupies to attack, and there qualify as a participant of a flank in any direction.

Large and larger creatures will take up cubes dependant on their orientation.  For example, a piscean of Huge size will occupy a number of vertical cubes, where as a Gargantuan serpent will fill a number of horizontal cubes.  Keep in mind that some creatures, such as the above serpent, may very likely be able to twist up or below, and even bend back on themselves, filling cubes on both vertical and horizontal axes.  In these cases, multiple dice (for each cube of the creature’s length) are used to determine where each segment of the creature is located, their order determined by die color or size.  This is called a creature's orientation, and in an essentially gravity-less environment such as underwater "up" is just an arbitrary direction.

Flanking Bigger Creatures

Flanking rules are still the same as in D20, but now can be inflicted in three dimensions.  The character and the ally must still be directly opposite each other with at least one cube of the victim between them.  There may be multiple cubes of the victim between them, but the line of cubes must be in a straight line from the creature to the ally.  If you can draw an imaginary line between the center of the cube the creature to the center of the ally, and that line crosses the line between the center of the first cube and the center of the last cube any of the cubes the victim occupies, the flank is legal.

3D Combat: Flanking Larger Creatures

The blue line overlaid on the serpent is the line from the center of the first cube it occupies to the center of the last cube it is in.  The direct line between an attacker and an ally must cross this axis to qualify as a flank.

Red lines are invalid flanks; green lines are valid.  In the above example:
Ceph 1 flanks the serpent with Ceph 3 and 4.
Ceph 2 flanks the serpent with Ceph 3 but not Ceph 4.
Ceph 3 flanks the serpent with Ceph 1 and 2.
Ceph 4 flanks the serpent with Ceph 1 but not Ceph 2.
None of the Ceph flank with the Mer.

Note: A sufficiently long creature that occupies enough cubes to wrap around a victim (5 or more) can flank with itself if it possess a natural weapon(s) on both ends (a bite attack and a tail slam, for example).  In these cases, the intervening sections (cubes 2 through 4) qualify as an ally for any other attacker.

There are creatures on the face of Elqua whose size dwarfs even the most Gargantuan of creatures that ruled over other worlds.  These Immense and Tremendous creatures are simply too large to be flanked by any creatures, even others of their own kind.  To foolishly attack one of these beasts is as effective as striking the ground or swinging at a mountain.  They are like forces of nature, and natives of the Endless Blue setting pray they never cross paths with these legendary threats.

Friday, February 19, 2010

Endless Blue - Week 08 - Buoyancy


Physics


Buoyancy


Every child knows things either sink or float, but day-to-day existence in the oceans of Elqua requires a character to be able to maintain his level in the water.  Bedding down on ocean floor is of little use if when you sleep during the night you wake up to find you’ve risen to the surface as you slumbered.  Just as a hot-air balloon can maintain its altitude in the atmosphere, aquatic creatures can do much the same under water.


A body normally displaces water, and that water presses inward trying to refill that space. That produces an upward pressure that pushes a body to the surface and makes it float.  This is buoyancy.  Increasing a body’s buoyancy results in it rising to the surface, just as decreasing it causes the same body to sink.  The further down in the depths of the ocean you go, the greater the forces push a less dense body upward, so the greater effort needs to be spent to overcome buoyancy.  A body’s floating point is the depth at which it’s no longer floats upward or sinks downward due to autonomic processes in the body.  In the Endless Blue setting, this point is usually categorized by whatever zone of water constitutes the creature native habitat – the Shore, the Shoals, or the Shelf.


A creature’s buoyancy does not prevent it from rising higher or diving deeper, just that it takes active effort swimming to overcome the natural inclination to return to their neutral floating point.  It is a move-equivalent action to maintain attitude at a water level different than the character’s buoyancy point.

Below the Waves
Buoyancy is achieved in Pisceans with a several redundant systems.  As a rule of thumb, the primary means is how aquatic life forms evolved their morphology to posses a lesser density than the water surround them, thus producing an intrinsic higher buoyancy to aid their locomotion and survival under water.  As a result, a dead piscean will automatically rise to the surface unless it is weighted down (several burial customs involve wrapping a corpse in their belongings or even rocks and seaweed to cause it to sink down).  Conversely, terrestrial and avian life have a lower buoyancy, and so will sink toward the ocean floor when killed – though they rarely reach significant depths before predators and scavengers devour the sinking meal.
The second process is via an organ called the swim bladder, which functions by diffusing or infusing gasses from oils and lipids in the expandable sac.  Because these infused oils are not compressible from ocean pressure, the swim bladder helps regulate the buoyancy by exuding more gases (which are compressible) to sink and reabsorb them to return to their neutral buoyancy point.  Creatures able to adjust their own swim bladders consciously may do so once per round for free as part of a move action instead of at the normal cost of their movement. This can only be accomplished when the creature is either unencumbered or lightly encumbered.
The final method is by the pelvic fins located at the socket-like notch called the acetabulum on each side of the pelvic bone, like the hips of terrestrial creature.  These webbed fins act like the wings of a bird, inducing dynamic lift.  Flexing of the spines changes the shape of the fins, allowing the creature to travel deeper.

Not all creatures are built for all depths.  While the Ceph can survive at any level, many creatures from the Shore would be crushed instantly in the dark trenches of the Shelf, just as a jellyfish native to the Shelf that has lived all it’s existence under the extreme pressures of the on the ocean floor would rupture outward from its internal fluids pressing outward and die were it marooned along the Shore.
A creature can voluntarily release its buoyancy to neutral, essentially becoming weightless.  This results in immediate movement as physics and gravity try to push the individual to the surface.  These creatures move their full movement (they cannot move less) directly upward until they readjust their buoyancy (by either a move action or for free as part of one) and cease their ascent.  They may then move normally.


The danger with this movement is a condition called “the pull”, or decompression sickness.  Early Elquans believed the pull to be a curse by the evil aberrations above the waves to claim more souls.  Usually the victim would die and the body’s natural buoyancy would cause it to rise to the surface (where it would become fodder for predators0 instead of sinking all the fathoms towards union with the gods.  Myth aside, every body is under pressure in the depths of Elqua’s oceans, and as a result of this pressure certain gasses are harmlessly dissolved and dispersed throughout their body’s fluids.  As an individual rises, the pressure eases and the dispersed elements coagulate back into gases.  Rising too quickly results in the gasses forming more quickly than the body’s normal means of eliminating them.

The Pull


Individuals can always rise a number of feet per round equal to their Constitution score without a risk of incurring the pull.  Moving greater than that requires a Fortitude save each round of moving so to avoid becoming incapacitated and helpless.  The DC for this is a base save of 15 for the first round, with and cumulative penalty of +2 for every successive round spent rising via positive buoyancy.  If a creature moves more than its Fortitude score in feet, it takes an additional penalty of +2 when moving its full rate, or a +5 if performing more than a single move action.


Rise up to Fortitude score in feet                           No penalty
Move over Fortitude in a single move                    +2
Move over Fortitude in a full round action             +5
Each round rising beyond Fortitude score             +2 cumulative


Failing such a Fortitude save results in immediate spasms and wracking pain.  The victim of the pull becomes disabled and begins taking 1 point of temporary Constitution damage per round he continues to rise.  Should the creature’s buoyancy become neutral and he stops rising, the Constitution damage stops accruing.  The Constitution damage can be restored at a rate of 1 point per day spent at a lower depth, and the victim is allowed a new Fortitude save each of those days at a flat DC 15 to remove the disabled status.


Above the Surface


For native creatures, survival above the life-giving waves of Elqua is not unlike survival underwater for air-breathers.  An aquatic creature essentially holds their breath on the surface to avoid asphyxiation.  The muscles of the gill-slits press the flap down and seal the organ so gravity cannot cause the water to spill out, preventing speech but keeping water already in the lungs around the oxygen-extracting gills.
A creature can hold their breath for a number of rounds equal to twice their Constitution score.  After that period expires, the creature must make a Constitution check (DC 10) to subsume their semi-autonomic breathing reflex, with a cumulative +1 each subsequent round.  Failure is a little more torturous for an aquatic than a terrestrial, resulting instead with the creature passing out, becoming helpless, and automatically taking 1 point of permanent ability score damage to all abilities (Constitution, Strength, Dexterity, Intelligence, Wisdom, and Charisma) each round until they are submerged under water again.  Should any one of those abilities reach 0 before re-submergence happens, the creature dies.