Trajectory,
in regards to archery, is defined as the curve of an arrow’s flight
path between the bow and its target. It takes an arrow a certain amount
of time to reach its target. The flatter and straighter an arrow’s
flight path is, the faster it will hit its mark. However, this also
reduces range as a missile with a flat trajectory descends more quickly.
To acquire good distance, one has to give the arrow a more elliptical
trajectory; more arc, more range. Since trajectory is directly related
to arrow speed, the slower an arrows’ speed per second, the more
curved its flight path must be to hit a far off mark. Inversely, the
higher an arrow’s velocity per second, the less trajectory required
for it to strike its target.
Straight shots with a bow and arrow are simple enough for good aim is
all one really needs. Yet trajectory can be a tricky thing, and miscalculating
the trajectory necessary to achieve a particular range will result in
a miss. A good archer, however, can usually visualize the trajectory
needed to reach a mark. Though some archers rely on bow sights or visual
aids, the experienced ones and instinctive shooters can “feel”
and eye the proper trajectory almost effortlessly. Still, to simulate
some of the thought processes required in calculating curvaceous trajectories,
a GM could impose the rule that if the target is beyond the maximum
effective range of the bow, then the archer must spend one action mentally
considering the much altered arc of his arrow before he fires it.
For
simplicity’s sake, I have resolved that most arrows travel at
a default speed of roughly 225 feet per second, barring external influences.
Assuming a melee action is three seconds, then the arrow can travel
675 feet per action. If the arrow is intended to strike a target beyond
that range, then it will take two actions for the arrow to complete
its flight. Keep in mind that figuring out trajectory and flight time
with a bow and arrow is much more complicated than this. I’ve
highly simplified how it works for playability purposes.
Of course, there are many factors besides trajectory that affect the
flight time of an arrow, such as wind velocity, arrow weight, fletch
length, draw length draw weight, etc. Yet for simplicity’s sake,
I’ve ignored these things and focused directly on flight path.
However, if you want a more advanced method of determining arrow speed,
at least in relation to draw weight, increase arrow velocity by 7 feet
per second for every 20 lbs. of draw weight over 80 lbs. For every 20
lbs. of draw weight under 60 lbs., the arrow goes 7 feet slower per
second. This means, for example, that if a melee action is roughly 3
second long then a bow with a 100 lbs. draw weight could fire an arrow
21 feet farther per action than a 60-80 lbs. draw weight bow. If one
of the archer’s Archery Rate of Fire actions is equivalent to
two melee actions, then that means the arrow travels a total of 42 feet
farther.
Having short fletches (1.25 to 3.0 inches) as opposed to long ones (3.1
to 6.0 inches) decreases the arrows total weight and increases velocity.
Arrows with short fletches go 5 feet faster per second.
For
every one inch of the archer’s draw length beyond 28 inches, the
arrow travels 7 feet faster per second. For every one inch below 28
inches, the arrow goes 7 feet slower per second.
Hard
and moderately hard wooden arrows are the “grainiest” and
heaviest types of arrow wood. Arrows made of these materials fly at
the default 225 feet per second speed. However, soft wood arrows are
lighter, which means they can fly 25 feet faster per second than their
counterparts.
Fast Flight bowstrings increase the velocity of the arrow which reduces
trajectory requirements. This in turn shortens the arrow’s flight
time. The missile will only take one action to reach any target within
1,500 feet.
There
are other variables to consider, such as the length of the arrow, shaftment
and the weight of the arrowhead. As stated in the Arrow Construction
section, an arrow must be within a certain length range in relation
to the bow’s length in order to achieve optimal performance. For
each inch below the minimum recommended arrow length in relation to
bow size (see corresponding chart in Arrow Construction section) the
arrow’s velocity increases by 50 feet per second. However, using
arrows that are too short for one’s bow has obvious disadvantages
as explained in that section. War arrows suffer a reduction in speed
of about 30-50 feet per second based on diameter.
Arrowhead weight and shaftment possess a huge range of possibilities.
GMs will have to use their discretion since these numbers are slightly
arbitrary. Larger arrowheads like broad-tipped, bifurcated and cage
fire, as well as some blunt and whistling heads will weigh the most
and invariably cause a loss in speed ranging from 5-50 feet per second.
Arrowhead design also slows down an arrow; the more blades, the slower
(5-20 on top of the arrowhead type penalties). Using metal and stone
as the arrowhead material again increases weight and can result in a
loss of 5-15 feet per second depending on the type of metal or stone.
In regards to shaft material, bone and horn are generally no heavier
than most kinds of moderately hard wood. Metal, if used for shaftment,
is probably alchemically enhanced for lightness or some sort of light
weight alloy equal to hard or soft wood. Otherwise, it would not be
practical for use.
These
rules can be a little difficult to institute into one’s game because
of the ambiguity of a melee action’s length in the Palladium system.
It generally says that a melee action is 1-3 seconds but this is somewhat
subjective. Consequently, GMs will have to use their best judgment when
applying these rules. If your not afraid to do a some math or break
out a calculator (something I’ve found is very handy for my games),
then divide 15 seconds (a full melee round) by the character’s
actions per round and figure the result into the character’s Rate
of Fire. However, they also give archers more incentive to acquire bows
with higher draw weights or arrows with range modifiers.
Where
as maximum base range is the longest range possible with a particular
bow before any bow modifiers, maximum range is the longest possible
range after bow modifiers. MER is the furthest and most realistic distance
at which one could reasonably expect to hit a mark. For most short bows
and longbows, the maximum effective range is 270 feet before modifiers.
However, this does not include range modifiers provided by arrows. Arrow
range modifiers are applied after bow range modifiers (and maximum range)
have been determined.
As
the maximum base range of the bow is increased through design elements
and materials, make sure to increase the MER proportionately. For example,
if after all modifiers have been calculated the bow’s base range
has increased by 5%, then raise the maximum effective range 5% as well
(270 feet becomes 283.5 feet).
Also, the further an arrow must fly to strike its target the more its
velocity decreases and, consequently, the less damage it will inflict.
Any arrow fired within a bow’s maximum effective range suffers
no ill effects to damage or accuracy. However, for every 100 feet an
arrow travels beyond the bow’s MER, it will incur a -1 to strike
and -2 to damage. I am aware that these penalties should probably be
more severe when firing at targets a great distance away, but I don’t
wish to handicap archers too badly. Alter these modifiers as you see
fit.
To
showcase the above rule, let’s say one has a 1.9m self long bow
of straight limb curvature with a maximum effective range of 270 feet
and a maximum range of 825 feet. It has an 80 lbs. draw weight and is
of standard human make. The arrow being fired has a 30 inch alder wood,
barrel-tapered shaft of standard diameter (not a war arrow). It has
an alder wood target arrowhead, three parabolic short fletches and is
of standard human make as well. Due to its specific features, the arrow
receives a +70 feet to its range and a +1 damage (total damage from
the combined base damages of the bow and arrow is 3D6+1). Though the
long bow’s maximum range is 825 feet, the arrow can actually fly
895 feet.
Now let’s say that one is attempting to strike a target roughly
600 feet away. Since the maximum effective range is only 270 feet, the
arrow will have to travel around 330 feet passed the effective range
to hit. That means the attack will incur a -3 to strike and a -6 to
damage. If the attack is successful but the damage roll is low enough
(6 or lower), then the arrow harmlessly bounces off its target. However,
keep in mind that such ranged attacks are often hard to detect and may
count as a surprise attack on the archer’s part.
If this rule is too cumbersome to work into your game or you think its
too much math, just disregard it.