The following calculations are an attempt to describe the science of flight without destroying the fiction of super powered beings. The end result: science fiction rather than random rules. If anything I present here is above your head (physics- and/or math-wise) you may need to consult a physics textbook. A basic familiarity with one- and two-dimensional motion is required to solve these problems, as is some knowledge of basic differential equations.
Looking at the descriptions of the Flight powers in HU2 I find that a lot of info is missing, and some is incorrect. In the end, I'm only going to need one number from the HU rules: the maximum flight speed of a given power. With this value I can determine the following useful details:
There are several "stunts" one can perform while in flight which will increase your character's maximum velocity and damage potential:
After obtaining these results several possible applications and/or changes for the standard Palladium system present themselves:
- Frictional forces acting on a character depend on the density of air, as well as that character's cross-sectional area, shape, and velocity. A decent assumption for normal sized humanoid characters is that:
F_{friction} = ½ d A C v^{2} = c_{friction} v^{2} = ( 0.08125 kg/m ) v^{2}
- The maximum thrust a character can exert, equal to the amount of weight (including his own) that he can fly with is related to the character's maximum horizontal velocity, v_{max}:
F_{thrust }= [ ( m_{character} g )^{2} + ( c_{friction} v_{max}^{2} )^{2} ]^{½}
- Using that value of thrust, the maximum velocity your character can attain while carrying additional weight:
v_{max} = [ [ F_{thrust}^{2} - ( ( m_{character }+ m_{additional} )_{ }g )^{2} ]^{½} / c_{friction} ]^{½}
- For vertical acceleration the maximum velocity of the character, v_{max-direction}, depends on the direction his thrust is aimed (not necesarily the direction he is travelling). When accelerating upwards or downwards::
v_{max-up} = [ ( F_{thrust} - m_{total} g ) / c_{friction}
]^{½}
v_{max-down} = [ ( F_{thrust}
+ m_{total} g ) / c_{friction}
]^{½}
- The velocity of a character at any given time can be expressed as a fraction of his maximum possible velocity in a given direction:
v = N v_{max-direction}
- Flying characters can make horizontal turns (vertical turns are a little more complicated) on circular arcs of angle a and minimum radius (that take minimum time):
r_{turn} = m_{total} e_{N} / c_{friction}
t_{turn} = 2 pi ( a / 360º ) m_{total} e_{N} / ( c_{friction} v )
- Characters can accelerate/decelerate between standing still and a given fraction of their maximum velocity (either horizontal or vertical) in time:
t_{accel} = m_{total} f_{N}
/ ( c_{friction} v_{max-direction}
)
t_{decel} = m_{total}
s_{N} / ( c_{friction}
v_{max-direction} )
- Sample values for the N-dependent coefficients are as follows (where f stands for "faster" and s stands for "slower"):
N_{
} |
e_{N} |
f_{N} |
s_{N} |