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Flight School


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.

What do we know?

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:


Review of the Final Results

- 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:

Ffriction = d A C v2 = cfriction v2 = ( 0.08125 kg/m ) v2

- 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, vmax:

Fthrust = [ ( mcharacter g )2 + ( cfriction vmax2 )2 ]

- Using that value of thrust, the maximum velocity your character can attain while carrying additional weight:

vmax = [ [ Fthrust2 - ( ( mcharacter + madditional ) g )2 ] / cfriction ]

- For vertical acceleration the maximum velocity of the character, vmax-direction, depends on the direction his thrust is aimed (not necesarily the direction he is travelling). When accelerating upwards or downwards::

vmax-up = [ ( Fthrust - mtotal g ) / cfriction ]
vmax-down = [ ( Fthrust + mtotal g ) / cfriction ]

- 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 vmax-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):

rturn = mtotal eN / cfriction

tturn = 2 pi ( a / 360 ) mtotal eN / ( cfriction v )

- Characters can accelerate/decelerate between standing still and a given fraction of their maximum velocity (either horizontal or vertical) in time:

taccel = mtotal fN / ( cfriction vmax-direction )
tdecel = mtotal sN / ( cfriction vmax-direction )

- Sample values for the N-dependent coefficients are as follows (where f stands for "faster" and s stands for "slower"):

N
0.99
0.90
0.75
0.50
0.25
0.10
0.05
0.01

eN
4.9374
1.3812
0.68033
0.25820
0.06262
0.01000
0.00250
0.00010

fN
2.6467
1.4722
0.97296
0.54931
0.25541
0.10034
0.05004
0.01000

sN
0.7804
0.7328
0.6435
0.4636
0.2450
0.09967
0.04996
0.01000