 # 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:

• Should super abilities give players a maximum thrust or velocity?
• Sample of additions to character sheet (for characters with flight)

### 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 = Ẅ 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 / 360ẃ ) 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