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Power Stunts: Mass / Velocity Changes

- Dan Steiner

Many powers allow characters to alter their masses, either directly or as a consequence of their power. The rules of HU2 make no mention of the consequences of changing a character's mass while they are in motion, which would have very significant effects. My assumption during these changes:

These assumptions are easily confirmed using the typical, zero velocity case. A character with Alter Physical Structure: Metal uses his power to change into a more massive form while standing still. His momentum is unchanged (from zero), but he gains a significant amount of gravitational potential energy. This energy must have come from a biological reserve of some sort, along with the energy used to form the additional mass. the bare minimum energy needed to increae a character's mass without external material is huge ( E = mc2 ): 200 lbs of increased weight corresponds to 2.26x1012 kW-hr. As a comparison, the power usage in my house is typically less than 2500 kW-hr in a given month, meaning it would take the monthly power consumption of about 900 million homes to produce 200 lbs worth of mass. This assumes that no power is lost during the process, a very poor assumption. My point is that the energies involved here are immense; producing a little bit of kinetic energy is small change when you consider the big picture.

The end result is that when a character changes their mass while in motion there will be corresponding change in their velocity, determined by the Conservation of Momentum. In mathematical terms:

pinitial = minit vinit = pfinal = mfin vfin
vfin = ( minit / mfin ) vinit

If the character increases his mass by a factor of three, his velocity will decrease by a factor of three. If he decreases his mass by a factor of five, his velocity will increase by a factor of five. Characters who need a boost of speed or need to slow down quickly will find this change in velocity particularly useful. Characters could use this "trick" to jump higher, fly faster, or brake more quickly than before.

To put this effect into game terms, we will also need a relationship between a character's motion and the damage inflicted by various attacks. Damage done by the impact of an object should be proportional to the amount of kinetic energy tranfered to the target; the more kinetic energy a character has, the more damage he can do. Using the results above, we see that when a character changes his mass his kinetic energy changes as follows:

Kinitial = 1/2 minit vinit2
Kfinal = 1/2 mfin vfin2 = 1/2 minit2 vinit2 / mfin
Kfinal = Kinitial ( minit / mfin )

Damagefinal = Damageinitial ( minit / mfin )

The kinetic energy of a character who increases his mass will be decreased, meaning he will cause less damage to an object upon impact and will have less energy to get rid of if he wants to slow down. The reverse is true for characters that decrease their mass while in motion. It seems counterintuitive that a character causes more damage by becoming lighter, but the math presented here is pretty straightforward. Kinetic energy is proportional to the square of an object's velocity, but is only directly proportional to a character's mass.

Not all flying attacks involve the complete loss of an attacker's kinetic energy. The above calculation for impact damage is appropriate if the character charges headlong into a large unmoving object with no regard for his own safety, but this will rarely happen in game contexts. Characters with their own wellbeing in mind will more often use the speed to rapidly approach and attack a victim, applying the increased damage bonus. When using this stunt to increase velocity it seems more appropriate to use an increased damage bonus, adjusted below in the stunt details, than to use the straightforward damage multiplier. The attacking character will be somewhat out of control, and will always take some damage himself, but at least the victim of the attack suffers increased damage as well.

Specific Power Stunts using Changes in Mass while in Motion

    1. Speed Boost: Characters in motion, through whatever method they wish, will see their velocity increase dramatically if they suddenly decrease their mass. This boost will be short lived as the character is slowed down by the greatly increased air friction, but for a short time they will be travelling a great deal faster than their usual limit. As stated above, the character's speed increase will be proportional to their decrease in mass.

Duration: Air friction will quickly slow them down, likely within five-ten seconds per 100% speed increase. Higher velocity means that the character experiences greater air friction and slows down more quickly. Best judgement of the game master is required....
Attacks per Melee: This stunt counts as one hand to hand attack, but the character can't perform it again until he changes back to a massive state and gets back up to a high speed.
Limitations: Characters that perform this stunt while running will need to roll to maintain their balance once per melee for every 100% increase in speed they experience. Unless characters have a skill lending a superior sense of balance the base percentage is 20% +2% per level, plus their PP attribute divided by two.
Collateral Damage: Players with powers that permit extreme reductions in mass could easily break the sound barrier. Keep in mind that the sonic boom resulting from extreme acceleration is incredibly loud, and could cause damage to people and objects within close range.
Damage to Character: The accelerations involved could cause damage to the now lower mass (more vulnerable) character. Depending on the size of the acceleration and the state of the character this damage could be severe. The sheer number of possible situations require GMs to use their best judgement, with possible damage ranging from slight headaches to severe whiplash and spinal damage. Loss of consciousness is also a possibility, which has it's own consequences...

    2. Speed Reduction: Your character is about to impact an object and needs to slow down quickly; if they increase their mass they will decrease their velocity proportionally. If a character is about to strike a solid object and wishes to reduce their own impact damage this effect will also decrease their kinetic energy, and thus will reduce the damage they sustain on impact, as calculated above. Reducing your mass, however, will have the opposite effect, and you crash even harder.

Duration: Instant, unless character changes back into their less massive state before slowing down further.
Attacks per Melee: This stunt counts as one hand to hand attack, but the character can't perform it again until he changes back to a less massive state (which would increase his velocity).
Impact Damage Reduction: Treat this stunt like a Roll with Punch, Fall, or Impact when determining combat rolls, but the character's Roll bonus does not apply. Instead, the character gets a bonus of +1 at first experience level, with an additional +1 at every other additional level. Damage sustained by character (and inflicted on target) is reduced by the proportion of the character's increase in mass.

    3. Damage Boost: A character who reduces their mass while in motion will temporarily increase their kinetic energy, and thus the amount of damage they can cause upon impact with an object as calculated above. Keep in mind that the character also increases the damage done to themselves in the following manner:

The standard damage bonus due to speed is +4 per 20 mph. Calculate the total damage bonus appropriate for the character's attacking speed. Since the character is not in complete control at these "artificially" increased speeds, he then must roll percentile dice. After applying the appropriate modifiers (below) to the percentile roll, the character inflicts that percent of the damage bonus to his target. The remainder of the damage bonus is divided by two and applied to the attacker.

Duration: Instant
Attacks per Melee: This stunt counts as one hand to hand attack; in practice it turns a one attack action into a two attack action, a two attack action into a three attack action, and so on. The character can't perform it again until he changes back to a massive state and gets back up to speed.
Impact Damage Bonus: Treat this stunt like a Pull Punch when determining combat rolls, but the character's Pull bonus does not apply. Instead, the character gets a bonus of +1 at first experience level, with an additional +1 at every other additional level. A successful roll means that the character managed to change his mass and velocity at the appropriate moment. The roll to strike is independent of this "Pull Punch" roll; if the character fails this roll but succeeds in rolling to strike he will not be able to use the increased damage bonus but will strike the object as normal.
The attacker rolls percentile dice (modified as above) and applies that percentage of the speed induced damage bonus to his victim.
Damage to Attacker: The remaining amount of damage bonus is divided in half and is applied to the attacking character.
Penalties: Characters that undergo extreme accelerations will be disoriented, buffeted by incredible air friction, and will need lightning fast reflexes in order to be effective. For each increase of 100% velocity the character will suffer a penalty of -1 on all combat rolls, to a maximum penalty of -15.

Example: Shrapnel, a seventh level character with both Alter Physical Structure: Metal and Flight: Wingless, sees an old enemy and increases his flight velocity from 200 mph by transforming from his metal state to his normal human state (four times less massive). Pinion, Shrapnel's target, weighs about 300 lbs, while Shrapnel weighs only 200 lbs in his fleshy state. Shrapnel is now flying at 800 mph, giving a total damage bonus of ( 800mph * 4 / 20 mph = ) 160 points and he attempts to strike with a 2D6 punch. He succeeds in both his "Pull Punch" roll (due in part to his +4 bonus) and his strike roll. As for damage: Rolling the percentile dice produces a raw roll of 58%. Modifying the roll as above, the final percentile is ( 58% + 35% - 20% + 10% - 15% = ) 68%. The damage done to Pinion is 2D6 + ( 68% * 160 = 108.8 = ) 109 points. Unfortunately Shrapnel takes ( 32% * 160 / 2 = 25.6 ) = 26 points of damage himself.

    4. Super-Jumping: Characters who wish to leap (not-so) tall buildings will find that if they lower their mass just after they jump they will increase the kinetic energy the jump has given them. Neglecting air friction, this translates into a direct jumping boost. A character with twice as much kinetic energy can jump twice as high as usual! A character with Alter Physical Structure: Metal that can usually jump three feet off of the ground will find that they can leap up to twelve feet off of the ground if they time their mass change correctly.

Duration: Instant
Attacks per Melee: This stunt makes the jump into an attack that costs two attacks per melee. The character can't perform it again until he changes back to a massive state.
Height Boost: Timing is everything with this stunt; the character rolls percentile dice, and gets that percentage of their height boost. Ex: If the character decreases their mass by a factor of two, and rolls a 35%, they increase the height of their jump by ( 2 x 35% = ) 70% of normal. The character gets an additional 4% per level for these rolls; The percentage roll can never total more than 100% despite bonuses. Conservation of Energy can only be stretched so far....


Combining Flight and Shrink

Since the Flight powers give every character the same maximum speed, regardless of weight, it seems that the amount of thrust you can exert is roughly proportional to your mass. This means that the choice with Shrink of whether to keep your mass constant or not is really important. It might help to look at my Flight School before  reading this, even though it is toned down. The equation that determines your max speed is:

(Thrust)2 = (Weight)2 + (C Vmax2)2,

where C is an air friction constant. Since Thrust and Weight are proportional to mass, this will be easier if we group them together:

(C Vmax2)2 = (Weight)2 - (Thrust)2

If you reduce your height by a factor of 1/A (1/12, 1/100, 1/1000, etc), your mass typically decreases by a factor of 1/A3, and C will be reduced by a factor of 1/A2. If you do a little algebra:

1/A4 (C Vmax-shrunk2)2 = 1/A6 [(Weight)2 - (Thrust)2]
1/A4 (C Vmax-shrunk2)2 = 1/A6 [(C Vmax2)2]
(C Vmax-shrunk2) = 1/A (C Vmax2)
Vmax-shrunk = 1/A1/2 Vmax

So, if you reduce your height by a factor of 100 and your mass goes with (a factor of 1003 = 1 million!) your maximum sustainable speed is reduced by a factor of 10. This means you'll have momentum reduced by a factor of 10 million! Kinetic energy by a factor of 100 million! Very little damage, even if you do have good penetration do to 1/10,000 the surface area. Damage probably scales with kinetic energy and surface area, which means it will go down by a factor of 10,000.

On the other hand, if you keep your mass constant when shrinking the equations for max velocity look like:

1/A4 (C Vmax-shrunk2)2 = [(Weight)2 - (Thrust)2]
1/A4 (C Vmax-shrunk2)2 = [(C Vmax2)2]
(C Vmax-shrunk2) = A2 (C Vmax2)
Vmax-shrunk = A Vmax

Reducing you size by a factor of 100 without reducing your mass will increase your maximum speed by a factor of 100! I'm positive that my simple models for C aren't accurate for Sonic or super-Sonic speeds, but it's still a lot! Your momentum goes up by a factor of 100, kinetic energy by a factor of 10,000, which means your damage will go up by a factor of 100 million! Of course, Jeffar's point is valid and you'd probably just punch a half-centimeter hole through whatever you hit.... The down side is that this much damage will probably hurt even an invulnerable character, if you hit something tough enough.

Remember that the cases above apply to maximum sustainable speed. If you "magically" reduce your mass in-flight your velocity will increase to conserve momentum.... This means Shrinking to 1/100 size, reducing your mass by a factor of 1003 = 1 million will instantly increase your speed by a factor of 1 million! This increased speed won't be sustainable, and unless you're invulnerable will probably kill you (or at least send you into orbit), but it is pretty impressive. The math uses conservation of momentum:

Pnormal = Pshrunk
Mnormal Vnormal = Mshrunk Vshrunk
Vshrunk = ( Mnormal / Mshrunk ) Vnormal
Vshrunk = A3 Vnormal

Kinetic energy goes up by a factor of A3, which means your damage will go up by a factor of A5. For A=100 that's 10 billion! Obviously, this will be limited by penetration effects as well.

So to sum up:

Shrinking by a factor of 1/A while leaving your mass constant will increase your maximum speed by a factor of A, and your damage (technically) by a factor of A4.

Shrinking by a factor of 1/A accompanied by a reduced mass and constant density will decrease your maximum sustainable speed by a factor of the square root of A. The damage you inflict will be insignificant because your kinetic energy is reduced by a factor of A4. On the other hand, you have access to a power stunt that allows you to temporarily increase your velocity by a factor of A3 and your damage by A5.