[Torg] Jumping in Torg

[Benjmain Grant]

OK, you got me thinking, so be afraid - very afraid.  (grin)

This is the situation in physics as I understand it when it comes to
projectiles:

There are two possible ways to launch a projectile - using a ramp and using
a booster.  A ramp converts a forward velocity to a velocity that is part
forward and part upward - like when a stuntman jumps his motorcycle over a
line of cars, he uses a ramp to do it.

On the other hand, when one is (for example) running on a flat surface and
one jumps a gap, one is maintaining a constant rate of speed horizontally
and merely adding a second vertical vector.  To more clearly envision this,
imagine a rocket with two nozzles - one behind it for constant forward
motion, and one underneath it for a pulse tp push it briefly upwards.

Either way, the projectile winds up with a vector that can be separated into
its vertical and horizontal components.  As strange as it may sound, in
terms of determining the horizontal distance a projectile can cover before
falling back to earth, the vertical component of the projectile's velocity
is only useful to determine how much "hang time" the projectile has - how
long the projectile remains in the air.  This hang time is purely a function
of the vertical velocity - the horizontal component does not affect it.

Once the hang time is determined, than that plus the horizontal speed
absolutely determine the horizontal distance covered.

For example, let's imagine a car travelling along at 100 meters/sec.  It has
a rocket rigged underneath it that will when triggered fire a burst that
will launch the car of the ground vertically at a speed of 30 m/s.  How far
will the car travel (ignoring air resistance) horizontally before it hits
the ground again?

To figure out the car's hang time, we can ignore its horizontal speed for
now and focus on its vertical speed - which starts at 30 m/s.  We also know
that the force of earth's gravity is about 10 meters/second per second.
(It's slightly less, but I am going to use 10 for this conversation, it's
close enough for our purposes.)

One question we could ask ourselves is if we drop an object, how much time
does it have to spend falling for it to be going 30 m/s?  Well, at second
zero, the drop object has just been released and has zero speed.  At second
one, it is traveling 10 m/s.  At second two it is travelling 20 m/s, and so
on - every second it is going 10 m/s faster than the previous second.  This
means that after 3 seconds a dropped object is travelling 30 m/s.

Well since our car was launched upward at 30 m/s, this means that after 3
seconds the downward "speed" of the car will be equal to it starting upward
"speed", which means that after 3 seconds, this car has reached it's max
height of the ground and will shortly begin its descent back to earth.
Since the car took 3 second to get from the earth to its max height, it will
take another 3 seconds to come down.  That's 6 seconds of "hang time".

We know that the car is moving horizontally forward at 100 m/s, and that its
hang time was 6 seconds.  A simple bit of math reveals that the car
travelled 600 meters forward during that time, and therefore would have
cleared a 600 meter gap.

Using the same logic, a human being on a moving platform travelling at 100
m/s who jumps at the last possible moment would clear a horizontal distance
of his normal vertical hang time multiplied by his current horizontal speed.

Now maybe vertical jump height (and therefore hang time) is a function of
Strength more than Speed.  However, I personally can create a hang time of
at least one second when jumping upward from a standing position.  Therefore
if I am being moved horizontal forward by some force such as a moving
platform (or a super speed power), even if my vertical jumping (and
therefore hang time) is unaffected, the faster I go horizontally the farther
I travel during my one second of hang time.

So  even if the super speedster can only jump upward vertically normally
from a standing start, even if he can only get the same one second of hang
time as I can get in real life, if he can travel at 3350 m/s then when he
does jump, being in the air for one second gains him the ability to cross a
3350 meter gap.

Now if he has access to a ramp, even if he is a crappy jumper, he can
increase his hang time and I will tell you why.

A ramp will convert purely horizontal speed to part vertical and part
horizontal.  This increases his hang time, but decreases the amount of speed
he gets to apply to the hang time period.  However, the increase to his hang
time is not because he's a good jumper - jumping has nothing to do with it.
He simply is moving at a great speed, and converting via a ramp some of that
speed into vertical speed, allowing him to spend more time in the air.

So this is my conclusion.  If super speedsters were to exist in real life
and be no worse than dead weights under the same conditions of velocity,
then they wouldn't necessarily be good at vertical jumping and getting long
hang time, but their ridiculous forward speed makes them travel incredible
distances horizontally even with only moderate and normal ability at
jumping.  This may even be able to be augmented through the use of a ramp to
convert some of their forward speed into increased hang time.

Any other way seems logically inconsistent.  Just because we have super
powers in our games does not mean we have to abandon all sensibility and
consistency.

So I am fine with Strength being used to determine max hang time and
Dexterity being used to determine running Speed - and both together being
used to determine total distance.  (Of course, jumping from a standing start
is possibly all about Strength.)

But I do insist, apparently rightfully so, that a person's forward speed be
taken into account when determining his long jump distance.  The simple
truth of the matter is that going ten times faster *does* in all cases
(ignoring wind resistance) translate into going ten times farther.  A Super
Speedster should therefore go MUCH father - even *if* he has not extra
special jump powers and is only a normal jumper.

Make sense?

-Benn Grant
eFix Computer Consulting
benn at 4eFix.com
603.283.6601