[Torg] Jumping in Torg

[Travis James Hall]

> -----Original Message-----
> From: torg-bounces at justintimeadventures.com 
> [mailto:torg-bounces at justintimeadventures.com] On Behalf Of 
> Sam Frazier II
> Sent: Thursday, 11 December 2008 1:11 AM
> To: torg at justintimeadventures.com
> Subject: Re: [Torg] Jumping in Torg
> 
> I would agree that a velocity and strength would be needed to 
> determine the distance in a Long jump. There should be a 
> formula for it though. *ponder* Off the top of my head, Value 
> of speed + Value of Str - Value of Weight = Distance 
> traveled? Which would be V * Str / effects of gravity. 
> *thinks* something like that.
>  
> I haven't done the math, but I would start with something like this. 
>  
> I think there should be a fairly simple way to guestimate 
> without getting sin/cos/tan involved. *winks at Travis or 
> whomever mentioned sin/cos/tan in a formula. I forget* though 
> your forumla seems correct to me, I'll agree with your point.

Well, I did point out that sine maxes out at 1 for a 45deg jump, so you can
just ignore that factor to get your max and eyeball for a less than optimal
angle.

But now that you mention it, the reason we have trig functions involved is
because we need to split the velocity into horizontal and vertical
components, and sine and cosine represent those relationships. If we have
another means of getting values for the horizontal and vertical components
of velocity, we can avoid those, and since it's hard to judge the angle of a
long-jumper's leap, that may be an easier approach anyway.

An alternate formula for working up projectile range is d = -2v(y)v(x)/a
where v(y) and v(x) are the vertical and horizontal components of velocity
respectively. (Dratted ASCII, no subscripts - sorry about the
difficult-to-read notation.)

We can reasonably suppose that v(x) is equivalent to running speed.
(Probably a touch less, as the jumper would tend to lose a little horizontal
velocity in that last step/leap, when effort is devoted to pushing up as
well as maintaining speed, but close enough in terms of Torg scales.)

v(y) could reasonably be supposed to be proportional to Strength, as leg
strength would be used to provide that initial upward force. Whether it is
reasonable to simply reason Strength through the value chart, whether a
limit value should be applied, whether a modifier should be applied, or
combinations, is up to the GM (because this is well into house rule
territory). You'd have to try some examples and see if the figures come out
about right. (The world record for long jump is a little under 9m. If
characters are regularly beating that, you've got a problem.)

a is (as previously noted) about -10m/s, which means our long jump distance
is found with v(x)v(y)/5 . But remember, that's working with measures (in
Torg terms). The multiplication becomes nice, neat addition when working
with Torg values. The equivalent in Torg values would be something along the
lines of (DEX-5)+(STR-?)-4, with a limit value on the Dex of 10 (that's the
running limit value) and the -5 being because Torg running speed is in
metres per 10-second round and we need m/s. The question mark represents an
unknown factor for unit conversion for Strength into upward motion, similar
to the 5 for converting running speed to m/s. If we suppose Strength
converts to speed similarly to Dex, that becomes (DEX-5)+(STR-5)-4 =
DEX+STR-14.

A little suggested calibration... That gives a max value (for normal humans)
of 10+13-14=9, which becomes a jump distance of about 60 meters - obviously
too high. Before pushing, we need this to max out 3 to get long-jump results
in the ballpark. That's lower by six, so apply a limit value to the Strength
of 13-6=7.

So what you get is, add Strength (limit 7) plus Dex (limit 10) and subtract
14 (unit conversion and accounting for gravity), and read through the Torg
value chart to translate to an actual distance. Pushing should be done on
the Speed column using Strength (because that's the lower limit value, and
it would only be fair to use the more limited stat). Without pushing
characters would jump around 4 metres, with pushing up to around 10 metres,
which is about as close as we can expect to get to anything when reading
through the Torg value chart.

Or you can fiddle around with alternate factors and limit values. There's
other ways to get similar basic results (and each will give a different
effect from pushing).

But that's not so helpful for jumping cars off ramps, because cars don't
have the applicable jumping ability to allow Strength to add to the height
of the jump. For cars, it is back to the trig (if our available information
is just angle of the ramp and speed coming off the ramp).

Travis Hall