(TFT) how to hit a ball

["Jay Carlisle" <Jay_Carlisle@charter.net>]

When measuring american baseball bats the industry uses a pendulum system 
that grips the actual bat being measured at a point 6 inches (about 2 
Scale-hex squares or 2 palm-widths from the handle-end of the bat).
This gives a moment of Inertia equal to the period of the swing squared, 
multiplied by the product of the bats mass by the distance between the pivot 
point and balance point of the bat by the acceleration of gravity divided by 
four times the square of pi.
Recent research shows that the actual pivot location of a swung bat from a 
competent, adult, human batter results in a pivot point about 2.5 inches 
below the actual bat and roughly 1.5 inches behind the long axis, placing 
the moment of the instantaneous center of rotation still in the body 
(roughly between the wrists) of the Figure and NOT in the equipment itself.
This is important because the moment of Inertia factors in very strongly 
when considering bat speed and control.
A few years ago a study was done with a group of top level batters using two 
different sets of bats.
The first set of bats had the same total weight, but the weight was 
distributed differently so that the bats had different moments-of-inertia. 
The second set of bats had the same moment-of-inertia, but different total 
weights.
The results clearly showed that when the moment-of-inertia was kept the 
same, the bat-swing speed did not vary largely as the total weight of the 
bat changed. In contrast, the bat-swing speed for all players was noticeably 
slower for larger MOI bats than for smaller MOI bats with the same total 
weight.
In sports this is referred to as the bats swing weight and had I chosen to 
use tennis rackets or golf clubs as my model for a swing then I would have 
run across this information from the get go but baseball bat manufactures 
apparently consider this information proprietary.
So after studying some papers by Terry Bahill who developed the "Bat 
Chooser" machine that determines an individual's "ideal bat weight" I ran 
across a couple of his rules of thumb.

First he roughly defines a bats "sweet spot" as follows;
"When the ball hits the bat, it produces a translation that pushes the hands 
back and a rotation that pulls the hands forward. When a ball is hit at the 
center of percussion (CoP or sweet spot) for the pivot point, these two 
movements cancel out, and the batter feels no sting."

I say roughly because he actually uses 7 closely related points to describe 
an area for the sweet spot that allows for a general description of about 80 
to 85% of the total bat length measured from the knob to locate the sweet 
spot, or about 29 inches from the knob for Joe Average adult body type.

He also gives a rule of thumb for a batters ideal bat weight by taking the 
batters height divided by three and adding an additional 1 to 7 oz depending 
on their level of competition or skill.
Bahill has defined the ideal bat weight as the weight at which the batted 
ball speed drops 1% below the speed of the optimum batted ball speed bat 
weight.
For major league power hitters a bat weight of ~41 oz produces the maximum 
(optimum) ball speed.
A reduction of 1% of the maximum ball speed results if the bat weight is 
reduced to ~33 oz but the overall bat speed is increased significantly 
allowing for longer reaction times and greater bat control.

So if I take Joe Average as 6' tall then major league Joe would have an 
ideal bat weight of 24 + 7 = 31 oz as a rule of thumb.
For a 3' long bat, ML Joe's sweet spot at 29" is within the 80 to 85% rule 
of thumb for the bats sweet spot.

A three foot long bat is 11 Scale-hex squares long with the sweet spot 
located on the ninth Scale-hex square from the knob.
A Scale-hex is a total of 16 3.25" Scale-hex squares from side to side so a 
3 foot long bat is just under three quarters of a Battle map-hex in length 
with its sweet spot just past the hex center.

Now proportionally at 6 foot tall, Joe's arms are about three eights of his 
total height, or about 27 inches long.
Assuming Joe is standing with his center of gravity over a hex center his 
arm reach should be very close to the edges of the hex he's standing in 
meaning that Joe with a three foot long bat should be able to swing the bats 
sweet spot through the hex centers of the adjacent front hexes at full 
extension with the edge of the hex he's occupying loosely describing the arc 
of his wrists swing over roughly 270 degrees.
The swing can be broken into three separate phases each covering about 90 
degrees of arc; the push/pull phase, wrist rotation phase, and follow 
through phase.
Of these three the most important component of damage is going to be the 
wrist rotation, especially once we put an edge (or two) on this club.
Assuming proper training (Talent, skill) it is my opinion that a success 
check should be describing this portion of the swing with the die roll.

Now at this point TFT (like most games) uses two separate die rolls, one to 
hit and one to damage.
This would suggest that a batter in TFT would check to make contact with the 
ball and then check to see how hard they hit the thing if they made contact.
I don't feel this is a good model of what's happening.
While hand-eye coordination is unquestionably an extremely important part of 
the overall result I believe that the effort or tension level applied to the 
swing cannot be separated out into a different success check.
Your best hitters look nice and easy with their swings appearing fluid and 
under control. When a hitter is smooth and easy with their approach, they 
see the ball better and can react more efficiently to breaking balls during 
a swing. It is also easier to check a swing with a low effort level, giving 
the hitter more time to read the pitch before committing to swing.
Major league hitting coaches (at least the Oakland A's) teach hitters to 
swing with 75 to 85% of their full maximum effort.
When dealing with full blown combat we'll see that many attempted blows over 
the course of a group of shots are not meant to be very damaging but rather 
are trying to "set up" a damaging stroke.
In the more formalized world of batting though I still think the batter is 
making the decision of how hard to swing at the same instant they decide to 
swing at all.
If they hit the force of the swing is already in play so to speak.

Before I start writing about how I differentiate the 90 degrees of arc of 
the wrist rotation of a bat swing to integrate the force of a given roll to 
the right of the success point on the bell curve I'd be interested to see 
how far off folks think I am with all of this.

http://www.sie.arizona.edu/sysengr/publishedPapers/momentOfInertia.pdf
http://www.sie.arizona.edu/sysengr/publishedPapers/TwoMethods.pdf

Oh yeah...


Some properties of a professional boxer's (Frank Bruno ~'85) punch
Duration of trunk advance before start - 201 ms
Velocity of trunk and fist before start - 1.0 m/s (2.2 mph)
Time taken from start of punch to impact - 100 ms
Distance punch travels from start to impact - 490 mm
Distance of follow through - 110mm
Peak acceleration of fist before contact - 90 m/s2
Velocity of fist at impact - 8.9 m/s (20 mph)
Residual velocity after impact - 1.8 m/s
Rise time of force to peak - 14 ms
Rise time of acceleration to peak - 14 ms
Peak contact force - 4096N(0-4 ton)
Estimated maximum force to human head - 6320N(0-63 ton)
Impulse transmitted - 41N s
Acceleration induced in head mass model - 520 m/s^2 (53 g)
1N = 0.225 lb; 1 m/s = 2.24 mph; 1 g = 9.81m/s^2
(Of course the duration of the contact was brief, but it still lasted long 
enough to
generate an impulse capable of lifting a 100 kg opponent some 8 mm
off the ground and accelerating the target head at 520 m/s2 (53 g) well
beyond safety margins quoted by Johnson, Reid, and Mamalis. An
equivalent blow would have been delivered by a padded wooden
mallet [i.e. club] with a mass of 6 kg (13 lbs) if swung at 20 mph.)

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1419171/pdf/bmjcred00479-0016.pdf

IMO people in general have a real distaste for math.
This is very understandable to me actually because my own skills at 
mathematics are significantly less than my abilities to communicate well 
with English which are certainly questionable at best meaning Jay sucks at 
math.
C'est la vie, but I've got this nagging part of my thought process that says 
that using strong and sound mathematics to "design" the game helps to 
achieve two different things that I feel are important to a "good-game".
First, and most importantly, I feel that strong mathematical underpinnings 
helps' keep the "rules" "fair" for players and also easier for the GM to 
judge.
The better I can understand the mechanics of a sword swing, the better I can 
use game mechanics to model it, ergo less argument or bad feeling.
Secondly, and more personally, I feel that a math framework helps to 
"educate" younger players by providing more than a simple knowledge of what 
particular equipment / stat combos are most effective as a player masters 
the rules by implying an understanding of more basic principals (basic being 
the best "I" can do) behind the advantages of said set-up.
But design isn't play, and play shouldn't involve solving quadratics for 
every arrow and whatnot.
All this junk gets buried in the componets of play but "I" have to deal with 
it all to design the components properly.
If I can draw a bat properly against a Scale-mega-hex then I can show a 
whole lot of this stuff to players graphicly w/o forcing a bunch of math on 
the play session itself.
It's still gonna be REALLY simplified but it's going to be pointing players 
in the right direction for learning rather than;
...
Cutlass 2d-2 dam, ST 10, wt 1.5
Shortsword 2d-1 dam, ST 11, wt 2
Broadsword 2d dam, ST 12, wt 2.5
...
The dice should be a tool to model the situation.
I shouldn't be looking at a thesaurus for different words for sword to fit a 
range of dice.
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