(TFT) football, a deep out

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

A doxel count of a pass route.
In classical art the "heroic" Figure stands 8 heads tall by 3 heads in width 
and 1 head in depth and would fit in a 8 head by 3 head by 1 head box when 
standing at attention.
By these proportions the 6 foot Figure has a head that would fit in a box 9 
inches in height, 9 inches in depth, and 6 inches in width.
Now putting them in motion has some wiggle room to it.

http://www.brianmac.co.uk/economy.htm

"Using Atwater's results, the six foot athlete (1.8 metres) has an average 
stride length of 2.5 metres."
Where the average stride length is 1.35 times the athlete's height.

Atwater's work was done with a group of 23 sprinters with 100m times ranging 
between 9.9 to 10.4 seconds.

100 meters (track length) /  2.5 meters (avg. stride length) = 40 avg. 
strides per 100 meters
40 avg. strides / 10 seconds (100m sprint time) = 4 avg. strides per second, 
or about 10 mps.
1.3m (1 Melee-hex sts) + 1.3m = 2.6m, or 2 Melee-hexes, or ~1 stride.
4 avg. strides per second * 2 Melee-hexes per avg. stride = 8 Melee hexes 
per second to complete 100m in avg. strides.
MA 40 is ~24mph which is 35.2 fps, or ~10.7 mps which roughly check to 8 
Melee-hexes per second.

Yes it's not scientific, but for descriptive purposes 10.7 mps / 1.3m per 
Melee-hex sts is in the ballpark for a game and as I'm not counting a 
footrace against competition right now I don't need to count squares.

Keeping things general it seems my fictitious 6 foot tall, 10 second 100m 
running, wide-out moves his 24 head silhouette forward 8 Melee-hexes in one 
second.
A head is only 6 inches wide and there are three of them making 18 inches 
which is equal to 9" + 9".
It's probably a tad easier to just call the doxel a 9" cube.
That's 16 doxel's for the silhouette instead of 24 9" by 9" by 6" ones but 
how many doxel's across a Melee-hex?
1.3 meters is about 4.265 feet which is a bit under 51.2 inches.
I call square-hexes 52 inches across sts and use squares to argue 0.8" 
increments if necessary.
This works out to about 5.7 doxels across a square-hex or  ~45.5 doxels 
across 8 hexes.

So, on a long go route (7 step drop) straight down field using average 
velocities I get the following.

Play starts.
(Initiative here, see Rice's reaction times)

First sec
Wide receiver moves 8 hexes forward (have wideout snap ball)
Quarterback drops back 3.5 hexes (consider QB lined up on hex-side when 
under center so the half hex moves him to a hex center)
Separation between Figures is 11 hexes.

Second sec
Wide receiver moves forward 8 hexes to 16 hexes from start.
QB drops back another 2 hexes to 5.5 hexes from start.
21 hexes of separation between Figures

Third sec
Wide receiver moves forward 8 hexes to 24 hexes from start.
Quarterback drops back another 2 hexes to 7.5 hexes from start.
31 hexes of separation between Figures

Fourth sec
QB throws ball @ 20 MA per sec
Ball moves forward 20 hexes to 13 hexes from start.
Wide receiver moves forward 8 hexes to 32 hexes from start.
Separation between the ball and receiver 19 hexes

Fifth sec
Ball moves forward 20 hexes to 33 hexes from start.
Wide receiver moves forward 8 hexes to 40 hexes from start.
Separation between the ball and receiver 7 hexes

Now things get interesting.
We're at turn 2 by TFT and the ball is not quite there.
Of course, it's only been moving as a thrown object for 2 seconds and it's 
gonna get to the receiver in about another 2/3rds of a second or so, but 
this begs the question of when does the "turn" actually start.
It makes a real difference.

In another example a poacher is in the king's wood with a longbow, tracking 
a deer.

http://www.fcps.edu/islandcreekes/ecology/white-tailed_deer.htm
"White-tailed Deer run very fast, up to 36 miles per hour."

36 mph is about MA 60

http://www.africanarcher.com/howGood.html
"Whereas arrow speeds of 300 fps and more from compounds are often heard of 
and bragged about, a good traditional longbow will cast a 
ten-grain-per-pound-of-bow arrow (the old standard) at about 150 fps - no 
more."

Wow, that's hardly over 100 mph whereas 300 fps is about 200 mph.

So our wide receiver has an MA of 40 or about 24 mph.
The deer bolts at MA 60 or roughly 36 mph.
The QB throws a ball at an MA of 100 or around 60 mph.
The bow fires the arrow at an MA of 170 or about 102 mph.
MA 40 / MA 100 = 0.4
MA 60 / MA 170 = ~0.35
There's similarity there I think.

So the 16 doxel silhouette receiver moves 227.5 doxel's down field through a 
trail of 3640 doxel's 8 by 2 in one TFT turn.

NFL ball dimensions:
Short Circumference: 20 3/4"- 21 1/4" (~6.5" diameter)
Long Circumference 27 3/4 "- 28 1/2 " (~9" diameter)
Weight: 14-15 oz
So the ball can roughly fit in 1 doxel.
So far the ball has moved for 2 seconds and left a trail of at least 40 
doxel's along it's straight-line path.

Sixth sec
20 hexes per second is 2 hexes per tenth of a second.
8 hexes per second is 0.8 hexes per tenth of a second.

Sixth sec, first tenth
Ball moves forward 2 hexes to 35 hexes from start.
Receiver moves forward 0.8 hexes to 40.8 hexes from start.
Separation between ball and receiver is 5.8 hexes.

Sixth sec, second tenth
Ball moves forward 2 hexes to 37 hexes from start.
Receiver moves forward 0.8 hexes to 41.6 hexes from start.
Separation is 4.6 hexes

Sixth sec, third tenth
Ball moves to 39 hexes from start.
Receiver moves to 42.4 hexes from start.
Separation is 3.4 hexes

Sixth sec, fourth tenth
Ball moves to 41 hexes from start.
Receiver moves to 43.2 hexes from start.
Separation is 2.2 hexes

Sixth sec, fifth tenth
Ball moves to 43 hexes from start.
Receiver moves to 44 hexes from start.
Separation is a hex.

At 6.55 sec the ball is at 44 hexes from start and the receiver has not 
quite made it out of the 44th hex from start.

A 6 foot tall Figure in the middle of a 1.3m hex can hold their arms 
straight out and reach into surrounding hexes with their hands and wrists.

As this is a deep pass let's put the ball over the receivers shoulder and 
hit him in stride.

Sixth sec, sixth tenth
The ball is at 45 hexes from start.
The receiver is at 44.8 hexes from start.
The difference is less than a foot. more like a doxel.

An extra 5 one hundredths of a second has the ball at 46 hexes from start 
and the receiver at 45.2 hexes. a difference of about three and a half feet.

So somewhere between 6.5 and 6.65 seconds the receiver is going to make his 
catch check in an undefended, snap from center, deep pass route at a point 
downfield about 65 yards from the scrimmage line.
The average time it takes for a complete human blink is about 300 to 400 
milliseconds or 3/10ths to 4/10ths of a second.

There are a number of issues with this, one of the foremost being a total 
lack of arc on the balls flight path.
Nobody is throwing a frozen rope 65+ yards, at least nobody human.
No start from scrimmage, no cuts during the route, no defense. and other 
stuff like wingspan.
Generally wingspan relates to height so a 6 foot tall receiver should have a 
roughly 6 foot wingspan.
As about a foot of that width is the chest this leaves 5 feet of actual arms 
or about 2.5 feet for a single arm length.
2.5 feet is a little over three and a third doxel's in length.
The shoulder to the elbow is about 1.5 doxel's and the elbow to the wrist is 
about 1.5 doxel's leaving about 3 inches to represent the hand which is 
pretty good for most hand positions, although outstretched fingers roughly 
double hand length.
A baseball glove really ups hand area but that's another sport.
I've already posted some stuff on arm rotations for throwing.
How quickly a Figure can move their arms and the limits of their reach have 
a bit to do with catching the ball too and is part of the reason I'm messing 
around with doxel's because they help show the areas swept out by limbs, 
equipment, etc.
They're especially good for different proportions (or monsters). like a 6'6" 
receiver with a freakish wingspan who still runs a 10 sec. 100m.
A 4.5 sec. 40 yard dash is a little over 18 mph and a 10 sec. 100m is about 
a quarter faster than that.
While I personally wouldn't run a whole football game like this I certainly 
get a better visual of what a given "play" is meant to accomplish if ran 
perfectly by counting the route like this.
The visual gives me a pretty good idea about spatial questions like where on 
the field pursuit may catch up to a receiver.
As I use 1" hexes on 8" by 10" standard sized pages this let's me use a few 
pages to represent anywhere on the field rather than having to lay out the 
whole thing.
It also helps to assign effects to opposed checks that result in something 
other than complete failure for both Figures.
In bump and run man coverage a successful check against a Stat that beats an 
opposed Stat check that was also successful may get 1 square of "push" per 
point that it beat its opposition causing adjustment to the route.
And then there's those plays where the line of scrimmage is in the red zone, 
your team is down by 4 and there's 4 seconds left in the game.



http://www.youtube.com/watch?v=dN3nSuvUM0Q

http://www.youtube.com/watch?v=En6cTw1nGSo&feature=related

http://www.youtube.com/watch?v=hquBATZjsRk&feature=related



Kyle: Sam didn't even go to college.
Mom: Yes, he did, Kyle.
Kyle: For a month!
Mom: And we're very proud of him for trying. It's just that college made him 
sleepy.
-Reaper
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