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Rain Man
04-25-2005, 10:10 PM
I'm procrastinating a work deadline, so I got to thinking about the Chief player 40 times that I posted in another thread relative to their weight. It occurred to me that it might be interesting to see who generated the most momentum, and who creates the greatest force.

Whether you believe the 40 times are not, it's an interesting exercise.

My assumptions were that the player would accelerate for the first 20 yards of a 40 yard dash, and would then travel the remaining 20 yards at a maximum constant speed. I didn't bother converting to standard units, and I couldn't quite remember how to convert pounds-force to pounds-mass, so my units are all goofy. Nonetheless, the comparative figures are accurate.

My equations were based on knowing that:

V=(40a)^(1/2)
40 = a(t^(1/2))
20 = VT
t+T=C

where

V = terminal velocity (yds/sec)
a = acceleration in first 20 yards (yds/sec^2)
t = time to cover the first 20 yards (sec)
T = time to cover the second 20 yards (sec)
C = Recorded time in the 40 (sec)

This creates 4 equations and 4 unknowns, so if I know C, I can solve for the others.

I then calculated momentum as MV, where M = player weight and V = terminal velocity.

I also calculated player force as Ma, where M = player weight and a = acceleration in first 20 yards

Doing these things, I come up with the following rankings.

Players generating the most Momentum (lbf*yds/sec) at 40 yards.


Momentum (lbf-yards/sec)
94 SIAVIL Junior 6- 4.4 344 5.11 401.29 5.11 344 4039.138943
65 BLACK Jordan 6- 6.0 327 5.16 408.04 5.16 327 3802.325581
90 SIMS Ryan 6- 3.6 318 5.02 601.88 5.02 318 3800.796813
79 SAMPSON Kevin 6- 4.4 312 4.96 376.77 4.96 312 3774.193548
74 WILLIAMS Brent 6- 5.5 321 5.19 390.80 5.19 321 3710.982659
60 WILLIS Donald . 6- 3.0 330 5.34 467.08 5.34 330 3707.865169
68 SHIELDS Will 6- 1.0 308 5.04 650.22 5.04 308 3666.666667
67 BOBER Chris 6- 4.0 322 5.31 530.72 5.31 322 3638.418079
76 WELBOURN John 6- 4.0 317 5.26 278.63 5.26 317 3615.969582
89 DUNN Jason . 6- 4.0 278 4.62 550.32 4.62 278 3610.38961
54 WATERS Brian . 6- 2.0 302 5.03 660.40 5.03 302 3602.385686
93 ISSA Jabari 6- 4.0 295 4.93 406.29 4.93 295 3590.263692
98 HICKS Eric 6- 4.0 287 4.89 624.03 4.89 287 3521.472393
77 ROAF William 6- 4.0 313 5.38 745.46 5.38 313 3490.70632
62 WIEGMANN Casey 6- 2.0 293 5.04 717.85 5.04 293 3488.095238
93 BROWNING John 6- 4.0 286 4.94 518.77 4.94 286 3473.684211
0 JOHNSON Aaron 6- 5.0 305 5.27 332.72 5.27 305 3472.485769
96 WILKERSON Jimmy 6- 2.7 271 4.73 388.09 4.73 271 3437.632135
61 SHARPE Montigue 6- 3.0 287 5.01 373.24 5.01 287 3437.125749
73 BARNETT Tom 6- 5.0 305 5.35 367.68 5.35 305 3420.560748
46 HALL Joe 6- 1.7 277 4.88 319.57 4.88 277 3405.737705
60 INGRAM Jonathan 6- 2.0 296 5.25 366.25 5.25 296 3382.857143
69 ALLEN Jared 6- 6.0 265 4.71 450.76 4.71 265 3375.796178
69 MILLER Matt 6- 4.0 285 5.08 305.99 5.08 285 3366.141732
50 MITCHELL Kawika 6- 1.0 251 4.61 408.05 4.61 251 3266.81128
0 WALKER Demotrius 6- 2.0 261 4.81 328.62 4.81 261 3255.717256
40 WILSON Kris 6- 1.7 248 4.62 371.23 4.62 248 3220.779221
57 MASLOWSKI Mike 6- 2.0 255 4.76 581.40 4.76 255 3214.285714
97 HALL Carlos 6- 3.4 248 4.64 469.02 4.64 248 3206.896552
51 FUJITA Scott 6- 5.0 247 4.63 424.04 4.63 247 3200.863931
88 GONZALEZ Tony 6- 4.0 248 4.71 795.97 4.71 248 3159.235669
55 STILLS Gary 6- 1.0 237 4.56 400.33 4.56 237 3118.421053
0 CRUZ Ronnie 6- 0.0 237 4.63 322.54 4.63 237 3071.274298
97 BELL Kendrell 6- 1.0 232 4.55 697.28 4.55 232 3059.340659
59 BARBER Shawn 6- 1.0 225 4.43 414.26 4.43 225 3047.404063
52 CAVER Quinton 6- 3.0 232 4.65 417.90 4.65 232 2993.548387
27 JOHNSON Larry. 6- 0.7 222 4.45 477.49 4.45 222 2993.258427
91 SCANLON Rich 6- 1.0 228 4.58 355.41 4.58 228 2986.899563
83 GAMMON Kendall 6- 4.0 255 5.19 335.86 5.19 255 2947.976879
49 RICHARDSON Tony 6- 1.0 232 4.75 518.78 4.75 232 2930.526316
97 FOX Keyaron 6- 2.3 227 4.67 378.11 4.67 227 2916.488223
25 WESLEY Greg 6- 1.0 218 4.55 524.91 4.55 218 2874.725275
41 CONNOT Scott 6- 2.6 218 4.56 351.86 4.56 218 2868.421053
33 HOLMES Priest 5- 8.0 213 4.48 483.81 4.48 213 2852.678571
0 MOORE Chazz 6- 0.0 215 4.63 307.19 4.63 215 2786.177106
0 McINTYRE Jeris 5-11.2 203 4.41 366.65 4.41 203 2761.904762
7 CLAUSEN Casey 6- 3.4 223 4.87 333.59 4.87 223 2747.433265
26 BATTLE Julian 6- 2.2 204 4.47 454.83 4.47 204 2738.255034
15 COLLINS Todd S. 6- 4.0 224 4.96 462.30 4.96 224 2709.677419
11 HUARD Damon 6- 3.0 222 4.95 477.14 4.95 222 2690.909091
87 KENNISON Eddie 5-11.0 195 4.35 533.76 4.35 195 2689.655172
22 McCLEON Dexter 5-10.0 196 4.39 513.02 4.39 196 2678.81549
10 GREEN Trent 6- 2.0 212 4.75 570.84 4.75 212 2677.894737
82 HALL Dante 5- 7.0 191 4.31 503.70 4.31 191 2658.932715
21 WOODS Jerome 6- 2.0 202 4.56 507.89 4.56 202 2657.894737
38 CROUCH Eric 5-11.8 197 4.45 362.27 4.45 197 2656.179775
44 WARFIELD Eric 5-11.0 197 4.48 442.73 4.48 197 2638.392857
KNIGHT Sammy 5-11.0 205 4.69 591.44 4.69 205 2622.601279
20 BOOTH Jonathan 6- 0.0 196 4.50 348.63 4.5 196 2613.333333
24 BARTEE William 6- 2.0 192 4.41 480.79 4.41 192 2612.244898
19 SMITH Jon 5-10.0 194 4.61 406.61 4.61 194 2524.94577
80 MORTON Johnnie 5-11.0 190 4.59 492.99 4.59 190 2483.660131
18 PARKER Sammie 5-10.3 179 4.35 402.28 4.35 179 2468.965517
17 SMITH Richard 5-10.0 174 4.37 382.58 4.37 174 2389.016018
20 SAPP Ben 5-10.0 175 4.50 312.54 4.5 175 2333.333333





Players generating the most Force at 20 yards.


Force (lbf-yards/sec2)
94 SIAVIL Junior 6- 4.4 344 5.11 401.29 5.11 344 1185.657224
89 DUNN Jason . 6- 4.0 278 4.62 550.32 4.62 278 1172.204419
79 SAMPSON Kevin 6- 4.4 312 4.96 376.77 4.96 312 1141.389178
90 SIMS Ryan 6- 3.6 318 5.02 601.88 5.02 318 1135.696259
65 BLACK Jordan 6- 6.0 327 5.16 408.04 5.16 327 1105.327204
93 ISSA Jabari 6- 4.0 295 4.93 406.29 4.93 295 1092.37232
68 SHIELDS Will 6- 1.0 308 5.04 650.22 5.04 308 1091.269841
96 WILKERSON Jimmy 6- 2.7 271 4.73 388.09 4.73 271 1090.158182
98 HICKS Eric 6- 4.0 287 4.89 624.03 4.89 287 1080.206255
69 ALLEN Jared 6- 6.0 265 4.71 450.76 4.71 265 1075.094324
54 WATERS Brian . 6- 2.0 302 5.03 660.40 5.03 302 1074.270085
74 WILLIAMS Brent 6- 5.5 321 5.19 390.80 5.19 321 1072.538341
50 MITCHELL Kawika 6- 1.0 251 4.61 408.05 4.61 251 1062.953779
93 BROWNING John 6- 4.0 286 4.94 518.77 4.94 286 1054.762412
46 HALL Joe 6- 1.7 277 4.88 319.57 4.88 277 1046.845606
40 WILSON Kris 6- 1.7 248 4.62 371.23 4.62 248 1045.707539
60 WILLIS Donald . 6- 3.0 330 5.34 467.08 5.34 330 1041.53516
62 WIEGMANN Casey 6- 2.0 293 5.04 717.85 5.04 293 1038.123583
51 FUJITA Scott 6- 5.0 247 4.63 424.04 4.63 247 1036.996954
97 HALL Carlos 6- 3.4 248 4.64 469.02 4.64 248 1036.712247
59 BARBER Shawn 6- 1.0 225 4.43 414.26 4.43 225 1031.852392
76 WELBOURN John 6- 4.0 317 5.26 278.63 5.26 317 1031.170033
61 SHARPE Montigue 6- 3.0 287 5.01 373.24 5.01 287 1029.079565
67 BOBER Chris 6- 4.0 322 5.31 530.72 5.31 322 1027.801717
55 STILLS Gary 6- 1.0 237 4.56 400.33 4.56 237 1025.796399
0 WALKER Demotrius 6- 2.0 261 4.81 328.62 4.81 261 1015.296441
57 MASLOWSKI Mike 6- 2.0 255 4.76 581.40 4.76 255 1012.905162
27 JOHNSON Larry. 6- 0.7 222 4.45 477.49 4.45 222 1008.963515
97 BELL Kendrell 6- 1.0 232 4.55 697.28 4.55 232 1008.573844
88 GONZALEZ Tony 6- 4.0 248 4.71 795.97 4.71 248 1006.126009
0 CRUZ Ronnie 6- 0.0 237 4.63 322.54 4.63 237 995.0132715
69 MILLER Matt 6- 4.0 285 5.08 305.99 5.08 285 993.9394879
0 JOHNSON Aaron 6- 5.0 305 5.27 332.72 5.27 305 988.3735584
91 SCANLON Rich 6- 1.0 228 4.58 355.41 4.58 228 978.2422151
77 ROAF William 6- 4.0 313 5.38 745.46 5.38 313 973.2452564
60 INGRAM Jonathan 6- 2.0 296 5.25 366.25 5.25 296 966.5306122
52 CAVER Quinton 6- 3.0 232 4.65 417.90 4.65 232 965.66077
73 BARNETT Tom 6- 5.0 305 5.35 367.68 5.35 305 959.0357236
33 HOLMES Priest 5- 8.0 213 4.48 483.81 4.48 213 955.1379145
25 WESLEY Greg 6- 1.0 218 4.55 524.91 4.55 218 947.711629
41 CONNOT Scott 6- 2.6 218 4.56 351.86 4.56 218 943.5595568
0 McINTYRE Jeris 5-11.2 203 4.41 366.65 4.41 203 939.4233884
97 FOX Keyaron 6- 2.3 227 4.67 378.11 4.67 227 936.7735191
87 KENNISON Eddie 5-11.0 195 4.35 533.76 4.35 195 927.4673008
49 RICHARDSON Tony 6- 1.0 232 4.75 518.78 4.75 232 925.4293629
82 HALL Dante 5- 7.0 191 4.31 503.70 4.31 191 925.3826153
26 BATTLE Julian 6- 2.2 204 4.47 454.83 4.47 204 918.877528
22 McCLEON Dexter 5-10.0 196 4.39 513.02 4.39 196 915.3128097
0 MOORE Chazz 6- 0.0 215 4.63 307.19 4.63 215 902.6491704
38 CROUCH Eric 5-11.8 197 4.45 362.27 4.45 197 895.3414973
24 BARTEE William 6- 2.0 192 4.41 480.79 4.41 192 888.5186728
44 WARFIELD Eric 5-11.0 197 4.48 442.73 4.48 197 883.3904656
21 WOODS Jerome 6- 2.0 202 4.56 507.89 4.56 202 874.3074792
20 BOOTH Jonathan 6- 0.0 196 4.50 348.63 4.5 196 871.1111111
83 GAMMON Kendall 6- 4.0 255 5.19 335.86 5.19 255 852.0164389
18 PARKER Sammie 5-10.3 179 4.35 402.28 4.35 179 851.3674197
7 CLAUSEN Casey 6- 3.4 223 4.87 333.59 4.87 223 846.2320118
10 GREEN Trent 6- 2.0 212 4.75 570.84 4.75 212 845.6509695
KNIGHT Sammy 5-11.0 205 4.69 591.44 4.69 205 838.7850574
19 SMITH Jon 5-10.0 194 4.61 406.61 4.61 194 821.5658688
17 SMITH Richard 5-10.0 174 4.37 382.58 4.37 174 820.0283816
15 COLLINS Todd S. 6- 4.0 224 4.96 462.30 4.96 224 819.458897
11 HUARD Damon 6- 3.0 222 4.95 477.14 4.95 222 815.4269972
80 MORTON Johnnie 5-11.0 190 4.59 492.99 4.59 190 811.6536375
20 SAPP Ben 5-10.0 175 4.50 312.54 4.5 175 777.7777778





I have no idea what this illustrates, but I just thought I'd share it.

Pants
04-25-2005, 10:17 PM
LOL

Crush
04-25-2005, 10:36 PM
:clap:

Hydrae
04-25-2005, 10:38 PM
Hehe, Sapp is a puss. :D

patteeu
04-25-2005, 10:39 PM
Based on your calculations, I think Benny Sapp would just bounce off of me. Don't ask me to stand between Junior and a buffet line though.

ENDelt260
04-25-2005, 10:42 PM
While I recognize that "normal" people don't do stuff like this, I'll commend you for restraining the UMR geek within to a simple physics exercise on paper, and not succumbing to the urge to build some crazy contraption.

KCJake
04-25-2005, 10:54 PM
Interesting stuff. Your calculations are pretty accurate. I have always been taught, you should reach your top speed around the 10-12 yard mark. The rest of your 40 is all about being able to maintain that top speed. The first 5-7 yards are so critical!

Freekofnature
04-25-2005, 11:41 PM
Useless stuff.......

however interesting.

Too bad they dont play the game by running 20 and 40 yard straight.

Inspector
04-25-2005, 11:41 PM
Not trying to correct you or anything, but terminal velocity was a movie, not part of an equation.

I thought you would have known that being so smart and all....

DanT
04-26-2005, 02:35 PM
My assumptions were that the player would accelerate for the first 20 yards of a 40 yard dash, and would then travel the remaining 20 yards at a maximum constant speed. I didn't bother converting to standard units, and I couldn't quite remember how to convert pounds-force to pounds-mass, so my units are all goofy. Nonetheless, the comparative figures are accurate.

My equations were based on knowing that:

V=(40a)^(1/2)
40 = a(t^(1/2))
20 = VT
t+T=C

where

V = terminal velocity (yds/sec)
a = acceleration in first 20 yards (yds/sec^2)
t = time to cover the first 20 yards (sec)
T = time to cover the second 20 yards (sec)
C = Recorded time in the 40 (sec)

This creates 4 equations and 4 unknowns, so if I know C, I can solve for the others.

I then calculated momentum as MV, where M = player weight and V = terminal velocity.

I also calculated player force as Ma, where M = player weight and a = acceleration in first 20 yards



Hey Rain Main,

Cool Post!
I'm not sure I understand all your equations. If I understand correctly, you are assuming constant acceleration (of magnitude a) over the first 20 yards and then constant velocity (of magnitude V) over the next 20 yards.

So, I can see how you'd have

20=VT (because that's the equation for the last 20 yards) and
t + T = C (because that's the sum of the first and last 20-yard split times), but I don't understand where you got the other two equations:

V=(40a)^(1/2)
40 = a(t^(1/2))

Using the displacement equation for constant acceleration (http://physics.about.com/cs/acceleration/a/060703.htm), I can see how for the first 20 yards, the following equation would apply:

20 = 0.5 * a * t * t, but that reduces to
40 = a * t * t, not
40 = a * sqrt( t ), which is how I'm reading your "40 = a(t^(1/2))".

Also, wouldn't V = a * t, since the terminal velocity is attained after t seconds of constant accelaration a?

Being a simpleminded sort, I can offer a simpleminded alternative to computing a and V (and therefore, force and momentum). Based on my eyeballing of the 10-meter split times of the 40-yard dashes of the fastest women in this article (ASSESSMENT OF LINEAR SPRINTING PERFORMANCE: A THEORETICAL PARADIGM (8-page PDF) http://jssm.uludag.edu.tr/vol3/n4/2/v3n4-2pdf.pdf ), about 44% of the 40-yard time is spent covering the last 20 yards, so

20 = V * T = V * (44% * C), or
V = 20 / (44% * C)

and

a = V / t = V / (56% * C ).

Duck Dog
04-26-2005, 02:41 PM
Somebody needs to get laid more.

DanT
04-26-2005, 02:42 PM
By the way, I just found out that there's a book by Nebraska physics professor Timothy Gay, Ph.D. on football and physics:
http://football.about.com/od/football101/gr/footballphysics.htm

He was featured in a New York Times article about the same subject:


http://www.nytimes.com/2004/11/16/science/16foot.html?ex=1258347600&en=02b0178a662a2d99&ei=5088&partner=rssnyt
Crunch! Oof! Well, That's Physics
By HENRY FOUNTAIN

Published: November 16, 2004


LINCOLN, Neb. - It's third and long midway through the second quarter, and Baylor's quarterback arcs a pass 30 yards down the field into Nebraska territory. The ball is thrown in front of the intended receiver, however, and two Nebraska defenders converge on it from opposite directions. Their eyes on the ball and not on each other, they collide at nearly full tilt and the ball pops away.


To the 77,000 fans at Memorial Stadium on this October Saturday, all but a handful dressed in red in tribute to their beloved Cornhuskers, this is just a typical bruising hit, made slightly more interesting, and alarming, because it involves two players on their team. But Dr. Timothy Gay sees it differently.

"Wow, cool, a three-body collision!" Dr. Gay said from his seat in the stands. The forces in this encounter are enormous, but the players don't appear to be injured. Their pads and helmets and the shortness of the collision help protect them, and the third "body" - the ball - absorbs a little bit of the momentum.

Weekdays, Dr. Gay is an experimental atomic physicist at the university who spends most of his time smashing electrons in a basement laboratory, studying the way they scatter as a means of understanding what might go on in the plasma of a fusion reactor or a star.

On fall weekends, when the Huskers play, he makes the short walk across campus to Memorial Stadium, to pursue his avocation - football physics.

To watch a football game with Dr. Gay is to view the sport through a different lens, one where talk of fly patterns, blitzes and muffed punts is supplemented by discussions of vector analysis, conservation of momentum and strange forces that can affect the flight of the ball. At Dr. Gay's perch a dozen rows back on the 35-yard line, Isaac Newton is cited as often as Vince Lombardi, and the X's and O's of the game are enhanced by delta-V's and delta-T's.

Back at his lab after the game, he does a quick estimate of the forces involved in that defender-on-defender hit. The players, who weigh about 200 pounds each, are running at about 20 feet per second, and after they collide they bounce back at perhaps half that speed. It's easy to calculate the acceleration - change in velocity, delta-V, over change in time, delta-T - and force, which by Newton's second law is proportional to mass times acceleration.

The rough result is that the players encounter a force of about 1,800 pounds and an acceleration of 9 g's, or 9 times the force of gravity. Such forces would be bone-breaking and capillary-draining if applied over time, but in the split-second of this collision the players can withstand them. The third body helps a little too - with its much smaller mass, the football is sent flying toward the sideline by the momentum imparted to it.

Dr. Gay draws a parallel to his work. "The three-body collision - that's the kind of thing I do for a living in the lab," he said. "In atom-molecule collisions, you cannot make a certain chemical reaction go unless you have a third body in there to take up some of the momentum. It's essentially the principle of catalysis."

Dr. Gay is as much a teacher as he is a researcher, and for the past five years has been intent on teaching fans of football something of the science behind it, first with a series of humorous one-minute videos shown on the scoreboard at Nebraska games and now with a book, "Football Physics: The Science of the Game."

"My connection to football is deep because what I do is collisions," he said. "I'm really interested in what happens if I send an electron in, where it's going to scatter to, how much momentum will it transfer."

"You see that all the time in football," he added. "You see guys colliding. Obviously the physics is a bit different. In football we use Newtonian physics, in atomic collisions we use quantum mechanics."

Using Newtonian physics, he explains later in the game why it was so easy for Nebraska to score on a short goal-line plunge.

[continued on next post]

DanT
04-26-2005, 02:43 PM
[continued from previous post]

Crunch! Oof! Well, That's Physics

Published: November 16, 2004


(Page 2 of 2)



"It's just the classic advantage of the momentum of the offense," Dr. Gay said. Because the offense knows when the ball is going to be snapped and the defense doesn't, the offensive line has about two-tenths of a second to build up momentum before the defense can react.

In Newtonian terms, momentum is simply mass times speed. The Nebraska linemen are both large (on the order of 300 pounds each) and speedy (they can run a 40-yard dash in about 5 seconds), so in that two-tenths of a second the line has built up a lot of momentum - something like 10,000 pound-mass-feet per second in the sometimes arcane units of physics.


Dr. Gay put it more plainly: "They've got a head of steam so they can just bowl over the defense, which hasn't started moving yet. It's Newton's first law in action."

Dr. Gay traces his interest in football and physics to his years at prep school in Massachusetts. He wasn't good enough to make the squad, but he worked as team manager. At the same time, he took his first serious physics course. The two interests coalesced.

"Plus, this was football in New England in the fall," Dr. Gay said. "It doesn't get any better than that."

Of course, it has gotten better. With degrees from Caltech (where he was good enough, or rather the team was bad enough, that he played on the offensive line) and the University of Chicago, Dr. Gay has for the past 11 years been at Nebraska, home to one of college football's blue-chip programs and some of its most loyal fans, who have sold out every home game since 1962. Lincoln is the state capital and a college town, but every fall it is swept up in football mania. Even the portable toilets are done up in Cornhusker red.

This year, after decades of a "three yards and a cloud of dust" philosophy, in which a strong running game is crucial, Nebraska has a new coach and a new way of doing things. It's called the West Coast offense, and it relies far more on the passing game, with the receivers running quick, precise routes and the quarterback timing his throws.

In physics terms, the team has gone from relying on mass and force to emphasizing kinematics, the science of motion and time. The problem is, most of the players were recruited for the old system. So in football terms, the team has gone from good to mediocre - at least by Nebraska's standards.

In the previous week's game, momentum may have been conserved, but pride was not. "Everybody knew we were going to have a tough year," Dr. Gay said. "But we didn't expect to lose, 70-10, to Texas Tech."

This week, though, Nebraska is having an easier time with Baylor, a perennially weak opponent. After a game in which fans pleaded with the team not to throw the football, Nebraska has resorted to more of a ground attack, led initially by running back Cory Ross, who at 5 feet 6 inches and 195 pounds has a low center of mass and is hard to bring down. The Cornhusker line is also throwing its mass around, and Baylor is getting the worst of most collisions. "They're losing the battle of Newton's first law," Dr. Gay said.

That first law - and the second and third, for that matter - are old hat to physicists. "Many of my colleagues say, 'Tim, why are you doing this? This really isn't a very interesting problem, this football physics,' " Dr. Gay said.

"In a narrow sense, they're right," he added. "It's not like we're discovering new physics."

But while it's often described as a collision sport, football is not just about hitting and getting hit. The flight of the ball, for one thing, presents interesting issues. "In this case, I really think there is something new to be learned," he said.

On a basic level, a ball's trajectory has much to do with how tight the spiral is. A wobbly pass presents more surface to the wind, incurring more drag and failing to travel as far. That's one reason, no doubt, why that second-quarter Baylor pass fell short of its target. A tight spiral generally requires that the ball be thrown faster, for reasons of torque. "The harder you throw it, the more torque you apply as it leaves your hand, so it spins faster," Dr. Gay said. "That means that it's more stabilized, and you get a tighter spiral."

Dr. Gay was particularly interested in something an old prep school colleague, now a coach for the New England Patriots, told him about punts - how they tend to drift to the right or the left, depending on the direction of spin and whether they "turn over," dipping front-end down after they reach the high point of their arc.

Drawing on work by another physicist, Dr. Marianne Breinig of the University of Tennessee, Dr. Gay described the forces at work. As the spinning ball moves through the air, one side is moving in the same direction as the air moving past it, while the other is moving in the opposite direction. This results in different relative velocities, and "you actually get a pileup of air on one side," he said.

"Because the friction and drag force are bigger, you get turbulence and a force that shoves the ball." This is the Magnus force, which is what makes a spinning baseball curve.

The Magnus effect doesn't create problems on kickoffs and field goal attempts, he said, because the ball is rotating on a different axis, end over end. It might cause the ball to move up or down, but not side to side, so accuracy wouldn't be affected.

As physics concepts go, the Magnus force is fairly ethereal. Back on the field, the situation is much more concrete: Nebraska is thumping Baylor. The Huskers go on to win by 59-27, aided by Ross and another back, Brandon Jackson, who have scored three touchdowns between them. Dr. Gay, objective physicist, is also a subjective, and happy, fan, left to wonder what it is that makes players like Ross and Jackson so good.

Science, he finds, offers only a partial explanation. "As biomechanical machines they're so complex," he said. "You can talk about overall patterns and features and stuff like that, but it's difficult to say why one running back is better than another.

"You know, heart, the will to win. Physics isn't going to touch that."

Braincase
04-26-2005, 02:44 PM
God Bless Geek Culture!

HemiEd
04-26-2005, 02:48 PM
Very interesting, so you are saying the biggest and baddest will hit you the hardest? :)

KC Dan
04-26-2005, 02:51 PM
RM,
Step away from the crack pipe! Slowly!

Warrior5
04-26-2005, 02:52 PM
This thread needs a Gaz option.

elvomito
04-26-2005, 02:53 PM
no boomer?

Skip Towne
04-26-2005, 03:04 PM
You really have a lot of free time don't you?

DanT
04-26-2005, 03:30 PM
The simplifying assumption that all players accelerate at a constant rate for the same fixed percentage of their 40 yard-dash time and then move at a constant velocity from then on leads to a simple formula for the relative force that a player generates:

divide the player's weight by the player's 40-yard time

and then use that to compare different players.

For example, Shield's relative force would be 308 / 5.04 = 61.1,
while Roaf's would be 313/5.38 = 58.2, meaning that future Hall-of-Famer Shields is approximately 5% more forceful than future Hall-of-Famer Roaf on plays where the approximation would apply, like on a sweep.

chiefsfan58
04-26-2005, 04:16 PM
And I though I was a nerd. ;)

Rain Man
04-26-2005, 05:07 PM
Hey Rain Main,

Cool Post!
I'm not sure I understand all your equations. If I understand correctly, you are assuming constant acceleration (of magnitude a) over the first 20 yards and then constant velocity (of magnitude V) over the next 20 yards.

So, I can see how you'd have

20=VT (because that's the equation for the last 20 yards) and
t + T = C (because that's the sum of the first and last 20-yard split times), but I don't understand where you got the other two equations:

V=(40a)^(1/2)
40 = a(t^(1/2))

Using the displacement equation for constant acceleration (http://physics.about.com/cs/acceleration/a/060703.htm), I can see how for the first 20 yards, the following equation would apply:

20 = 0.5 * a * t * t, but that reduces to
40 = a * t * t, not
40 = a * sqrt( t ), which is how I'm reading your "40 = a(t^(1/2))".

Also, wouldn't V = a * t, since the terminal velocity is attained after t seconds of constant accelaration a?

Being a simpleminded sort, I can offer a simpleminded alternative to computing a and V (and therefore, force and momentum). Based on my eyeballing of the 10-meter split times of the 40-yard dashes of the fastest women in this article (ASSESSMENT OF LINEAR SPRINTING PERFORMANCE: A THEORETICAL PARADIGM (8-page PDF) http://jssm.uludag.edu.tr/vol3/n4/2/v3n4-2pdf.pdf ), about 44% of the 40-yard time is spent covering the last 20 yards, so

20 = V * T = V * (44% * C), or
V = 20 / (44% * C)

and

a = V / t = V / (56% * C ).


You're right on the second equation. I'm out of town right now and just solved everything on a sheet of paper at my desk, so I'm hoping that I just typed it wrong. It was just the equation S=.5at^2+Vot where Vo=0 and S = the first 20 yards of acceleration. I'm thinking it was a typo since I can crank through the accelerations and times and come up with a distance traveled of 40 yards.

The first equation (hopefully I remembered it right) is V^2 = Vo^2 +2as, where Vo=0, hence V^2 = 2as = 40a. I used that equation because I needed to get V as a function of S, which was known.

Rain Man
04-26-2005, 05:09 PM
The simplifying assumption that all players accelerate at a constant rate for the same fixed percentage of their 40 yard-dash time and then move at a constant velocity from then on leads to a simple formula for the relative force that a player generates:

divide the player's weight by the player's 40-yard time

and then use that to compare different players.

For example, Shield's relative force would be 308 / 5.04 = 61.1,
while Roaf's would be 313/5.38 = 58.2, meaning that future Hall-of-Famer Shields is approximately 5% more forceful than future Hall-of-Famer Roaf on plays where the approximation would apply, like on a sweep.

I started out doing that, and then started wondering if the fact that it was a two-phase problem (acceleration and cruise speed) would somehow impact the numbers. Plus it was more fun to try to figure it out.

DanT
04-26-2005, 07:23 PM
You're right on the second equation. I'm out of town right now and just solved everything on a sheet of paper at my desk, so I'm hoping that I just typed it wrong. It was just the equation S=.5at^2+Vot where Vo=0 and S = the first 20 yards of acceleration. I'm thinking it was a typo since I can crank through the accelerations and times and come up with a distance traveled of 40 yards.

The first equation (hopefully I remembered it right) is V^2 = Vo^2 +2as, where Vo=0, hence V^2 = 2as = 40a. I used that equation because I needed to get V as a function of S, which was known.

Thanks, Rain Man.

Now I see what you mean. By the way, that first equation is implied by the constant acceleration condition. Assuming zero initial velocity and position, the constant acceleration condition implies that V_t = a * t, which implies that the position at time t is s_t = 0.5 * a * t * t (i.e. the second equation), which implies that
2 * a * s_t = a * a * t * t = V_t * V_t.

SLAG
03-10-2006, 04:00 PM
So what does this all mean?

Donger
03-10-2006, 04:02 PM
So what does this all mean?

ROFL

Thig Lyfe
03-10-2006, 04:08 PM
Rotational velocity of William Bartee's neck = 0

SLAG
03-10-2006, 04:12 PM
Rotational velocity of William Bartee's neck = 0


ROFL


Rep

Coach
03-10-2006, 04:15 PM
Rotational velocity of William Bartee's neck = 0

Hahaha, so true.

ROFL

FAX
03-10-2006, 04:15 PM
Mr. Rain Man, this is awesome. You should also take into account Injury=I and Failure to Remember the Play=FRP.

V should be reduced by I as a total amount of time derived from adding IR time and missed practices due to injury, etc. divided by Total Possible Playing Time=TPPT. V = (V / (I / TPPT)

Then, V should be divided by FRP (Failure to Remember the Play) which is to the number of plays f*cked up by the player=F divided by the Total Number of Plays=TNP. Or, FRP = (TNP / F) V = (V / (FRP / TNP)

That should give you the total impact of the player's force on the Teams Winning Percentage=TWP.

FAX