(Insert complex mathematical equation here) - Thearon W. Henderson
Putting the "smart" in smart football analysis.
Since the day the Seahawks traded for Marshawn Lynch, fans have been fascinated with his brash, hard running style that practically demands physicality. And why wouldn't we? After countless broken tackles, stiff arms and "get off me!" moments, the surprise and "wow" factor of such physical mentality has still made countless fans squeal in joy and amazement. There is no doubt that the title Beast Mode is one that Lynch has fittingly and rightfully earned.
Yet I'm not satisfied. Why? Why could Lynch play as well and as physical as he can despite just being another football player? A man I really admired once said "It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning" and I guess part of the mystique behind Lynch's play is the mystery. But the inner science geek in me demands to understand why Lynch can be Beast Mode, and even the most ridiculous plays in the NFL can be broken down into science and physics.
This is a breakdown of the play:
7:52 - Lynch fakes the taking of the handoff, briefly slows down (but he's still moving) on the 26 yard line
7:51~7:50 - Lynch swings towards the left before reaching the numbers on the 30 yard line and again slows down for the ball
7:49 - Lynch catches the ball and re-adjusts his feet
7:48 - Lynch accelerates towards the 35 yard line before decelearrating
7:47 - Lynch sets his feet again and meets Goldson head-on on the 36 yard line
7:46~7:45 - Lynch drives Goldson 6 yards before being pulled down
The play starts. Lynch gradually jogs at constant speed (therefore a an acceleration = 0) through the fake, after one second has elapsed from the play. He plants his foot on the ground on the 26 yard line to move left.
To essentially change his direction from forward to out left, Lynch must exert an amount of force that the opposing coefficient of friction force from the turf must stop his forward movement. (This is also where Newton's Third Law, for every action there must be a equal and opposite reaction, comes in. Thanks Doug!) Force = Mass x Acceleration, so we first have to figure out how fast Lynch accelerates to before he pauses again briefly to catch the ball by Wilson.
So from what I can gather, Lynch's acceleration from resting time (from where he stomps his foot to the ground) to his deceleration again at the 30 yard line is calculated as:
a = (vf - v0) / (tf - t0)
a = (3.048 - 0) / (3 - 1)
a = 1.524 m/s^2
From then on, we can calculate the Force that Lynch exerts to stifle his movement from forwards to the left:
F = m x a
F = (215lbs or 97 kg) x 1.524 m/s^2
F = 97 x 1.524 = 147.83 Newtons
4.4 N = 1lb, so (147.83/4.4) Lynch steps with approx. 33.6 lbs of force onto the ground - simply to shift directions (and keep in mind, he's jogging!)
After maintaining constant speed (a = 0) to catch the ball, Lynch begins to accelerate again to near-full speed, peaking between the 32 and 34 yard lines, 4 seconds into the play. The average maximum speed a running back usually runs would by about 10 yards per second, or about 9.8 m/s. Let's compare that to how much ground Lynch gains before he re-adjusts to face against Godson one on one.
In about one second, Lynch has already covered 5 yards of open ground. This would be around 4.572 meters / second. And while we know Lynch is not a burner or a speedster on the field, he does have an amazing initial burst, as shown by his acceleration from where he originally started. (The orange line is the period/distance covered which Lynch maintained constant velocity (around .9144 m/s, or about a yard per second).
The acceleration would then be calculated as:
a = (4.572 - .9144) / (5 - 4)
a = 3.6576 m/s^2
A definite and immediate increase in acceleration from earlier.
Finally, the last part of the play happens when Lynch resets and decelerates into constant velocity again to prepare to matchup against Goldson. He again returns to around .9144 m/s before accelerating, this time with his body lowered.
The acceleration is also slows, coming in at .9143 m/s^2.
What allows Lynch to bulldoze the blockers the way he does is not only due to his quick burst, but also his momentum, as calculated by mass times velocity.
p = m x v
p = 97kg x 2.743 m/s
p = 266.97 kg-m/s
This is where Goldson comes in and, in turn, fails.
To make the tackle, he must come in with a greater impulse, or opposing force, than Lynch is driving at. Since impulse is defined as force x the amount of time the force is applied to, Goldson must either continue to hold on to Lynch for a long period of time or impact with a greater force. This is evident in a basic football, as the longer you hold on to a ball carrier or the harder you hit him, the more likely he will go down.
Even before he meets up with Lynch on the line, Goldson comes to a complete stop. He hesitates to ready the tackle: bent knees, arms ready to punch outward and wrap up, all the basics. He comes up to the 38 yard line from the 36 in about one second, giving him an velocity of about 1.828 m/s an an acceleration of .9144 m/s^2.
The Force would then be:
F = (200lbs or 90.72 kg) x .9144 m/s^2
F = 82.95 N
Goldson applies the tackle for two seconds. The impulse would then be 82.95 x 2, or 165.91 kg-m/s^2, significantly less then what Lynch has. Therefore, Goldson is driven backward while Lynch keeps moving forward. This is the rule of conservation of momentum, where the momentum of the two objects must remain the same after they meet. In this case, since Lynch has the greater momentum, he gets more push towards Goldson and thus, lets him "drive". In the same manner that Goldson held on to the tackle rather than bouncing him off, Lynch does not accelerates after contact, as now the speed is determined by both of the players' mass.
You might be asking yourself why this doesn't last forever. After all, why couldn't Lynch have continued to move forward and carry Goldson with him to the endzone? This is due to where Lynch's center of mass is. The center of mass, or where mass is most concentrated on in the body, is usual around the bellybutton. As you can infer, the closer you are towards the center of mass, the more mass will apply, and thus more force will be required. This is why coaches always stress tackling low - not because it's procedure or anything, but because it's farther away from where the body is. If anything, it is easier to get a 300 pound lineman on the ground through tackling through his shoelaces and feet rather than pushing him down.
When Goldson meets Lynch, he meets him high - more bad news for him coming in with such low momentum.
Lynch drives forward, but Goldson holds on to him steadily, gradually increasing his impulse while decreasing Lynch's momentum. It is only when Goldson loses his balance does he take Lynch down with him.
The force to which Goldson carries with him to the ground is calculated through the Earth's gravitational acceleration, where g = 9.81 m/s^2 .
F = 90.72 kg x 9.81 m/s^2
F = 889.96 N, or around 202.26 lbs.
Since it only took Goldson one second to take Lynch down, the impulse would also be 889.96 N or 889.96 kg-m/s^2, which is now suddenly greater then 266 kg-m/s^2 (which has considerably lowered following Goldson grabbing and holding on to him). Lynch finally falls forward for a 12 yard gain, half of which his momentum was generated through 415 pounds of mass.
To clarify, he's a quick recap of what happened:
This is only a brief, albeit shorthand version of all the things that go onto a football field, and most coaches and players probably won't translate such stuff onto the field anyways. Nevertheless, if there's anything important that science has taught us is that one time, Marshawn Lynch ran so hard only gravity could bring him down.*
(*The numbers calculated above are in no way 100% accurate.)