The Physics and Paradoxes of the Snatch

The first contested lift in the sport of weightlifting, often called olympic style weightlifting or olympic weightlifting, is named "the snatch" (and is often on the receiving end of jokes). The rules are relatively simple. A weighted barbell starts on the floor, and the lifter takes it from the ground to a position overhead, standing fully, arms locked out. Essentially, you start like this:

and end up like this:

The first picture is Greg Everett of Catalyst Athletics, and the second is Lu Xiaojun of the Chinese national team. 

Seems simple enough, right? It is, until you consider the fact that in the picture above, Xiaojun is holding 160 kilograms overhead, or approximately 352 lbs. It's even more impressive when you consider the other fact that this is over twice his bodyweight. Xiaojun competes in the 77 kg weight class, or approximately 170 lbs. 

So, how did he do this? As strong as he looks, I don't think anyone would make the argument that Xiaojun is capable of simply rowing this weight off the floor and pressing it overhead. I have purposefully addressed only the beginning and end states of the snatch. What happens in between these two positions requires a requisite level of athleticism that defines weightlifting as an olympic sport. 

As strong as the men and women of the sport of powerlifting are, their particular sport simply measures one of what I call "the parameters of athleticism," namely strength. To be a successful powerlifter, you must possess near Hurculean strength. However, you are not required to possess speed, agility, flexibility, explosiveness, or be, ironically, particularly powerful. 

Yes, I did just make the claim that powerlifters aren't particularly powerful, but let me make a qualification. Powerlifters aren't powerful compared to weightlifters. The definition of power is the time rate of change of work. Work is a vector combination of force and displacement (specifically the "dot" or "inner" product), and itself is a scalar, i.e. not a vector. Put succinctly, to be powerful you must perform your work in a short period of time.

It will be instructive to see the snatch in action. In the video link below, Chad Vaughn, a former American competitor in weightlifting, is shown performing the snatch in slow motion with a weight of 129.5 kg, or 285 lbs.

Chad Vaughn snatch.

In the video you can see that Vaughn doesn't lift the weight particularly high. He pulls the weight first to his hips, and then applies some more pull after that which elevates the bar to slightly above hip level. He then, almost magically, places himself directly under the bar and catches it in a deep squat, after which he stands. In real time, the elapsed time from when he first breaks the bar from the ground to the point where he has received the bar is less than one second.

It is this portion of the lift that makes it so powerful. Take Vaughn's lift of 130 kg. Let's say in the process of the lift, he elevates the bar 1 meter, and this process takes him 0.8 seconds. The work performed is:

W = Fd = (130 kg)(9.81 m/s^2)(1 m) = 1275.3 N-m

and the power output is

P = dW/dt = (1275.3 N-m)/(0.8 s) = 1.594 kW

This is approximately equal to 2.1 horsepower, which is impressive considering the definition of a horsepower is the power required to raise 75 kg by 1 m in 1 second, historically attributed to an effort accomplishable by a horse lifting the weight via a pulley.

A measurement of the accelerations of the bar would be interesting and enlightening, but requires more sophisticated software that is currently available to me. 

The physics of the lift are relatively simple. The bar is accelerated off of the floor, and then maintained at nearly a constant velocity until the bar is near the hips. The lifter then uses the strength of the hips to accelerate the bar again. This second acceleration is key to a successful lift.

With no acceleration, the lifter is applying a force to the bar that is exactly equal to the weight of the bar. If the force of the lifter is then removed, the bar will immediately reverse direction and begin accelerating toward the floor, under the force of gravity. More technically, the bar begins in a state where the sum of forces acting upon it is zero, and ends in a state where the sum of forces is non-zero. 

Now take the case where the lifter is applying a force greater than the weight of the bar. In this condition, the bar is accelerating in the direction of the lifter's force, i.e. upwards. The more force the lifter applies in excess of the bar's weight, the higher the acceleration will be. The higher the acceleration is, the larger the velocity will be when the lifter stops applying force. 

Why does this matter? It matters because the lifter needs to get underneath the bar, and this requires time. And in this time, the lifter must execute something paradoxical: they need to be both strong and fast at nearly the same time. More on this later. But first, an energy balance on the bar will show why the final explosive acceleration is needed. If the initial state of the bar is the point where the lifter stops applying force, and the final state of the bar is the moment it reverses direction in the air, then setting the kinetic and potential energies equal yields:

(1/2)(m)(v^2) = mgh

and therefore:

h = (v^2)/(2g)

The higher the velocity is at the point where the lifter stops applying force, the higher the bar will travel. This is because gravity needs time to reverse the upward velocity of the bar, and hence to reverse the bar's momentum. The bar's velocity is increasing upward during the final explosive pull with the hips. This changing velocity takes more time to stop. A constant velocity takes nearly no time to stop, since the instantaneous force on a constant velocity object is zero. Physicists enjoy pointing out the fact that energy balances such as this are independent of the mass (and hence the weight) of the object. That is, an anvil and a tennis ball that are launched directly upward from the same point at the same velocity will travel to the exact same height. This is the converse situation from dropping the tennis ball and anvil from the same height and observing that they reach the ground at the same instant. However, inertia dictates that it is much more difficult to accelerate an anvil to the same speed as a tennis ball. 

To observe that a non-accelerating object will reverse direction almost instantly, take any object that you don't mind dropping on the ground. Move it upwards at a constant speed (or as close as you can get) and then release it. You'll see that the object reverses direction and begins falling toward the floor nearly instantaneously. Compare this to first accelerating the object prior to releasing it. The object will continue to travel in the direction of acceleration for some time prior to reversing direction. For the purposes of inertia, an object moving at a constant velocity is about the same as an object not moving at all. This should not be confused with momentum, of which a stationary object obviously possesses none. 

The stronger a lifter is, the more force they will be capable of applying in excess of the weight of the bar, the more they will be able to accelerate the bar, and the higher the bar will travel, giving them more time to get underneath the bar before it reverses direction. 

Now consider this... think of the last time you tried to jump as high as you could. Or, try it right now. In the jumping position, was your body relatively tense or relaxed? With a little experimentation you can see that jumping from a relaxed position results in a higher, more easily executed jump. This occurs due to much of the same reason as the above discussion on acceleration. Tensed muscles are in a condition where the are already applying force (in order to contract). When this is the case, there is less of a force differential in the muscle prior to jumping. Compare this to a relatively relaxed condition, where the build up of force occurs rapidly. A large change in force applied over a distance in a short period of time. This is, again, power. You are more capable of generating power in this position. A pre-contraction of the muscles almost parasitically removes force from the jump.

And herein lies the paradox. While performing a slow lift, such as a deadlift or a squat, the lifter wants tension in the body. This tension prevents unwanted accelerations of the weight. It puts the lifter in a position where they are in full control of the lift, and their muscles are at their strongest and most structurally solid position prior to putting them under load. This type of muscular tension results in a slow, controlled lift, as seen in powerlifting and strongman competitions. 

The first part of a snatch is almost like a deadlift. In fact, sudden accelerations of the weight in the first pull of the snatch are undesirable, as it may put the lifter in a poor position to receive the weight overhead. From the floor, the lifter slowly builds tension to break the bar from the ground. Some acceleration here is inevitable, but the first pull is completed at nearly a constant velocity. The lifter completes the next part of the lift by a sudden acceleration imparted to the bar by the hips, transmitted through the tension in the arms, and ends up in this position:

The lifter shown is Mat Fraser. At this point, Fraser is in a position of high muscular tension. He has used nearly all the muscles of his posterior chain in a powerful way to accelerate the bar over a very short distance, but he must now rapidly get under the bar. 

Being tense and being fast are almost physiological opposites. It is difficult to move quickly while carrying tension in the muscles; just ask any martial arts instructor on the philosophy of throwing a punch. From the point that Fraser is shown in, he must shed nearly all tension and rapidly move into a position to receive the bar. Once he's in position to receive, he must then immediately rebuild tension to provide a solid structure to carry 305 lbs overhead. This tension-speed-tension cycle happens very, very quickly, and is the reason weightlifting is one of the most challenging sports.

There is one last use of physics that makes this part of the lift possible. Recalling the previous discussion about the falling anvil and tennis ball, a second paradox arises. The lifter's feet are not attached to the floor, and so the lifter cannot apply a force with their legs to assist in accelerating towards the ground. That is, the legs can simply remove tension and allow gravity to pull them down. But the barbell will also be accelerating toward the ground at the same rate. Assuming the lifter is performing a near-maximal effort lift, how can it be possible to the lifter to get under the bar faster than the bar gets to the floor?

Upward acceleration was discussed previously, but at near-maximal loads the acceleration will be small, and so the window of opportunity for gravity to move the lifter all the way under the bar before it begins returning to the ground will not be large enough. The lifter will lose the race... or, more correctly, the lifter and the barbell will tie each other.

There is a way for the lifter to actually push themselves downward... the barbell. As the barbell is accelerating upwards, the lifter removes tension from the legs and uses their arms to apply a force upward on the bar. As a result of Newton's third law, the barbell will then apply a force downward on the lifter. The lifter now has the force of gravity and the force of their arms pulling down and then pushing up on the barbell to assist in accelerating them into the receiving position, catching the barbell at the apex of its travel.

Oh, and by the way, that rebuilding of tension thing needs to happen again in order to successfully catch a heavy load overhead. And the lifter still needs to be able to stand up.

Why is the snatch so difficult? During execution of the snatch, this entire blog post happens in less than one second. This also makes successful execution of the snatch one of the most rewarding feelings in all of sports.