Great, let’s all train for power. However, to do that we need to know just what power is, and that’s aim of this article.

How Hard Are You Working?

We know that when we push or pull against an object we’re applying a force (if you don’t know this, see my article on force-time curves), and if we push or pull hard enough the object will move, in accordance with Newton’s first law of motion. When the object you’re applying force to moves in the same direction, you’re performing work – the product of force and distance.

This is very useful, because, like impulse, work adds greater detail to any description of the mechanical characteristics of a movement by combining effort (force) with outcome (displacement). We can get a pretty good idea of how much work is been performed by first estimating the force applied to the mass and then multiplying it by the distance that it travels.

A Lifting Based Example – The Deadlift

If you load a barbell up to 200 kg and your deadlift range of motion is 50 cm, the vertical work that you perform can be calculated like so:

Force = 200 (barbell mass) × 9.81 (acceleration of gravity) = 1, 962 N

Then multiply this by the distance you lift the barbell:

1, 962 × 0.50 (meters) = 981 J (joules) of work

Pretty simple, right? However, we must remember that other work was performed during this lift. For example, work was performed to move our body’s center of mass. However, unless you have access to the sort of kit that’s typically only found in well-equipped biomechanics laboratories you won’t be able to measure this. For those of you who are interested, Dr. John Garhammer provides a range of examples in his excellent review of power measurement (see the reference list at the end of this article).

If we we’re feeling ambitious, we can take the example of the vertical jumper from the force-time curves article and calculate the work he performed like so:

Jumper weight (force) = 787 N × 0.27 m (his jump height) = 212.5 J

Quite a difference, and this is where power comes in.

What About Energy?

But hang on, what about energy? Mechanical energy can be defined as the capacity to perform mechanical work. Humans possess mechanical energy, and this is typically found in the form of either potential energy or kinetic energy, where the former can be simplified as existing as a consequence of position:

Potential energy = mass × acceleration of gravity × height (or distance)

And the latter can be simplified as existing as a consequence of motion:

Kinetic energy = mass × velocity² ÷ 2

This gives us a little more information, but means that we need some way of measuring how quickly the mass we’re interested in is moving. It also highlights that what we’ve been able to calculate so far is actually an estimate that can be made using the relatively little information we have. Ideally, we’d have a record of either motion or force (or both) recorded over known time intervals to obtain accurate records of work, energy or power. (Page 97 of Drechsler’s Encyclopedia of Weightlifting provides a relatively simple way this can be done.)

Interestingly, at the top of the vertical jump our jumper has potential energy:

Potential energy = mass (80 kg – ish) × acceleration of gravity (9.81) × height (0.27) = 212 J

Which should look familiar (see above), but he has no kinetic energy:

Kinetic energy = mass (80 kg – ish) × velocity² (0 – top of the jump) ÷ 2 = 0

Which shouldn’t come as a surprise! If we were to calculate the kinetic energy of our jumper at take off, though, it would be much more than 0:

Kinetic energy = mass (80 kg – ish) × velocity² (2.31 m/s at takeoff) = 5.34 ÷ 2 = 213.4 J

This number is starting to look familiar (give or take a few joules). So, we perform work by applying a force to a mass to move it. We do this and our capacity to perform work changes. Pretty simple.

The Definition of Power

Now we get to the fun bit – power. What is it? Power is simply the rate at which we perform work. So, it’s a combination of force and how quickly we can move something in a given direction, which is also known as velocity (think back to my first article). Therefore, power can be calculated in one of two ways:

Power = work ÷ time or Power = force × velocity

Why Is Power So Important?

To illustrate its importance let’s think back to the two examples we used earlier. (However, I’d once again recommend you find a copy of Garhammer’s paper for other examples, and a classic lifting-related example comparing deadlift and clean work and power can also be found in Dr, Pat O’Shea’s book: Quantum Strength Fitness II.)

Now, if you have a 300 kg deadlift the 200 kg lift we discussed earlier would represent about 67% of this one repetition maximum (1 RM), which means that you could probably lift it relatively quickly, in about 1.5 seconds. Therefore, an estimate of average power applied to the barbell could be obtained like so:

Force = (1, 962 – see above) × velocity (0.50 m ÷ 1.5 s = 0.33 (ish)) = 647 W (watts)

Of course, the heavier the lift, relatively to your 1RM, the longer it’s going to take to complete. The longer the lift takes to complete the less power you’ll be applying to the bar.

This demonstrates the simplest way to train power – train strength. Get stronger and you’ll be able to lift the same amount of weight (say 200 kg) faster. You’ll need to apply the same amount of (average) force, but velocity should be greater because you’re able to lift more quickly.

Of course, once you’ve saturated the whole ‘getting stronger’ thing there are other methods that can be used, some of which have been discussed on Breaking Muscle, and some that I’ll try and touch on in future articles.

Where Do You Stand?

Finally, let’s consider a simple method that will let you figure out where you stand. You can measure your vertical jump quite easily, and if you do this you can get a pretty good estimation of your peak power output by doing some simple math. You could obtain jump height from video footage (from your phone for example – see reference to Drechsler above) and, if you know how many frames it records per second, calculate ‘flight time’ – the time you spend in the air. Jump height can then be recorded like so:

Jump height = (flight time² × 9.81) ÷ 8

An even easier way of recording jump height can be found here – an excellent resource that also provides ‘power calculators’ toward the middle of this page. Of all of these I would recommend using the ‘Sayer’s Equation.’

So there, you have it. Power is the product of how quickly something moves when we push or pull it, and has obvious implications for sports performance. This, of course, is why such a big deal is made about it, and it’s something I’d like to go into more detail with in future articles.

References:

1. Baker, Daniel. “Differences in strength and power among junior-high, senior-high, college-aged, and elite professional rugby players.” Journal of Strength and Conditioning Research 16, no. 4 (2002): 581-585.

2. Drechsler, Arthur. The Weightlifting Encyclopedia: A Guide to World Class Performance. Flushing, NY: A is A Communications, 1998.

3. Garhammer, John. “A review of power output studies of Olympic and Powerlifting: Methodology, performance prediction, and evaluation tests.” Journal of Strength and Conditioning Research 7, no. 2 (1993): 76-89.

4. O’Shea, Patrick. Quantum Strength Fitness II (Gaining the Winning Edge). Patrick’s Books, 2000.

Photos courtesy of Shutterstock.

The post Power: What It Is, Why We Want It, and How We Generate It appeared first on Breaking Muscle.

Now, although very exciting, we didn’t really go into much detail, and detail can be important, especially when we’re talking about how we apply the forces that cause movement.

In my last article we covered a few of the relatively simple, but fundamental definitions that underpin sport and exercise biomechanics, relating them to the kettlebell swing.

Now, although very exciting, we didn’t really go into much detail, and detail can be important, especially when we’re talking about how we apply the forces that cause movement.

This article will focus on an important type of movement pattern: force-time curves, which illustrate how we apply force over time.

We’ll combine this with an explanation of Newton’s laws of motion and how they relate to the study of sport and exercise using countermovement vertical jump performance (in which the subject bends at the hips and knees before jumping). Understanding this creates a foundation for future review.

Recap: What is Force?

Recall that “… force is a pushing or pulling action that one object exerts on another.” So, if we want to move something, whether it’s barbell, kettlebell, or our own body, we have to push it or pull it – apply a force.

In the case of our jumper, force is applied to his center of mass, the point around which the masses of his segments (e.g. arms and legs) are distributed to help maintain balance.

Newton’s three laws of linear motion provide a framework of how we control movement with force, and the effect this can have on performance. Applying force to cause motion will only work if it is sufficient to overcome the inertia of the object – Newton’s first law: the law of inertia.

Inertia: It Won’t Move Itself!

Inertia is one of those words that is generally misused. In relation to Newton’s first law, inertia is the reluctance of an object to change its state, where state simply refers to whether it’s moving or not. It’s this state that is controlled by the application of force.

So, an object will remain stationary until it is pushed or pulled – force is applied. Or, once moving it will keep moving; until pushed or pulled, that is, by, you guessed it, applying a force.

But how do we control this state? The giveaway is the standard unit that inertia is reported in: the kilogram, the unit also used to report mass (well, in most of the world anyway).

This introduces perhaps the most basic type of force: weight, which is the product of mass and the acceleration of gravity. Therefore, to overcome inertia (move something) of an object we have to apply a force that exceeds its weight.

Force-Time Curves: A Basic Human Movement Pattern

From a practical perspective this is where it can get quite exciting. Human movement tends to be underpinned by the application of force to the ground through the feet (or hands, see Becca’s article on push up force).

Force platforms enable us to record these forces, and using Newton’s laws, we can manipulate them to obtain a better understanding of the mechanical demands of different types of movement (see previous article for example).

To get back on track though, Figure 1 shows the typical vertical force-time curve from vertical jump performance.

Figure 1. Typical vertical force-time curve from countermovement vertical jump performance, vertical force applied to the center of mass of our jumper.

One of the first things we tend to do to make sense of a force-time curve is determine the subject’s weight from the period of ‘quiet standing’ that can be seen in Figure 2.

In this case body weight is 787 newtons; dividing this by the acceleration of gravity (9.81) yields a body mass of just over 80 kg. We can then start thinking about applying Newton’s second law to get more information about how much force has been applied, and how much movement this will cause.

Figure 2. Annotated vertical force-time curve.

• The ‘y’ axis to point ‘a’ shows ‘quiet standing’, which is equal to the subjects’ body weight
• Point ‘a’ to ‘b’ shows ‘unweighting’ – the subject dips their knees, travelling in the same direction as the acceleration of gravity
• Point ‘b’ to ‘c’ shows the increase to peak force, where the subject slows downward movement to the lowest point of the dip
• Point ‘c’ to ‘d’ shows ‘active’ jumping (leg extension) force
• Point ‘d’ shows ‘takeoff’; points ‘d’ to ‘e’ ‘flight’ or ‘air’ time

Force, Mass, and Acceleration

Recall from the last article that force is the product of mass and acceleration (F = ma), and we can use this to decipher Figures 1 and 2.

If we know that F = ma, we can manipulate force data, like that presented in Figures 1 and 2, by dividing it by the mass of the subject, converting our force-time curve into an acceleration-time curve.

However, we need to remember Newton’s first law where we have to overcome the weight of our jumper: 787 newtons. We can simply subtract body weight from Figure 1 before dividing it by mass, which would render ‘quiet standing’ force zero.

Force would have to exceed zero to influence motion or accelerate the mass of our jumper. An example of our acceleration-time curve can be seen in Figure 3.

Figure 3. Annotated vertical acceleration-time curve – the acceleration of the center of mass our jumper during his jump.

This is great, but doesn’t tell us an awful lot. However, a little jiggery-pokery, in the form of some numerical integration, enables calculation of velocity – how fast our jumper moves.

Figure 4 shows velocity-time, and what are often referred to as peaks and troughs, which provide an indication of movement direction: troughs below zero indicate downward motion, peaks above zero upward motion.

We could take this a stage further and numerically integrate this velocity-time data to obtain displacement, or motion, but key measures like jump height can be quite easily obtained using equations of uniform motion.

To do this we need to determine the velocity of our jumper at takeoff, square it, then divide it by 2g (9.81 * 2), which in this case equals the following:

5.34 (2.31 [takeoff velocity²]) ÷19.62 (2g) = 27 (cm) (fairly mediocre)

Figure 4. Annotated vertical velocity-time curve – how quickly the center of mass of our jumper is moving during his jump.

We calculate mechanical power now by multiplying our force-time data by our shiny new velocity-time data, but let’s leave this to another article, where we can do the topic justice.

Before we finish however, we should consider the practical relevance of Newton’s third law.

Action: Reaction

This is perhaps Newton’s most famous law, and it states that for every action there is an equal and opposite reaction.

Perhaps without realizing it, this law has been at work throughout our analysis in as much as if our jumper had pushed against the ground and not met an equal an opposite reaction, jump performance would have been quite tricky.

You see it’s this reaction – in combination with Newton’s second law (and friction) – that enables us to control how we move, and it seems so much easier to understand once we understand laws 1 and 2.

Figure 5. Forces during vertical jump landing.

The one downside to this is that it also yields a mechanical consequence. For while the reaction enables us to move, it can also act as that all-important stopping force, bringing motion to a crashing halt.

This is illustrated in Figure 5, which focuses on the change in vertical force as our jumper lands. Indeed, up to this point, our analysis has focused on the first aim of biomechanics:to improve performance, while the forces shown in Figure 5 enable us to consider the second aim of biomechanics: to minimize injury.

Identification of problem areas, like jump landing, enables us to implement technique changes to landing strategies with the aim of reducing landing force, and thus minimize injury.

Our jumper came to a halt with the help of a force equal to nearly 7.5 times his body weight. As a final thought, Figure 5 can also tell us how quickly landing force was applied to the body. In this case it was 56 milliseconds (0.056 seconds).

Dividing landing force by landing time yields something called loading rate, which in this case was just under 132 bodyweights per second – potentially problematic.

To conclude then, we can use Newton’s law of motion to manipulate force-time data to get an idea of the different phases of performance, like the vertical jump, its demands and consequences.

We’re going to use this foundation in future articles, the next of which will cover power.

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I love my job! I teach and study sport and exercise biomechanics. It feels more like a hobby than a job, and the fact that I get paid to do it is a bonus. My research focuses on the mechanical demands of resistance exercise, and my own training interests have influenced this. In this article I want to combine my teaching head and research head to go over some of the basic terminology used in sports biomechanics research using examples from my research into kettlebell exercise mechanics.

Swing Biomechanics

Recently a colleague, Dr. Mike Lauder, and I published two kettlebell related research papers. Indeed, our sports biomechanics laboratory at the University of Chichester, here in the United Kingdom, is one of only two that I’m aware of currently studying the biomechanics of kettlebell exercise. Breaking Muscle contributor, Andrew Read, recently presented an excellent review of our second study, which was a training study that quantified the effect of six weeks of bi-weekly swing training on maximum and explosive strength. I’d urge interested readers to take a look, although the study essentially showed this training program improved maximum strength by about 10% and explosive strength by about 20%. However, it’s our first kettlebell related study that I want to focus on in this article, and I want to use it to provide a foundation to clarify what we’ve studied, why we’ve studied it, and what our results mean.

‘Mechanical Demands’ – Come Again?

Our first study was titled: “Mechanical demands of two-handed kettlebell swing exercise.” Sounds very exciting, if you like that sort of thing, but what does it mean? This is a good question from which the other points I want to cover can be answered. Simplistically, mechanical demands refers to the biomechanics of the exercise. First things first though. Let’s make sure we don’t leave anybody behind and begin this next section with a couple basic definitions, the first of which should focus on just what biomechanics is.

Sure, we’ve all heard of biomechanics, possibly used it in training related conversation, but let’s make sure we know what it means. According to Bartlett (2007), sports biomechanics is: “…the study and analysis of human movement patterns in sport,” and we use mechanics – a branch of physics – to study these. To quantify the mechanical demands of the swing we decided to measure how far and how fast the kettlebell moved and what underpinned this. In this case all of these measures represent a human movement pattern, and plotted against time provide a record of that movement that can provide important information if you know what you’re looking at.

How Far, How Quickly?

Okay, now it’s time for definitions two and three. To describe the motion of an object in a given direction we use displacement, how fast it moves in a given direction, velocity. These are excellent examples of a human movement pattern, and the direction component is important because swing movement is relatively unique because of the way horizontal (forward and backward) and vertical (up and down) motion combines. I would go as far as saying it is a combination of this movement pattern and its movement velocity that led to significant improvements in both maximum and explosive strength seen in our training study.

The trajectory, or flight path, of the kettlebell can be obtained by plotting vertical displacement against horizontal displacement, and typical kettlebell trajectory is displayed in Figure 1 below. To give you an idea of what this means, the total kettlebell displacement was equal to about 71% of the subjects height, or about 128 cm, and the ‘bell produced an arc-like trajectory. I say ‘resultant’ because we were aiming for maximum impact, which tends to require getting to the point, so rather than report both horizontal (forward and backward) and vertical displacements individually we calculated and presented the resultant. This is calculated in much the same way one might calculate the hypotenuse of a right-sided triangle (the adjacent side would be the horizontal, the opposite the vertical displacement for the kettlebell swing). We studied 16, 24, and 32 kg swing performance, and load didn’t affect this displacement. Figures, when you think about it. Of course, there will come a point when load will effect displacement, but for our subjects 32 kg wasn’t it. However, their swing performance did slow (by about 12%) as load increased.

Figure 1. Typical kettlebell trajectory during two-handed swing performance. Sx = horizontal displacement; Sy = vertical displacement.

Not the Whole Picture

This may have important implications, from a training perspective, but this is the outcome. We need a little more insight to achieve a more rounded picture of the effect on movement mechanics, which will ultimately influence one’s training response. We can find this out by studying the force that’s required to cause this unique movement pattern.

Force

What causes this relatively unique movement pattern? To get to the bottom of this we’ll need to get a few more definitions out of the way. Let’s start with one we’ve all heard of: force. There’s lots of different ways to define force. However, force is essentially how hard one pushes or pulls another object. Remember Newton’s Law of Motion? According to his second law, force is the product of mass and acceleration, or: F = ma. Therefore, we apply force by simply standing still. However, it’s the force that causes motion that we tend to be most interested in and from a sport or exercise perspective study of force with respect to time is the way to go. One way of doing this is to study impulse.

Impulse

Impulse takes this a stage further, considering both how hard one pulls or pushes and the amount of time it’s applied. According to Newton’s Second Law of Motion, impulse (force * time) is equal to the change in momentum. Momentum seems to be one of those terms that are used to describe all sorts of things. In a mechanical context though, it describes the product of an objects mass and velocity. Because the mass of the kettlebell and lifter remain constant, impulse describes the change in their combined velocity. Motion is underpinned by impulse. No impulse = no motion. Its study provides far greater insight into the mechanical demands of a movement. Our results showed that combined horizontal and vertical impulse was maximized during swing performance with 32 kg, beating both back and jump squat equivalents.

The Wrap Up

So, we now know what biomechanics is. We also know how we use it to study one of our favorite bits of exercise equipment. If anybody feels a nosebleed coming on please get in touch, especially if you plan to follow future articles that will expand on the application of biomechanics to strength and conditioning.

References:

1. Bartlett, Roger. Introduction to Sports Biomechanics. Abingdon, UK: Routledge, 2007.

2. Lake, Jason., and Mike Lauder. “Mechanical demands of kettlebell swing exercise.” Journal of Strength and Conditioning Research 26, no. 12 (2012): 3209-3216.

3. Lake, Jason., and Mike Lauder. “Kettlebell swing training improves maximal and explosive strength.” Journal of Strength and Conditioning Research 26, no. 8 (2012): 2228-2233.

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