The other week a blog was linked on a board I read, and it was a discussion loosely titled as “explosive movements don’t make you explosive”. This is a recurring theme amongst some elements of the strength & conditioning field, most notably the more rapid later-comers of the HIT and SuperSlow schools of thought.

I added a few comments to the discussion, because I felt the gentleman in question was mistaken on a few assumptions. Firstly, I linked to several studies that showed the addition of elastic bands to regular strength-training to be more effective at developing both strength and power when compared to regular weights (PMID: 16686552, PMID: 18550975).

This sparked a tangential discussion – namely, what does variable resistance training (the fancy name for adding bands or chains or anything that changes the normal resistance curve) have to do with training explosively?

As I explained, explosiveness has to do with force production in the working muscles. My opponent however was under the impression that explosive training implied high speed. Since this is a misconception that comes up all the time, I figured it’d make for a good blog post.

* Disclaimer: This post is going to involve a tiny bit of math.* For you folks that may be somewhat hazy on the subject (like myself), I’ll be keeping this as visual and non-technical as I can, though you do have to invoke some small amount of calculus to discuss the topic meaningfully. Don’t worry, I don’t understand it that well either so this isn’t going to be equation-heavy. More equations means more room for me to screw up – and if any of you readers more savvy than I catch errors, please bring them to my attention.

### A Little Math Background

The first and most important thing to understand when talking about any motion-related value is that we’re dealing with *rates of change*; we’re dealing with how some value *x* changes over time *t*.

The classic example of this is the relationship between position and velocity. Position is just what it sounds like; the location of an object in relation to some other point. It can be a set of coordinates on a graph or it can be “down at the corner of 5th and Main”.

Now the object moves. If you plot this motion on a graph, showing how the object’s position changes as each second passes, you’ll get a line that represents *position with respect to time*; this is the velocity of the object. Phrased in other terms, each point on that graphed line represents the *rate of change of position*. The value of each point on this line represents the object’s velocity (which is the rate of change of position, just so you don’t get confused).

You’ll usually see velocity given by the formula Δx/Δt (the Δ is the Greek letter delta, which means “change in value”) – the change in position *x* with respect to the change in time *t*. However this is only the formula for the average velocity over a given interval of time. If you want to know the velocity at any given point on that interval, we have to use other trickery. That’s where calculus comes into the picture.

There’s a method used to find that value for any point on a graphed equation like this, which is called taking the derivative. The derivative is just a way of finding the curvature at any point of the line – which in turn gives you the rate of change at any point. Note that this works for any quantities that change with respect to another quantity; in the physics of motion this tends to be a change with respect to time, but any quantities will work.

To reiterate, we’re looking at how a value changes over time. The specifics of the math are helpful to understand it, but that’s the key point to remember.

### The Force-Time Curve

Analyzing human movements mathematically will come down to plotting *force with respect to time* – called the force-time curve. Or, how force changes over the duration of the movement.

I want to point out that force created by your muscles is responsible for any and every movement your body makes. This is regardless of speed or any other property – it all comes down to the contraction of your muscles to create force.

It’s also important to distinguish between internal and external activity. Regardless of any movement in the barbell, or dumbbell, or shotput, or your own body, or anything else that you’re moving, your muscles always have to contract to create force. The external action (what moves) and the internal action (what your muscles do to make it move) are not identical.

From that understanding, we can go on to look at the other properties of movement.

### Defining Speed and Power

I’ve already mentioned that velocity is the rate of change of an object’s position. This is effectively the same thing as the object’s speed, although there is a subtle difference – speed is just the magnitude of the object’s motion, while velocity has both magnitude and direction. I bring this up just for the sake of correctness; for my purposes here it won’t really come up.

Speed of movement is usually tied up in most people’s understanding of “explosive training”, and both of those terms get conflated with “power” – a term that is so misused that it hurts me deep down inside.

I want to point out that speed is a purely external property – that is, it’s only relevant to the object being moved. Your muscles still have to contract to apply force, one way or another; creating speed is only one outcome of that. Remember this, because it will be important soon.

So we know what speed is. What about power?

Power requires us to talk about a slightly different concept: work, which can be thought of as how far a given force moves an object. If you move a 100kg barbell over half a meter, you’ve done work with that barbell. This is one instance where internal and external action are important to note: if you hold that barbell in place, the bar isn’t doing any work because it’s stationary. Your muscles, however, are having to do work to hold the bar in place – they have to overcome the force of gravity to hold it there.

That’s all I’m going to say about that because you don’t really need to know much more about work itself. Now that you have an idea of that, we can say that power is the rate of doing work, with average power being given by the formula W/t. To continue with the idea of rates of change, *power is the change in work with respect to time*. If force is constant, then power can be defined as Force times Velocity. Unfortunately force is rarely constant, so we usually have to look at the integral equation for power…which I’m not gonna do.

You can just think of power as being the motion that results from force in a given amount of time; a high power value implies that a relatively large force created a relatively large motion. This is why plyometric exercises and the Olympic lifts are considered high-power exercises – they both involve very large (if brief) forces that create rapid motion. Both of these “fast” movements do a large amount of work in a short interval of time.

I would have you note that both speed and power are related quantities, in that they both imply “fast” external motion. Note that high power doesn’t always involve maximum velocity, or vice versa. I do need to point out something else: both speed and power are often used synonymously with the word “explosive”, which is wrong.

Power is related to explosiveness, yes. The speed of an object is related to explosiveness in the same sense. Yet neither of them actually implies “explosive” movement. So what’s going on here?

### So What is Explosiveness, Then?

Go back to the force-time curve I mentioned before, and recall what I said about how each point on the graph gives you the rate of change at that point. On the force-time curve, the slope of the graph at any point is the *rate of change in force with respect to time*. If you plot that value on a graph, you get another piece of terminology: * Rate of Force Development* (RFD). Mathematically, this is defined as (dF/dt), or the derivative of force with respect to time.

Force itself is defined as the change in the momentum of some mass; this is the source of the commonly-cited F = ma equation. Force implies a change in an object’s motion. I’d have you notice that there are some implications to this: namely, a large mass with a low acceleration can still imply high force just as a small mass with a high acceleration.

This is why you see coaches speaking of different “kinds” of strength. A heavy but slow maximum-effort lift requires a lot of force to move, even though it’s going slow. Likewise, a low-mass object that is accelerated very rapidly, aka speed-strength like the baseball or tennis-serve examples, requires a lot of force to move. There are differences in how force is developed and applied in both cases, but high muscular forces are involved regardless.

Which brings me, finally, to explosiveness. If you consider the RFD curve, which can be defined as “how quickly force is developed by the working muscles”, then explosiveness is simply the maximum value of that curve. Phrased differently, we can say that *explosiveness is the ability to produce maximum force in minimum time*.

Explosiveness (or explosive strength if you prefer) is given by this equation: S_{e} = F_{max} / t_{max} (as Newtons per second). For any given force created, the lower the time value (i.e., the faster that force is applied), the more explosive the movement. In real terms, a 100kg bench press completed in 0.5 seconds is more explosive than a 100kg bench press completed in 3 seconds, and a 150kg bench press done in 2 seconds is more explosive than the same lift in 3 or 4 seconds.

Effectively, explosive strength is an “internal” or muscular value; it applies only to what’s happening within your muscles as they work to produce force against the external object. The actual speed or power of that external movement is largely irrelevant. I say largely because obviously there is a very real overlap with power here.

Paraphrasing Dr. Zatsiorsky who summed the issue up in *The Science and Practice of Strength Training*, “a powerful athlete is always strong, but a strong athlete is not always powerful”. The implication is that a powerful person must be strong, and thus capable of producing high forces; but being able to produce high forces alone is not a guarantee that a person will be powerful.

You can see that explosiveness as defined by the RFD curve really has nothing to do with fast movement, although they can be closely related. A fast movement and a powerful movement will result from a high RFD, but a high RFD doesn’t always mean that a movement was fast or powerful. This is why using bands and other methods of accommodating or variable resistance qualifies as “explosive training” – they involve rapid generation of force in the working muscles.

Now as noted there is a difference between rapid, impulsive generation of force, as with the baseball pitch, and slower movement like the 1-rep max lift. You always hear a lot of HIT and SuperSlow aficionados talking about how momentum “lifts the weight for you” in “explosive” (fast) movements. That’s not strictly true; any moving object has momentum. You can define a subtle difference in the momentum of a slow lift, whereas a faster motion will tend to be more impulsive (responsive to change in velocity), but momentum is there in both cases.

What is relevant is the amount of time that force is generated in the working muscles. I’ve discussed before why this is probably a factor when you’re talking muscle-building goals, for the simple reason that hypertrophy seems to be a result of maximizing the force-time curve (see? It’s everywhere!) for the targeted muscle(s). On that same note, though, the working muscles don’t seem to differentiate between very heavy/impulsive reps or somewhat lighter sets with a more gradual tempo – as long as the total “area under the curve” is similar, the specifics don’t seem to matter.

In practical terms, this means if you want to do short, explosive sets, you’ll need to do a lot of them to equal the same growth stimulus as a handful of longer, slower sets (aka what bodybuilders already tend to do). If you’re after strength gains or especially athletic performance, though, you’re going to be better off doing a combo of heavy/slow training, lighter/faster training, and stuff in the moderate “power” range that’s both moderately heavy and moderately fast.

Practically, we tend to find that there are optimal RFD and power values for any given movement and resistance, so you’ll need to train specifically for your goal (who’d have thought???). That said, it appears that there are some benefits to training heavier and/or lighter than your target, as well. Powerlifters in the last 10-15 years have started to learn the benefits of explosive or “speed” training, and it’s long been known that improving maximum strength almost always improves power and speed (or at least lays the foundation for that improvement).