If you like this, you might also like my Instagram channel Nerd on Bars @nerdonbars where I calculate the power output of various athletes and myself.
Why do people hit the gym? What is their goal?
For some, it is to put on muscle and look good. For others, it is to be healthy and live longer. For yet others, it is to have fun, because doing sports is fun. None of these are mutually exclusive.
In this post, I will not focus on any of these. I will focus on the goal of getting strong and building power. I write this, because I feel like people are doing exercise more and more for appearance’s sake, and less to get strong. And it has to do with economics.
Before the industrial revolution, over 80% of the population were farmers. The average human had to do physical labor to survive. The average human could not help but to “bodybuild”.
Since then, humans have built machines to harness the power of nature and do the physical labor for them. What made the human civilization so powerful robbed individual humans of their own power, quite literally. The average pre-industrial human could generate a higher wattage than the average post-industrial human of today—they had to.
Before the industrial revolution, humanity’s total power output was bottlenecked by human physiology. Humanity has since moved up in the Kardashev scale. Paradoxically, the more power humanity can generate, the less physical exercise the average human can economically afford, and the weaker their body becomes. Strength has become a luxury.
This is why most modern fitness terms make me sad, because they remind me of what has been lost.
Consider “functional training”. There used to be no training other than “functional”, because most physical effort had to create economic value. The term is used to differentiate between exercises with machines which target specific muscles, and exercises that are composed of more “compound movements” that mimic real-life activities. It used to be that people did not have to do any training, because physical exercise was already a part of their daily life.
This is why I dislike “building muscle” as a goal as well. Since strength is a luxury now, people want to maximize that in their lives. However, they end up trying to maximize the appearance of strength, because increasing actual strength is harder than building muscle.
When I say it is harder to get strong than to look strong, I mean it in the most materialistic sense: Increasing your body’s power output in Watts is harder and economically more expensive than increasing muscle volume in Cubic Centimeters. Increasing wattage has a higher time and money cost, requires more discipline and a lot more effort. It is a multi-year effort.
Contrarily, muscle can be built quicker in a matter of months, without getting relatively stronger. Many bodybuilders can’t do a few pull-ups with proper form. Their strength doesn’t transfer to other activities. They are sluggish and lack agility. In that sense, bodybuilding culture today embodies the worst parts of capitalism and consumerism. Empty, hollow muscle as a status symbol. Muscle for conspicuous fitness.
To meet up the demand, capitalism has commoditized exercise in the form of the modern machine-laden gym: a cost-optimized low-margin factory. Its product is the ephemeral Cubic Centimeter of Muscle™ which goes away quickly the moment you stop working out.
These gyms are full of people whose main motivation for working out is feeling socially powerless and unattractive. However, instead of going after real physical power, i.e. Watts, they go after the appearance of power, muscle volume. They compare themselves to people that just look bigger, people with higher volume.
The goal of this post is to convince you that it is superior to chase Watts than to chase muscle volume. It is psychologically more rewarding, the muscle gained from it is more permanent and has higher power density. However, it is more difficult and takes longer to achieve.
Goals
Goals matter. For example, if you purely want to maximize your muscle mass or volume, using steroids or questionable supplements is a rational thing to do. Enough people have criticized it such that I don’t need to. Disrupting your hormonal system just to look bigger and be temporarily stronger is extremely dumb.
I personally want to:
feel powerful, and not just look like it.
live as long and healthily as I can.
I believe that the best way to do that is to increase my power output in Watts and do regular strength training in a balanced way that will not wear out my body.
If I had to define an objective function for my exercise, it would be:
\[f(P, L) = \alpha P + \beta L(P)\]
where $P [\text{Watt}]$ is my power output, $L(P)[\text{year}]$ is the length of my life as a function of my power output, $\alpha$ and $\beta$ are weights that I assign to power and longevity. I won’t detail this any further, because I don’t want to compute anything. I just want to convey my point.
Notice how I don’t constrain myself to any specific type of exercise, such as calisthenics or weightlifting. As long as it makes me more powerful, anything goes. Is wrestling going to get me there? Count me in. Is working in the fields, lifting rocks, firefighter training or Gada training going to get me there? I don’t differentiate. As long as it makes me more powerful, I am in.
Calculating power
How can one even calculate their power output?
It is actually quite easy to do, with high-school level physics. You just need to divide the work done by the time it took.
For example, consider a muscle-up:
Left: Muscle-up starting position. Right: Top of the movement.
I am at the starting position on the left, and at the top of the movement on the right. In both frames, my velocity is 0, so there is no kinetic energy. Therefore, we can calculate a lower bound of my power output by comparing the potential energies between the two frames. Denoting the left frame with subscript 0 and the right frame with subscript 1, we have:
\[U_0 = mgh_0, \quad U_1 = mgh_1\]
where $U$ is the potential energy, $m$ is my mass, $g = 9.81 m/s^2$ is the acceleration due to gravity and $h$ is the height.
The work I do is the change in potential energy:
\[W = U_1 - U_0 = mg(h_1 - h_0) = mg\Delta h\]
And my power output is the work divided by the time it took:
The distance I traveled $\Delta h$ can be calculated from anthropometric measurements:
Various distances on the human body.
I will denote the distances from this figure with subscripts $d_A$, $d_B$ and so on. Comparing this with the previous figure, we have roughly:
\[\Delta h \approx d_A - d_G\]
To understand how I derive this, consider the hands fixed during the movement and that the body is switching from a position where the arms are extended upwards to a position where the arms are extended downwards.
I have measured my own body, and found this to be roughly equal to 130 cm. Given that it took me roughly 2 seconds to do the movement and my mass at the time was roughly 78 kg, I have found the lower bound of my power output to be:
It is a lower bound, because the muscles are not 100% efficient, some energy is dissipated e.g. as heat during the movement, my movement is not perfectly uniform, etc.
Still, the lower bound calculation is pretty concise, and can be made even more accurate with a stopwatch and a slow-motion camera.
Aiming for 1 kilowatt
When I was first running to calculations, I wanted to get a rough idea of the order of magnitude of the power output of various exercises. It surprised me when I found out that most exercises are in 10-1000 Watt range, expressable without an SI prefix.
I have been training seriously for almost a year and regularly for a couple of years before that. I have discovered that in my current state, my unweighted pull-ups are in the 500-1000 Watt range. For the average person, 1000 Watts, i.e. 1 kilowatt, is an ambitious goal, but not an unattainable one. 1 kilowatt simply sounds cool as a target to aim for, as if you are a dynamo, a machine. A peak athlete can easily generate 1 kilowatt with their upper body for short durations.
How does this reflect to the muscle-up example I gave above?
If I am not adding any additional weights to my body, that means the duration which I complete the movement would need to decrease. We can calculate how much that would need to be. Moreover, we can derive a general formula which calculates how fast anyone would need to perform a muscle-up to generate 1 kilowatt.
To do that, we first need to express power in terms of the person’s height. Previously, we had $\Delta h = d_A - d_G$. Most people have roughly similar anthropometric ratios, so we can use my measurements to approximate that ratio. Multiply and divide by $d_B$ to get:
\[\Delta h = \frac{d_A - d_G}{d_B} d_B\]
For me, $d_A = 215 \text{cm}$, $d_B = 180 \text{cm}$ and $d_G = 85 \text{cm}$, so:
The formula is really succinct and easy to remember: Just multiply the person’s mass in kilograms by their height in centimeters and divide by 14000.
Calculating for myself, I get $78 \times 180 / 14000 \approx 1.00$ seconds.
This confirms that I need to get two times faster in order to generate 1 kilowatt. Alternatively, if I hit a wall in terms of speed, I could add weights to my body to increase my power output. (TBD)
My friend and trainer J has agreed to record his muscle-up and various other exercises, so I will add his numbers and compare them soon.
TBD: Add the data from J.
Extending to other movements
I chose the muscle-up because I’ve been working on it recently. However, this method can be applied to any movement, as it’s just an application of basic physics.
For example,
Do you want to calculate the power output of a pull-up? You just need to change the height $\Delta h$, it’s roughly half the distance for muscle-up.
Do you want to calculate the power output of a weighted pull-up? You just need to add the additional mass to your body mass $m$.
Do you want to calculate the power output of a sprint start? Just measure your top speed at the beginning and the time it took to accelerate to that speed, and divide your kinetic energy by that time.
Do you want to calculate the power output of a bench press? You need to set $\Delta h$ as your arm length and $m$ as the weight of the barbell.
See the next section for a more detailed example.
Power-weight relationship in a bench press
In the bodyweight examples above, we had the same bodyweight, and it was being moved over different distances.
Then a good question to ask is: How does the power output scale with the weight lifted? The bench press is an ideal exercise to measure this in a controlled way.
25% slowed down and synced videos of a bench press with increasing weights. Top row left to right: Rounds 1, 2, 3. Bottom row left to right: Rounds 4, 5, 6.
I asked my friend to help me out with timing bench press repetitions over 6 rounds with different weights. You can see these in the video above.
Before we even look at the results, we can use our intuition to guess what kind of relationship we will see. If the weight is low, power is low as well. So as we increase the weight, we expect the power to increase. However, human strength is limited, so the movement will slow down after a certain point, and the power will decrease. We should see the power first increase with weight, and then decrease. This is indeed what happens.
In each round, my friend did 3 to 4 repetitions with the same weight. I calculated the average time it took to complete the repetition and the total weight (barbell + plates) lifted in that round. Then, I calculated the power output for each round using the formula above. The height that the barbell travels during the ascent is $\Delta h = 43 \text{cm}$.
Round
Total Weight $m$ (kg)
Average Time $\Delta t$ (ms)
Power $P$ (Watt)
1
40
580
291
2
45
623
305
3
50
663
318
4
55
723
321
5
60
870
291
6
65
1043
263
The visualizations below are aligned with the intuition:
Total weight vs average time in a bench press. Time taken increases monotonically and super-linearly with weight.
Total weight vs power in a bench press. Power first increases with weight, then decreases.
Average time vs power in a bench press. Similar to the weight vs power plot, but with time on the x-axis.
The figures matches the perceived difficulty of the exercise. My friend said he usually trains with 45-50 kg, and it started to feel difficult in the last 2 rounds. His usual load is under the 55 kg limit where his power saturates. That could mean he is under-loading, and should load at least 60 kg to achieve progressive overload and increase his power.
Reinventing Velocity Based Training, Plyometrics etc.
Power is a factor of speed and force. So in a nutshell, this project is about maximizing speed and force at the same time.
While starting this project, I wanted to have a fresh engineer’s look at powermaxxing, and did not want to get influenced by existing methods or literature. I knew that sports people were using scientific methods to measure and improve performance for decades, but I wanted to discover things on my own. I will continue to stay away from existing knowledge for some time, before I look at them in more detail.
Also: I have personally not seen any person on social media that tracks power output in Watts, or visualizes it with a Wattmeter.
If you know about such a channel, please let me know.
Not-conclusion
This is a work in progress, so there is no conclusion to this yet. I will add more content as I learn more.
