Problems with the critical speed model: Can power laws predict running performance better?

Digital art image of a runner with math equations in the background

The critical speed model—also known as critical velocity, CV, or critical power—is a powerful concept for understanding what running speeds are sustainable at a metabolic steady-state and what speeds are not.

Critical speed is not without its detractors, though, and the critical speed model is certainly not without its flaws.

I just posted a huge article on understanding the science of critical speed, critical velocity, and critical power for runners. That article goes in-depth on what critical speed is, how the model works, and how you can use it in your training.

I was originally planning on including the major criticisms of critical speed as a part of that article, but it’s long enough as it is.

So here, separately, is a summary and analysis of the main problems with critical speed (and, by extension, critical power) as a model for endurance performance, plus some rejoinders as to why alternative models, like the power law model of performance, are not always better.

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The science of critical speed, critical velocity (CV), and critical power training for runners

Female athlete running in front of scientific graphic paper

Critical speed is the boundary that separates running speeds that can be sustained at a metabolic steady-state from speeds that cannot. Sometimes called critical velocity or “CV,” critical speed is known in the running world in partly due to its popularization by Tom “Tinman” Schwartz and his proteges, including Drew Hunter.[1]

Critical speed is increasingly becoming the gold standard among physiologists for identifying the limit of what runners would call “high-end aerobic” or “steady-state” running speeds, and is gaining traction as a training tool as well. The critical speed model explains the body’s response to different speeds better than older models based on the lactate threshold.

Among exercise physiologists, critical speed (or a semi-related concept, the maximum lactate steady state, which we’ll also discuss) is rapidly becoming the gold standard for capturing the aerobic fitness of athletes.

Critical speed has its roots in early work in the 1960s, 70s, and 80s, but didn’t really start to emerge as the strongest physiological model for intense exercise until the last 15 years or so.

In this article, we’ll take a detailed look at the critical speed phenomenon, understand how it works on a mathematical and physiological level, see some of the problems and controversies surrounding it, and learn how to apply the concept of critical speed in your own training.

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A comprehensive overview of Canova-style percentage-based training for runners

Percentage-based training is a mathematical approach to planning workouts for runners. Percentage-based methods are used by many top international coaches, most notably Renato Canova, to train runners at distances from 800m to the marathon. 

I could write a whole book about percentage-based training for runners (in fact, maybe I will someday), but the goal of this post is to give a clear, comprehensive, and readable overview of percentage-based training as a system—a set of principles that can be used to guide training decisions.

To this end, we’re going to focus on the concepts and rationale behind the percentage-based training method, as opposed to exact training calendars. This post does include an appendix with recommended workouts for every event from 800m to the marathon (even the 3k!), but event-specific full training calendars will be a project for another day.

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How much glycogen is stored in a runner’s liver?

Carbohydrate-rich foods in the shape of a liver in the style of a scientific illustration

Liver glycogen is a major source of carbohydrates for your muscles to burn when you’re running. The glycogen molecule is just a big long chain of glucose molecules which is optimized for long-term storage.

When your body needs carbs during a run during a run, your liver can break down glycogen into glucose, shuttle it into the bloodstream, and send it to your active muscles to be burned for energy.

Stored glycogen in your liver is particularly important for running the marathon and ultra distance races, since the glycogen that's locally in your muscles isn’t sufficient to get you to the finish line. But exactly how much glycogen do you store in your liver? And can training increase this amount?

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Introducing Running Writings Apps and the workout pace percentage calculator

Screenshot of the Running Writings workout pace percentage calculator web app

This week I launched Running Writings Apps, a new platform for me to host some of my more technology-heavy running-related projects. During my PhD work I did a lot of data analysis and data visualization, and picked up some strong programming skills along the way. I’m excited to incorporate more of that alongside my long-form writing here.

This week I launched my first project: the Running Writings workout pace percentage calculator! Check it out!

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Training intensity and capillary growth: Do you believe all the studies, or just a few? 

Color microscope image of muscle fibers and capillaries

Recently I’ve been diving back into the world of exercise physiology research, especially as it relates to running performance. I got behind on following ex phys in grad school (too busy following biomechanics!), so it’s been a few years since I’ve caught up on the latest research.

This weekend I was reading about capillarization: the growth of new, tiny blood vessels–capillaries–that run between and around individual muscle fibers. Capillaries are super important for aerobic performance, since they’re the place where oxygen diffuses out of red blood cells and into muscle fibers. 

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The Keys to Marathon Training: Modern changes to Renato Canova’s elite marathon training methods

While researching my blog post on Renato Canova’s marathon training book, I came across a lecture that Canova gave at a coaching conference put on by Spanish marathoner and coach Antonio Serrano in 2017. The talk, called The Keys to Marathon Training[1] was held in conjunction with the 2017 Valencia Marathon.

This lecture directly answers one of the questions I had when writing up my analysis of Canova’s book–what’s changed since 1999? From his answers in a 2011 interview, I knew that Canova believed some important things had changed, but that video didn’t go into too much detail. Canova’s talk at this conference goes into much more depth, so I wanted to do a more formal write-up on it.

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Review and summary of Marathon Training - A Scientific Approach by Renato Canova

Photo of the book Marathon Training - A Scientific Approach by Renato Canova and Enrico Arcelli

How do the best marathon runners in the world train? While you might catch a workout or two on Instagram or hear rumors about epic training weeks on message boards, there’s precious little information on the systematic approaches that elite coaches use with top marathon runners–and even less information on the science that backs up these approaches for designing marathon training programs.

One exception to this general rule has been the Italian coach Renato Canova, arguably the greatest living running coach and the topic of several of my previous posts on Running Writings. Canova freely discusses his training philosophy and posts example workouts or even full training schedules for the athletes he has worked with, which include Olympic and World Championships medallists.

In 1999, Canova even co-authored a book on the science of marathon training—however, there’s a bit of a catch: this book was printed through the IAAF (now World Athletics), not a traditional publishing company or printing press. As a result, Canova’s book is extraordinarily rare. I had heard of this book probably a decade ago, but in the intervening years I couldn't find any substantive information on its contents. Until now.

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A scientific guide to treadmill training and workouts for runners

Stylized image of treadmills in a gym

Though many runners treat treadmills as a necessary evil, treadmill access is a must-have if you live anywhere that gets extreme cold or extreme heat and want to train seriously year-round. Being from Minnesota (and having coached many runners in the Midwest), I’ve had plenty of experience modifying workouts and training sessions for the treadmill. 

On top of that, I’ve just wrapped up a biomechanics study as a part of my PhD dissertation that involved 60 runners completing a treadmill run in a motion capture lab, so I have a lot of experience working with biomechanical data from treadmill running. 

When you’re doing treadmill workouts, you can’t always just translate your outdoor workouts 1:1 and expect everything to go well. There are several important physiological, biomechanical, and psychological aspects of treadmill running that differ from outdoor running. 

Moreover, I’ve found that a lot of runners have ideas about treadmill training that aren’t in alignment with the scientific research on treadmill running. So, this article is designed to refute some of these incorrect ideas, and provide some guidance on how to incorporate treadmill running, when necessary, into your own training. 

Just want to know the most important info before you hit the treadmill? Click the link below to go directly to my seven scientifically-supported best practices for treadmill training.

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Advanced versions of strides and accelerations for runners

The homestretch of a track at night

When runners ask online about ways to improve their running form or increase their footspeed, a common response is “add some strides.” It’s assumed or implicit in such a response that everyone knows what strides are and how to do them optimally.

As with many things in training, it’s worth spending some time to dig into what constitutes “doing strides,” and how we might incorporate them into training in a more thoughtful way. 

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Did you know I have a book? Check it out here!