**R**amblings **A**bout **N**umerical **T**hings is a series of articles sharing my thoughts and opinions on the meaning or application of numbers in a particular area of interest. I’ll try not to go overboard on the numbers themselves, but rather focus on how you can use numbers to meet your goals.

For most triathlons, you spend the most time on your bike. If you want to be a faster triathlete, it makes sense to be faster on the bike. So if you are doing long course races (70.3 to 140.6), this means that you can cut substantial time off your total race by maximizing your bike speed… right?

The short answer is yes & no. Yes, you can have a good bike split, but it may result in a really poor run… more than negating the gains you made by riding fast. Here’s why: The physiological cost of increasing your speed is not linear. In the following example for a full IM, **a 5% increase in bike speed will “cost” you more than 21% in additional total physiological stress on your body.**

Let’s play with some numbers:

- If I average 18 mph on the bike for 112 miles, my total ride time would be 112 miles / 18 mph = 6.22 hours (6:13).
- If I can squeeze out 5% more speed, my average speed would be 1.05 x 18 = 18.9 mph. Getting an additional 0.9 mph can’t be too hard, can it? At 18.9 mph, my total ride time would be 112 miles / 18.9 mph = 5.93 hours (5:56). Basically 5% more speed translates to a 5% time savings, or nearly 17 minutes on a 112 mile ride. That is a big savings.

Of course… there’s a cost of going faster. And as mentioned above, the relationships are not linear.

First, a brief background on bike power. Whether you train with a power meter or not, it is important to understand the basics of bike power. The total amount of power it takes to achieve a given speed is a function of aerodynamic drag, rolling resistance, transmission losses (chain/gear friction) and the effects of gravity if you are on a hill. What is important to understand is that while the impact of gravity and rolling resistance is linear relationship, changes in speed impacts the aerodynamic power component as a cubed function. Unless you are climbing or cruising at less than 10 mph, this means that changes in speed require a much greater corresponding change in power. For example, using the speeds above and an online speed / power calculator, the resulting power is:

- At 18 mph (see note 1 below for model / input), the required watts on a flat road is 116.51.
- At 18.9 mph (same input conditions), the required watts on a flat road is 131.93.
- The increase in power required is 131.93/116.51 – 1 = 13.23%. So to go 5% faster… you need to produce 13.23% more power (physical work).

That isn’t really the end of the story, as you also need to consider the impact of this increase in power on your body. A common factor used to quantify the total physiological impact of a workout on the body is Training Stress Score (TSS). Essentially it combines the intensity of the workout (Intensity Factory – IF) and duration, to come up with a single factor of how hard you worked your body in the workout or race (see note 2 below). TSS is calculated by:

TSS = IF x IF x Duration (hrs) x 100

The Intensity Factor is simply how hard your average output is versus what your maximum output is for a 1 hour period. So, if you could produce 185 watts for 1 hour at maximum capacity, your IF for a ride at 116.51 watts would be: 116.51/185 =0.63. At 131.93 watts (second scenario), your IF would be: 131.93/185 = 0.71. Using these to calculate Total Stress Scores:

- TSS for 18 mph = IF x IF x Duration x 100 = 0.63 x 0.63 x 6.22 hrs x 100 = 246.9
- TSS for 18.9 mph = 0.71 x 0.71 x 5.93 hrs x 100 = 298.9
- The resulting increase in physiological stress: 298.9 / 246.9 – 1 = 21.1% increase.

So the question is: Is the 5% bike speed increase is worth the 21.1% increase stress on your body? As a rule of thumb, the upper limit of TSS scores during an IM is around 280 for a strong IM athlete and an upper limit of 260 for weaker runner or novice IM athletes. Few pro’s push to 299 TSS values, so likely the 5% increase above would likely result in a poor IM run overall (see note 3 below for more information).

Ideally, you balance your pacing to get close to the target TSS values without going over and resulting in a significant negative impacting your run… meaning your run turns into a long and leisurely stroll. I’ll discuss strategies for this in a future RANT blog.

Notes:

- Calculator example. I used 165 lbs for the rider, 20 lbs for the bike, CdA of 0.271, CRR of 0.004, Rho 0.076537, 3% drive loss, with no incline (these are similar to my numbers). There are several similar calculators online, converting speed to power or power to speed. Note these models assume constant speed, and don’t factor in acceleration. With hills, turns, stop/starts, your average speed versus average watts will be quite a bit different than you will see in these models (higher average wattages for lower speeds). They are still useful tools at comparing scenarios, if used properly. Other bike power/speed calculators I use are here and here.
- Note that universally a 5% increase does not exactly represent a 21.1% increase in physical “cost” across the board, as it is a function of your specific IF factors as well as the starting point (speed) you are referencing. If you were comparing 20 to 21 mph, your “cost” would actually be higher than this (due to the increased aerodynamic drag) and it would be lower if you were comparing 15 to 15.75 mph. The math stays the same, as does the general trend… increasing your speed 5% takes a much larger toll on you body.
- Definition of NP, IF, TSS (TrainingPeaks).
- Joe Friel IM Bike Pacing blog (TrainingPeaks).
- One caveat to Joe’s site above and my comments on Ironman TSS values, is that if you look at the pro women, they seem to run higher TSS values than the guys (overall) and do push into the 300 range. Here is a list of files for 2013 and 2012 for reference. Two top age group female athletes have shared IM files with me, and I have noticed that they also seem to be able to push higher TSS values and still run well, making me wonder if women are able to hold higher biking IF values for longer duration than men.

Great stuff, GG. More people need to read this type of analysis before racing – it’d save them unnecessary bonking and gain them some serious time!

Thanks for this writeup GG. I just put together my own numbers using your examples. It was a very interesting exercise.

You race Iowa Games today?

Sent from my iPad

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No. I live in Idaho. And the current games are Senior Games, which is older than me.

Sorry… I was trying to reply to another person posting. I’m glad you found the blog helpful. I’m in the process of evaluating some new software for modeling bike data that is REALLY interesting (for geeky people like me… 🙂 ), and should have some more posting about long course modeling out shortly. Thanks for your comments.