Aerodynamics Pt. 2

A few days ago I sized myself up for some compression socks. As a triathlete, you see, I have a duty to be as sartorially challenged as possible. It should be clear from the photo below that I take this duty very seriously.

Anyhow, to determine the proper size sock for myself, I referred to a handy compression sock sizing chart. Men's size small corresponds to a calf diameter of 12.5 to 15 inches, medium to a 15 to 17.5 inch diameter, and large to a 17.5 to 20 inch diameter. "Hmm," I thought sarcastically to myself, "what size might I be?"

Just to be sure I didn't have to have to order women's socks, I decided to measure up my legs of steel. After pulling a shoe lace from a nearby pair of trainers, I wrapped a length of the lace around my calf and then measured that length. "13 inches," I exclaimed aloud to no one, "now I don't have to cross dress every time I want moderate pressure applied to my lower appendages!"

What do my supermodel (5'10" 115 lb. female supermodel, that is) sized calves have to do with aerodynamics? Well, yesterday when I posted the drag formula (~50g of drag = ~0.5s/km time saving = ~5W) I left off one aspect. An additional 50g of drag is also roughly equivalent to an increase of 0.005 m^2 of frontal area. This additional bit of info allows us to estimate with relative precision the aerodynamic advantage my calves offer relative to a typical male triathlete.

As illustrated in the figure below, my calves are each about 4 inches wide when viewed from the front (seriously, I just measured with a tape measure). We can also approximate a man's calves as extending 8 inches vertically.

As a result, each of my calves has a frontal area of 32 square inches, which can be converted to 0.0206 m^2 per calf.

Now, let's estimate the typical triathlete as having slightly beefy calves from copious amounts of cycling. An 18" diameter seems reasonable as a comparison. Approximating a calve as a round tube, we can estimate the width of the ordinary triathlete's calve to be 5.7 inches. 5.7" x 8" = 45.6 sq. inches = 0.0294 m^2 of frontal area per calf for the typical triathlete.

Now to calculate my calves' aerodynamic superiority:
2 calves * (0.0206 m^2 - 0.0294 m^2)/calve = -0.0176 m^2 (this is the frontal area of my calves relative to the ordinary triathlete's)
0.0176 m^2 * 5 W/0.005 m^2 = 17.6 W (power savings)
0.0176 m^2 * 50g/0.005 m^2 = 176 g drag (reduction in drag)

Amazing! My calves save almost twice the difference between a Cervelo P3C and a Kuota Kalibur! Who needs a P4/Shiv/Speed Concept when you've got legs like mine?

Aerodynamics

Okay, while I admit to reading Slowtwitch pretty regularly, I rarely post. However, I had an aerodynamics question that I was hoping one of the aero nerds on the forum would have some insight on. Here's my post reproduced:

Drag numbers, like those illustrated in the graph below, are typically reported for a wind speed of 30 mph, correct?


The question I want to explore is how the results change when drag is scaled to a more realistic speed for an Ironman. Let's make a few simplifications. First, we'll use Tom A.'s rough formula that at 30 mph wind speed ~50g of drag = ~0.5s/km time saving = ~5W power savings. Second, let's estimate the difference between, say, a Cervelo P3 and a Kuota Kalibur to be 100 g of drag (we're simplifying here because the difference varies with yaw angle, but for the sake of simplicity we'll just consider the case of a 100 g difference).

Computing the time savings of a P3 vs. the Kalibur over 180 km, we get 100g = 10 W = 1s/km = 3 minutes for 180 km. Great, I'd take a 3 minute savings for an IM.

However, that 3 minute time savings is calculated using a formula based on a 30 mph wind speed, and to get a more realistic estimate of the time savings from a P3 to a Kalibur we should scale down to a more realistic speed. One point I'm not sure that most people recognize is that drag is a function of the square of wind speed and power savings is a function of wind speed cubed (i.e., we can not linearly scale these numbers). To scale our results for 20 mph -- a much more realistic speed for most AGers -- we can multiply Tom A.'s drag numbers by (20/30)^2, or about 45%, and we can multiply the power savings by (20/30)^3, or about 30%. So scaling our numbers indicates that the difference between a P3 and Kalibur would be 45 g and the power savings would be 3 W at 20 mph. While I recognize that every watt saved is valuable, 3 W isn't much. (A note: I recognize that the speed one is traveling is not necessarily equal to wind speed relative to the frame -- sometimes the wind speed relative to the frame would be greater and sometimes it would be less depending on wind speed and direction.)

Additionally, I know Gerard at Cervelo has said that the slower one goes the greater the time savings. Yet it seems strange that 3 W could save more than 3 minutes over 180 km at 20 mph. I don't recall any formula for time savings from my fluid dynamics classes. Does anyone have any insight here?

Feel free to critique my reasoning, as I just whipped this out without thinking it through too much (that's what you're here for, ST aero nerds).
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And now for more over-analysis:

My point is that the graph above, taken at face value and not considered as advertising, exaggerates the differences between bikes for most people. Based on a 3 W power savings for a rider putting out 200 W, analyticcycling.com estimates a time savings of a bit under 2 minutes for an Ironman when switching from a "slow" bike (the Kalibur) to a "fast" bike (the P3). However, another estimate based on the assumption that the % of time savings stays relatively constant regardless of a rider's speed gives an estimated time savings of a bit under 4 minutes between the bikes. (I have no idea what the basis for this assumption is.)

Don't get me wrong, 2 minutes is a nice savings. But differences in comfort and handling between two bikes might be able to provide similar savings (note that I say "might", as this is pure speculation), only those differences aren't so easily quantifiable.

Plus, the entire discussion above requires that one take the drag differences between bikes as fact and disregard that the company promulgating these results is the same company that happens to be shown in the best light. (In Cervelo's defense, every other company in the industry seems to view Cervelo's bikes as the gold standard, so I don't mean to criticize Cervelo. Plus other companies release their own data that should also be questioned.) So many ads say shifters or pedals or sunglasses can result in several seconds time savings, and many of those ads look ridiculous.

I am thinking about this because many triathletes have had great success on "slow" bikes. Normann Stadler and Torbjorn Sinballe both had amazingly fast rides on bikes that would be considered slow. I would expect the differences in ability between world class athletes to be very small, so if the difference in bikes were as great as many people say then I wouldn't expect so many wins on slow bikes. Winning, after all, is what matters.

A bad week (not too bad, though)

I've felt indefatigable for the past two months or so. However, after six weeks averaging about 20 hrs/week, and without a day off since January 5th, I finally had a lackluster week of training. On the plus side, I got in a fair amount of intensity including two trainer rides focusing on raising my FTP. (This will be obvious to many of my two readers, but if you know you're going to have a low volume week then up the intensity to compensate.)

Somewhat oddly, I was exhausted this Monday despite my low volume the proceeding week. In all honesty, I also had a stressful event this past Saturday, and I think that stress really took a toll on my body. I had planned for a super-tough HIM simulation ride on Sunday, and I could not get my legs going. I ended up bagging the workout after just over an hour (well, two hours if you count my swim beforehand). Paying attention to my body is tough when my body says to back off and my mind says "don't be a slacker," but I remind myself that sometimes taking it easy is the best option.

Anyhow, one low volume week isn't the end of the world. A 12 hour week with some tough efforts isn't going to set my training back much if any, and I'm ready to crush it these next three weeks before tapering for IM Cali. In fact, yesterday I got in a 1.5 hour trainer ride with 5 x 8 min low gear work (60 rpm) at 270 W. My HR got a bit higher than expected, and the workout left my legs beat, but it was a nice quality session.

I followed that ride up with a 1:15 run by feel. I think my HR hovered a bit above 150 bpm, and my pace was often around 7:00/mile despite running on packed down snow. This run gave me confidence that my running legs are intact -- I can run after a hard bike without feeling much (if any) of a negative effect.

I may try a HIM simulation ride this weekend by holding 155 bpm for as long as possible and seeing what wattage results.

Crushing a brick

Today's first workout: a brick consisting of (1) a 1:20 ride including 6 x 8 min at 160 bpm and (2) a 0:40 run with the first 18 minutes at ~160 bpm. I averaged 6:16/mile at 162 bpm for the first 18 min of the run, though the first 18 minutes of the run were slightly uphill at about a 1% gradient on average. Also, if I don't take my HR into consideration until it reached a steady state my average HR would be more like 165 bpm. A HR of 165 bpm means I was going about HIM pace, perhaps a tad slower. Regardless of this over-analysis, a solid workout.

Oh, and I'd like to add one other comment regarding my weekly volume (~20 hours/wk) for any neophytes that may read my blog. The workouts I typically post are generally some of the harder ones that I do. A few of my workouts each week are extremely easy, yet still count toward my total volume. For example, yesterday and the day before I rode for an hour per day in addition to some other workouts. Both of these rides were recovery rides with an average HR of under 115 bpm. Don't think that you need to put in 20 hours per week of HR>140 bpm or anything like that. Go easy when you're tired, and work harder when feeling rested (or at least not too fatigued).

I should go through my workouts for the past few weeks and look at how many hours of intensity I'm doing. "Intensity" isn't a very exact term, but I'll consider it to include time at 150 bpm or greater on the bike and at 160 bpm or greater while running. My goal is to be in the 4-5 hour range this week, increasing to about 8 hours per week before tapering for Cali 70.3. Of those 8 hours, perhaps 1 hour will be running, 4.5 hours will be biking, and 2.5 hours will be swimming.

The Moutains are Beautiful

Yesterday Stacey had the day off so we headed up to Boulder to run Mesa Trail. There were four to six inches of snow on the ground, though most sections of the trail were pretty well traveled so the snow was packed down pretty well. The trail is hilly and makes for a great running strength workout. After an hour and a half or so, my legs were so tired that reaching a moderate HR (say, 150 bpm) became tough. I averaged a stellar 10:30/mile (!) at 141 bpm thanks to the snow and tough terrain. The run in graph form:


Mesa Trail is one of the most beautiful places I've ever run. The trail was especially beautiful yesterday because the sky was cloudless, the sun was shining brightly, and the snow was that puffy, low-density type that can pile up 6 inches high on tree branches.

I snapped a few pictures during the run, including one where Stacey can barely be seen in her red jacket off in the distance:

Boring Training Update

Yesterday Stacey and I rode from Boulder to Ward and back. Ward is a formerly prosperous gold-mining town sitting at about 9,200 feet. Gone is any sign of wealth from the town's bygone mining days, replaced by rusted cars and feral dogs. It is one of the more unique communities I've seen.


As is apparent from the elevation profile, the ride involves a fair amount of climbing.


I tried to hold 150-155 bpm on the climb, except during the occasional turn-around to ensure that Stacey was doing fine on her way up. This allowed me to get in about 1.5 hours at slightly below HIM intensity, making for a solid and specific workout in prep for Cali 70.3 in seven weeks.

It was snowing by the time I reached Ward, and the sun was only occasionally peaking out from behind a layer of clouds. The descend back to Boulder of almost 4,000 ft. at 30 mph on an overcast 35-40 degree day made for a chilling experience.

As Stacey and I approached Boulder on Hwy 36 we saw three groups of police cars along with several other emergency vehicles. A fire truck was a few hundred yards off the highway out in the middle of a field. We wondered what was going on. Turns out we narrowly missed witnessing a mid-air collision between two planes.

Avoiding the bucket

This entry is in response to an email from Chuckie asking for athletes's thoughts on an article about being "in the bucket", i.e. exhausted from training. Being in the bucket can wipe out one's motivation, can require copious amounts of sleep to recover from, and is generally a detriment to improvement.

I have a few thoughts after reading the article. First, I'm not sure I've ever "been in the bucket". I am almost always motivated for training, and when I'm not motivated it's typically not because I'm physically tired. (Though training surely contributes to my occasional mental tiredness.) I've never been so shelled that I operated at reduced capacity outside of training. Perhaps I haven't been in the bucket because I typically train alone and thus am rarely tempted to go harder than the training plan calls for. With masters and potentially some group running in my future, avoiding excess intensity is something I'll have to be more attentive to in the future.

My second thought is: If there is any secret to training, that secret would be how to strike the perfect balance between work and rest. The reason training can be complicated is because each person has a unique balance that leads to optimal results, both compared to other people and compared to that same person at a different time. Like most athletes, I err to the side of too much work (though it's very possible that another athlete with more mental resolve would disagree with my self-assessment). If I'm a bit more fatigued than normal at the start of a workout, I typically tell myself to toughen up and do the workout. Only when I'm feeling extraordinarily tired do I bag a workout. Tapering, however, is an exception during which I err to the side of rest.

One other thing I should be careful of is that my desire to improve dictates that I increase my training load from year to year. (A quick aside applying the platitude "If you keep doing what you're doing, you'll keep getting what you're getting," to training: Assuming one is improving with training, will continuing that same training lead to additional improvement, or will it lead to stagnation? I think the answer is that doing the same training may continue to lead to improvement, but after a certain point it will lead to stagnation. Testing can indicate when training is no longer leading to improvement.) While I expect to be able to handle a greater training load each year, each increase in my training load has the potential to upset my heretofore successful balance between work and rest. A recent interview with Linsey Corbin on Slowtwitch comes to mind (you can bet I was shocked to find something of substance in a triathlon interview). Linsey said something like she want to get faster so she trained harder, but her harder training only caused her to become slower. In response to becoming slower, she trained harder still but only became even slower.

While going easier goes against what most athletes view as the way to improvement, I hope that if my training becomes unbalanced as a result of an increased training load that I will respond by going easier, not harder. After the fact I'm sure it's very apparent when one takes on too large of a training load, but in the heat of things working harder seems so logical. I can understand that pros feel the need to push their boundaries even more than age-groupers, as without taking risks no pro is going to be the best in the world (plus, thanks to Chrissie Wellington female pros must feel a giant need to push their training to the limits). The takeaway is this: don't be afraid to go easier. I write this more as a note to myself than as a warning to others. Hopefully by typing this out I will be more likely to have the confidence to back off if I sense (or better yet, measure) that my training load is too great.