The Rule of the Thumb

Base: A New Definition

Mitochondria: Aerobic Engines

Stripped Down

Project: Rolling Resistance

Stems

Power Meters

Wheels

The Rule of the Thumb…

10/24/2004 - Words and images by: Kraig Willett

I was recently accused of having too much time on my hands. This brutally honest feedback was dished out in response to a little study I recently completed which dealt with, ironically, hand position during cycling time trials. In my defense, I’d just like to say that by using some simple digital image processing techniques, it doesn’t take very long for armchair scientists like me to conduct a “poor man’s” virtual wind tunnel test by measuring frontal area. What the heck is frontal area, and why does it even matter, you ask? Quite simply, the smaller the hole you punch in the wind, the faster you will go, and frontal area is one way to learn just exactly which position produces a smaller, and ultimately faster hole…

Frontal area is but one variable that affects the overall aerodynamics of a given object. The equation minded folks out there might recognize the following equation for aerodynamic force:

Where: F= aerodynamic force

= air density

u = air speed

Cd = non-dimensional force coefficient (function of the shape of the object)

A = frontal area

In order to simplify things, it is often convenient to rearrange the above equation such that all the terms that don’t change during a comparative analysis are on one side of the equal sign and everything else is to the other. In this case, the simplification looks something like this:

You may have heard some of the geeky types like myself refer to a thing known as “CdA” – well, the above formula is what this term references. It is simply a way of describing the aerodynamics of an object. The “A” is the projected frontal area; while the Cd is the force coefficient and is a function of the shape of the object (e.g. a flat plate has a higher Cd than an equivalently sized sphere…)

Let’s take a look at an application of this un-wieldy equation: a 0.5 meter tall by 0.5 meter wide piece of plywood presents a frontal area of 0.25 m^2 (i.e., 0.5 x 0.5 =0.25) when it is placed broadside to the wind. Cd for a flat plate has been documented in the literature as ~1.12 -> this Cd value has also been shown to be independent of frontal area. The resultant CdA for this particular piece of plywood is therefore 0.28 (or just a shade worse than Tyler Hamilton’s standard time trial position - heh, does that mean that TH’s position is not a whole lot better than a piece of plywood???)

The logic of the argument presented then follows that if Cd is constant and the frontal area is subsequently decreased, the overall aerodynamics of the smaller frontal area object will be better (since the product of Cd and A will be smaller). Looking at the plywood example presented earlier, we can determine that a 0.4m by 0.4m piece of plywood presents a frontal area of 0.16 m^2 and therefore would have a CdA of ~0.18 – which means that the smaller piece of plywood has a smaller CdA (due to its smaller frontal area) and therefore, is more aerodynamic. If these pieces of plywood raced bikes, and produced the same amount of power, the smaller CdA piece of wood would go faster simply because it was more aerodynamic. Pretty easy stuff, huh?

Well, the underlying assumption that this type of analysis relies on is that the Cd of the object (in this case, a cyclists’ hands) does not change for small changes in orientation. This assumption is more than likely a pretty good one, and indeed there does exist some tunnel data out there (based on cyclists, not cyclist’s hands, however) that supports this constant Cd assumption. Furthermore, from my previous work in the wind tunnel where I studied fork aerodynamics, projected area by itself is an excellent proxy for evaluating aerodynamics outside of a wind tunnel.

The Straight Aero Bar Extension Trend

Jan Ullrich, or was it Jens Voigt, has made the straight aero bar extension the latest fad/trend in the TT product world. The internet is full of people describing just how they took a hacksaw to their $400 one-piece bars (like the Easton Attack, CSC Vision Tech, Profile Carbons, etc...) so that they could adopt the Ullrich/Voigt hand position. I mean heck, those guys are winning with those style of bar extensions, so it MUST be fast, right?

Applying the tenuous “constant Cd” assumption discussed previously, I set out to see how these straight aero bars, or more precisely, the resultant hand position required to grab onto that style of bar affected measured frontal area. The reasoning goes that if the frontal area was smaller with a particular hand position, well, that would be the aero bar extension that everyone’s just “gotta” have…

The experiment consisted of sitting myself in a chair while wearing lots of black (so that my hands would be easy to extract from the digital picture) and rotating my hands downward in ~ 10 degree increments.

Figure 1. Wide angle shot of the hand position frontal area sweep setup.

After processing these images to determine frontal area, I was able to create the following table:

Figure 2. Straight aero bar extensions put your hands in a position somewhere between #3 and #4 above.

I would estimate that the hand position necessary to grab onto the straight style of aero bar extension is somewhere between that illustrated by position #3 and #4 above. Interestingly, the frontal area measurements show these two positions to have the highest frontal area by up to 20% as the chart below also illustrates:

Figure 3. Hand position and frontal area.

It should be noted that the minimum frontal area was measured with hand position #2. Upon closer inspection, the minimum frontal area hand position can best be described by looking at the relationship between the thumb and the forearm.

Position #2 is obtained when the thumb is parallel to the forearm and the forearm is also held parallel to the ground. An easier way to visualize this relationship is if one places a ruler on top of the forearm. Ideally, when the minimum frontal area hand position is achieved, the ruler should touch the forearm and thumb along its entire length as seen below:

Figure 4. The rule of the thumb - keep it inline with the forearm for smallest frontal area.

Hand positions #3 and #4 significantly deviate from the line projected off the forearm as is illustrated in figure 5.

Figure 5. This hand position results in a larger frontal area.

My “Rule of the thumb” should be clear by now; I think that for best aerodynamics people should keep that thumb and forearm in contact with a “virtual” ruler that extends out from the forearm. The resulting hand position based on the “rule of the thumb” setup has been shown to present a slightly smaller frontal area and perhaps, ultimately, faster TT times. In summary, the thumb metatarsal should be kept as flat as possible, and honestly, that’s quite tough to do when one lops off the upturns on their appropriately shaped conventional aero bars and opts to go the straight bar extension route.

And to think that someone had the audacity to claim I had too much time on my hands…