Part 5: Tire Pressure and Aerodynamics

We will start this post with a quick refresh on the state of modern wheel aerodynamics.  
Rim Shape and Tires
In 1991 Steve Hed and Robert Haug patented a rim shape that would go on to be known as the 'Toroidal' shape.  The toroidal rim was unique in the it had no flat surfaces, a deep tire well for tubular tires and curved in such a way that the combined rim and tire formed an ellipse. 

Image from Steve Hed Toroidal Rim Patent #US5061013
In simplistic terms, this patent covers any rim that is wider than the tire and comprised completely of curved surfaces.  Now the problem with the patent was that actually making this rim turned out to be impossible with the technology of the day.  The Hed CX rim was roughly toroidal, but with an aluminum cap at the tire well and brake track could not make the beautiful curvature required for ultimate aero, and even at that, the angled aluminum brake track was problematic.
In 1997, Zipp (who owned the Haug half of the Toroidal patent, but had never made a rim of this shape) patented the 'Hybrid Toroidal' rim shape.  This patent took the concept of having the rim be wider than the tire in order to control the airflow, yet matched it with parallel brake tracks to make the concept more manufacturable. 

Sargent/Zipp Hybrid Toroidal patent
The Rule of 105%
The rims of this era were all 19-21mm wide, and the Zipp and Hed rims were typically 23mm wide at the widest point, which was optimized for a 19-21mm tire.  During the early part of my tenure at Zipp 1999-2013 I noticed in the wind tunnel that any time the tire approached the rim width, the aerodynamics were compromised and from that formulated the rule of thumb we called the Rule of 105(%).  The Rule of 105 states that the rim must be at least 105% the width of the tire if you have any chance of re-capturing airflow from the tire and controlling it or smoothing it.  

Rule of 105 (%) Formulated in 2001 Based on Early Wind tunnel work with 21 and 23mm Tires
One of the most interesting aspects of the Rule of 105 is that before 2001, nobody was tunnel testing with 21 or 23mm tires.  The conventional wisdom was that you TT'd or raced Triathlon on 18-20mm tires and that was that.  However, I was at the Texas A&M Tunnel with US Postal in 2001 and Johan Bruyneel was talking about the amazing ride and grip of these new 21mm tires they received from the team sponsor.  He had made the decision to abandon narrower tires, even for the TT as the riders so preferred this new tire.  We immediately went about testing wheels with 21mm tires and found that the 21 and 22mm rims of the time just weren't wide enough.  
This would be the beginning of an amazing game of chicken and egg within the cycling industry as wheel manufacturers made rims that worked with wider tires and tire manufacturers and athletes kept pushing the limits by using tires even wider still.  In 2007 we struggled to convince cyclists at Paris Roubaix to use 27mm tires when they had always preferred the 'already very wide' 24mm tires by Paris Roubaix 2016 we had cyclists at Roubaix on 30mm front and 32mm rear tires with 25mm tires being used in TT's!
Why the Rule of 105
This CFD image from Bontrager does a great job in showing the 'Why' of the Rule of 105.  While the cycling industry has always liked to talk about aircraft wings, the reality is that no aircraft wing has ever had a bicycle tire as a leading or trailing edge.  This was the realization in the early 2000's that propelled Zipp, then Hed, then Simon Smart/ENVE, Bontrager and now many others to completely rethink the problem.  The real problem/opportunity is how to best take the dirty air off of the tire and smooth it with the rim in the front half of the wheel, and how to use the rim to impart some flow structures that will close up nicely around the tire on the rear half of the wheel. 

Image from Trek/Bontrager D3 Rim Shape White Paper Showing 25mm Tire
This is an image from the Trek/Bontrager white paper of 2011, you can see in the top image how the separation (in blue) is completely dominated by the tire as the rim is narrower.  The 'Zipp' image has the rim and tire at the same width as the tire, and the Bontrager at the bottom has the rim wider than the tire and able to 'recapture' the separated airflow from the tire.  These subtle differences can make for very large changed in drag, and even greater differences in handling.  Many brands have similar CFD imagery to this on their sites, the critical point is that subtle variations in rim shape can and will change aerodynamic drag as well as handling, but none of it is possible unless the rim is at least 105% of the tire width.
The Link to Tire Size and Pressure
So now that we understand how we got to now on this topic, let's revisit our Caliper Measured tires and rims from Part 1.

Actual Measured Widths of Tires On Various Bead Width Rims
The link between pressure and aero starts to become clearer as you look at the chart above.  Between 87 and 115psi most of these tires will grow by nearly 1mm in width.  In strict aerodynamic terms, this added width comes at a cost of roughly 1watt per 2mm of tire at low yaw angles.  However, the big penalty can come at moderate yaw angles as the tires approach the width of the rim.
First let's look at a Zipp 404 Firecrest, a rim with 26.5mm outer width and 16.5mm Bead Width.  With a 23c tire, we see less than 10 grams of drag difference between 6Bar, 7Bar, and 8Bar.  However, with a 25c Tire, we see some significant effects to the aerodynamics of the wheel with changing pressure as the tire growth over those pressures takes rim from being 102% of Tire Width to only 98% of Tire Width.

Effect of Pressure on Zipp 404 Firecrest with 25mm Continental GP4000sII 25c Tire
All 3 pressures on the 23mm tire made a difference roughly equal to the margin of error of the wind tunnel (A2 Wind Tunnel), so 6Bar, 7Bar, or 8Bar would all be within 10 grams of the blue line .  However, the 25mm Tire is approaching the threshold of aero efficiency due to the inflated width of that tire on a 16.5c bead width rim, and at this tire width, your pressure can make a relatively large aero difference.  
At yaw angled between 10 and 20 degrees, the difference between 7 and 8 Bar tire pressure (100.5 and 115psi) in this instance would be between 1 and 9 watts.  When you consider that a full ceramic bearing upgrade for this same wheel set represents a savings of 0.8-1.0 watt it becomes clear that these aero differences related to tire pressure may be small, but are most definitely non-zero!
Recommendations
For setups where the rim is 105% of the measured tire width or greater, tire pressures will have very small aero effects.  Our friends at FLO Cycling recently completed a very detailed study on 23mm tires on one of their wheels in 5psi increments (rim was 105-108% of tire) and found 0.5-2.0 Watt Difference.  You can read the results HERE. For their setup, the optimal pressure turned out to be 95psi for the 23c Tire on 17.5c Rim.
Again, these are very small numbers, however, at the margins of performance, they may be critical to performance, and best of all, these gains are free of charge to those willing to experiment.
We continue to recommend measuring your tire width and carefully logging your tire pressures to help you better understand these effects.  The thinking should be that wider tires require lower pressures, and if you are violating the Rule of 105 for an Aero Critical event, then perhaps consider downsizing your tire or try and see if a slightly lower pressure may be the solution.
BONUS: Tire Wear and Aerodynamics
As an added bonus we've decided to thrown in a fun graph showing a new 23c GP4000SII and one that has seen 1000 miles of use as a rear under 175lb athlete.  The effect of tire wear was something I first noticed in the wind tunnel 10+ years ago and have been interested in ever since.  While your tire wear will vary based on surface conditions and rider weight, we can unequivocally say that tires with visible center tread wear or flat spotting on the crown of the tire are costing you time out on the course.  
This is logical if you think about it, the crown of the tire will wear flat, and flat, is a terrible aerodynamic shape!  For the sake of our limited data collection time and money, we have used a USED Rear Tire.  Front tires will wear more slowly, but remember, the aero performance of the tire will be slowly degrading every time you use it, so for 'A' races we recommend tires will low mileage!