An incorrect but widely held view among many cyclists is that they will always go faster uphill with lightweight, shallow-section wheels. For years marketing departments have sung the benefits of these lower-weight wheels, noting their lower rotational weight. But those claims, and their importance, are most often overblown. After researching wheel technology, I now believe most cyclists will benefit from deeper, more aerodynamic wheels — even on climbs.
Science says go deep
Should you be riding deep-section wheels to go faster on climbs? According to some compelling research and testing, the answer is absolutely yes. This information comes from wheel-building and testing guru and engineer Bill Mould, test engineer Russ Willacker, and aerodynamics engineer Jean-Paul Ballard, himself a former Formula 1 aerodynamicist, CEO of wheel maker and aero consulting company Swiss Side, and aerodynamics consultant to Team Ineos.
Team Ineos riders used its full aero road setup in almost all stages of the 2019 Tour de France; a key exception occurred during stage 14 for eventual-winner Egan Bernal. The stage finished atop the Tourmalet, and Bernal used lightweight climbing wheels. All teams recognize that in a three-week stage race, cumulative fatigue must be minimized.
A rider’s aero drag is reduced by about 50 percent when sheltered in the peloton, so if aero wheels would save a solo rider 10 watts at 45-50 kph (in a straight line, and can save 20-30 watts in the right crosswind conditions), those climbing wheels will still cost a consistent five watts while sheltered in the peloton and will cost the guy at the front 10-30 watts. While climbing with aero wheels on stage 18 over the Galibier, Bernal overtook on GC his teammate, Geraint Thomas.
Weight and moment of inertia
The figure above represents a rider climbing a constant-grade hill with 1,000 meters (3,281 feet) of elevation gain, gliding to a stop at the top. By lifting himself and the bike to a higher elevation, he converts kinetic energy (the forward movement of his body and bike) into potential energy.
The increase in his potential energy is the product of three things: the total mass (m) of the rider and bike, the gravitational constant (g) — which is 9.8 m/s2 — and the height (h) of the hill. Factors like drivetrain friction and rolling resistance are small and can be ignored here. We will also ignore wind resistance for the purpose of this illustration.
If the mass of the bike and rider is 100 kilograms (220.4 pounds) and the height of the hill is 1,000 meters, the energy required to climb the hill (mgh) is:
- 100kg x 1,000m x 9.8 m/s2 = 980,000 Joules.
Since one watt is one Joule per second, if he were to pedal at a power output of 200 watts, the time to climb the hill would be 4,900 seconds, or 81.7 minutes. If we were to remove 200 grams (nearly half a pound) from the weight of the rims, hubs, bike, or rider, his time becomes 4,890 seconds, a mere 10-second gain in a climb of an hour and 22 minutes. Furthermore, as long as he does not apply the brakes, it doesn’t matter where the weight is located; the “rotational” weight (a.k.a., moment of inertia) of the wheels does not play a role.
Why does our experience lead us to believe that we climb faster with wheels with a lower rotational weight — and consequently, a lower moment of inertia? Wheels with a lower moment of inertia spin up faster, but they also slow down faster. This can be easily measured in a laboratory or demonstrated by spinning the front wheel on a bike.
Unless you are pedaling uphill with exactly constant power output throughout every pedal stroke (which nobody does), the speed of your bike will be constantly changing. During the most effective part of your power stroke with one leg, you feel the bike accelerate, but you slow down over the top and bottom of the stroke until your other leg begins the most powerful part of its stroke.
Riders generally produce peak power between approximately two o’clock and four o’clock on the pedal stroke, when viewed from the bike’s drive side. That’s when the bike accelerates, and it then slows down when the feet pass the dead spots top and bottom. We sense the increase in speed and are less aware of the decrease that immediately follows.
The figure above illustrates, in red, a constant average speed going up the hill and, in blue, the constant changes in speed above and below the average with each pedal stroke. The lower the rotational weight of the wheels, the larger the swings up and down in instantaneous velocity (right graph). Because of the flywheel effect of the spinning wheels, wheels with more rotational weight smooth out these variations (left graph), and we don’t feel them as much.
Although the total kinetic energy of a bicycle is the sum of translational and rotational kinetic energy, rotational energy is only a tiny part of the total. Reducing rotational weight of rims, tires, and tubes saves energy only when the wheel is accelerating, and, as long as the rider doesn’t hit the brakes, he or she gets that energy back when the wheel is decelerating.
This is not to say that wheels with low rotational weight are pointless. In an uphill sprint, the quick acceleration of low-inertia wheels at slow climbing speeds is an advantage, and after the rider crosses the finish line, it doesn’t matter that the bike slows down faster; the race is over! Light wheels with a low rotational weight offer advantages in criterium and cyclocross races, because the flywheel effect from heavier wheels is dissipated when braking in the many corners, and regaining the speed that was lost in the corner burns more of the rider’s available energy.
Despite all of the braking and accelerating in a criterium, however, heavier, higher-inertia, deep-section aero wheels still have a clear advantage over lightweight, shallow-rim wheels, according to Swiss Side’s computer simulations of criterium races. It has confirmed those simulations in real-world measurements. Ballard suggests anyone with a power meter try it themselves. Run the same course and look at your average power; Ballard is certain that you will measure either a time savings or a power savings with the aero wheels on the same course.
One reason that bike racers tend to believe so strongly in reducing weight — and rotating weight in particular — while thinking less about aerodynamics, is that aerodynamic drag is hard to measure, whereas weight, and even rotating weight, is easy to measure and, in some cases, feel. Take cyclocross, where a rider sprints for the holeshot from a dead stop, then brakes into and accelerates out of hundreds of turns, before lifting and carrying the bike a dozen or more times. It’s obvious what a difference lower weight and lower wheel inertia makes.
Another case in which a wheel with a lower moment of inertia is beneficial is when accelerating rapidly to jump up onto a log on a mountain bike. There is no corollary on the road to these circumstances, however, and thinking that low rotational weight will grant extra speed when climbing a long, steep grade is a false hope.
Drag and thrust
Deep-section aero wheels can help climbers, too. Despite the measurable benefit of aero wheels, the left pie chart above shows that around 75 percent of the head-on drag that a rider works against is created by his or her body. If the wheels only account for about 8 percent of the total drag, how is it that aero wheels have such a huge effect?
It’s the result of the “sailing effect” — or, the production of lift — as well as thrust from the front wheel in crosswinds.
All wheels produce lift in a crosswind like an airplane wing tipped in the air, caused by the air moving on the top traveling faster than the air moving underneath. Generate enough lift and thrust is produced, driving the wheel forward.
Other parts of the bike see drag reductions in crosswinds, but the front wheel is the only part of the bike that actually produces thrust, and it takes a very aerodynamic wheel with the right tire to produce it. Just like the wings did in the two crashes that grounded the Boeing 737 Max, an aero wheel stalls when its angle of attack (yaw angle) goes beyond a certain point; the airflow can no longer stay attached, and the drag suddenly goes way up. All aero wheels stall at 20 degrees of yaw.
The right-hand pie chart above shows that there is little contribution from the body and the bike to the sailing effect. That pie chart uses data from an aero bike and a rider in an aero position with an aero helmet, so it would be far less when sitting up and climbing on a standard road bike. Given the swirling air encountered by the rear wheel, most of the drag reduction (sailing effect) occurs on the front wheel; negative drag (thrust) only occurs on the front wheel, and only with the correct tire.
Swiss Side’s wind tunnel data shows that with the wrong front tire, the sailing effect is lost. Apparently, some sidewall tread is required to “trip” laminar airflow into a turbulent boundary layer, which is thicker and more resistant to shear stress. The flow remains laminar with a slick tire, which causes the wheel to stall very early when the air comes around the shoulder of the tire and separates.
The best functioning aero tire in Swiss Side’s testing is Continental’s older GP4000S II, a slick with hatched patterns in fin-shaped pairs on the sidewalls. The newer Continental GP5000, a slick with single, more widely-spaced fin-shaped hatched patterns on the sidewalls, is aerodynamically good, but not as good, and is better in rolling resistance. That tire is available tubeless, and an equally efficient tubeless tire aerodynamically is the Schwalbe Pro 1, a slick with widely-spaced hatched patterns in long, angled rhomboid shapes on the sidewalls.
Velocity vectors allow us to determine the effective wind angle that a rider experiences. To a physicist, speed and velocity are not the same thing. Speed is simply a magnitude—how fast something is going, expressed in distance per unit time (20 miles per hour, for instance). Velocity, however, is a vector; it has both magnitude (speed) and direction.
The rider’s velocity is in the bike’s direction of travel, which we’ll call zero degrees. The wind’s velocity may be at any angle relative to that zero-degree bike direction. The “yaw angle” (or simply “yaw”) — the effective wind angle the rider experiences, is the direction of the vector sum of those two velocity vectors.
Conceptually, vector sums are straightforward. If the wind speed and rider speed are equal and the wind is at 90 degrees to the direction of the bike, then the yaw angle is 45 degrees. Similarly, if the wind speed and rider speed are equal and the wind is at 45 degrees to the direction of the bike, then the yaw angle is 22.5 degrees. And if there is no wind, then the yaw angle is the same as in a direct headwind or tailwind, namely zero, and the effective wind speed is the speed of the rider. The math becomes more complicated with varying wind angles and differing speeds of the wind and the bike. In the real world, the speed and direction of both the rider and the wind are constantly changing.
If the rider is pedaling hard, even if huge side gusts make the instantaneous yaw angle at 45 degrees or more, the average yaw angle will generally be in a narrow range—usually within 20 degrees or so of the rider’s direction.
The legendary bike leg of the Ironman World Championships in Kona has been well-studied in this regard. Ballard’s measurements show that, despite riding on a wide, hot strip of black tarmac across black, treeless lava on Hawaii’s west coast, exposed to huge crosswinds, the average yaw angle top riders encounter in that race is 15 degrees.
You can see from the chart above that 15 degrees of yaw is near to optimal for the sailing effect of wheels of various depths, with the shallower ones stalling at lower yaw angles than the deeper ones. Only the deepest ones, 62.5mm and 80mm deep, go to negative drag (thrust). The 80mm-deep Swiss Side Hadron 800 with a Continental 4000S tire goes from consuming 15 watts at 45kph and zero yaw to -11 watts (adding 11W to the rider’s power) at 18 degrees of yaw, a net swing of 26W of power.
A boat can sail upwind by tacking back and forth, making its average direction into the wind, because the wind pushing on a sail that is angled from the centerline of the hull produces a forward force. The greater the sail angle, the greater the forward force relative to the side force.
The boat only goes forward because the keel keeps it from sliding sideways in the water. Similarly, the tires on the road are the rider’s keel. A rider could get a bigger benefit with a solid front disc wheel, but a passing semi-truck would send him flailing back and forth like a potato chip in a dust devil.
Albeit less drastically, gusty wind conditions can readily make a bike with an 80mm wheel depth uncontrollable. Some aerodynamic benefit is necessarily exchanged for better front wheel control in stormy conditions. A low rim section is 30mm or less; aero rim depths start at 40mm. A wheel up to 60-65mm deep is absolutely rideable for road racing, while 80mm is too scary on windy descents for all but the heaviest of riders. In the drag-curves chart above, the Hadron 625 is 62.5mm deep and representative of aero wheels (485 is 48.5mm deep and 800 is 80mm deep).
Climbing on aero vs. lightweight wheels
It would be nice to provide an elegant formula into which you could plug the gradient of the climb, your weight and average climbing power, and the weight and aero drag coefficients of various wheels, and it would spit out which wheels would be fastest for you in that circumstance. The fact is, though, that taking rolling resistance into account as well as aerodynamics and weight would add complexity. And it would still be too simplified to give you an answer you could hang your hat on.
Instead, running simulations using a powerful computer program with the ability to factor in a lot more of the variables that you would have to ignore in order to manually solve such a problem, like variations in wind speeds and angles, variations in terrain, and even in road surfaces and tire widths, types, and air pressures, is going to yield more useful result.
Swiss Side, which has been doing similar simulations as the official race and aerodynamics simulation partner for Team Ineos, created two climbing simulations for this article comparing aero and lightweight wheels in Figure 8. The simulated total base drag coefficient (CdA) for the bike and rider is 0.320, and the simulated rider weighs 70kg (154 pounds).
Three different power outputs for the rider were simulated: 200W (recreational rider), 300W (racer), and 400W (pro racer). The computer ran a series of climbing gradients for each given power level to determine at which gradient the weight savings of lightweight wheels brings more time savings than the aero savings of aero wheels. In the graphs, the horizontal zero axis is where the speed with either setup is the same.
Scenario 1 (10% saving comparison):
- 7.5kg bike weight with a typical CdA of 0.095 for the bike only.
- This represents the Specialized Tarmac with pedals and is the average CdA of road bikes measured in a recent extensive wind tunnel test.
- We apply a 10 percent Bike CdA saving and then separately a 10 percent Bike Mass saving
Scenario 2 (Real-world comparison):
- A typical lightweight bike of minimum UCI legal weight of 6.8kg and CdA of 0.095 with 1380g Lightweight Meilenstein Evo Clincher climbing wheels.
- Compare to a Canyon Aeroad CF bike with a total weight of 7.5kg and CdA of 0.066 with Swiss Side Hadron Ultimate 625 clinchers.
- Weight difference is 700g; aero drag difference is approximately 30 percent (since 0.066/0.095 = 0.7).
In the left graph (Scenario 1), you can see that dropping the aerodynamic drag by 10 percent makes the rider putting out 200W faster than he or she would be with a 10 percent lighter bike until the hill steepness reaches 3 percent, at which point the lighter bike is faster. Due to his or her higher climbing speed, the rider putting out 300W is not faster with the lighter bike until the hill is steeper than 3.7 percent, and the pro rider (400W output) is not faster with the lighter setup until the hill is steeper than 4.2 percent.
Going to the real-world comparison of a lightweight bike and an aero road bike, Swiss Side’s computer simulations show that an average cyclist (200W power output) would have to climb a gradient of 5.2 percent before the lighter bike becomes faster than the aero bike.
For a rider putting out 300W, the simulation finds the break point to be at 6.8 percent, and a pro riding at 400W would need to be on an 8.3 percent gradient to be faster on the lighter bike. Since that gradient would have to apply to the entire course, such a stage only exists in an uphill time trial. The average gradient of most stages, even mountain ones, is close to zero.
The Col du Tourmalet climb to the stage 14 finish averages 7.4 percent. Bernal chose to pedal a bit harder the rest of the day with lightweight wheels to get an advantage over Julien Alaphilippe (and Thomas) on that crucial final climb.
Using these types of computer simulations, Tour de France riders choose deep section carbon composite wheels, even on mountain stages, because their aerodynamic benefit makes the rider faster despite extra weight.
Team Ineos has developed its “Virtual Pitwall” in collaboration with Swiss Side (the engineers in Formula 1 sit on the wall of the pit and run simulations to optimize their team’s equipment in a race). It will be cloud-based, allowing the team to run any simulation they want while at a race, using this tool. The team can input terrain and predicted wind, weather, and rider power; even how a rider feels on a given day can get factored in. Then the team can select the optimal equipment setup for the day.
For instance, modeling windy Tour stages that split the race into echelons could aid in wheel selection and other preparations for a lightweight rider who cannot control as deep of wheels in strong crosswinds as bigger riders.
Mentioning pro racing is only for illustrative purposes; don’t let anyone tell you that aero is only important if you perform at a high level. The science is very clear. Even if you are an average recreational rider, drag reduction and the accompanying aerodynamic benefits will accrue to you, too, and perhaps even more.
Any time you are going faster than 15 kph (9.3mph), aerodynamic drag is the biggest resistive force you have to overcome. And since you will be out on a given course longer than faster riders and will encounter larger yaw angles, resulting in a larger sailing effect on your front wheel, you stand to benefit even more from aero wheels than a pro would.