It pays be to be compliant: the physics of indoor track and “optimal” surfaces

45 years ago, a young lad hailing from a southern suburb of Dublin ripped around the interior of Madison Square Garden 11 times. By doing so faster than six other gentlemen making the same prestigious rounds, he was crowned champion of the 1977 Wanamaker Mile. 

6 years later, in 1983, that same lad, a bit stronger and a bit wiser, ripped 10 laps for a mile around the interior of Byrne Arena in East Rutherford, New Jersey on a track designed to his specifications. This time, he did it in 3 minutes and 49.78 seconds, faster than anyone had ever covered that distance indoors (with the previous fastest person being his own 1981 vintage), and faster than anyone would cover it for another 14 years. 

11 years later, in 1994, that same lad, now a lot wiser but perhaps a bit less strong (in sinew, at least), ripped around the interior of Harvard University’s Gordon Field House 8 times, this time on a track designed by a couple brilliant locomotor scientists, but still covering one mile. He completed that grand prix in 3 minutes and 58 seconds, becoming, at 41 years young, the first master’s athlete to run a mile in under four minutes.

Aside from occurring under a roof and being protected from the outdoor environs by walled confines, each of these performances had something unique in common. They were all conducted on the surface for which our protagonist, a one Mr. Eamonn Coghlan, was the esteemed Chairman. They were run on boards.

Coghlan winning his first Wanamaker title in 1977. 

Photo: W. Jacobellis/New York Post via Irish Times

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The surfaces on which we run have distinct effects on our biomechanics, and consequently, our energetic efficiency and speed at which we can cover a distance over them. When we run on stiff surfaces like hard asphalt, our bodies–behaving like giant springs1–actually “soften up”, putting our joints through slightly greater ranges of motion and reducing the overall stiffness of its spring dynamics to counteract that of the surface. When we run on compliant surfaces, like a bouncy boardwalk, our bodies “stiffen” up as springs, tightening up the range of motion in the joints and preserving the vertical excursion of the body2. Stiffer spring characteristics are linked to better efficiency3, and faster runners tend to run as stiffer spring systems4

Our bodies behaving as giant springs when we run.

Image: Burns et al. (2021) with frames adapted from Muybridge (1887)

When we run on a compliant surface that dampens–meaning it doesn’t bounce back well and dissipates the energy we put into it, like sand–we have to do work against the surface. As a result, the efficiency of our muscle-tendon complexes (e.g., the Gastrocnemius/Soleus-Achilles complex) drops. A group of researchers in Belgium actually followed runners around a custom-built sand runway in their laboratory (with rakes to scrupulously maintain the surface). They measured the energy cost on the compliant-yet-dissipative sand at a whopping additional 60% compared to firm ground5.

If that compliant surface is more resilient–meaning it returns the energy we put into it and bounces back, like that boardwalk–our bodies start to really like it. To examine this, a group of researchers at the University of Colorado actually rigged up a treadmill with a soft EVA foam belt–the same foam used in most running shoes–providing a cushioned surface with modest resilience (EVA typically returns 60-65% of the energy put into it). They found that runners running barefoot on the soft foam improved their efficiency by 1.6% compared to running barefoot on a stiff treadmill deck6, akin to an asphalt surface. They termed this “the cost of cushioning”: the work that our bodies have to do to sustain the impact of each step on a stiff surface. On a soft, compliant surface, we can offload that work to the ground. If it’s not so soft and dampening that we lose more energy than we save, the effect can be advantageous.

If the surface is compliant and resilient, we not only offload the cushioning cost to the ground, but we can actually store and recycle energy from each step in the ground and get it back for the next step cycle. This effect can be quite advantageous, and it was executed quite nicely in a novel piece of footwear for road racing around 2016 (note: shoes are surfaces that you carry on your feet). The results changed the sport as we know it. 

Running on a compliant-yet-dampened surface is not particularly efficient. A scene from the sand study. Photo: The Company of Biologists

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Understanding those principles of the grounds on which we run, we can move to the matter at foot–the tracks on which we race. The search for the faster tracks had a fire lit in the 1960s and 1970s. These were, of course, the glory days for which we all wax romantic (even those of us who wouldn’t be mentally or physically conceived for decades to come). It was spearheaded by a gentleman named Floyd Highfill. Originally an engineer, he started a company called Tracks West and took to designing and building tracks in the 1960s 7 .

He had several key design principles, informed conceptually by his background in physics and mechanics but executed practically via his intuition as a former collegiate runner. First, he knew the track had to be well banked (see part 1). But the implementation of the banking was one of his big innovations. Tracks then, and most still today, use a symmetric banking–gradually rising to its apex in the middle of the turn, then gradually falling to the next straightaway. Highfill thought this constant change was disruptive to the stride of the runner, so his tracks aggressively rose to the maximum bank angle early into the turn and carried that angle consistently through about 75% of the turn, then more gradually dropped into the straightaway. He referred to this as “asymmetric” banking. Again, most modern tracks use a simple symmetric bank construction. Except for Boston University, which still to this day uses Highfill’s asymmetric banking design.

His second key principle was a bit simpler, but perhaps more critical–his ovals had to be made of plywood. He sensed that the bounce of the wood was best for a runner. Many of his tracks didn’t even have a synthetic surface–just brightly colored paint over some plywood boards that would have to be replaced as spikes chewed them up. The boards were typically placed on longitudinal two-by-four supports running beneath the lane lines and spaced four feet apart. They could be taken down and set up for meets hosted in multipurpose arenas and field houses.

Floyd Highfill with a characteristic well-banked plywood track

photo: Sports Illustrated

His tracks were the canvases for many of the great indoor meets of the era and saw countless world records. They included the 160-yarder in the San Diego Sports Arena–which saw several Coghlan-authored world records in the mile (3:51 and 3:50), the 176-yarder in Tingley Coliseum at Highfill’s alma mater in Albuquerque (and one of his early test kitchens)–which saw an 880y WR of 1:47.9 in 1969, the 176-yarder at Cole Field House at the University of Maryland– site of the famous 1975 Liquori vs. Prefontaine CYO Mile (where a young Villanova Wildcat named Eamonn Coghlan finished 5th, barely missing the sub-4 barrier in 4:00.2), and 220-yarder in Pocatello, Idaho–which still is used today.

He also helped design the track that would go into Madison Square Garden for the Millrose Games, to be used and abused over the next decades for some of the world’s great indoor racing. For that particular project, he collaborated with a biology and engineering professor at Harvard University, one whose name any running biomechanics researcher might struggle to write a paper without citing: Tom McMahon.

Top left: A Highfill/Tracks West construction at Cole Field House at the University of Maryland, site of many epic battles on boards at their annual CYO meet (e.g., top right). Bottom left: Prefontaine’s 1974 8:20 American Record in the two-mile on Highfill’s famously fast and superbly steep installation in San Diego. Bottom right: Marcus O’Sullivan ripping around the Highfill/McMahon & Greene collaboration in Madison Square Garden.

Photos: UMD Archives (top left); AP (top right)); Chip Gale/T&F News (bottom left); Running Past (bottom right)

At the same time that Highfill was designing and constructing tracks out of intuition, McMahon was coming up with some pioneering and clever experiments to understand the mechanisms of how we run on different surfaces. Note: it’s one thing to sense something intuitively, but it’s another thing to understand it mechanistically. The former helps us move towards something better quickly, but the latter is necessary to tweak, refine, and determine an ideal robustly–to “tune” the variables. 

The track coach at Harvard approached McMahon in the late 1970s seeking advice on the design of a new track to reduce injuries and possibly even improve performances. The wheels in the scientist’s mind begann spinning (or rather, the limbs began bouncing). Together with his post-doctoral research fellow Peter Greene, they set out to determine the optimal surface for running and ultimately build a “tuned” track for the runners at Harvard. They built a series of runways of different surface stiffnesses and studied the stride characteristics of the runners as they moved over them. The tracks ranged from stiff asphalt to plywood boards to platforms with soft squishy pillows beneath8.

Left: McMahon (right) and Greene (left) conducting their experiments on the runway whose surface they adjusted. Right: A subject running over a stiff surface (top) with little deformation underfoot and the super-compliant pillow track (bottom) with substantial deformation underfoot.

Photos: Scientific American

Their work was motivated by the concept of treating the runner as a bouncing system similar to that aforementioned giant spring, but this time with a dampening (i.e., energy dissipating) element. Modeling the surface beneath the runner as a spring in series with them, they postulated that they could calculate a theoretical “ideal” frequency at which the whole system–runner and track–would bounce together. The modeling predicted that as the surface got softer and softer, the runner’s step length would increase. It also predicted that as the surface got softer and softer, the ground contact time of the runner would first dip a little bit, then sharply rise. Within that range of surface stiffnesses where the contact time slightly dips and the stride length starts to see an uptick, the surface should be advantageous for the runner. Factoring in the mass differences between the runner and the track boards and the runner’s energy dissipation, they predicted that a track about 2-4 times as “stiff” as a human runner would be “optimal”9.

Left: The 1977 runway set-up where they could measure and swap surfaces. Right: the six surfaces tested and their respective stiffnesses.

Figure and Table: McMahon and Greene (1979)

In their actual observations of runners on the different surfaces, they found that ground contact time remained relatively constant as they moved from higher to moderate stiffnesses, until that sweet spot, where it got a bit more varied. Then, at the softest surface (the “pillow” track), it markedly increased. Their stride lengths also increased as the surfaces got more and more compliant, as predicted. So, in that particular surface stiffness range, just before the contact time went up substantially and where the stride lengths ticked up a little bit, they concluded track should be optimal for running fast. The materials that they used to achieve this sweet spot were their experimental plywood boards.

With these results, they built a track at Harvard tuned to that stiffness–about 195 kN/m. The following two seasons, the Harvard athletes would run 3% faster on their home track compared to their best time elsewhere. The previous season, they had run an average of 0.3% slower at home due to their cinders. Runners from other schools also ran 2% faster on the Harvard track. A 2% or 3% improvement in performance is a substantial change–5 to 7 seconds for a 4:00 mile–but remember that in addition to that optimal surface, they also put a modest bank on the track (about 10°), so that’s a 2-3% improvement over tracks that may have been varying in their suboptimality, flat or otherwise. 

While McMahon and Greene’s work started to really dig at the mechanisms of why boards might be faster, there were some gaps that remained. First, the runners in their experiment were running at sprint speeds, and only the support mechanics were being observed, not the energetics at controlled speeds. Second, their treatment of the runner as a vertical spring-dashpot wasn’t quite in line with the pendular motion it exhibits, not fully characterizing our mechanical adaptations over the surface changes. Third, and perhaps most importantly, they were examining the mechanism for performance improvement through the lens of resonance and runner-track frequency matching, ignoring the potential role for storage and return of elastic energy. This was exemplified by the their most compliant surface–the pillow track–also being a substantial dampener, which has its own effects on support mechanics and efficiency.

Tom McMahon tragically passed away in 199910, but one of the final studies with which he was involved pulled all of these concepts together and serves as perhaps the best illustration of the effects of a compliant, resilient surface on running efficiency. For that study, the research team built a treadmill with adjustable supports beneath the deck so that the surface stiffness could be modulated11. They measured the running economy and mechanics of runners across a range of stiffnesses, from 75 kN/m (softer than the plywood tracks) up to 985 kN/m (approaching firm ground). For context, recall that McMahon and Greene had posited that 100-200 kN/m would likely be optimal for a runner. Critically, the treadmill here was also highly elastic–it returned more than 90% of the energy put into it through each step.

As the researchers lowered the stiffnesses, the runners ran with very similar support mechanics. The differences only appeared at the extremes, where on the most compliant set-up, the runners had a modest 4% decrease in contact time and step length. However, with the decreasing treadmill stiffnesses, the energetic cost of running steadily decreased. At the most compliant setting, the 75 kN/m surface, the runners had a whopping 12% reduction in their energetic cost at that speed. 

From the Kerdok et al. bouncy treadmill study. Note the relatively consistent step parameters (left panels), the significant increase in leg stiffness of the runner to maintain the overall system stiffness (middle panels), and the drastic decrease in metabolic demand for the given speed on the softest surface (right panel).

Figures: Kerdok et al. (2002)

Because the surface acts like a linear spring, the softer the spring, the greater the displacement for a given force, and thus the greater the amount of energy that can be stored in it. The researchers here observed surface displacements of 2 mm at the stiffest surface and up to 25 mm at the most compliant. For a typical ground reaction force of 2000 N, the stiffest surface would have returned approximately 2 Joules to the runner each step. The most compliant surface would have returned 23 Joules! For reference, when running at 6:00 mile pace, there’s approximately 100 Joules of energy exchanged with each step, and the arch and Achilles have been estimated to store about 17 and 35 Joules of that, respectively12. Operating at about 78% efficiency, those structures return about 13 and 27 Joules during propulsion, respectively. A compliant, resilient surface–like that treadmill or a well-tuned plywood track–can thus take up a significnat portion of that work that our body's elastic structures (many of them requiring metabolic energy to operate) otherwise have to do.

“This close relationship [between the reduction in metabolic demand of running and the mechanical power returned by the track to the runner] strongly suggests that, when a greater share of the elastic rebound elevating the center of mass in the latter portion of the contact phase is provided by the elastic recoil of the running surface rather than the biological springs in the runner’s leg, the metabolic cost of running is reduced”
–Kerdok et al. (2002)

Getting back to racing surfaces, a tartan track with a steel or asphalt substructure, like most modern indoor and outdoor tracks, has a surface stiffness of approximately 1600 kN/m13. This means that it only returns about 1 Joule to the runner under the aforementioned loads. On the original “tuned” plywood track at Harvard, the surface stiffness was 195 kN/m. With a similar design, Boston University’s current indoor track is likely within that range. This would indicate that a well-constructed plywood track can return about 9 Joules per step, substantially more than a typical indoor or outdoor venue.

It’s further curious that Kerdok et al. observed the metabolic efficiency of the runners to continually increase across the range of stiffnesses, with the lowest surface stiffness being the most efficient. One is left to wonder: if they had a surface as compliant as the pillow track (14 kN/m) but with the resilience of their treadmill set-up, what that efficiency would have looked like? They noted that the softest surface had a resonant frequency that was approximately equal to that of the contact time of the runner, which is necessary for the energy to be returned in time for takeoff. A softer surface would lower that frequency and extend the time it takes to fully bounce back and return the energy. But would a runner extend their ground contact to take advantage of it at an even softer surface? Building on this point, the runners were tested at a constant speed of 3.7 m/s, which is about 7:15 per mile or 4:30 per kilometer. As runners speed up, the time course of that energy storage and return might need to speed up as well. It may be that for the faster speeds of an elite track race, the 100-200 kN/m surface of plywood tracks is optimal. But where that ideality lies and how it changes across speeds and architectures remains to be elucidated.

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McMahon’s legacy lives on across the running world, as the shoes and spikes that are ripping record books to shreds are a direct implementation of these ideas. From his academic lineage, Rodger Kram pushed these ideas further, including the aforementioned “cost of cushioning” explorations and collaborations with Nike and Ineos on their Breaking2 and 1:59 projects. One of Rodger’s charges, Wouter Hoogkamer, led the original study that robustly demonstrated the beneficial effects of the VaporFly14 and now works with Puma to develop fast footwear.

Highfill’s legacy is a bit more splintered (pun intended). Many of his tracks have been torn down or replaced. Tracks West is no longer, and most indoor tracks built today follow a somewhat pre-fab construction model using steel sub-structures. However, one venue still has his fingerprints (or maybe footprints) on it: the Track and Tennis Center at Boston University. 

When Boston University renovated their indoor facilities in 2002, former BU coaches Pete Schuder and Bruce Lehane seized the opportunity to implement the features of the fast tracks they had known so well from the previous decades. They worked with the architects to design the plywood structure with a steep 18°, asymmetrical banking to facilitate faster racing. They even managed to pull Floyd Highfill out of retirement to help consult on the project. It’s been repaired and resurfaced over the years, but it maintains the distinct plywood substructure that provides an ideal surface to elevate distance running performance. The staggering number of records that are continually cranked out there year after year is a testament to the intuition and ingenuity to pursue a sort of ideality. Despite the demonstrable effect that’s been supported by clever science and decades of performance data, it is one of the last of its kind.

The Boston University indoor track at their Track and Tennis Center. Anyone who sets a record here should send a “Thank You” note to Pete Schuder.

Photo: FIU

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So if all of this talk of compliant and resilient surfaces facilitating faster footraces sounds familiar, you’re not imagining things. As alluded to earlier, this same concept is what has made the new generation of racing shoes so effective at slashing apart record books. The PEBA foam that Nike tuned so well for the VaporFly is so much softer and more resilient than anything before it–just like a properly supported plywood board versus asphalt or steel. That foam, in essence, brings that optimal surface to your foot (and because its density is so low, its light enough to carry with you each step), enabling that same beneficial elastic energetic storage-and-return assistance within each step cycle.

Load-deformation curves from testing old (left) and new (right) portable surfaces. The red arrows indicate compression and blue arrows are decompression. The area within that loop is the energy lost, so the fatter the loop, the less efficient the spring. The slope of the line is the stiffness–how much force is required for a given displacement. The old shoes were stiff and dissipative, and the new ones are compliant and resilient. Note that the stiffnesses of the super shoes are much lower than the beneficial tracks. Shoes and ground comparisons aren’t apples to apples, but it might suggest that a more compliant, resilient ground might also be able to further advance the benefit.

Figures: G. Burns

One could extend the analogy even further: just as the super shoes are predominantly performance-enhancing from the elastic effects of that foam, and the curved plate is an architectural accoutrement that facilitates and elevates its performance-enhancing potential, the BU track is predominantly performance-enhancing from the elastic effects of its surface, and the steep bank is an architectural accoutrement that facilitates and elevates its performance-enhancing potential. The shoes without the plate might be better than old shoes, but not as transformative, and a flat board track without the bank would be better than a flat track, but not nearly as record-smashing. Add those architectural features to facilitate the faster running–a curved plate with just the right rigidity and radii or a steep bank with just the right pitch and asymmetric implementation–and magic happens.

And what about super shoes on a super track? The effects aren’t likely linearly additive, but they’re still likely more beneficial together. That’s speculative, but it is based loosely on the idea that when you add springs or dashpots in series, their properties sum inversely. So, if the BU track helps a runner run 2.5 seconds faster in a mile compared to a steel indoor track, and the spikes help them run 2.5 seconds faster in a mile compared to old spikes, together they might help them run 3 or 4 seconds faster. Again, that’s just some napkin prognostication, but the concept is that a little bit of that beneficial surface effect goes a long way–either in shoes or surface–and a lot more might be just a little bit better. But still better.

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All of this leaves one to wonder–why are more tracks not made out of plywood? Again, many modern banked indoor facilities now use steel substructures. It’s necessary for the hydraulic constructions that have become popular, and it’s a lower burden to maintain. Plywood does deteriorate in quality, with different boards wearing at different rates and needing to be replaced more frequently. If the entire substructure is plywood, it can even change the accuracy of the distances over time, necessitating careful attention to the maintenance. Those hydraulic constructions are also appealing to cater to a wider spectrum of athletes and races. A very steep permanent bank makes running slowly a bit uncomfortable, and it biases against some women’s distance racing at the collegiate level. However, a modest bank with a plywood substructure would still likely be substantially advantageous for all and could facilitate a wide range of racing. The original “tuned” indoor track at Harvard only had a 10° bank, which is the pitch at which many hydraulic tracks now are set for the entirety of meets.

All of this would lend ample evidence to the speculation that athletes were more assisted by tracks in the 70s and 80s, where the plywood constructions and steep banks were advantageous compared to the constructions of today. We may now have super shoes, but the racers of those glory years had super tracks. 

It also begs the question–why are more athletes not chasing fast times year-round on these tracks? I would argue that Boston University’s track is faster than any outdoor track. The banking nearly offsets the effect of the tighter turns, and the plywood substructure elevates it to something better. Even if it was dead even to an outdoor track, the climate is perfectly controlled inside the facility, meaning there’s zero chance of wind or heat or rain. Consider that many athletes run their lifetime personal bests on that track (or close to them), and they do it in the winter when they’re not at peak fitness. Think what they could do in the summer on top form on that nearly ideal surface with no weather implications. Could we get Jakob Ingebrigtsen and Tim Cheruiyot to come over for an 8-round title fight in July? I wouldn’t doubt the possibility of them seeing the other side of 3:40. 

Moreover, athletes are allowed to qualify for outdoor championships with indoor marks. That strikes me as a loophole in the World Athletics rulebook, but it’s one that if I were an athlete or coach, I would be exploiting prodigiously on BU’s track. I suspect the primary reason that athletes or coaches don’t try and arrange this is predominately one of an entrenched assumption that indoor is slower than outdoor. This may be the case for most indoor tracks, but for some, namely the one at Boston University, I would argue it’s an erroneous assumption.  

So what are the options? BU is the gold standard with its steep bank and careful construction, but it’s certainly not the only wooden track left. The Tyson Center at the University of Arkansas is also, to my knowledge, built on a plywood substructure. That track has seen its fair share of records and shockingly fast performances. Its bank is modest, about 10° purportedly, but with the plywood, it’s probably close to BU in its benefit. A Highfill-designed track is also still in use at Holt Arena in Pocatello, Idaho. It’s also seen its fair share of records over the years, and they still host the annual Simplot Games on it, which is one of the largest indoor meets in the world. In the UK, Birmingham’s fast fixture is plywood, and Beynon and Mondo still offer permanent wooden indoor track constructions. The indoor track constructed by Beynon for the Portland 2016 World Indoor Championships was a plywood base on a steel substructure. That track now lives at the University of Iowa. There are more around the country, but it’s also important to note that not all wooden tracks are equal, some missing the mark with the board constructions, using surfaces or supporting elements that reduce beneficial effects. Highfill knew how to do it well, McMahon certainly knew how to do it well, and Schuder and Lehane implemented those lessons and maintained the track at BU to continue to do it well.

The Highfill/Tracks West construction at Holt Arena in Pocatello, Idaho.

Photo: Simplot Games

It would be great to compile a listing of all the available wooden tracks for athletes and coaches. What if there was a series of races held on the best plywood tracks in the country? Get the best runners around the country or the world duking it out to chase fast times on the fastest surfaces. It would be a missed opportunity not to call it The Circuit Board.

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Running is, at its mechanical essence, a well-orchestrated forward bounce. That bounce is a dance, and the runner’s partner is the ground. They briefly-yet-intimately interact several times a second, and the mechanical nature of both the runner and their partner can have distinctive effects on how efficiently they carry their tune.

Like all great relationships, it’s about give and take. The runner gives some potential energy from their airborne aerial phase to the ground as they engage, and if the ground is properly compliant, it’ll willingly take some of that energy from the runner as they collide. Then, as the couple prepares to depart, if the ground is timely and resilient, it’ll give the energy back to the runner, who will willingly take it back into the air and bring it along to their next meeting. And the next, and the next, and the next, until the dance is done. With a well-calibrated give and take, the runner and their partner are likely to finish that dance a little bit faster. And for just about any runner, some simple timber might be that perfect partner. One need not be the Chairman to have a good board meeting.

Photo: Bob Hagedohm/Sports Illustrated

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Part 1 on optimal bank angles:
There’s money in the bank: the physics of indoor track and “optimal” speeds

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  13. Willwacher, S., Fischer, K., & Brüggemann, G. P. (2013). Surface Stiffness Affects Joint Loads in Running. ISBS-Conference Proceedings Archive. https://ojs.ub.uni-konstanz.de/cpa/article/view/5634

  14. Hoogkamer, W., Kipp, S., Frank, J. H., Farina, E. M., Luo, G., & Kram, R. (2018). A comparison of the energetic cost of running in marathon racing shoes. Sports Medicine, 48(4), 1009-1019. https://doi.org/10.1007/s40279-017-0811-2

Geoff Burns