Sunday, 4 October 2015

Racewalking: The hidden flight path

Anyone who has watched racewalking intuitively knows it's different from running, hence it has as much credibility as classic technique in XC skiing, or the butterfly stroke event in swimming. And anyone who's tried race-walking knows it's very hard to do well, painful (especially the shins) and frustrating (especially if you get DQd moments before finishing). For most of its contemporary existence it has been a maligned sport.

What are the technical differences between walking and running? According the official rules,
  • Racewalking is a progression of steps so taken that the walker makes contact with the ground so that no visible (to the human eye) loss of contact occurs.  
  • The advancing leg must be straightened (i.e., not bent at the knee) from the moment of first contact with the ground until in the vertical position.
We know there is a flight phase with each running step. Walking, by contrast, both your feet should never both leave the ground. Rule #2 is less intuitive but in fact a better way to differentiate running versus walking. Interestingly this rule only came into effect in 1995.

There are another technical differences. For instance in a runner's mid-stance phase, i.e. when the foot swivels under the hip, the body's centre of mass (COM) is at its lowest. For walkers, because of the straight knee, their mid-stance COM is at its highest point. I only mention this because because I find that both running and walking, when you really think about them, are weird, complex movements.

Returning to rule #2, it is easy enough to visualize (and enforce) to make it a fair visual criteria in a judged sport. However there is a fundamental problem with Rule #1 that I will now explain. There is already plenty of research that observes a flight phase in race walking. For instance in a recent (2014) literature overview, Pavel et al note
From an overall view, race walking athletes seem to adhere to the ‘straightened knee’ rule, but at race speed they do not observe the ‘no-flight time’ rule. 
Admittedly flights times spoken of are small; Pavel estimates between they range 0.01 and 0.05 seconds. But those small flight times add up. Moving at 4 m/s, a single 1/100th second of "flight time" can earn a bonus distance of 4 cm (after all, distance = speed x time). So in a 50 km walk race, given a stride frequency of 3 steps/s (180 steps/min), one takes over 37,000 steps. That tiny flight time and 4 cm per stride adds up to a total distance gain of 1.5 km! Importantly the human eye cannot visually process a flight time of 10 milliseconds yet a race walker is less likely to win without this clear flight-time advantage. Indeed, in one study flight times were found positively correlated with speed.

Video of a race-waller leaving the ground (at 0:13):

Unlike some judged sports where small "cheat" advantage stay small (such as making a single illegal V-shape move with your skis in classic racing), because of the cumulative effects of undetectable millisecond flight times, we now know a completely honest race walker is at a permanent disadvantage over one who can eke out a bit of air time for each stride.

Small flight times matter, but it still seems unfair to characterize all racers as deliberately breaking rule #1. Perhaps a better way to envision race walking is the attempt to minimize air flight time, rather than to eliminate it entirely. So if that's all you are interested in, the discussion ends here and you can enjoy either mocking or defending racewalking, or do something else entirely.

But even if the discussion is only academic, there is more to understand. Observationally we know high-speed cameras can catch a flight phase in non-DQ'd walkers, but how can one go about detecting this with pure physics? At a deeper level it seems possible that using stride angles and F=ma would tell me if it's theoretically possible to race 'fair' at the typical speeds of a competitive walker.

Race walking angles. Left is mid-stance phase, Right is the landing phase.
Stride length L is about 1.23 m for elite men, 1.08m for women.
A 1.8m-tall person has a leg length of 0.9m, roughly, and b = 0.45.
Recall the technical note where I said the leg is straight at the mid-stance phase. Moving this way, the body appears to behave like an inverted pendulum (heavy side on top instead of at base). Hence because of the fast swivelling rotation over the straight leg, there appears to be a balance of centripetal (Fc) and gravitational (Fg) forces. Their relative strength is measured by the Froude Number (Fr), a ratio of Fc and Fg, and a function of total leg length (2b), forward speed, and gravity. Fr is NOT a function of mass.
At this point I may have disinterested most of my theoretical audience, so for an intermission enjoy some classic XKCD:


Moving back to the Froude number, whenever Fc exceeds Fg (Fr > 1) then you leave the ground. If we restrict to Fr exactly 1, then vmax2 = 2bg. So for b = 0.5 m, vmax = 3 m/s or 10.7 km/h.
But race walkers routinely run faster than this. Men can racewalk over 14 km/h for 50 km distance, averaging 3.9 m/s. With this simple analysis we have proved all race walkers must cheat, right? Well, not exactly.

Referring to one article titled "Body centre of mass trajectory shows how race walkers elude "Froude law", they say
The pattern of race walkers’ [COM] was found to be dynamically opposite when compared to walking... Although a variation of walking, race walking is not a pendulum-like gait, thus it does not undergo the “Froude Law”
It turns out out original assumption about the pendulum-like gait was flawed. Here is a better picture:

Hence around the mid-stance phase where the body "ought" to be lifting off the ground, the COM is being carried forward in a mostly-horizontal movement. A 2015 conference paper by Hanley et al shows a similar stick figure model. It's also supported by the relatively flat ground forces under the foot during this mid-stage.

Hip rotation does not eliminate the option for lifting, but considerably extends the upper limit vmax before the walker must be airborne. The opportunity for lifting must come after the hip is rotated but before landing of the foot (obviously). This is partly why race walkers have such an exaggerated hip movement (not to consciously avoid flight time, but to maximize speed with a straight landing knee).

There is less than a half-leg swing to become airborne; at 3.2 steps/s there are less than 0.156 seconds for something 'illegal' to happen, but that is enough time. From the first figure I calculated the body will fall a height of about 0.3*b meters from mid to end stance phases. For b = 0.5m, a fall of 13cm would take about 0.175 seconds. But that means the leg can be fully extended in front of the body with 19 milliseconds to spare. Even though the time is tiny and officially undetectable, at 4 m/s this would be enough to travel a further 7.6 cm before landing. During 'normal' walking the Froude number is < 1, hence no liftoff.

It's still hard to say what vmax is before liftoff, but estimating from the second figure, we see the radium of rotation L' is e extended by the foot to 2.4b. In that case if b = 0.5m, the vmax would be to be around 3.4 m/s. This is higher than the previous 3 m/s estimate, but still slower than the 4 m/s observed in competition. As far as I can tell, that would require a leg extension of 1.6m, or else I'm doing the math wrong. Either way speekwalking is a more complex action than it first appears, but it seems likely competition speeds are physically impossible without some amount of 'liftoff'.

Hanley and Bissas have published analysis showing that elite racewalkers had a mean flight time of 0.03 seconds, and moving 12 airborne centimeters per step. To think we can float a full 12 cm while appearing to be in contact with the ground, even to a well-trained eye. [Aside: It amazes me how poor our visual processing becomes for short time periods]. Hanley goes on to say
very brief but non-visible flight periods were recorded for all athletes... Although longer flight distances were clearly advantageous to this group of athletes, it is not advisable for race walkers to deliberately increase flight time when attempting to walk faster as this also increases the risk of disqualification. The best advice might therefore be to try to maximise flight distance with the minimum of flight time (i.e. avoid upwards rather than forward movement)
So although racewalking remains recognized as a legitimate form of racing, I do have qualms with a sport that cannot be won unless obeying the strange mix of avoiding 'visible' leaps while still leaving the ground. Most judged sports are improved by including recorded and/or electronic footage (Football, baseball, hockey, and tennis, for example). Race walking is the only sport where such accuracy would effectively disqualify all the competition. As a compromise I wonder what would happen if we removed rule #1 entirely and allowed slight time, but kept rule #2 (keeping the leg straight). What would competitions then look like?

No matter what, the physics of race walking are an interesting test of human locomotion, and argue the inevitability of the running motion instinct. There are plenty of other areas to discuss and explore, like why, for instance, do humans usually transition from walk to run when Fr = 0.5, rather than 1? And amazingly enough this 0.5 transition point is found in other animals too.

So there's precedent for walking to be better accepted for what it is, but given the strong physical evidence that contradicts Rule #1, I would recommend revisiting the exact phrasing in the rule books. Or just make the entire race up a mountainside where walking will be your only choice.