For an outdoorsy, not-so-tall girl, it’s not uncommon to wind up at the back of a pack of significantly taller, male hiking companions. Sweaty and panting, I watch their backpacks recede further away up the trail, and even the sweep guy might abandon his role to bolt around me. In an endurance situation, mental fatigue sends the foggy brain into rhythmic, ineffectual loops. Unable to do mental arithmetic while moving, one can only see that the negative space triangle formed by others’ legs is larger for taller people, and imagine that this reflects some advantage… but how much advantage?

Later, off the trail, pen and paper in hand, one can focus on calculating the magnitude of how much this height advantage adds up to, in terms of explaining how a physically fit person might lag so far behind:

Height of the taller person | inches | |

Walking cadence | steps per minute | |

Stride angle (angle between legs at full extension point) | degrees | |

Height of the shorter person | inches |

Meanwhile, the shorter person has an assumed leg length of inches. Despite using the same stride angle and walking cadence as her companion (i.e., putting in the same amount of effort), each of her steps is smaller and she therefore covers ground more slowly...

*merely due to being shorter*!

In order to keep up, the shorter person must work harder, by either:

(a) making her small steps more rapidly, at a faster cadence of steps per minute; or

(b) matching her companion's same walking cadence, but making each step longer by widening her stride angle to degrees. (As efficiency-conscious runners well know, increasing step length beyond what is optimal for one's height has a dramatic effect on tiredness.)

Alternatively, if the shorter person exerts only the same effort as her taller companion, she will fall behind miles after one hour of hiking. In such case, the taller person will get to stop and rest minutes every hour, while waiting for the shorter person to catch up.

[Note: We’ve made the simplifying assumption of leg length as a fixed proportion (45%) of overall height – a reasonable constant, given that average ratios of leg length to height, and step length to leg length (a function of stride angle, which correlates positively with speed) enable trackers to infer height from footprints.]

Other factors driving differential physical effort between two companions are undoubtedly afoot during a hike: aerobic fitness, anaerobic endurance, strength-to-weight ratio, movement/form efficiency, backpack contents, stomach contents, sufficiency of recent sleep, injuries, performance of clothing/gear, and who’s chatting more than listening. Still, the point here is that leg length alone has a substantial impact on rate of travel. Regardless of which physical issues contribute to the exertion asymmetry, the optimal solution for both hikers (assuming they value fairness and social interaction) is to “put Herbie in front” — i.e., have the disadvantaged hiker set the pace.

Eli Goldratt’s 1984 classic The Goal vividly illustrates this principle of operational efficiency with….a hiking example! Herbie (the fat kid in the book; in our case, the short hiker) is the bottleneck. When the fast kids hike at their own pace with Herbie in the back of the single-file line of boy scouts, Herbie falls behind. They impatiently wait for him at trail intersections, but only to immediately take off hiking again as soon as he catches up and before he catches his breath. Herbie gets more and more tired, and thus even more physically disadvantaged, since fatigue initiates a negative feedback loop in terms of physical performance. Meanwhile, the fast kids get periodic rest, and so the effort differential increases from both directions. Putting Herbie in the front of the line — combined with distributing his backpack load among the fast kids — ensures that the hikers stay together and evenly spaced, and that the physical effort difference is somewhat lessened. (The effort saved by fast kids hiking slower than their capabilities is less than the effort saved by Herbie avoiding being in chronic, desperate catch-up mode.)