Photo : Alexis Martín

In trail running or orienteering people say that if you have to run 100 m of elevation up and down it would take the same time as running flat for 1000 m. We can find a similar old rule of thumb and more recently, some researchers (Davey, Hayes & Norman, 1994 ; Scarf, 2007) added a little science to this vernacular knowledge but with few data points (2 athletes and 300 race results, respectively).

Could we add some modern massive data to check this saying ? Using our dataset scraped from ITRA on 16 949 race results from 2 802 runners, we can fit a basic non linear model to estimate the parameters :

> (model <- results %>% 
>   nls(heures ~ (dist_tot + deniv_tot / k) / v, data = .,
>      start = list(k = 100, v = 8)))

Nonlinear regression model
  model: heures ~ (dist_tot + deniv_tot/k)/v
   data: .
     k      v 
87.239  9.565 
 residual sum-of-squares: 313542

Number of iterations to convergence: 3 
Achieved convergence tolerance: 1.292e-06

> confint(model)

Waiting for profiling to be done...
       2.5%     97.5%
k 81.672165 93.296957
v  9.332102  9.809812

So we see that the average flat speed sustainable over a long period of our sample (which is biased towards elite runners) is around 9,6 km⋅h^-1 and that 1 km flat is equivalent to 87 m [82 – 93] of height gain, not far from the old 100 m. Of course these values will vary according the athlete shape, the total race length and profile and many other parameters…

References