RunMotion Coach

What is the equivalent flat speed when running?

Equivalent speed

Speed ​​is a relative notion in running. Many parameters can influence the speed of your run, in particular the altitude difference and the nature of the terrain: track, road, muddy path, mountain path, etc… The weather conditions also play a role in the performance and speed of the runner. The flat equivalent speed aims to take into account the most important parameter: the altitude difference.

What is equivalent flat speed?

A speed is the ratio between a distance travelled and the elapsed time. It is commonly expressed in miles or kilometers per hour, but for runners it is usually expressed as minutes per mile or kilometer.

During a constant effort going from flat to uphill, the speed decreases, however if one goes from flat to downhill, the speed increases.

It is therefore possible to correct this real speed with the altitude difference. It is the speed equivalent to flat, like if you were running on a totally flat ground.

How to calculate this equivalent flat speed?

The formula is:

Flat equivalent speed = Virtual distance / time

Flat equivalent speed = (Distance + k1 * positive elevation gain – k2 * negative elevation gain) / time

With k1 and k2 correcting coefficients. If you go uphill, it’s like if the flat distance was greater than the actual distance, and if you go downhill, it’s the opposite, it’s like if the flat distance was less than the actual distance.

k1 and k2 depend on the slope and are not equal, since we do not make up for the lost time uphill.

How does RunMotion Coach calculate this parameter?

From the activities we receive from Strava, or from your GPS watch, we have access to the altitude difference and the distance. So for each lap or kilometer (or mile) we can calculate this flat equivalent speed with the formula above. Our research gave us coefficients k1 and k2 which best describe the influence of the slope.

The only limit to our calculations lies in the technicality of the course. The applied coefficients were validated in road races, that is to say on a hard ground and without any sharp turns.

On technical roads, or if the ground is muddy, the efficiency isn’t as good. It would therefore be necessary to add another corrective term to the virtual distance. It is possible that the equivalent flat speed is underestimated during your trail running. The heart rate is therefore sometimes a more accurate indicator of the effort made on this terrain.

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