Estimating travelling speed using only your eyes

Here is a fun trick (I think) invented by Martin Rolfs and Casimir Ludwig.

You are in a train and would like to know the speed of the train – but no phone, GPS or speedometer – here is how you do it.

Voyager GIF - Voyager GIFs
Person pondering how fast she is going –

Here is how to do it:

  1. Stretch out both arms, thumbs up.
  2. Make eye-movements from one thumb to the other, focus on the eye movements going in direction of the train
  3. Slowly increase/decrease the distance of the thumbs, effectively changing (in a controlled manner) how large your eye movements are.
  4. Notice the rail sleepers of the nearby track – at some point of (3) your eye-velocity will perfectly match the angular speed of the train, and you will be able to see the rails crisp as day – during an eye movement (take that saccadic suppression! – but seriously, check out that Wikipedia article, it explains step 3 in more words)
  5. Now measure (somehow) how many thumbs-width’ your two thumbs hands are apart and take this times two (1 thumb-width are approximately 2° visual angle). For our example, let’s say we measured 7°.
  6. Gauge the distance to the neighboring track, let’s say 2m.

7. The final ingredient is the log-log relationship between eye-movement size & eye-movement speed: the Main Sequence of Eye movements. A 7° saccade is ~130° / s fast.

Collewijn et al., 1988

8. Let’s solve for the train’s speed: $ v=\frac{130°/s}{2*\pi} *2m=20\frac{m}{s} = 72\frac{km}{h} $

Now remember or print out the main sequence from Collewijn & you will never not know how fast the train is going 🙂

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