{"id":458,"date":"2022-02-04T12:03:27","date_gmt":"2022-02-04T10:03:27","guid":{"rendered":"https:\/\/benediktehinger.de\/blog\/science\/?p=458"},"modified":"2022-02-04T12:10:11","modified_gmt":"2022-02-04T10:10:11","slug":"estimating-speed-using-only-your-eyes","status":"publish","type":"post","link":"https:\/\/benediktehinger.de\/blog\/science\/estimating-speed-using-only-your-eyes\/","title":{"rendered":"Estimating travelling speed using only your eyes"},"content":{"rendered":"\n

Here is a fun trick (I think) invented by Martin Rolfs and Casimir Ludwig<\/a>. <\/p>\n\n\n\n

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.<\/p>\n\n\n\n

\"Voyager
Person pondering how fast she is going – https:\/\/tenor.com\/JuRb.gif<\/figcaption><\/figure><\/div>\n\n\n\n

Here is how to do it:<\/p>\n\n\n\n

  1. Stretch out both arms, thumbs up.<\/li>
  2. Make eye-movements from one thumb to the other, focus on the eye movements going in direction of the train<\/li>
  3. Slowly increase\/decrease the distance of the thumbs, effectively changing (in a controlled manner) how large your eye movements are.<\/li>
  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<\/a>! – but seriously, check out that Wikipedia article, it explains step 3 in more words)<\/li>
  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\u00b0 visual angle). For our example, let’s say we measured 7\u00b0.<\/li>
  6. Gauge the distance to the neighboring track, let’s say 2m.<\/li><\/ol>\n\n\n\n
    \"\"<\/a><\/figure><\/div>\n\n\n\n

    7. The final ingredient is the log-log relationship between eye-movement size & eye-movement speed: the Main Sequence of Eye movements. A 7\u00b0 saccade is ~130\u00b0 \/ s fast.<\/p>\n\n\n\n

    \"Image\"\/
    Collewijn et al., 1988<\/figcaption><\/figure><\/div>\n\n\n\n

    8. Let’s solve for the train’s speed: $ v=\\frac{130\u00b0\/s}{2*\\pi} *2m=20\\frac{m}{s} = 72\\frac{km}{h} $<\/p>\n\n\n\n

    Now remember or print out the main sequence from Collewijn & you will never not know how fast the train is going \ud83d\ude42<\/p>\n","protected":false},"excerpt":{"rendered":"

    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. Here is how to do it: Stretch out both arms, thumbs up. Make eye-movements from one thumb to the other, focus on the eye movements going in direction of the train Slowly increase\/decrease the distance of the thumbs, effectively changing (in a controlled manner) how large your eye movements are. Notice the rail sleepers of the nearby…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-458","post","type-post","status-publish","format-standard","hentry","category-blog"],"_links":{"self":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/posts\/458","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/comments?post=458"}],"version-history":[{"count":0,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/posts\/458\/revisions"}],"wp:attachment":[{"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/media?parent=458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/categories?post=458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/benediktehinger.de\/blog\/science\/wp-json\/wp\/v2\/tags?post=458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}