Coriolis I. The Coriolis Effect according to Coriolis. 6/2/2016 1st Coriolis lecture Anders Persson, Uppsala

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1 Coiolis I The Coiolis Effect accoing to Coiolis 1

2 The scientific-mathematical basis fo these lectues 2

3 When eaing a lot of liteatue ealing with ynamic meteoology I saw an asie comment that the Coiolis effect ha been eive by its iscovee in a quite iffeent way compae to all ou moen textbooks Gaspa Gustave Coiolis Futhe, I coul ea, Coiolis was inteeste, neithe in the atmosphee no in the oceans but in machines 3

4 1835 4

5 Coiolis was inteeste in how the centifugal effect acte on moving pats in otating machines The common centifugal foce The total centifugal foce The Coiolis foce The common centifugal foce A stationay object in the otating system An object moving (inwas) in the otating system The Coiolis foce was the exta foce that ha to be ae to the common centifugal foce fo an elatively moving object 5

6 A A A which applie on R an yiels R R R R ) ( ) ( R R 6/2/ st Coiolis lectue

7 ) ( ) ( R R ) ( 2 ) ( 2 simplifies into an then The Coiolis acceleation!! The Coiolis foce (pe unit mass) The centipetal acceleation The centifugal acceleation 6/2/ st Coiolis lectue

8 Fom the Coiolis foce to the Coiolis acceleation The Coiolis foce -2m : 1. Fictitious foce 2. To the ight of anti-cl. motion 3. Non-inetial system The Coiolis acceleation: +2 : 1. Acceleation cause by a eal foce 2. Pointing to the left of anti-cl. motion 3. Inetial, fixe, system The Coiolis acceleation is cause by the eal foce we have to apply to pevent the Coiolis Effect fom eflecting the object Also note that the Coiolis acceleation (foce) was eive in conjunction with the centipetal (centifugal) foce. That the Coiolis acceleation (foce) can not be eive sepaately was conjectue in my QJRMS 2015 aticle. 8

9 The absolute fame of efeence was use by Eule when he in 1759 eive the Coiolis acceleation The next step of pogess was at the en of the 18th centuy when Laplace eive his tial equations But neithe he no Eule eally unestoo physically what they ha mathematically eive 9

10 It was the 1803 expeiment in the Schlebusch mines in Saxony that fo the fist time confime ageement with theoy Ion pebbles wee oppe in a mine shaft in Saxony Laplace an Gauss compete about calculating the eflection 10

11 Fom Simeon e Laplace s pape

12 Fom Fieich Gauss s pape

13 Scatte of the hits in the Schlebusch mine shaft Peicte efection 13

14 Galileo tie to estimate the eflection of falling objects, but got the maths wong Isaac Newton woul have the mathematical (an Robet Hooke the technical) to make the 1804 expeiment 120 yeas ealie 14

15 One of the fist things Newton i in Pincipia was to eive an expession fo the centipetal acceleation Note: eveything in absolute fame of efeence 15

16 In my 2015 QJRMS aticle I showe how Newton, with his mathematical technique coul have eive the Coiolis acceleation Raial elative motion 16

17 The same fo tangential elative motion So why in t Newton o it? 17

18 Because in Newton s ays scientist ha no feel o knowlege about statistical estimation theoy. Hooke mae some expeiments in 1680 but was put-off by the lage spea of the falling objects just like in 1804 But in 1804 scientists ha some feel an knowlege about statistics, the value of aveages an how to calculate them 18

Also Johannes Keple (1571-1630) coul have eive

19 Also Johannes Keple ( ) coul have eive the Coiolis acceleation fom his 2 n Law An imaginay line joining a planet an the sun sweeps out an equal aea of space in equal amounts of time. 19

20 How Johannes Keple coul have eive the Coiolis acceleation by using his 2 n law Deflection of falling boies Deflection of boies shot vetically upwas But he in t ealise the law was also vali fo eathly objects 20

21 -Isn t it tue that the Coiolis foce is only a fictitious foce? -Yes, that is tue! -Isn t it also tue that the Coiolis foce cannot o any wok? -That is absolutely tue, it is always iecte pepenicula to the motion an can only change its iection, not its spee (its kinetic enegy) -So isn t the Coiolis Effect just an optical illusion??? -No because when cannot use fictitious an wok in thei colloquial, eveyay meanings 21

Being fictitious an unable to o wok oes not mean the Coiolis Effect can be seen as an illusion One example: In the 1950 s an 1960 s planne to ceate atificial gavity on thei space stations by letting

22 Being fictitious an unable to o wok oes not mean the Coiolis Effect can be seen as an illusion One example: In the 1950 s an 1960 s planne to ceate atificial gavity on thei space stations by letting them otate. This was nicely epicte in Stanley Kubick s 1969 movie A Space Oyssey : Ko4CqF8_xFhOGFvxKcYafafA0yy4qJOLEyy9E-A- 6ou7TNub_e9DNKLtfamKKTqQ_HhYpnX_z5ZZG8mZpbPLBq QgTkA 22

23 But the asto- an cosmonauts woul get sea sick! R Fo R=100 m it nees a otation 300 faste than the eath s to povie a g = 9.81 m/s 2 g = 2 R That means 300 times stonge Coiolis foces! 23

24 So the Coiolis foce might be fictitious an unable to o wok but it was still able to thwat the Ameican an Soviet plans to ceate atificial gavity on manne space stations which is still an unsolve poblem 24

25 Is it a too povocative title? 25

26 An coming to optical illusions: I foun this on the web 26

27 The most stupi of all stupi Coiolis explanations: an aiplane eflecte when taking off eastwa along a geat cicle: 52º 52º Okay, eflecte to the ight on the Nothen Hemisphee... but eflecte to the left when taking of in the othe iection! 27

28 Summay: 1. The Coiolis foce (acceleation) can be egae as an extension to the Centifugal (Centipetal) foce fo a boy moving elative to the otating system 2. The Coiolis foce is inee fictitious an unable to o wok but is theefoe not some optical illusion 3. The Coiolis Effect coul mathematically have been iscovee aleay in the 1600s by Newton an even Keple, han t thei insights been blocke by simple, but pofoun misconceptions. What simple misconceptions block ou visions toay? 28

29 ...pehaps this one? The popula, but eoneous Haley s Pinciple using consevation of absolute velocity 402 m/s 464 m/s 62 m/s 30 N 298 m/s 104 m/s 50 N 30 N Common explanation: the excessive wins ae etae by fiction 29

30 Beak 30

31 31

32 32

33 33

ω = θ θ o = θ θ = s r v = rω

ω = θ θ o = θ θ = s r v = rω Unifom Cicula Motion Unifom cicula motion is the motion of an object taveling at a constant(unifom) speed in a cicula path. Fist we must define the angula displacement and angula velocity The angula displacement