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Let's suppose that an airplane flying at a uniform airspeed follows a perfect, level, closed circular trajectory with respect to the mass of air. Now, seen from the ground, and in the presence of a constant wind, will no longer be a circumference. What would it be...?

Steve V.
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xxavier
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1 Answers1

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It will be this :

http://www.aeroexperiments.org/images/grndtrck.gif

Pilot's of slow-flying aircraft like hang gliders and paragliders see tracks like these all the time on their GPS displays, as they circle in a thermal updraft in the presence of strong wind.

Depending on the strength of the wind, the "curliques" may become so stretched out that they don't form enclosed loops at all, just "points", i.e. a "scalloped" line. This happens when the windspeed is greater than the airspeed. That means that the aircraft never makes any progress in the upwind direction at any point in the circle.

Related: http://www.aeroexperiments.org/nocss.shtml http://www.aeroexperiments.org/introcircles.shtml http://www.aeroexperiments.org/circles.shtml

quiet flyer
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  • But if the 'air curve' is a closed one, the 'ground curve' has to be closed too, since a transformation of the reference system cannot 'open' a closed curve... – xxavier Oct 15 '18 at 07:11
  • @xxavier as shown by the first image, the ground track is indeed open. there is no reason why it should be closed. your "if the 'air curve' is a closed one, the 'ground curve' has to be closed too" is not correct. – Federico Oct 15 '18 at 07:19
  • @quietflyer I don't know where your "curliques" names comes from, but the proper name is Prolate Cycloid http://mathworld.wolfram.com/ProlateCycloid.html or Trochoid http://mathworld.wolfram.com/Trochoid.html – Federico Oct 15 '18 at 07:21
  • @Federico Yes, you are right. If I have two plates in relative, parallel relative motion, and I trace a closed curve on one, its 'image' on the other will not be closed. My mistake came from imagining the first curve already existing, and not in the process of being traced... – xxavier Oct 15 '18 at 07:25
  • Thanks for the terminology note. I just decided to call the shape a "curlique" because I couldn't think of anything better. It is not really the right word and apparently I am mis-spelling it to boot. https://en.wikipedia.org/wiki/Curlicue – quiet flyer Oct 15 '18 at 07:33
  • Now here's the fun part-- what precisely is the source of the force component that causes the acceleration component that makes the magnitude of the groundspeed vary? Someone could ask that as a question, if they don't see the answer already. – quiet flyer Oct 15 '18 at 07:34
  • @quiet flyer. Not such a force exists because that acceleration is related to the image of the aircraft, that has no mass. The only mass is that of the real aircraft, that flies in the air. Its image, moving on the ground, has no mass... – xxavier Oct 15 '18 at 07:51
  • The real aircraft has a real airspeed and a real groundpeed and if the real groundspeed is changing in magnitude, a real force component, acting parallel to the groundspeed vector, is causing it. – quiet flyer Oct 15 '18 at 07:59
  • Forces are only involved in the aircraft-air relationship. The aircraft has no physical relation with the ground while in flight, and hence, no forces ground-aircraft exist at all... – xxavier Oct 15 '18 at 08:03
  • Never mind the chat, I need to call it a night. – quiet flyer Oct 15 '18 at 08:04
  • Actually the answer to acceleration question is given in one of the url's attached to the answer above. The "introcircles" one – quiet flyer Oct 15 '18 at 08:06
  • In the particular case where the airspeed is equal to the wind speed, the curve traced is a cycloid, which is the same path traced by a point on the tread of a bicycle wheel rolling along the ground without slipping. – PJNoes Oct 17 '18 at 00:05