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Reynolds number question.

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Reynolds number question.

Old 03-19-2002, 04:50 PM
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Default Reynolds number question.

I have a question. I observed that a scale Cessna and full version of this same airplane have different Reynold numbers, primarily due to different characteristic lengths. Thus, I concluded that scale cessna and model cessna will have diffrenet dynamic behaviour. Can someone explain to me exactly how this dynamic behaviour is different?

What I am trying to get at, is to compare the behaviour of the small plane to its real size counterpart especially the plane behaviour during windy conditions. I am trying to get a "seat of the pants" grip on whether the scale 182 responds to a 15 mph wind in the same fashion as the real one.

This question stems from a comment that I heard at the field. Someone said that us flying at 15 mph is like the real pilots flying the real plane at multiple of that wind speed. The person said that to find out what wind corresponds to the 15 mph wind for a model, you multiply the wind speed by the scale factor. So assuming the model Cessna is a 1/4 scale, it gives the full scale wind of 60 mph. I am almost sure this is wrong, becuase the individual did not give me any theoretical or mathematical explanation. That is why I started to look at some underlying theories.

I apologize for my naive tone of post, but I am not a mechanical or aeronautical engineer and I do not know anything about fluid dynamics. This is why I hope that someone knowledgeable will be able to explain this to me.

Thank you
Old 03-19-2002, 05:16 PM
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Default Reynolds number question.

Reynolds numbers are unitless values given to flow situations so that one can compare apples to apples. It's sort of like a representation of the number molecules flowing over a surface over a given period of time, but not exactly. You are right that a full scale wing section will behave differently than a scale model wing section of the same airplane. For small wings the air seems more "syrupy", if that makes any sense. Laminar flow is preserved over a much larger percentage of the wing than at larger reynolds numbers, which correlates to larger wings and/or higher airflow speeds. Insects take full advantage of this.

If I'm not mistaken I believe Mr. Reynolds was actually in charge of the sewer system in England over a hundred years ago and developed a system for calculating fluid flow through the pipes under London.
Old 03-19-2002, 06:21 PM
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Default Reynolds Number

A quick approximation of Reynolds Number is given by the following:

777.7 x Velocity in mph x chord in inches
Old 03-19-2002, 06:41 PM
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Default Reynolds number question.

I did not know that about Mr. Renolds. Isn't it amazing how studying the flow of turds under the streets of London can contribute in no small way to the development of beautiful aircraft such as the Concorde and SR-71.


I don't think that there is a theoretical mathematical explaination for scale wind speed for a 1/4 scale aircraft. Look at it this way; if you want to fly a 1/4 scale plane at scale speeds, then you'll have to fly that plane at 1/4 the speed of the real plane. So it follows that a 15 mph wind for a 1/4 scale plane would be equvalent to a 60 mph wind for a full scale plane. I think that the guys at the field were only talking about how the wind's speed effects the scale speed of the 1/4 scale plane and they are correct with their math. I'm not sure what more you think there is to this scale wind speed subject or maybe I have missed your point.
Old 03-19-2002, 08:13 PM
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Default Scale Speed

Scale speed has more to do with the visual perception of flight characteriatics than the theory of fluid flow and Reynolds number.

In judging scale competition flights, flying in a scale like maner garners additional points.

For example: For a 1/4 scale plane to appear like its scale counterpart in flight it would have to:
1. Be 1/4 the distance from the viewer as the full scale plane it was being compared to.
2. Cover the same visual angle as the fullscale plane (at 4 times the distance) in the same elaped time.

This means that to appear scale like in flight the 1/4 scale model must fly at 1/4 the speed of the full scale plane. If the wind is blowing at 5 MPH and the full scale plane stalls at 44 MPH, the ground speed of the full scale plane will be somewhat above 44-5=39 MPH.

In the same 5 MPH headwind the 1/4 scale model will have an airspeed a little in excess of 11 MPH and a ground speed a little in excess of 11-5=6 MPH. To have a ground speed 1/4 of full scale, the wind speed can only be 1.25 MPH for the model.

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