This page is devoted to Reynolds Number 

                          and the affects of scaling 

                                        in the real world.  

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Reynolds Number is a very basic principle.  It is a fundamental scale value that lets you know if you are talking about grasshopper wings or Cessna wings.  If you are thinking that "wings are wings" and scale means nothing, then you are thinking wrong.  Before we get into the math of scaling, you have to know this basic truth:   You can not expect a full size Cessna 172 wing to fly correctly if you scale it down to a 1/5 scale model of a C-172.  The act of changing the wings size will change the way it affects the air it flies thru.  Even if you could magically scale up a housefly to the size of a pony,  it would not be able to fly.  Its wings would not generate enough lift (even though they are scaled correctly in proportion).   

Ok,  so now you know that scaling big things down changes the way they fly.  They may still fly, but not the same as the big versions.  Scaling little things up is really a bad idea.    As the Wright Brothers discovered   thru experimentation and brilliant engineering observations,  birds and planes do not fly the same.  What is a great shape for a bird wing is not necessarily a good shape for an airplane wing.  Both scale and speed make a very big difference in what shape flies best.    

You just know that there is math in this discussion.  The exact formula is :

                             RN = ( C * V )  /   0.0001564      

where :   V = velocity in feet/second        and      C = chord length of the wing in feet

Yea,  great formula, but a bit exacting for this discussion.  There is a really simple version of the RN formula.  It is only an estimate, but it is close enough for most everything :  

                        RN    =        C   *  V   *  10,000

where :   V = velocity in  miles/hour            and      C = chord length of the wing in feet

Examples of the math would look like this :  

A full size (4 passenger) Cessna 172 wing has a chord length of about 5 feet wide and is optimized to fly along at about 100 miles per hour.  The exact RN value would be : RN = ( (100*44/30)  *  (5.0) ) / 0.0001564  =  4,688,832.1     and the approximation would be RN = 5 * 100 * 10,000  =  5,000,000.  

A 1/5 scale model (remote control) Cessna 172 wing would be about 12 inches wide ( 1.0 ft chord) and would be optimized to fly along at about 30 miles per hour.  The exact RN value would be : RN = ( (30*44/30)  *  (1.0) ) / 0.0001564  =  281,329.9    and the approximation would be RN = 1 * 30 * 10,000  =  300,000.  

Now you know how to get the Reynolds Number and that it is important.  But what does it all mean? ? ?  Well, take a look at the graphic below.  It is a general range of operation for each type of flying machine. 

But this is website about tandem wing aircraft and more specifically about DragonFly aircraft.  So where does the Dragonfly's canard and aft wings fall on this graphic???

As you can see, the original GU25 canard is a low Reynolds Number foil.  At best, this seems like a curious choice.  This foil is is optimized for use in the 100K to 500K range.  Lets do the math.  RN =  Chord * speed * 10,000.  So all we need is the average chord of the dragonfly's canard and a projected stall speed (we really only care about the low speed characteristics for now).   From the plans, we see the average chord is about 2.5 feet and the projected stall is about 50 mph.  So........  RN = 2.5 * 50 * 10,000  =  1,250,000.  Hummmmmm.  That is way above the top of the range of the GU25.  Well,  all airfoils fly better the faster you push them............ don't they???   Lets shelve that question for a moment and take another look at the range of C * V that this foil was created for.  Reversing the equation and solving for speed, we see that V = RN / 10,000*C.  So for a chord of 2.5 ft and a RN of 500,000 (the top of the RN range) the projected speed for best performance of this foil is V = 500,000 / 10,000 * 2.5   or V = 20 mph.  Wow ! !  This airfoil is designed to top out at 20 mph.  That seems a bit slow for a plane that claims to fly 150 mph.  In fact, it seem more like a glider's speed.   Kinda like what you would expect for a large chord, slow moving, human powered flying machine. 

Now before you go thinking the GU25 was foolish choice (remember I said it was curious choice) you have to understand the whole story.   First of all remember that this choice was made back in the dark ages....... like 1974 or 75.  Also,  the Dragonfly did not exist yet.  The forerunner of the Dragonfly and Q-2 aircraft was a tiny little thing called the  Quickie.  So the story starts here.  With this little 18 hp toy airplane that has an 18" average chord canard.  When the great father in the desert was looking for airfoils there was not a lot of data on high lift, low speed canard foils.  Why "Low Speed" you ask ???   Remember that the most dangerous time in a canard's flight envelope is the stall range.  For the size of the canards that was envisioned (about 1.5 ft chord) and the stall speeds wanted (about 45 mph) you are now looking for an airfoil that is optimized in the RN = 675,000 range.  If you choose from any of the General Aviation airfoils out there ( and there are literally hundreds) you will see that there is no performance data less than RN = 3,000,000.   In airfoil performance analysis, you cant make generalizations.  If your data curve stops at RN3E6 (that is 3,000,000 written in shorthand) you cant just say the airfoil will act the same at RN2E6 because it is really close.  For the same chord, the difference in RN of 3E6 and 2E6 may only be 10 mph.  but the airfoil may simply stop flying completely 1 mph less than the tested RN you see on the curves.  So the real task is to find "hard and reliable data" for your flight envelope.  The only airfoil at the time that had such data in the 650K range was the Glasgow GU25(11)5-8 "human powered flight research foil".  Any data is better than no data.   The GU25 had research data that proved it flew well down to RN1E5 (that was way below where it was needed to fly) and we all know that airfoils always fly better the faster you go, so, this was the perfect choice of foils for the little Q-1's canard.  Not a bad line of reasoning if you follow it from the beginning.   

Unfortunately, this is a nasty foil if you allow it to get dirty or wet.   Neither of these things would happen in a human powered flyer test, but canards getting dirty happened all the time in the real world to the planes that had GU25 canards.  The canard got dirty, or wet, or buggy and it forgot how to make lift.  

Now there is a fix but the real answer was to find a replacement airfoil.  The replacement airfoil was the R1145MS "Roncz Rain Canard".  It was developed by an aero wizard that was part of the great father's team, and was based upon the LS(1)-0417 mod  NASA airfoil.  The initial shape (developed by NASA for general aviation) was tweaked to reduce the nasty stall behavior and some of the rotational moment and the final product was a great canard airfoil.  

Authors note:  The Bottom line is ..... Scale is everything in designing for the optimum performance of a flying surface.  Birds and Boeings do not fly the same.  

revised 04/11/2002