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Old 02-02-2005 | 04:07 PM
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Default Reynolds Number

A Brief Explanation of Reynolds Number.

Judging from many comments in this forum, there seems to be a bit of confusion regarding Reynolds number. This isn’t surprising because flow in the boundary layer is quite complex.

Although basic aerodynamics assumes a perfect fluid that is incompressible and without viscosity, in the actual world, air is both compressible and viscous. Fortunately, aircraft of moderate size and flying at moderate speeds behave almost as they would in a perfect fluid. At high speeds, the compressibility of air must be accounted for and at low speeds, viscosity becomes a factor to be considered. Of course, Mach number is used as a measure of the need to consider compressibility, and Reynolds number relates to the influence of viscosity.

Reynolds number is a dimensionless number that is inversely proportional to the coefficient of kinematic viscosity and proportional to the velocity and some arbitrary dimension. The dimension is usually the chord of the wing but in case of a sphere or cylinder, may be the diameter.

The effect of Reynolds number on flow is far from linear. In fact there are some definite breaks in the curve. At very low R the flow close to the body (boundary layer) is smooth and layered (laminar flow). It very closely resembles perfect fluid flow. As R is increased, the flow separates at the widest point but remains laminar, creating a large wake, and the drag increases noticeably. As R increases further, the flow changes from laminar to turbulent and doesn’t separate until further aft of the widest part, reducing the size of the wake. When this occurs, drag drops significantly. This point is called the critical Reynolds number. For a sphere, this is around R=385,000. Unlike compressibility effect, which begins sharply with formation of a shock wave, the critical R is a rather wide band, and can vary considerably depending on the energy in the stream.

The use of Reynolds number is twofold. One is to compare bodies of different sizes (scale effect). A large body moving at a slower speed will have similar flow characteristics to a smaller body moving at a faster speed provided that the Reynolds number in both cases is the same. (This assumes that the higher speed is not so great as to encounter compressibility effect.) The second is to predict flow characteristics based on test data collected at a different R. Here is where a problem arises. Boundary layer flow is so complex that it defies rational analysis without sufficient test data. And extrapolation very far out of the range of the data collected, can be almost a WAG.

As an example, engineers at Boeing, and Lockheed, when designing the B747, and the C5A respectively, estimated drag by extrapolating from data from smaller aircraft, as well as wind tunnel data. During flight testing, it was discovered that the drag estimates were too high and both aircraft exceeded their design range figures by a significant amount. In those cases, the final results were better than estimated. As more such large aircraft have been built, test data at these large Reynolds numbers has accumulated making drag estimates on large aircraft a bit more accurate. At the other end of the spectrum, with very low Reynolds numbers, the estimates are likely to be overly optimistic.

If the R being considered is near a transition such as that involving laminar separation, or near the critical Reynolds number, any extrapolation is libel to yield questionable results. If well away from a transition R, extrapolation can give good results.

Anything that adds energy to the stream will affect the critical R and usually keep the boundary layer attached reducing drag. Thus a turbulator wire can be of benefit when operating near the critical R, but note that for R well outside of the critical range, there is little or no effect.

In designing the typical R/C model, dependable test data in the range of Reynolds numbers encountered is pretty sparse. Without such data, design becomes sort of hit or miss. Fortunately if you don’t stray much beyond typical design parameters the results are likely to be satisfactory. If you are designing for specific competition, the secret is to test, test, and test. It also helps to keep good notes.

[One test is worth a thousand expert opinions.]
Old 02-02-2005 | 06:02 PM
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Default RE: Reynolds Number

Nice explanation, Lou.
Old 02-02-2005 | 07:36 PM
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Default RE: Reynolds Number

Bravo, Lou!! Good stuff! [sm=thumbup.gif][sm=thumbup.gif]

Cheers!

Jim
Old 02-03-2005 | 10:10 AM
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Default RE: Reynolds Number

Lou- your write up is about a dead ringer from what I studied (on my own).
When I tried to boil it down to what I build/fly- my models all fell into the "very low R" catagory.
so I simply tried different airfoils for aerobatic models and found that they did not mean much -if anything --except for rigidity.
The thinner /lighter stiffer the wings got the better the models worked.
On another note ---
I don't see much mention in this forum regarding airframe construction and power plant developement.
My own gut feeling is that improvements in engines and airframe materials influence development in aircraft - far more than any changes /improvements in the aerodynamics leg of this 3 legged stool.
What do you think?
Old 02-03-2005 | 10:54 AM
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Default RE: Reynolds Number

Dick, I’ll address both parts of your comments. First, your models are indeed in the lower extreme range of Reynolds number where up to now there is little actual data. That may be changing with the new military interest in very small remote controlled spy craft. There’s nothing like such interest to generate the money to do a lot of basic testing and research. Until such time as that data is made available, you are pretty much on your own in that range. As I suggested, if you could record results of your many experiments including measurements rather than relying on memory and gross impressions, that would be a great help in understanding what is happening in these rather unexplored flight regimes. On the other hand I know you are in this for fun and such notes would be too much like work.

I agree with the emphasis on engines and airframe construction. Aerodynamics is perhaps more significant for full scale machines since available power and weight reduction are somewhat limited. With our model-sized craft, power is almost unlimited. Modern model aircraft engines are a marvel of power to weight engineering and it’s almost a given that vertical flight is usually possible.

Weight reduction while retaining structural integrity is always a challenge. This is clearly one area where most models could achieve noticeable gains.

Your analogy of a three-legged stool is appropriate. And in such a stool, each leg is necessary if the stool is to stand.
Old 02-03-2005 | 01:35 PM
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Default RE: Reynolds Number

An excellent write up. Once we distill all this down I'd like to copy it to the Aerodynamics FAQ in the top section.
Old 02-05-2005 | 11:12 AM
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LouW,
I've been building a 1/6 scale turbine U-2A for the past 3 years. I've had some concerns about the aerodynamics of the high aspect ratio wing. With a wingspan of 160", root cord of 23" and tip cord of 6", I worry about tip stall. With advice from another modeler/engineer I've come up with this: A turbulator strip(3 layers of trim striping tape,1/8" wide) about 5% aft of the leading edge on top on the outer 1/4 panel. The ailerons are 30" long so I'll probably cover this area. Your comments, recommendations? Jack

Here's the wing sections:
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Old 02-06-2005 | 12:50 AM
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Default RE: Reynolds Number

Bruce, feel free to post this wherever you like.
Old 02-06-2005 | 12:40 PM
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Default RE: Reynolds Number

Vortex, the ribs shown in your first pic with the increase % thickness, added camber, forward high point and washout as shown will most likely be all you need to avoid the tip stall problem. Whoever made the decisions on shape and angles looks like they did their homework and has incorporated every trick I've ever seen for delaying the stall at the wingtips. Save the turbulators for later if you need a slight boost but I suspect you'll be fine with it as is.

If you have not thought about it yet I would suggest a large degree of differential aileron action in the throws and coupling in the rudder to the ailerons to further assist with reducing any adverse yaw. Also you can take a page from aileron glider fliers and ensure you keep the glide speed up a little during the approach pattern. Only once you are commited to the flare should you approach the stall speed just prior to touch down. The adverse yaw has the most effect on tip stalling when the airflow is close to the stalling point and only a little more is needed to force it to break away. I see that you are using flaps on this magnificient model so slowing down during the final approach won't be a problem.

Also train yourself to use smaller aileron deflections when flying slowly and closer to the stall point. Just breath on the stick and give the model time to slowly roll into and out of the turns. No "Bank and Yank" at those speeds or even close. That's another glider pilot trick to avoiding tip stalls.

In fact with 3 years invested you may want to look into building a small scale hack ship that is prop powered just for fun. A simple box fuselage with block tops to give you a "stand back and squint" semi scale look to the model and a similar planform wing and airfoils. 60 to 72 inch span and powered by a 25 to 40 depending on the span and it'll teach you all you need to know about how the wing and the airfoils will perform on the big one. For my part I'd recomend the 72 inch span with the 25 and load it up to a "scale" wingloading to compare to your model. Each wing area size range of model has it's preffered wing loading from light and floaty to heavy and tank like. Figure out where you big U2 fits within that wing area range and reflect that into the 6 footer so it tests the wing properley. Such a lightly powered model would ensure you are investigating the WING'S performance and train YOU at the same time in all the aspects of flying your big one rather than just scooting around with far more airspeed than you need.

While you're at it try it out with some motor assisted thermal soaring. Learning to hold the model at it's happy speed while cruising and in turns that range from shallow to tipped up is a requirement for glider fliers that want to be succesful and it would be a good skill to pick up for you and your U2 I suspect. The emphasis here being on smooth entries using small and smooth control inputs and coordinating the elevator input to hold the model's airspeed even.

If you've read much on the flying of the full sized U2 at altitude, as I'm sure you must have, you'll realize that this is how the pilot's fly the real ones during the missions. That bit about the ceiling being limited by the stall speed rising and the mach speed falling to the point where they are dealing with a 5 to 10 mph envelope floored me. The description about how to deal with turbulence in the turns (is the inside wing stalling or the outside wing hitting compressability?) was fascinating and reflects the smooth and gentle inputs I'm suggesting here. You can still tip it up for sharp turns but the idea is to slowly roll and recover from the high bank angles while controlling the elevator to avoid any stalls or dives. Done well it'll look like one of those graceful aerobatic sailplane airshow routines.

And of COURSE you'll be fitting cameras into BOTH versions....
Old 02-06-2005 | 08:52 PM
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Default RE: Reynolds Number

Bruce,
First of all, thank you for taking the time to reply to my concerns on the large scale U-2.

With the approach of the systems testing and radio programming for this complex airplane, I appreciate your input. Large differential aileron and rudder to aileron coupling will be incorporated. The idea of the smaller version powered glider was thought about some time ago. The closer I get to the first flight the more likely I am to to practice with something not so critical. I need to be sure I'm not in the bank and yank mode since I fly the short-wing turbines. I had an 80" ducted fan U-2 but it flew much too fast. It's demise was met while in a turn, unable to roll out.

For additional roll control and to counter aerodynamic dampening, the flaps will be mixed with the ailerons to a max or 5^ up. I prefer to mix only the outboard flap but this gets too complicated with the radio. There should be plenty of drag as the large speed brakes extend >45^.

I was told that the Reynolds Numbers that this model operates at, is much like the real one was at altitude. Not Sure.

Yes, I have done extensive reading on the U-2 and retain a copy of the Air Force -1 (flight manual) of the early one. There were many flying lessons written in the manuals in those days. Perhaps because of the many losses.

I have the onboard camera standing by as well as an anxious 1/6 scale test pilot!! First flight in '05

Jack
Old 02-07-2005 | 12:37 AM
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Default RE: Reynolds Number

The tiny speed envelope at max altitude -is not peculiar to the U2-
Check with any guys who drive commercial jet stuff.
the window can get pretty tight.
(I know this is not a model thing -just commenting )
as far as fretting over the airfoil - -just make it as equal as possible from wing panel to wing panel.
On this type planform (aircraft as viewed from above)--the real evil doer will be the DIFFERENCE in airspeed between wing tips.
One of my first experiences in RC modeling -35 years ago - was a model laid out in a very similar setup -- close coupled - small stab.
It was extremely easy to yaw the model at low / landing speeds -OR in a slight crosswind - trying to visually level the model-- get a difference in tip speeds .
the result was always a drop of the slower panel- and correction was always impossible .
The lateral area on the U2 makes yaw control touchy -- we do this on some models to make them good in wild aerobatics - but in this setup - I would sure make sure I had the landings and takeoffs well up to speed so that the plane is ON the ground anytime speed is below positive control on all surfaces

great looking project.
Old 02-10-2005 | 04:45 PM
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Default RE: Reynolds Number

Dick - the thing is you are riding a horse that has already been broken. It is easy to design airplanes that fly well when for the last 100 years folks have been designing airplanes and refining the configurations and airfoils. They have also put their results in print for all to see and benefit from. With our power availability it is possible to get away with a host of aero sins and in some cases developing wrong conclusions for why things happened leading to more wrong conclusions (not that you have done anything like that ;-)

However if you start out from scratch - two teams - one with aero resources, one without - and both design airplanes to do a specific job that is going to be made or broken depending on how well the airplane is designed --- I would put my money on the guys with aero resources.

To add to what Lou mentioned - With respect to Rn differences from wind tunnel to flight test there is a correction that can be made for Rn but we also found a correction that is dependent on the wind tunnel. Something that isn't necessarily determinable but a correction determined from previous experiences with similar airplane types in different tunnels and in flight tests. We had a Mcair Polysonic, a Cornell and a AEDC 16 foot transonic correction. It usually shows up in a drag increment to get more precision in estimates of range, etc.

It was interesting that in looking at the CL break point at high angle of attack the Hi Rn windtunnels gave a more flight test like break.

I recently saw a graph in one of the many modelling magazines that I take (so have totally forgotten which one it was) that plotted the log of the Rn verses a factor of the wing chord. It covered Rn from the size of a fruit fly wing and flight speed to the super monster people haulers. It was interesting that for the most part a straight line could be drawn through the whole data set.

When looking at small segments of the curve you could see smaller slopes in areas and in come cases exceptional airplanes would fall off the curve.

However it did indicate that everything that swims or flies in the air that we love is doing so in a fashion that is appropriate to the maximum efficiency at that Rn. Flat wings for flies, curved wings for birds, and the airfoils that we love and know for our airplanes and above. Keep in mind that a flat airfoil that we use for our little foamys is not in any way efficient, just practical for something that doesn't need a range greater than 100 ft and is nicely separated at 45-50 degrees.

Being a very practical engineer for almost 40 years I depended on a heck of a lot of test reports, experience and airplane specific testing to get answers. By now I have a lot of accumulated data and experience that makes me reasonably effective in the field, however, when it came time to develope a supercritical airfoil for a particular configuration it was nice to go to the computational tools to save cutting several dozens of wings for the wind tunnel.
Old 02-10-2005 | 06:38 PM
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Default RE: Reynolds Number

OK- did I step on your toes here ?
I re read what I wrote - I don't see any glaring errors - just comments on a short coupled model which if you look at it- can be a handful.

It would seem you refer to my efforts as clumsy , non scientific puttering -
Maybe I mis read you
.
Old 02-10-2005 | 08:18 PM
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Default RE: Reynolds Number

No, no toes stepped on (although it is good for you to reread what you write:-). You said way early up in the thread -

------ I don't see much mention in this forum regarding airframe construction and power plant developement. My own gut feeling is that improvements in engines and airframe materials influence development in aircraft - far more than any changes /improvements in the aerodynamics leg of this 3 legged stool.
What do you think? --------

and I answered that I thought it isn't necessarilly so and said so. To my thinking the improvements have all pretty much gone together, otherwise we would still be flying biplanes made of carbon fiber with jets on them. (Ignore the fact that the Franklins have a jet powered biplane that they use in airshows, a great show if you have never seen it, fire and smoke and noise everywhere). It takes a big engine to push bad aerodynamics but good aerodynamics can use a small engine. I think the 3 legged stool needs all three legs, aero, propulsion and structures but you must admit that you tend to think the aero leg can be pretty short.

Of course the reason you don't see much regarding airframe construction and power plant developement here is that the forum is labeled Aerodynamics or some such label (sorry, couldn't resist).

Are you the Hanson that did the Edge 540 review in 3-DFlyer? If so it was a good read and I am a little jealous, that must have been fun.

Did you see the error in Jason Noll's talk about propellers? He talks about the 2 bladed prop having a disk area, the smaller 3 bladed prop having a smaller disk area and therefore the smaller disc size means there will be less drag on the down lines.

He forgets that there are 3 blades making drag compared to the 2 blades. The concept of disk area is valid only when thinking about props of the same number of blades. It is just a simplification of the more complex way looking at the change of the local angle of attack on the prop blade due to the forward velocity and rotational velocity and resultant lift and drag vectors. But not understanding the aero of the problem gives misunderstanding of the physics.
Old 02-10-2005 | 09:43 PM
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Default RE: Reynolds Number

I misread you and you, in the earlier read - mis read me .
You have assumed I have no respect for aero engineering .
Not so
vehemently not so.
My only argument is a mis conception that formal engineering knowledge is the end path to any development of new ideas.
On the three legged stool thing - --my whimsical thought was "what if -for some unknown reason --engine power and airframe materials were "magically" far improved?
Would the airplane have developed as it did ?
I don't think so - but there is no way to prove such a thought .
I stand tho, by by premise that most -if not almost all advances in aircraft have been a direct result of better , lighter powerplants .
Next the advances in airframe structures and lastly (by no means unimportantly -- the aerodynamic TESTING and development used to utilize these two advances .
Let's turn it around
If we try for an advance in aeronautic improvement with no improvement in power or airframe technology-- the changes would me comparitavely small.
N/Y?
From th Wrigh Bros Flyer - the real advances came from bette powerplants -- then th airframes were improved to utilize this .
So what if say Glen Curtiss - a motorcycle racer had come up with a 200 hp power plant on his first try.
Would the June Bug ever have materialized?
The Japanese Zero Sen was brilliantly engineed simply to take advantage of th only engine available a small powerful aircooled design.
(Aircooled engines are NOT easy to streamline )
The The ME262 - jet engines -(what if the Jumos were as powerful as those on a Lear?)
This is why I am so keen on power to weight/wingloading testing.
My own doodling simply reinforces my earlier thoughts .
In models (this is a model forum) weight and power are the driving forces in new development.
The art of streamlining/ airfoil selection,adherance to windtunnel airfoil data tc., is secondary- important -but the ability to develop designs using these factors (power and weigh reduction) provides aircraft (toys to be sure ) that do things their full scale counterparts can not even approach.
But what IF that power were available ?????
Old 02-10-2005 | 09:58 PM
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Default RE: Reynolds Number

Yes I did/ do a number of reviews for 3D Flyer - th EDGE is a good flyer
And I read Jason's review --
3 bladed props get some really interesting commentary.I was a bit puzzled by some of his comments.
Our own finding- is that they are not as efficient in these small sizes as two bladed designs (at least all of those I have used ).
But if you have the power to make em pull the model - they are quieter and the reason, may be one never mentioned
Here goes ---------
The blades deliver pulses of air NOT in sync with the exhaust pulses .
We have noted this sound difference in flight on our big gassers and this is an idea I came up with .
The prop blades produce a whup whup sound in sync with two stroke putt putt. and if the three baldes put the putt and whups out of sync - may not the result be some sound cancelling?
Wanna think on that?

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