What Goes Up

[John Cole]

"Wings develop a good 10% more lift in winter than they do in summer".

 

Well I guess it must be colder in Liverpool than I thought.  Nearest location the BBC publishes average conditions for is Aberystwyth:

January average day max 7 degrees C (280 Kelvin)

August average day max 18 degrees C (291 Kelvin)

 

Suggests nearer 4% to me.

[David Burton 2]

Hi John,

 

Thanks for your comment.

 

For the figures you quote I totally agree, but I must admit to taking somthing closer to the max and min, rather than the means! 

 

For a cold winter's day here I took 0 degrees C. Not that untypical at the moment - in fact a week ago I was flying at the patch and it was -4!

 

For a warm summer's day I took 30 degrees C. OK, a little optimistic maybe - but I have known it to reach that here! Not very often - but it does happen and we can all dream!

 

At 0 degrees air density is 1.292Kg/m3

While at 30 degrees air density is 1.1644Kg/m3

 

A difference of 9.88%

 

In the original draft of the article I did in fact cite the temperatures - but in the inevitable editing for length that detail was one of the casulaities! Anway thanks for your point.

 

David

[John Cole]

I used to live near Chester Zoo, and I remember cheering when summer temperatures got beyond 20!  JSC

 

Oh, and don't forget humidity.  Water vapour's lighter than dry air.

[John Bunting]

David:

Having asked about the lift of symmetrical airfoils, after Part 1, I've been looking forward to your comments on it in Part 3.

The nub of the matter seems to lie in your words, "this wing wil 'flip' from significant down-force to significant lift as we pass through the zero singularity that it never manages to actually occupy!".

This leads one to wonder just what the lift curve actually looks like, for these very small angles of attack. It seems to suggest that the slope of the curve may be larger there than it is for larger angles; or else that there may be a small hysteresis loop around zero, so the wing goes very slightly beyond the theoretical zero lift angle, before the up or down force 'flips' from one state to the other. I wonder if any wind-tunnel tests, or even mathematical modelling, show any such behaviour.

Talking of maths in general, I read the 'Aeromodeller' from 1945 onwards, and the amount of maths then was frightening, compared to today. Most of it, unfortunately, based on full-size data, at much higher Reynolds numbers than for model flight. I remember covering sheets of paper with figures, to work out the angle of incidence for maximum L/D or power factor. But the one that really sticks in my mind was a series of articles, stuffed with equations, entitled "Counteracting the effects of engine failure in twin-engined model aircraft". Happy days!

[David Burton 2]

Hi John,

 

Good question. About three years ago I developed an interest in what happens to symmetrical aerofoils at very small angles of attack. I had notice that very few published lift curves actually indicated that the zero alpha position had actually been measured. There were measurements at, say plus minus 1 degree, but at the zero point the line was simply drawn through the origin - as you might expect without an actual experimental point. But I wanted to know what happened at very small angles - less than half a degree.

 

I would need a very accurate symmetrical wing section to do this. So I designed a symmetrical aerofoil using "Solid Works" (a professional 3D design software suite suite) This meant that, at least in the computer, the section was perfectly symmetrical because I simply designed one half and mirrored it.

 

To make the section - I had it machined from a single block of Araldite using a Bridgeport 5 axes CNC Machining Centre. (An advantage of working in a University - we have lots of specialist kit around!) Using this means that the section is going to be about as accurate as I could possibly get it.

 

To check it was accurate I measured it using a optical 3D measurement system we had developed - it showed that the section was accurate to the computer model, at all points, to better than 50microns (i.e. 1/20 of a millimetre). It also showed that such errors as there where were random - there was no structured error leading to unintentional camber.

 

So I now had a "perfect" symmetrical section aerofoil. The next problem was that the force balance and the section rotational stages fitted to our wind tunnel would not be accurate enough for what I wanted to do. So I used a micrometer screw rotational head to control the position of the section and a new fibre optic strain sensor based on a Bragg grating system that had been developed by the research of a close colleague to measure the force. The important thing about this force sensor was that it had a very high sensitivity and responses almost flat to signals from static all the way to 2MHz - very fast.

 

With this I set about obtaining a lift curve. The micrometer screw limited the angles I could use to only approximately plus minus one and half degress - very small but that didn't matter - as I was only interested in small angles.

 

Continued in the next post.......

[David Burton 2]

The first lift curve we got is shown below:

 

Nothing too surprising there. The points even fit a straight line very well, and the line pretty well goes through zero. So far everthing is as expected.

 

Then I tried at smaller and smaller angles. The result of this is probably best summarised by the lift curve below:

 

Between 0.4 degrees and 0.1 the section is behaving more or less as we would expect. But once we got below, somewhere around 0.07-0.05 degrees the Cl value started to become constant - at approximately 0.06-0.07. This was the case on both sides of the zero point. The two data points at angle zero are in reality the mean of a series of readings around that point - plotting them all confuses the graph.

 

So, in this range close to zero the Cl value plateaus - remaining almost constant at a value we might call Clcrit. If you start at say minus 0.05 degrees and steady increase the angle to plus 0.05 what happens is that the Cl value remains around minus 0.06-0.07 and then suddenly switches to plus 0.06-0.07. It prooved impossible - despite many attempts to get any stable reading between these two points. And no amount of careful adjustment would produce a "zero-lift" condition.

 

So I think this is the answer to your question - at small angles, less than about minus 0.05 degrees, the lift curve runs almost horizontal at minus Clcrit, nominally at zero it switches to plus Clcrit and it runs at this value until about plus 0.05 degrees.

 

The cost of producing the wing section meant I was not able to repeat this experiment for other symmetrical sections - but I have no reason to believe this result is untypical in any way.

 

I hope this is helpful.

 

David

 

[John Bunting]

Thanks, David: all most interesting. I hardly imagined that my guesswork would turn out to be so closely investigated in your experiments! Can you also tell us the chord and thickness of the test airfoil, and the tunnel flow speed(s)?

It occurs to me that if the facilities are still available, one further case might be examined: a flat plate airfoil, which should be cheap to make.

[John Cole]

Looking at the graph, I think you are referring to a hysteresis effect between -0.05 and 0.05 degrees, with Cl being at either -0.006 or 0.006, not 0.06 as you say in your text. Do I read your graph correctly? The effect appears to be present at e.g. 0.1 degrees, where you show Cl of about 0.008, where a straight line would give nearer 0.005.

 

I don't think you say what aerofoil section you used, but the results of your first graph show a low slope of less than 0.05 / degree. I would expect end-corrected data to be significantly higher that this for common symmetric sections. Is your data end-corrected? If not, that might explain the low value.

 

Fortunately, these numbers are quite small (order of 1% of Cl at cruise). Although symmetrical wings are not often flown at such low (subsonic) alpha as you are examining, stabilisers may be - though I have to note that the range in which you've observed the effect is small compared with e.g. wing-induced downwash at the horizontal stabiliser, If the effect were larger, or observable at greater angles, then control would be hard to maintain!

[John Cole]

Yes, wind tunnel data for low and zero alpha is hard to find. But this is from Moran's "An Introduction to Theoretical and Computational Aerodynamics"

ISBN: 0486428796

 

The graph is a bit of a mess as it shows Cm as well as Cl, and lines for both the basic NACA0012 but also this section with a deflected split flap! So ignore the two Cm lines, effectively horizontal at Cm = 0.0 and -0.23, and the upper Cl line which shoots off the page.

 

The Cl line for "straight NACA0012" has points plotted at both +1 and -1 degrees (triangle marker for Re of 6*10**6), and also at zero degrees (hard to say what's plotted there though!).

 

The effect that you have observed is quite small compared to the scale of this diagram: smaller than the thickness of the lines as drawn, I think. To show the scale, I estimate the height of e.g. the individual triangle point-markers to be equivalent to Cl of 0.045, about 7.5 times the size of the effect you have observed.

[David Burton 2]

Hi,

 

sorry I haven't been back for little while, but to respond to some of these points:

 

John B: I'll have to go off memory as I am away from the office at the moment, but if I recall correctly the aerofoil section was about 17% thickness ratio and its chord would have have been of the order of 35-40cm. Air speed, again from memory, about 30m/s or thereabouts. So Re approx 7x10**5.

 

One day I will get round to the flat plate experiment - I need to convince an MSc student it would make a good project! And then dig out the fibre optic lift balance kit again!

 

John C: no the data is not end corrected.

 

It could be a hysteresis effect (let's face it, it could be a lot of things!) but I doubt it. The reason for that is the instability the flow exhibits at this point. Anywhere in that range the flow can continually "flip" between plus and minus about 0.06. So it isn't just that we "only get these values and no zero" its the ocsillation between them at a fixed (albeit very small) alpha which is so distinctive. and unusual.

 

David

 

 

[John Cole]

You did not comment on my spotting what semed to be a typo (from examining your graph): saying Cl = 0.06 when it looks like 0.006 to me. And you have repeated that in your latest posting (saying 0.06), making me wonder if the graph is incorrect? The values of +/- 0.06 are the greatest-magnitude values on your upper chart, at alpha = +/- 1.5 degrees. Please note: if the effect is the smaller value, that doesn't make it less important or interesting!

 

I suggest that your first description does suggest a hysteresis loop, and that if the alpha were e.g. exactly zero and Cl was continually flipping between +0.006 and -0.006 then your balance would record it as zero unless it had extremely quick response!

[David Burton 2]

Sorry John, you're quite right 0.006 not 0.06! Tired eyes!

 

The balance actually did have a very fast response because of the fibre optic strain gauge. The data logging was at 2MHz sampling rate - which is slower that the frequency response of the fibre optic system. So we could get very good temporal resolution. I did have some graphics of this, Cl vs time - not sure I can find them - I'll take a look.

 

The basic effect was that the aerofoil would not oscillate a constant speed between the two values - oscillate is not really the right word. I know it is the one I used - but in tetrospect it does not describe accurately what we observed. The lift force would sit at one value of Cl, stable for a short period, and then flip to the other, again for a short period before flipping back again. The period for which it was stable would be anything from approx 0.1sec to 1-2sec. Without any decernable pattern. And this behaviour was the same for all alpha values between about -0.07 and +0.07 degress.

 

David

[John Cole]

Then what you describe is not hysteresis or Cl would be stable at -0.006 with increasing alpha up to the flip angle (of say alpha = +0.07 degrees) when it would flip to +0.006 and remain at that value with alpha decreasing until it reached -0.07 degrees when it would flip back. I believe hysteresis is associated with +ve feedback, which would not seem to be the case here.

 

Maybe the reason others have not spotted this (apart from not looking for it!) is the timescale: maybe they weren't looking for such short-period signals. And I have only found that one graph (above) with points plotted AT alpha = zero. And the relatively-small size of the effect may mean it was too small to register on their equipment.

 

There's another "funny" in your second graph: you might expect the slope of Cl vs. alpha to be constant as alpha moves towards zero, and then reduce as it approaches the zone between +/- 0.07 degrees. But there seems to be something else happening at around -0.3 and +0.3 degrees. Both these points seem to be well off the straight line drawn through zero / zero. To help make the point, here's your graph, superimposed on itself and inverted (rotated through 180 degrees), to show the effect is the same + and -. Comments?

 

Edited By John Cole on 31/01/2011 16:05:45

[John Bunting]

If you ever do the flat plate tests, David, I wonder if you'll get similar results to F W Schmitz. I think he got a funny boomerang-shaped lift curve, with a sudden decrease of slope at about α=5°, Cl=0.5.

[John Cole]

I had difficulty finding flat-plate data. Here's what I found. It's from NACA report 319 by Briggs & Dryden of the Bureau of Standards. The report is dated 1928; they were looking at a range of sections for use in airscrews, and therefore looked at high speed airflow from Mach 0.5 to 1.08. The data is not end-corrected.

 

I have re-plotted their data for the flat plate for Mach 0.5 (c. NTP, I guess), from the tables on page 31. The flat plate has a thickness of 4% and a chord of 1 inch, Re about 5x10**5 I think. They also looked at wedges and curved plates as well as typical (Clark / RAF) sections of that day.

 

It all supports my view: you don't need fancy airfoil sections to fly: just a powerful engine. Fancy sections are all about reduced drag, not increased lift. I wonder if that's what's in Part 4!

 

 

 

[David Burton 2]

Hi John,

 

re your observations - I agree, that's why I didn't think it was hysteresis.

 

The "S" shape curve into the instability region was quite repeatable - happening in most cases if not all. I don't find the second part of this "S" so surprising - when the angle is below |0.2| as the lift nears the instability. If it didn't do this there would be a risk of the curve having an actual first order discontinuity - which would be very unlikely indeed. But the second part of the "S" - the "hump" around 0.3 degrees is something we considered at the time but, to be honest, can't really explain - even with a hypothesis. If it only happened on one side of the plot I would be tempted to dismiss it an effect of a manufacturing error on one side of the section. But its there both sides of zero alpha - and I've no measurement evidence from the section of a systematic error that occurs on both sides. Indeed, as I stated above, measurement of the section's form indicated a complete absence of systematic form error - only random errors.

 

Well, one thing about research I have found out: do an experiment and you get some answers - but you also invariably get more questions! Its a sort of technical job creation scheme for researchers! I think I'll just have to put the "hump" down to that for now!

[John Bunting]

Just reading Part 4, which arrived this morning, and am intrigued by the references to 'vortex shredding', in the photo captions. Now there's an idea: shred the vortices, and maybe you'll get the drag down a bit!

[David Burton 2]

LOL! Oppps! Now there's one that escaped the proof reading! Well spotted John.

 

It should of course read "shedding"! Although now you mention it shredding them might be an effective strategy.

 

I will be sending some videos into David for this in the next day or two, so watch out for them.

 

David

[Robin Kearney]

David, many thanks for these informative articles, I'm thoroughly enjoying reading them.

I recently pranged my Multiplex Merlin in what I now know to be a text book tip stall, the flight path was almost exactly as in the powered glider tip stall video you posted to the forum.

 

I've read quite a few people complain the Merlin has some design flaw which leads to a 'death spiral' (as some are calling it) but having now suffered one such incident and reading these articles I'm convinced the error is with the pilot and not the aircraft.

 

I'll be more mindful when I use the elevator at low speed in future!

 

Thanks for a great series.

[David Burton 2]

Hi Robin,

 

really glad you are enjoying the articles and finding them useful.

 

I certainly wouldn't feel too bad about realising that stalling might be at the root of the issue with the Merlin - we've all been there! Every R/C pilot has stalled his/her share of models - but it wouldn't it be nice if we could all recoginise the causes, see the danger signals before they develop too much and hence start to avoid a few of these prangs!

 

Here's hoping eh!

 

David

[Tom Wright 2]

David Hello.

 

I have been following your excelent articles with great interest. The resultant comments and discussions are absorbing and stimulating.

The absence of in house professional jargon and mathematical restraint is refreshing.

 

My current interest is the projected and actual characteristics of flat plate wings at low reynolds numbers - and at very low speeds.

I have an intuitive theory that suggests that the rate of increase in CL at low angles of attack ,remains low ,as speed is increased,this effect seems noticeable up to about 7 degrees and of course assumes a uniform rate of acceleration.

My observations are made by flying a 10ft span model with an aspect ratio of 5 and an AUW of 12 LBS the resultant effect seems to be a very docile pitch sensitivity within the

AOA range stated and a high degree of pitch stability.

Several other flat plate characteristics have also been noticed when small changes to L/E and T/E profiles have been made ,but i will leave questions on those until a later date.

My question ... Is there any substance in my intuitive theory or is it a misconception ?

 

Tom.

 

 

Edited By tom wright 2 on 12/05/2011 02:46:28

Edited By tom wright 2 on 12/05/2011 02:49:19

[Simon Chaddock]

 

DB2

There has been quite a bit of discussion about the term 'tip stall'.

I believe not a recognised aerodynamic term other than a wing may stall at its tip but your videos show clearly what can happen when it does.

My point is that getting into this situation is the beginnings of a spin and should be recognised as such with the result it will require significant height to recover.

 

My own view is that it is not "I crashed because of tip stall" but "I crashed because I put it into a spin".

[Tom Wright 2]

I have just spotted the post by John Cole which includes a graph for a flat plate but there is no mention of the L/E or T/E profiles my original question is based on a parallel top and bottom surface chord 24in thickness 1 in but with no profiling - just flat faces at the t/e and l/e . I suspect this arrangement acts rather like a turbulator and may account for the benign change in lift within the - 7 TO + 7 AOA range.

Sorry if this basic question lowers to thread tone a bit but this subject is of interest to compare with my practical experiments.

 

Hi Simon.

I assume you were the Blue Bird pilot ? I have the same model and found it was prone to incipient  spin antics that soon develop if prompt action is not taken .

Did some mods to mine and it is now better behaved.

 

Tom.

Edited By tom wright 2 on 12/05/2011 19:30:55

[John Cole]

If you look at the original report NACA 319 and then go to Figure 44 (p 342 of the combined papers) you will see that the flat plate has a rectangular cross-section. JSC

Edited By John Cole on 12/05/2011 19:35:06

[Tom Wright 2]

Thanks JSC.

TW2.