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Author Topic: Induced Drag  (Read 971 times)
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Sundance12
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MAAC #25680, VE4BDF (amateur radio callsign)

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« on: June 13, 2018, 08:26:02 PM »

Riddle me this,

Doubling the chord of a wing increases the drag four times.

Sundance12

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« Reply #1 on: June 14, 2018, 02:25:21 AM »

Hi,
I won't cause confusion by throwing formulae onto the page, but here goes:-
Induced drag only makes any sort of contribution to the overall drag when the lift coefficient of lift of the wing is high, which will be at high angles of attack and thus probably at slow speeds. However when such conditions occur induced drag will be inversesly proportional to Aspect ratio, so, theoretically doubling the chord (and keeping wingspan the same) will halve the Aspect ratio and double the induced drag - but, as there will be twice the area the lift coefficient will be halved to fly at the same speed, so the induced drag would be about the same.
However, normal wing drag will double because the wetted area has doubled. So a fourfold increase? no.
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« Reply #2 on: June 14, 2018, 05:19:30 AM »

Hi Sundance, thanks, just what I needed to stir my brain of a morning Wink

So assuming that you are keeping everything else constant - speed, weight, span and air density - then there will be no change in actual induced drag. By doubling the chord you are doubling area and halving aspect ratio.

If you look at the equation for Induced Drag (Di) and not Induced Drag Coefficient (CDi) you will see that there is no representation for area or aspect ratio and so changing these has no effect.



In the above we can assume that lift (L) is the same as Weight. Air Density (ρ or rho), Speed (V) and span (b) are unchanged so the resulting actual induced drag (Di) remains the same.



The Induced Drag Coefficient (CDi) will change however because area (S) is there in the formula:



Looking at the first version there - S is doubled, so for Di to remain constant, CDi must be halved.

Looking at the second version ie rearranged to show aspect ratio - it's easy to get hung up on the 'effect' of aspect ratio. But don't forget that the CL also changes too Smiley because S is involved in the formula:




In fact CL and CDi are both halved and so actual drag Di still remains the same.


To think of it practically, induced drag can be visualised as the effect of tilting the wing back as you increase angle of attack. The greater the angle of attack (and CL), the more the lift vector is tilted rearwards. This rearward component of the lift is the induced drag, a force acting against the direction of travel.

If you double the wing chord but keep everything else including speed constant, the wing will be flying at a lower angle of attack ie half the CL. The CDi is also halved. But the actual total induced drag remains the same.


The overall drag may well change a little. Profile drag may be reduced due to doubling the Reynolds number, but wetted area will have increased. The aircraft will also be in a different attitude which may affect parasite drag if the fuselage alignment has changed.

All of this is a little counterintuitive because it's easy to get hung up on the CDi formula and misunderstand the effect of aspect ratio. In reality all that matters for total Induced drag is span - the more the better! Where span and weight is fixed then aspect ratio doesn't change as much as you might think.


(All of this assumes you want to keep speed as a constant. If you want to keep CL constant then the speed would change and the total drag would also.)


Jon
Induced Drag
Induced Drag
Induced Drag
« Last Edit: June 14, 2018, 05:29:56 AM by Yak 52 » Logged
Sundance12
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« Reply #3 on: June 14, 2018, 08:14:13 AM »

Thanks for the responsees, I will have to re read both to make sure I understand the suggestions. I am considering a standard class 100 inch span sailplane that has a very large chord, like 15 inch chord. And was intrigued by the phrase in the first post and wondered how a large chord sailplane was going to be effective.

I realize that it would have to be a light model so that it could be flown at low angles of attack.

Bruce
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« Reply #4 on: June 14, 2018, 10:32:52 AM »

Well explained there Jon. That's correct as the formula for induced drag - the first Jon shows, indicates span (b) is the critical factor.
However there is another factor that you should consider Bruce, and that's the nose down pitching moment of the airfoil.

The actual nose down moment from the wing for a given speed and angle of attack, is proportional to the pitching moment of the airfoil x the standard mean chord.

The formula for the airfoil pitching moment, M=0.5xρxV^2 xCmxCbar where Cm is the airfoil pitching moment and Cbar is the standard mean chord of the wing.

What this means for your wide chord 100" glider Bruce is that the wide chord will produce a strong nose down tucking moment which you will need to balance either with a large tail trim load or by moving the Cg back -how far back will depend on the tail volume of the design and the speed - ie CL at which you desire to have the best sink. This for a thermal glider will usually be at a high CL near the stall.

If the model is to be light(low wing loading) enough to fly at a low CL then that actually could make the issue worse as the Cg will need to move a long way aft to balance the pitching moment. This is because both the wing lift and pitching moment vary with speed squared x the coefficient(CL and Cm) for a given wing and while the CL will be low the CM stays relatively the same.

The problem is worse if you use a more highly cambered wing such as a Clark Y or similar as these airfoils have a much higher Cm than the lower cambered ones.

The tail volume could obviously be increased by increasing the size of the tail or increasing the tail boom length. Both will add weight to a degree and the increased tail size will add drag as well.

This idea of large chord wings for limited span wings was tried in the late 80's( on 2m models) or so and was not very successful for the above reasons.

It was found that if trimmed for say low speed at a high CL then they were prone either to dive out of control when trying to speed up or if the tails were big enough to trim, to have very poor glide angles at speed due to the high tail plane drag.

If you do wish to go this way Bruce then at least I would suggest that you use a modern low cambered airfoil of no more than say 2% camber at the most and stick to a reasonable wing loading of around 9-10oz/ft2 at a guess, so that the required CL for any part of your flight does not drop too low. Thus your model will actually end up heavier than a more conventional 100" model of AR's of around 10-12(these are the minimum AR's I would use).

You will need a larger Tail Volume to enable a Cg of something like 40%(or possibly more) of the standard mean chord of your wing, and still retain sufficient stability - either a larger tail or longer boom or mix of both.


Sorry to be a wet blanket.

John



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Sundance12
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« Reply #5 on: June 14, 2018, 11:11:17 AM »

That ok John
Wet blankets put the fire out from time to time.
My review of wide chord designs is loosing intrigue.

Dick Sarpolis (flying models) Designed one of these wide chord gliders
https://www.rcgroups.com/forums/showthread.php?2576909-L-A-R-S-Low-Aspect-Ratio-Sailplane-Flying-Models-Dick-Sarpolus
And this is part of my investigation into the point of the original post.
I will use some of the formulas and reasoning on this design as a rechsearch paper.
Regardless of the nature of the aerodynamic features of LARS, I still like the style of the particular airplane.

Observations welcome.

Sundance12

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« Reply #6 on: June 14, 2018, 07:57:19 PM »

I especially liked the comments by GT on that thread Bruce. GT is a well known successful Discus Launch glider designer and his views on airfoil performance are worth considering - I believe he is right.

However I noticed that the increase in pitching moment was not mentioned that I could see on a quick scan through the thread.

Certainly the low drag, modern low camber foils would work better in this regard(pitching moment) but accuracy would be an issue as GT points out, to obtain any worthwhile improvement.

Even though a couple of LARS models mentioned were supposed to have performed better than their contempories - they would have trouble competing against conventional modern models in my humble opinion.

I actually flew (in the late 90's) a 1.5m glider of around 10:1 AR against 2m gliders and it was quite successful due I believe to the pressed glass on foam wing using the then new Selig DLG section - S4083. The wing wasn't the best example of a pressed foam wing but would still outperform most 2m models with built up wings.

John
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Terry Fitzpatrick
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« Reply #7 on: June 16, 2018, 11:06:09 PM »

A low aspect ratio 2metre glider was designed and built by Martin Simons the author of "Model Aircraft Aerodynamics ". The benefit he was designing for was large wing area, low wing loading for for soaring, combined with the ability to carry huge amounts of ballast for speed tasks. He says it worked. I would be inclined to believe considering the technical quality of his book. There is a picture of the model on page 94 of the 5th edition of his book. If you are interested in seeing a picture of the model I will scan the page and post it on this forum.

From memory I think the Dick Sarpolus model had a high camber wing which was probably not the best selection.  The  modern  Martin Herppele aerofoils for flying wings have a slight positive pitching moment(nose up) and still manage fairly good lift coefficients . The 230 series NACA aerofoils (e.g. 23012) from the 1920's have almost no pitching moment but there would be better ones around for model gliders these days.

regards Terry Fitzpatrick
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« Reply #8 on: June 16, 2018, 11:27:11 PM »

The performance of a model that you can see will be much better than one that you can't, unless you have software and an on board GPS to do the fun part for you. So a wide chord can be useful.

The low aspect ratio designs I've seen used airfoils that were capable of far more lift than required, so I contend they haven't had a fair test. An airfoil with nearly zero pitching moment and capable of only moderate lift ought to be sufficient. With the higher Reynolds number obtained, a slightly thicker airfoil ought to perform ok.

To get more performance, all the radio gear could be hidden inside the wing. If necessary, a very narrow carbon tube with a streamlined pod just big enough for a bit of lead could be the "fuselage" nose. Or, maybe a careful study of the tradeoffs would show that a bit of sweep could do the same job. It might be that all control linkages could fit inside the wing too. The rear fuselage could be a conventional tail boom.

I don't think this would be the ultimate performing 100 inch model, but it might win a cross country race with such a model, depending on the visual abilities of the contestants.

I only have the 2nd edition of the Simons book. I don't think it has the picture. Is there a lot of other new stuff since the second edition?

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« Reply #9 on: June 17, 2018, 02:46:07 AM »

I believe there is Lincoln and you may be able to pick up the 5th edition at a good price .

Terry if that is the Martinet 2M? then I saw it flying many years ago and it was a good performer for it's time in Australia. models around at that time were Sagitta 600's, and similar with a few Algebra 2M models (British). The Algebra was a god performer - largely due to it's sheeted wing. Most of the 2m models of this time were around
600ins2  from memory - ie an AR of 10:1.

As airfoils improved and following a move to sheeted foam core wings no one has campaigned a 2m with an AR less than 10:1, that I'm aware of.

With better performing low speed airfoils available now - there doesn't appear to be an advantage to using low AR's for fixed span gliders. For non span limited classes then span is king and generally the AR will be relatively(above 15:1) high to give good penenetration at a low empty weight - typical for current competition F3j and F5J models.

An example of a current F5J (f3J with an electric motor) is the ArtHobby Avatar of 3.4m(134") WS of AR 21:1 at an empty weight of 1.4kg.(50oz.), using a Selig SD7084 on a veneered foam wing. It's performance is bettered by the all composite modes.

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From memory I think the Dick Sarpolus model had a high camber wing which was probably not the best selection.  The  modern  Martin Herppele aerofoils for flying wings have a slight positive pitching moment(nose up) and still manage fairly good lift coefficients .

Reflex airfoils unfortunately will not match conventional airfoils in efficiency at high or low angles of attack. They always have more drag.


Quote
To get more performance, all the radio gear could be hidden inside the wing. If necessary, a very narrow carbon tube with a streamlined pod just big enough for a bit of lead could be the "fuselage" nose. Or, maybe a careful study of the tradeoffs would show that a bit of sweep could do the same job. It might be that all control linkages could fit inside the wing too. The rear fuselage could be a conventional tail boom. 

Lincoln ,I believe this has been tried on a F3B model by an Italian flyer around 1985? He had a slight amount of sweep, and no nose but with a tail boom and conventional tail. It was nicely done but was not copied. The chord was not excessive but it was a lower AR than the more conventional models of the era. It didn't establish a trend however.

Quote
From memory I think the Dick Sarpolus model had a high camber wing which was probably not the best selection.
Yes I think you are right there. High camber airfoils were in vogue then.

John



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« Reply #10 on: June 17, 2018, 11:21:12 AM »

May I add some historical notes about the Italien model John OZPAF mentions.

The builder was Eugenio Pagliano from Turin, professionally a car designer with Bertone. The model flew so well that the Austrian team AME from Innsbruck asked to have it on rent to compare it against there PFEIL, the leading F3B model at the time. And it did win the competition!

Urs
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« Reply #11 on: June 17, 2018, 08:22:50 PM »

Thanks Urs. Yes it was a very impressive model and apparently the Swiss amongst others did copy it. Eugenio also had another model - the Crescendo which while still innovative was a more conventional design.

Check this page for more info
https://www.rcgroups.com/forums/showthread.php?1315244-A-little-bit-of-F3B-history/page3.

Apologise for the shift off the topic.

John
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Terry Fitzpatrick
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« Reply #12 on: June 17, 2018, 11:46:46 PM »

OZPAF The model I was referring to was the Martinet 2M. What is the current aerofoil of choice for RC gliders?

LINCOLN There is a a lot of new material in the 5th edition even compared to the 4th edition. Get one! Ive got 4 editions. Its the best source of model design information I have come across.

regards Terry Fitzpatrick
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« Reply #13 on: June 18, 2018, 02:07:42 AM »

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What is the current aerofoil of choice for RC gliders?
 

That's no longer an easy question to answer as there are many in house foils being used however here are some of the current F3J/F5J airfoils being used:-

Avatar 3.4 F5J  SD 7080 9% thick  Selig Donovan.

Stork 8 F3J   HN 254 modified  Hubert Norbert.

Supra from Vladimir AG series AG40/AG41/AG42/AG43 Drela

Note all these airfoils are 2% camber or less and most around 8% thick. This trend has developed along with the lower weight and wing loading of these aircraft.

The other noticeable trend that has developed with the full design approach now used is for a series of transitional airfoils as shown by the Drela AG series used on the Supra.

The old thermal favourites SD 7037 and MH 32 are rarely seen these days.

There are many other top Airfoil designers/developers around at the moment - many like Dirk Phlug of Germany (DP foils) who are modellers and Aero engineers.

For a straight F3J model of either sheeted foam or moulded I would recommend Drela's foils. For a built up wing F3J - probably SD7037 would be reasonable for a sports glider.

Competitively nothing thicker than 8% and no more than 2% camber for a flying weight around 1.5kg max n a 3.4m wing or more.

John
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