Induced drag rectangular wing

[truffaldino]

Hello,

I am wandering if anybody has a table (or formula, if exists) for Oswald's efficiency factor of a rectangular wing (depending on AR). Will be grateful for info

Truffaldino

[HerkS]

This sort of analysis really breaks down at model Reynolds Numbers because the profile drag of the wing is so affected by low RN effects.

However you may find information that's helpful to you in this article.
http://nal-ir.nal.res.in/1675/01/jasi_v53_2002.pdf

Unfortunately they didn't include the charts that provide one of the factors necessary to complete the equation for e. I've reproduced it for you in the attached document. The factor charts are from Perkins and Hage and are on the second page of the attachment.

[truffaldino]

Thank you a lot!

I neeeded this graph to check the code I have written to calculate induced drag for my sailplane.

Truffaldino

[HerkS]

Sounds interesting -- let us know what you come up with - H

[eflightray]

I don't know if this site is of any help - Glider Aerodynamics (http://www.gliders.dk/aerodynamic.htm)

[truffaldino]

I have just written a simple program solving Prandtl lifting-line integral equation to calculate induced drag. I have checked it on elliptic planform and efficiency was 100%. Then checked on rectangular with ar=10 and efficiency was about 93%. I was surprised by such a high efficiency and thought that there was a mistake in the program, but as follows from the charts you have provided this true indeed and there is no problems with the code.

Now I do not see much reason of doing tapered or more complex planform for my sailplanes, as few percents of gain in induced drag will be compensated by profile drag increase due to reducing Re number. As for me, reducing total drag by 1-3 percent is not worth building a complicated wing. As far as I see, the main reason for doing complicated planform on slowly flying sailplanes is some structural considerations (lower center of gravity, lesser lifting force arm on each half of the wing etc).

[truffaldino]

Just an addition to my previous post. I also found out from your charts and the program that efficiency of rectangular wing decreases as ar grows, so induced drag is not really inversely proportional to AR but is more complicated function for non-elliptic planforms. In the case of big AR (about ar 20 and higher) you can feel a significant difference in efficiency and my statement from previous post are wrong, but for AR around 10, there seems no much difference between elliptic and rectangular planforms.

[HerkS]

truffaldino -- thanks for sharing your conclusions.

This is very interesting. Low RN does spoil some of the advantage of high AR on models.

Also a rectangular planform does usually have good flying and handling qualities.

Perhaps when you build your model, you will start a thread to tell us how it works for you.

[truffaldino]

Thanks Herk,

I am attaching a graph of efficiency factor for AR from 5 to 160 calculated with the simple program I have written, extending your charts (calculations with lifting-line theory do not make sence for AR less than about 5). Maybe anyboudy will need this chart.

As for building a model: It is already built: I just wanted to change a planform, but after doing the above calculations I decided not to replace the wings. actually I do not have ideally rectangular planform, but it is rectangular with an aerodynamic twist (washout) toward the tips. This washout increases efficiency by about 3% also increasing stability.

My goal in building this model was to avoid sophisticated building techniques, using the most primitive tools and matherials. Also I modified the sd7037 profile to have caspidal trailing edge, so that aerodynamic twist can be achieved by simple cutting part of trailing edge toward the tips as well as .5 to 1mm errors could be tolerated without reducing performance. This type of profile and planform allows to build wings by simply cutting, folding, sanding and gluing depron sheets.

The glider has 2.4 meter wingspan, wingloading is 22g/dm^2. By my estimates the minimum sik rate of the model is about 0.4m/sec (72ft/min).

[truffaldino]

Today I found an interesting program on the web. It is called XFLR5 and it is uses 2d panel approximation method instead of lifting line approximation. It turns out that the efficiency of rectangular wing calculated in this approximation is about 3% higher than that of the lifting-line, i.e. about 96-97% for AR=10. From this point of wiew it looks quite meaningless to use complex planforms on slowly flying models.

[nmasters]

I remember a few threads about induced drag and the planform compromises due to low Re. Here are two I participated in (mostly as an agitator and gopher):
http://www.rcgroups.com/forums/showthread.php?p=10688453&highlight=planform+induced+drag+reynolds+drela#pos t10688453
http://www.rcgroups.com/forums/showthread.php?t=747983
One of the links I dredged up for that first thread goes to a description by Mark Drela of how he designs a wing.

--Norm