Mean Chord vs MAC

[CloudyIFR]

What's the difference between the Mean Chord i.e. (area / span) versus the Mean Aerodynamic Chord which is (area*mean chord / area)

Thanks
Curtis
Montana

[HugePanic]

there are specifications that explain all this in detail.

as i remember correct:

it should be the same at a rectangular (hershybar) wing.

it is different at swept wing, delta wings and so on...

for example: the mean chord of a delta is much larger than the chord lenght at the wingtip. the MAC is somewhere between.

for each wing its possible to create a virtual rectangular "replacement wing", that has the same characteristics than the original one (at normal speeds/AOA).

this replacement wing defines the MAC.

pleas correct me if i am wrong

[CloudyIFR]

Would it be correct to say:

Mean Chord is the average Geometric Chord of the wing and:
Mean Aerodynamic Chord is the average Aerodynamic Chord?

Thanks
Curtis
Montana

PS Bitte Ein Bit!

[MarkusN]

Seems to be the same thing. Look at your formula: area*mean chord/area. If you solve this equation you get MAC = mean chord.

If I remember right the term MAC is used when you talk about the spanwise position of said chord. This is important when calculating things like CG on a swept wing.

[eflightray]

Here's a handy page of info - Airfield Models MAC (http://www.airfieldmodels.com/information_source/math_and_science_of_model_aircraft/formulas/mean_aerodynamic_chord.htm) , as he says, average chord is not mean aerodynamic chord.

Even shows an elliptical wing calculation.

[HugePanic]

i just checkt my university-scripts, seems that i was right.


rectangular wing: chordlength = MAC

deltawing: MAC = 2/3 inner cord length

trapezoid wing: MAC = 2/3 * innerchord * ((1+lambda+lambda²)/((1+lambda))
(lambda = outerchord / innerchord)

elliptical wing: MAC = 8/3 * pi * innerchord

MAC is used to have a dimensionless value for a position (like ca, cl...)
for example: COG = 29% of MAC (this works for all wings, if MAC is calculated correctly)

Thats what WIKIPEDIA (http://en.wikipedia.org/wiki/Chord_(aircraft)) says:

Physically, MAC is the chord of a rectangular wing, which has the same area, full aerodynamic force and position of the center of pressure at a given angle of attack as the given wing has. Simply stated, MAC is the width of an equivalent rectangular wing in given conditions.


i hope this helped

:)


P.S.: nich lang schnacken, kop in nacken.... (aber des zeug in hamburg kann ja keiner trinken)

[CloudyIFR]

But what would I use a definition? Is what I wrote before accurate, Geometric vs Aerodynamic?

Thanks
Curtis

[HugePanic]

Yes

[CloudyIFR]

Thanks so much!

Spangdahlem Airbase 1996 -2001 F4G Wild Weasel Maintainer!

Bitte Ein Bit!

[JetPlaneFlyer]

COG = 29% of MAC (this works for all wings, if MAC is calculated correctly)


Perhaps I'm taking the statement out of context but it would be incorrect to assume that CoG should be at 29% MAC for all aircraft. CoG position depends on the aircraft layout and static margin.
Tailless aircraft will have a CoG well ahead of 29% MAC and aircraft with large horizontal stabs and/or long tail moments will have Cog well behind 29% MAC... sometimes behind 100% MAC ;)

Steve

[CloudyIFR]

For a flying wing a balance location of 29% MAC would result in a static margin of minus 4%, I'm thinking that would be a very dicey flight!!!

Curtis
Montana

[MarkusN]

deleted for nonsense

[ciurpita]

even a rectangular wing has an elliptical-ish lift distribution. the tips aren't as productive . so an elliptical wing would produce more lift than a rectangular wing of the same area and span.

therefore, the area of a rectangular wing with the same span and lift as an elliptical wing, will be greater than the elliptical wing, and its chord would be greater than the mean (geometric average) chord length of the elliptical wing.

see quote in comment #6. the chord of a rectangular wing having the same lift and span of an arbitrary wing planform depends on the actual lift distribution of that wing. there are, however, reasonable approximations.

[mnowell129]

The Mean Aerodynamic Chord is a "virtual" wing chord of a given wing that can be used to calculate the pitching moments and stability for the wing. The Mean Aerodynamic Chord has a chord length and a fore and aft position.
The Mean Aerodynamic Chord is hard to calculate because factors such as twist, section changes, wing protuberances, varying reynolds numbers across the span, etc. etc, factor into the calculation. For example a swept wing where the outer 1/3 is washed out with a low lift curve slope will shift the Mean Aerodynamic Chord forward, since the inner (more forward) part of the wing will be more heavily weighted in the calculation of MAC.

The Mean Geometric Chord is an estimate of the Mean Aerodynamic Chord using only the wing planform (i.e. it's geometry) and ignoring the other factors.
For most situations including models the MGC is a good enough approximation for the MAC that it can be used for normal CG calculations and tail sizing. The posted calculations are correct for computing the MGC as an approximation for the MAC, but should not be construed as actually computing the "real" MAC. Virtually the entire modeling community misuses MAC when in fact they are referring to the MGC.

The Mean Chord is just the average chord and differs from the Mean Geometric Chord in that it doesn't indicate position fore and aft, merely the average chord length, MGC is a chord whose length is equal to the mean chord but also fixed as to it's fore and aft position.

mick

[feihu]

mick:
Well said.
Here is a page from "Perkins & Hage, Airplane Performance Stability and Control".
feihu

[Texas Buzzard]

What's the difference between the Mean Chord i.e. (area / span) versus the Mean Aerodynamic Chord which is (area*mean chord / area)

Thanks
Curtis
Montana
.................................................. ................
For us modelers it doesn't make any difference what you call it. The mean chord IS the same as the Mean Aerodynamic Chord for our purposes in determing where the C of G is supposed to be.

Just find the 28% from LE at the root then find the 28% from the front of the tip. Connect these with a straightline.
Go out half way to the tip and draw a line parallel to the root. Where the two lines cross will be where the C of G needs to be for testing.

Then carry the line thru' that CG placement to the root....it will be behind the 28% mark on swept wings or tapered wings ( LE tapered)...thats it folks.

[CloudyIFR]

Oh, thanks for all the help folks.

If you're interested in why I ask stay tuned to Radio Controlled Soaring Digest and you may go here for an MS Excel Spreadsheet.

See the "Files" Page.
http://h1.ripway.com/cloudyifr/index.html

Curtis
Montana

[JetPlaneFlyer]

.................................................. ................
For us modelers it doesn't make any difference what you call it. The mean chord IS the same as the Mean Aerodynamic Chord for our purposes in determing where the C of G is supposed to be.

Just find the 28% from LE at the root then find the 28% from the front of the tip. Connect these with a straightline.
Go out half way to the tip and draw a line parallel to the root. Where the two lines cross will be where the C of G needs to be for testing.

Then carry the line thru' that CG placement to the root....it will be behind the 28% mark on swept wings or tapered wings ( LE tapered)...thats it folks.

That would be miles out for many aircraft Buzzard...

For starters the 28% figure is not true for all layouts.. Tailless aircraft must have their CG ahead of 25% to be stable, so if you used this method on a tailless model it would be unstable and crash :( ... Also aircraft with large tails can have a CG way behind 28%... somethimes behind 100% MAC!

Also the idea of using a point half way along the span is flawed because this would only be correct for a parallel chord wing... A wing that has any taper will have it's MAC located elswhere, difference can be quite large for a wing with significant taper ratio.

[mnowell129]

mick:
Well said.
Here is a page from "Perkins & Hage, Airplane Performance Stability and Control".
feihu
Thanks. And thanks for the reference.

[mnowell129]

.................................................. ................
For us modelers it doesn't make any difference what you call it. The mean chord IS the same as the Mean Aerodynamic Chord for our purposes in determing where the C of G is supposed to be.

Just find the 28% from LE at the root then find the 28% from the front of the tip. Connect these with a straightline.
Go out half way to the tip and draw a line parallel to the root. Where the two lines cross will be where the C of G needs to be for testing.

Then carry the line thru' that CG placement to the root....it will be behind the 28% mark on swept wings or tapered wings ( LE tapered)...thats it folks.
This only works for constant chord wings with simple sweep, it doesn't work for all planforms. For example if you use this method in the two cases below you will get very nose heavy setup and in the other a very tail heavy setup.
I think it's good to simplify things but your method only works for rectangular wings that are straight or swept, with a conventional tail of a certain size and placement (essentially for models with the same tail volume (Vt)). If you state that up front then your method is correct, it's just not universally correct for all models.

[Flight Engineer]

Good luck with this one!!!!!! :o

after this i gave up (http://www.rcgroups.com/forums/showthread.php?t=664201)

[ciurpita]

there are several tools available for calculating lift distributions of arbitrary planforms
http://www.amadistrictii.org/cjrcc/wing2/wing.html

once the lift-distribution is obtained, excel could be used to calculate the aerodynamic center of lift. it's not out of the question even for us modelers.

[macboffin]

there are specifications that explain all this in detail.

as i remember correct:

it should be the same at a rectangular (hershybar) wing.

it is different at swept wing, delta wings and so on...

for example: the mean chord of a delta is much larger than the chord lenght at the wingtip. the MAC is somewhere between.

for each wing its possible to create a virtual rectangular "replacement wing", that has the same characteristics than the original one (at normal speeds/AOA).

this replacement wing defines the MAC.

pleas correct me if i am wrong It is not necessary to make a equivalent oblong wing.Just do it direct! Add root chord to tip chord, halve it, that is the MAC.

[CloudyIFR]

http://www.rcsoaringdigest.com/

You may be interested in a article I wrote in the April 2008 issue of Radio Controlled Soaring Digest.

Curtis
Montana

[HugePanic]

It is not necessary to make a equivalent oblong wing.Just do it direct! Add root chord to tip chord, halve it, that is the MAC.

the MAC is NOT the mean chord length!! so this is not correct

[woolebugr]

Since some of you guys seem to know what you are talking about here, I have a question. I built a mini Mugi Evo and calculated the cg using this (http://www.palosrc.com/instructors/cg.htm) calculator. I read in another post that for flying wings the cg should be between 17% and 22%mac so I calculated for both and marked the wing for balance somewhere in between those marks. Anyway, she seemed very nose-heavy. Here (http://www.rcgroups.com/forums/showthread.php?t=846877#post9528135) is the post about it. It may have just been too heavy to fly, but do you think I was using the correct mac for a delta or should it have been higher? I used this calculator for another scratch-built fff wing and the cg seemed dead-on when she maidened.

[Brandano]

what most people seens to forget when calculating MAC is that all of the plan view of the plane should be considered as a sort of wing surface. A large fuselage can create a lot of lift, like in the case of the F15 that landed without a wing. The static margin "somewhere in front of 25%" is a rule of thumb, and erring in the direction of a nose heavy plane is safer than ending up with an uncontrollable tail heavy plane. Every calculator will give you something to start with, but not necessarily what you will end up using. Incidentally, if the flying wing was the one in your avatar then you should look to generic CG for a delta wing instead. Incidentally, the MAC should consider the tail surface contribution to lift as well, otherwise how would you handle tandem wings? If you work on this assumption you will see that the calculated CG for flying wings and conventional planes are much closer than if you use the wing are alone, and that the same rules can be applied to canard planes as well.

[nmasters]

Deltas are weird. Obviously if it doesn't have a tail it's a flying wing but a delta is also a very low aspect ratio wing and other considerations apply because of the low AR and high taper. There is a very long bit of calculus to find the CG for different stability factors of a flying wing. This chart (http://www.rcgroups.com/forums/showthread.php?p=6190131#post6190131) shows a graphical method to find the safe CG range of high AR 'wings based on a table of results of that formula. The graphical method breaks down at really small AR so here's an adapted version (http://www.rcgroups.com/forums/showthread.php?t=666614) for deltas


--Norm

[woolebugr]

Thanks, most of that is way over my head but I think I can sort some of it out.

[Derfy]

...Anyway, she seemed very nose-heavy...

It's all to do with the aerodynamic centre not being at the traditionally accepted 25% MAC point when you are dealing with swept, low taper ratio wings.
From what I can remember, the AC can be at as much as 30-35% MAC, depending on the degree of sweep and taper and of course, the aspect ratio.
If you use the traditional type CG calculator with the AC set at 25% MAC and base your CG on this, you are going to end up with the CG too far forward.


If you are looking for a good CG calculator that can cope with swept, multi-panel wings, try this one (thanks to Julez):

http://home.arcor.de/d_meissner/W_Laengs4_V23.zip

It's interesting to note that this calculator gives both an aerodynamic and a geometric centre. I wonder why?

I've tried this with the original Mugi and it's spot on. :)

By the way, Norm's right, deltas are weird. :D

:cool:

[woolebugr]

Thanks Derfy, I used that calculator and this is what I came up with in the photo below. It shows the geometric center to be at 135mm. Would this be my cg?

[HugePanic]

keep in mind that the MAC doesn't know which type of horizontal stabilizer you have. MAC is only calculated by the wings shape. you have to select a COG at the MAC that fits you design. this is about 25-30% at a conventional tail-design.

your tests show that is completely different for pure-deltas. ;)
you just need good COG positions (relative to MAC) from a similar design....

[Derfy]

...It shows the geometric center to be at 135mm. Would
this be my cg?...

No, you want to click the Aircraft tab, and then making sure you have 1 Wing and Automatic choice of stability selected, click the Calculate button. This should give you CG locations for two different stability factors (4% & 8%) and the aerodynamic centre location. If you want to enter your own stability factor, select the Manual choice of stability radio button.

The results I get for your figures are:

x_cg(8%): 136.0mm
x_cg(4%): 142.8mm
x_ac: 149.7mm

Now I'm not sure what the ideal stability factor for a delta wing is (maybe someone a bit more knowledgeable can help here) but the original Mugi used around 6% which gives:

x_cg(6%): 139.4mm

Hope this helps and please let us know if it works. :)

:cool:

[woolebugr]

Thanks Derfy, that's exactly what I needed. I checked on that delta and the cg I had calculated was about an inch further forward than what you came up with. On a model with only a 9.5" root, that's a lot! No wonder she nosed in like she did. Anyway, I have already removed the servos on this delta to use on another model but when my lighter motor and lipo arrives I will give her another try. Thanks again, Murray

[nmasters]

I recommend 132. 7mm doesn't sound like much but on my graph 139 falls behind a critical point that usually indicates whether or not tip stall is likely to occur. Of course if you don't have enough washout CG position is kind of moot
--Norm

[woolebugr]

I decided to tape the elevons in one place and I added ballast to balance her out at about 134mm. I then took it out in the back yard and did a couple of glide tests. Success!! :D
She floated across the yard without any tip stall or nose-in. I may just put the electronics back in and give her another try. Thanks for all your help guys, Murray

[Derfy]

Great news!

Of course, assuming you accurately scaled the original plan, you could have scaled the CG position as well.
Doing this, funnily enough, gives 132.7mm for the CG position.
That Norm's a clever guy. :D

:cool:

[jinal007]

Mean chord is the average geometric chord i.e 1/2 (chord root + chort tip). It hardly has any physical meaning.

Mean aerodynamic chord is the width of a rectangular wing that will produce the same aerodynamic loading.