Are My Calculations Right???
 

I'm trying to find the CG on a Straight Tapered Wing. Root Cord 12" - Tip Cord 6.750"

MAC 9.625"
25% Of MAC = 2.375
30% Of MAC = 2.875

RE: Are My Calculations Right???
 

You mean you're trying to find the Mean Aerodynamic Chord of that wing. Finding the CG for a model involves not only the wing but also the fuselage tail arm length and the stabilizer area. There are links to some online calculators in the sticky resource threads at the top of the forum listings. Check them out. They tell you where to place the CG in terms of distance back from the leading edge of the wing at the root.

RE: Are My Calculations Right???
 

Puff, I didn't do the calcs, but you are on the right track. http://www.geistware.com/rcmodeling/cg_calc.htm#cg

Now if you want the balance caculator, it is at http://www.geistware.com/rcmodeling/cg_super_calc.htm

The CGwill be the same in both for the same wing..

Don.</p>

RE: Are My Calculations Right???
 

Ok thanks. One more question?? Since my wing is double tapered, do I enter the wing sweep or use 0, and treat it like a rectangular wing. I plugged in both and there is quite a bit of difference.


Rectangular Wing = 2.41" to 2.89" for 25% to 30% from root leading edge.

Sweeped Wing = 3.65" to 4.13" for 25% to 305 from root leading edge.

RE: Are My Calculations Right???
 

PtMG,

At www.TailwindGliders.com there is a FREE MS Excel spreadsheet as well as an article/tutorial called "Sailplane Calc" that will answer these questions as well as calculate these complex formulas for you as well. The spreadsheet does a little more than the links already provided but the article may help quite a bit.

All the best.
Curtis
Montana

RE: Are My Calculations Right???
 

Your graphic calculation of the MAC is correct.

From that point on, forget about the shape of your actual wing.

You have found the Means Aerodynamic Chord of your actual wing.

As stated above, you have to decide on the location of the CG along that MAC.

Of course, your measurements for that location will need to be respect to the root of the actual wing.

RE: Are My Calculations Right???
 

I use a quick n dirty method for this type stuff:
measure span (60")
1/2 span is then 30 "
and 1/4 span is 15"
measure in 15" from tip- and make two marks -one at 25% and one at 30% from leading eage -
do this on each panel
now connect the dots
this gives two straight lines,parallel from tip to tip
the CG should fall between them
Depending on speed o model -type of model wing loading of model - the "best " cg will be at front or rear of these lines
really light aerobatic - aft
really fast heavy model - front
I will bet you can't do it any better with a computer full of calculations.
CG is simply the " best compromise" location.

RE: Are My Calculations Right???
 

Puff,

For a symmetrical quadrilateral, like your Straight Tapered Wing is, the span is irrelevant.

MAC = (12 + 6.75) / 2 = 9.375 = 9-3/8"

MAC LE location measured aft from wing's root LE = (12 - MAC) / 2 = 1.31 = 1-5/16"

0.25 MAC location measured aft from wing's root LE = (MAC / 4) + 1.31 = 3.65 = 3-21/32"

MAC is the chord of an imaginary rectangular wing that accomplishes the same aerodynamic function of your Straight Tapered Wing (equivalent area and lift).

0.25 MAC is considered the neutral point of the MAC (where the lift force is applied).

Those are your fix numbers.

The CG location is more flexible and depends on many other factors and preferences of pitch stability degree, as explained above.

RE: Are My Calculations Right???
 

Puff, it's not you that says the wing is swept or not. The "S" or "Sweep" term in those calculators is the leading edge sweep only. In your case with the double taper the root and tip chords along with the leading edge sweep as shown indicates that the wing is not actually swept when you look at the 1/4 chord line. Or at least any angle is quite insignificant. However your leading edge sweep distance IS significant and must be included. The "S" term is used to allow for how the wing is tapered. Using a value of 0 for "S" you are then describing a wing with a straight across leading edge rather than the double taper shape you show.

RE: Are My Calculations Right???
 

Thanks a Million everone. Balanced my plane between the 25% &amp; 30% and she flies like a dream.

RE: Are My Calculations Right???
 

I am a model builder and have quite a bit of experiance with Models and Real Aircraft.And have to make that dicision alot when altering the design of crashed aircraft.It's usually found by suspending the aircraft by the wingtips and usualy slightly forward of the center othe wing width.The fuselage should balance and stay level if your close enough to fly.add weight if needed either inthe tail or nose.Loking at your wing I would say suspending it from the forward wingtips or very near will get you close? Good luck Alittle nose heavy can be corrected by changing the angle of attack raising the nose and adding power if you have any.But tail Heavy is almost doomed from the start never being able to get the nose down or even level to recover from a stall situation! Stay Safe

RE: Are My Calculations Right???
 

It should have a full tank off fuel itwill effect it ?And then again empty should get you in the ballpark!

RE: Are My Calculations Right???
 

You always balance with an empty tank. If you balance with a full tank, as it burns off, you are going to a tail heavy mode. While It may fly fine on take off, it will be badly out of balance at landing. If your tank is centered over your CG, then it doesn't mater if you balance full or empty. Pattern guys use pumps and put the thank back over the CG just for that reason, it flies the same at the finish of the flight as it did at the beginning. You don't need to worry about a full or empty tank if it is an electric.

Don

RE: Are My Calculations Right???
 

Sorry, Lnewqban, you are wrong there.
What you have defined is NOT the MAC (= Mean Aerodynamic Chord)
You have calculated the Geometric Mean Chord. The MAC IS INDEED 9.625" as calculated by Puff right at the start, though as BMathews was right to point out, wings do not have a CG, that belongs to the whole aeroplane. The CG position will depend greatly on the stabiliser and fuselage, and any other bits attached thereto.

The MAC is defined in Aerodynamics as the integral of c^2.dy over integral c.dy but is easier to find by that graphical method shown

RE: Are My Calculations Right???
 

The calculator and my graphic where 100% the same. Now I know.

RE: Are My Calculations Right???
 

The SWAG approach works as well as any for this application
Here is the math
Take one pencil
draw four straight lines which make a scale representation of the the wing planform (a bird's eye view) and roughly draw in the tip shapes .
using scissors-cut out the the little drawing
THIS is the shape which is doing the lift work- so cut carefully and watch your fingers!.
Fold each tip to the center
Unfold and note the location of each fold
make a dot on each fold - 1/4 back from the leading edge.
connect the dots.
make a second set of dots 1/3 back from the leading edge
connect these dots
the space in between is a workable location for a flyable CG location
You could use math and calculate all the various parameters of the model
But
this approach will give you the same results and you will also learn how to use a pair of scissors
This works for 3D , one ounce flat foam aerobats AND 100 pound scale Piper Cubs and all the others in between.
The best location - in that range -will vary somewhat

RE: Are My Calculations Right???
 

alasdair,

You are correct; however, the equivalent rectangular wing is a concept easier to understand for many people than integrals.

Copied from http://en.wikipedia.org/wiki/Chord_(aircraft)

"Standard mean chord (SMC) is defined as wing area divided by wing span:

SMC = S/b

where S is the wing area and b is the span of the wing.
Thus, the SMC is the chord of a rectangular wing with the same area and span as those of the given wing.
This is a purely geometric figure and is rarely used in aerodynamics.

Mean aerodynamic chord (MAC) is defined as:

MAC = (2/S) Integral between zero and b/2 of c^2 times the derivate of y

where y is the coordinate along the wing span and c is the chord at the coordinate y. Other terms are as for SMC.

Physically, MAC is the chord of a rectangular wing, which has the same area, 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.
Therefore, not only the measure but also the position of MAC is often important. In particular, the position of center of mass (CoM) of an aircraft is usually measured relative to the MAC, as the percentage of the distance from the leading edge of MAC to CoM with respect to MAC itself."

In summary, MAC is the mean value of all the chords along the semi-span of a wing.
The important things to determine are the length of that mean chord and the location of its projection over the fuselage.

Another simple way to find it for wings of quadrilateral shape is using the centroid:

http://en.wikipedia.org/wiki/Centroid

http://en.wikipedia.org/wiki/List_of_centroids

Note that the triangle centroid location is similar to the location of the MAC of a delta wing.

RE: Are My Calculations Right???
 

Yes, I just wanted to clarfiy that the MAC is not the same as the SMC or GMC that you used.
It makes little difference unless the wing is sharply tapered.

In Aerodynamics the MAC is the correct value of mean chord to use in calculations.

Just to enlarge on what you said, the MAC is the chord passing through the centroid of the wing shape, indeed the midpoint of the MAC (MAC/2) IS the centroid of a trapezoidal wing, or even a wing with 2 panels with different sweep and taper. The MAC does not even need to lie entirely on the surface.

A formula for the MAC of a swept tapered wing (or a panel) whose root chord is Cr and taper ratio is t (where t=Ct/Cr) is
MAC = 2Cr/3(1+t+t^2)/(1+t)

The two photos show the MAC of a two panel wing balanced on a steel ruler. Note that since it balances on the midpoint of the MAC, that must be the centroid of the shape.
Note also that the MAC extends slightly off the TE of the wing in this case.

RE: Are My Calculations Right???
 

someone else knows the value of scissors