Calculating CG

[SoarScale2]

Folks, I thought I would post a quick message regarding the calculation of the CG for a standard type sailplane. This method is relatively simple and provides a starting point for the CG based on the structure of the wing and the camber of the airfoil used.

The camber of the airfoil is involved in the calculation because the centroid of mass for differeing cambered airfoils changes as the camber changes and therefore the CG changes also. In this discussion I will use the Quabeck airfoils as the reference for AIRFOIL CG position based on camber.

So, to that end, let's first look at the Quabeck airfoils and their respective CG position as it relates to camber.

1% Camber - HQ1/xx - CG Position = 29%
1.5% Camber - HQ15/xx - CG Position = 32%
2% Camber - HQ20/xx - CG position = 34%
2.5% Camber - HQ25/xx - CG position = 36%
3% Camber - HQ30/xx - CG position = 39%
3.5% Camber - HQ35/xx - CG position = 42%

These CG positions ONLY relate to the airfoil and NOT the wing itself.

The percentage numbers above must be factored with the wing. We start by calculating the effective or standard mean chord of the whole wing - essentially rationalizing the wing into a non-tapered straight plank.

Most wings are tapered structures with one, two, three, four or more tapered sections. Our first calculation is to identify the SMC (Standard mean chord) of an eqivalent straight, non-tapered plank-type wing. This is fairly simple.

Please reference the attached drawing. Here, I have chosen a dual tapered wing.

Step 1: Calculate wing panel area

Our first step in calculating the SMC is to calculate the AREA of the wing. In the drawing below, the area of the panel is calculated by the following formula:

Area of panel = (((C1+C2)/2)*L1) + (((C2+C3)/2)*L2)

Since each section of the wing is a straight taper the standard formula:

(((Larger Chord at root of section + smaller Chord at end of section)/2) X Length of section) applies.

If you have more than two tapered sections, you simply calculate the area of the tapered section and add it to the total area being calculated.

This can be done in any units you choose to select - inches or millimeters. The result is in inches^2 or millimeters^2. Whichever unit of measure you select, make sure you keep that unit type in ALL your calculations.

Step 2: Calculate total wing area

We now need to calculate the area of the both wings so multiply the area of panel result by 2

Total area = area of panel x 2

Step 3: Measure wingspan

Now measure the wingspan with the plane assembled and record it.

Step 4: Calculate Standard Mean Chord (SMC)

We are now in a position to calculate the SMC.

SMC = total area (in^2 or mm^2) / span (in or mm)

The result of this calculation tells you the chord of a an EQIVALENT STRAIGHT PLANK-TYPE wing.

Step 5: Locate SMC LE location on wing.

Now we need to find the location of the SMC on the wing itself. Let's say that our SMC is 190mm and our root chord is 220mm. Move along each wing and mark the location along the span where the chord is equal to the SMC - 190mm in this case. Mark the location on each wing with a piece of low-tack tape.

Step 6: Locate LE of SMC on root

Now stretch a piece of string between the two marked SMC positions. This piece of string will CROSS the fuselage and may be difficult to do with the plane assembled. An alternate method is to do the same excersize with ONLY the wings laying flat on your bench. If you choose this latter method, it is important that the wings be aligned on your bench in exactly the same way as if the wings were mounted on the fuselage. In most cases, the wing root is at 90 degrees to the center line of the fusegale and so simply matching the wing roots together on your building bench will provide the data you need.

The goal here is to locate the LE of the SMC as it crosses the root of the wing and mark this location on the root. See the second drawing for a diagram of this excersize.

Step 7: Calculate location of aircraft CG.

Once you have marked the SMC LE location on the root, you are ready to calculate the CG location on the root.

The CG location can be calculated using the following:

CG Location = SMC x Airfoil CG Location

So in our example above, SMC = 190mm
Lets say we are using the HQ30/xx 3% camber airfoils

The CG would therefore be: 190mm X 0.39 (39%) = 74.1. (C1a in the third diagram attached)

The location of 74.1mm is the distance of the CG on the root BEHIND the SMC LE location on the root which we previously marked. Lets say our SMC LE was located 30mm back from the LE at the root as shown in the forth drawing.

Our final aircraft CG location is therefore 30mm + 74.1mm = 104.1mm from the LE at the root. This equates to 39% of the SMC for the whole aircraft using our 3% cambered Quabeck airfoil.

It is always recommended that you start with a CG location slightly forward of this position just in case your measurements were not that accurate. In the example above, I would personally start by balancing the aircraft at about 95mm back from the root LE and then perform flight tests and CG adjustments until I was happy with the flight characteristics of the aircraft.

So, In summary, here are the steps:

1). Calculate the area of both wings
2). Measure the wingspan
3). Calculate the standard Mean Chord (area/span)
4). Locate the LE of the SMC on the root of the wing
5). Identify the predominant airfoil CG location and mutiply that value by the SMC (SMC x 0.XX%)
6). Mark the location of the airfoil CG just calculated from the SMC LE location marked on the root.
7). Balance the aircraft a few millimeters forward of this position for flight tests and adjust as necesary.

[SoarScale2]

Folks, I noticed that in the first drawing I used the nomenclature of MAC (mean Aerodynamic Chord) instead of SMC (Standard Mean Chord). Note that in my first drawing, MAC has been replaced by SMC in consequent drawings - apologies if this causes confusion. In my posts, MAC = SMC - they are the same.

Tony Elliott

[SoarScale2]

Let's work an example.

The attached drawing shows a two tapered section wing panel.

Step 1. Calculate area of panel.

Panel Area = (((220mm+190mm)/2x1000mm) + (((190mm+120mm)/2)x975mm)
Panel Area = 205,000mm^2 + 151,125mm^2 = 356,125mm^2

Step 2. Total area of wings = 356,125mm^2 x 2 = 712,250mm^2

Step 3. Assuming the fuselage width is 125mm, Span = 1975 + 125mm + 1975 = 4075mm

Step 4. SMC = Area / span

SMC = 712,250 / 4075 = 174.78.........mm or rounded to something you can actually measure - 174.8mm

This is the chord of a straight plank wing with a total span of 4075mm that would have the same area as the multi-tapered wing in the drawing attached.

proof: total area calculated for the wing is 712,250mm^2
SMC x span should equal the same area.
174.78....... x 4075 = 712,250 !!

Step 5. Now locate the position on each wing panel where the chord is 174.8mm and mark these locations. Stretch the string between them and mark the LE of the SMC on the root of the wing. Let's assume this is located 20mm behind the LE of the root.

Step 6. Calculate the CG of the airfoil used. In this case we will use the 2.5% cambered airfoil with a CG location of 36%.

Airfoil CG = SMC x Airfoil CG = 174.8 X 0.36 = 62.928mm

Step 7. Aircraft CG = Distance between LE of SMC on root and root LE + Airfoil CG

Aircraft CG = 20mm + 62.928 = 82.928mm

I would personally start by balancing the aircraft at around 77 to 78 mm behind the LE at the root and then flight test the aircraft and adjust as necessary.

The process is not that difficult with a calculator in hand.

There is also a graphical method of calculating the CG but I personally do not use it. This has worked very well for me for all my scratch built aircraft.

Tony Elliott

[SoarScale2]

You will note that the CG location as a percentage of the root chord is greater than the airfoil percentage. Specifically:

82.928mm / 220mm = 37.7%

This is correct for those of you who observed the difference between airfoil CG and aircraft CG. Remember we are calculating the CG of an equivalent straight plank wing that represents the area of the tapered shape of the wing. The effect of this is as shown above as it relates to the root airfoil because the root airfoil is not the reference for CG calculation, the SMC is.

As I have stated earlier, it is always a good idea to start flight tests with a slightly forward CG and adjust the CG by removing small amounts of weight from the nose over a few flights. The primary reason for this as you will find out if you use this method is that accurately identifying the SMC LE on the root is not always an easy task and can lead to errors in measurement. This is especially the case when you attach the wings to the fuselage and try to locate the SMC LE on the root. Parallex errors will undoubtedly occur as you transfer the string location of the SMC LE to the root. The more accurate way is to lay the wings on your bench in the exact alignment that they would be if mounted to the fuse. Again, if you make errors here, they could translate to errors in the final CG location so accuracy is important here too.

This is why I always balance the plane ahead of the calculated CG and adjust through flight tests.

FINAL NOTE: When taking measurements from the aircraft or wing structure, I would recommend that you measure each item three times to ensure you have as accurate a measurement as possible.

Hope this info helps

Tony Elliott