August 12

Find Centre Of Gravity

This post covers a very important aspect of setting up your model plane to fly correctly and be fully controllable once airborne. Any plane, whether it be full size or a model, needs to be balanced both in pitch (fore & aft) and laterally (side to side). Today we are going to look at the factors affecting the “Pitch” stability.

The Pitch Stability of your model plane depends almost entirely on you locating the correct Centre of Gravity (I apologise to my American readers for the English spelling of “centre”). So it is most important that you find Centre of Gravity (CofG) of your plane at the outset. The term “pitch stability” refers to the longitudinal balance of the plane whilst flying. A nose heavy pitch will cause the plane to be unresponsive to controls and drop its nose when power is reduced. A tail heavy pitch will make the plane climb excessively when power is increased but,even worse, it will be over responsive to the controls and, in the very worst case, impossible to fly.

The neutral point and centre of gravity of a model plane
Neutral Point & Centre of Gravity

If you purchase an ARF plane the correct CoG position should be provided by the manufacturer. In the first instance ensure that your plane balances at this position. This should ensure that your plane is flyable from the word go.

In our diagram above the CoG is shown both ahead of and behind the “Neutral Point” and the “Aerodynamic Centre”.

Neutral Point (NP)

Without going into detail, this is a mathematical analysis of the longitudinal static stability of a complete aircraft (including horizontal stabilizer or tailplane) that yields the position of centre of gravity at which stability is neutral. The significant word here is “static”, i.e. when the plane is stationary without lift being generated. This position is called the Neutral Point.

Aerodynamic Centre (AC)

 It has been found both experimentally and theoretically that, if the aerodynamic forces on a plane are applied at a location 1/4 of the way from the leading edge of a rectangular wing at subsonic speed, the magnitude of the aerodynamic moment remains nearly constant even when the angle of attack changes. This location is called the wing’s Aerodynamic Centre and because it is affected by dynamics during flight and has to take account of lift generated by the wing, it is normally positioned slightly ahead of the Neutral Point.

Top view of plane with constant chord wing
Constant Chord or Rectangular Wing

In order to obtain good Longitudinal Stability the Centre of Gravity (CofG) should be as close as possible to the main wings’ Aerodynamic Centre (AC). This occurs because the lift due to the horizontal stabilizer has only a very slight effect on conventional R/C models.

Most model aircraft with rectangular wings (typical of a trainer design) have an “Aspect Ratio” of between 4.5 and 8.5 . Now I hear you asking: “What is the Aspect Ratio (AR)?”  This is the ratio of wing span (the full length of the wing, tip to tip) to wing chord ( the width of the wing, leading edge to trailing edge). So if we have a 60″ wing span and a 10″ wing chord, our Aspect Ratio is 60/10 = 6. The maths to find a formula for locating the position of our CofG is fairly complicated and I don’t intend to strain your brain cells with such tedium. So here is such a formula that you can use to calculate the CofG position for any plane where the Aspect Ratio (AR) falls within the range 4.5 to 8.5.

CofG position = 0.1 + (0.4 x V-bar)

Here we have a new term to explain. “V-bar” is the “tail volume ratio”. In other words the size and area ratio of the stabilizer compared to that of the wing and its distance behind the aerodynamic centre. Practically it is found by the following method:

1)  Measure wing span – S

2)  Measure wing chord – C

3)  Mark a point 25% of the wing chord from leading edge of wing.

4)  Measure the “mean” stabilizer chord (mark a point halfway along one half of the stabilizer and measure the chord at that point) – TC

5)  Mark a point 25% from leading edge of the stabilizer at this “mean” chord position.

6)  Measure stabilizer span( tip to tip both sides of the stabilizer) – TS

7)   Measure distance from the 25% wing mark in (3) to the 25% stabilizer mark in (5) – TA(tail arm)

Stabilizer Area(SA) = TS x TC       Wing Area(WA) = S x C     

V-bar = (SA/WA) x (TA/C)

So now let’s repeat the final formula for your CofG:

CofG position = 0.1 + (0.4 x V-bar)

depending on the units of measurement you have used, this figure will be the number of those units measured from the wing leading edge to your Centre of Gravity location.

Worked Example

Let us do a calculation based on some typical dimensions for a trainer plane:

S = 60″      C = 10″    TC = 6″     TS = 20″     TA = 28″

Stabilizer Area (SA) = 20 x 6 = 120 sq.ins.

Wing Area (WA)= 60 x 10 = 600 sq.ins.

V-bar = (120/600) x (28/10)

= 0.2 x 2.8 = 5.6

CofG position = 0.1 + (0.4 x 5.6) = 2.34″ from wing leading edge

I know all this sounds complicated but if you take the time to do a practical exercise with your trainer you’ll find it is easier than you think. Try it and have some fun, it will be interesting to see how close you are to the kit manufacturers suggestion.

Check Your Centre of Gravity

Once you have calculated the theoretical CofG position it’s time to check it. There is a very simple way to do this using just your fingertips.

Finding The CofG Using Fingertips
Fingertip CofG Locating Method

Mark the position of the CofG on both wing tips lightly in soft pencil and using just one finger of each hand place them under the wing tips in alignment with the marks and gently lift. If your plane is correctly balanced it should remain horizontal. If it drops its nose it is nose heavy and if the tail drops, it is tail heavy.

Usually slight adjustment to the location of either the receiver battery in a nitro plane or the lipo in an electric plane should correct the situation. If such adjustments do not correct the balance then you will need to add some additional weight either to the nose or the tail. Because the nose moment is much shorter than the tail moment, the amount of weight for the tail will be proportionally less than for the nose.

Tool to find Centre of Gravity

You can actually buy a special balancer for more accurate results. Below is a photo of this device:

A frame for finding the CoG of a model plane
CoG Balance Frame

You can purchase this frame on-line in the USA by clicking on the image. UK visitors can buy using this link: CofG Balancer

I really hope that you will have a go at this practical exercise to find centre of gravity for your own plane. Take your time and I think you will feel a sense of achievement at the end of it. Good luck and come back and let me know how you get on.

Colin



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Posted August 12, 2015 by Colin in category "General Flight Training

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