Lateral Stability 2: Paper Aeroplanes & The ‘Keel Effect’

There are a number of ways to give paper aeroplanes ‘lateral stability’ – the ability of an aircraft to fly the right way up, and not to roll as it travels through the air.

One method is to use the ‘dihedral effect’ as outlined in my earlier blog post here.

Another method is to make use of the ‘keel effect’.

The keel effect involves the positioning of the plane’s centre of gravity. The centre of gravity is the average location of all the gravitational force on an object. In simple terms, it is the point where an object (e.g. an aeroplane) balances. Some people call this point the ‘centre of mass’, because, in most instances you encounter, centre of gravity and centre of mass are the same thing… although the two concepts can be different out in space!

In very simplistic terms, the keel effect means that aeroplanes with a centre of gravity below the wing are more stable than those with a centre of gravity above the wing.

To start understand the physics of why the keel effect works, let’s look at a diagram. The diagram below shows a simple front view of a weight suspended beneath a wing with a dihedral angle of zero (so we can ignore the dihedral effect totally). Let’s say that in this second of time, the lift forces are entirely equal to the gravitational force on the aeroplane, which means that it is neither rising nor falling. The lift forces on each wing are equal, so that the centre of lift of the plane is exactly in the middle of the two wings. Also since there are no sideways forces at all, the plane is moving straight forward with zero sideslip.

Keel Effect - 1

Now let’s look at what happens if the plane is disturbed during flight and starts to tilt to one side.  At this point two things start to happen simultaneously.

Firstly, because the wings are no longer level with the horizontal, so part of the lift force is directed horizontally. This causes the plane to begin to side slip.

Secondly, because the wings are no longer level and some of the lift force is directed sideways, there is less upward force. This causes the plane to descend.

Let’s go through factor number 1 using diagrams.

When the plane tilts, the lift force of the wings no longer point up, but a bit to the side…

Keel Effect2

We can represent the forces on the wings by breaking them down into two components, and upward force and a horizontal force. Given that there is now a force acting to the right (our right), the plane starts to move (‘side slip’) to the right.

Keel Effect 3

Once the plane starts moving rightwards, air starts to hit it in a leftwards direction.

Keel Effect 4

The pink line in the diagram above shows the horizontal position of the centre of gravity. As you will see more air is hitting the plane above the centre of gravity than below it.

Keel Effect 5

Bingo!

Now lets look at factor number 2!

Keel Effect 6

Keel Effect 7

Keel Effect 8

Bingo again!

So what lessons can we learn from this when designing paper aeroplanes?

Well one key lesson is that if we make our planes so that the wings are above the centre of gravity, then they should have more lateral stability. This is already the case with most of the planes I’ve posted on the main website, with (at the moment) one exception, which is the piranha. The piranha is a slightly special case as it is not a plane that produces much lift, so the force vectors around the wings are different.

Another lesson is that we can make our planes MORE stable by lowering the centre of gravity further below the wing. If you draw the diagrams yourself, you will see that the further down below the wings that you place the centre of gravity, the stronger the stabilising forces get.

One easy way to do this is to make the fuselage higher and the wings stubbier. Unfortunately, this does mean that you also lose some lift; however, you can counter this by tweaking the back edge of the wings upwards very slightly upwards. This is the same thing as turning the elevators on the tailplane of a normal aeroplane upwards, often called ‘up elevator’.

If you try making the lion or the merlin you can experiment with folding the wings higher up the fuselage than I do in the video. In fact, if I ever fly a plane in a competition, I usually DO make the wings slightly higher than I do in the video and add up tweaks to the back of the wings … this improves stability, at the expense of making the plane look slightly uglier!

If this doesn’t work, it is usually for one of two reasons… either your wings aren’t producing enough/any lift! You can easily solve this by tweaking a tiny section of the trailing edge of the wings upwards by a very small amount. Without lift, you can’t have unbalanced force vectors causing the neccessary side slip. Another reason is that you have made the wings at an anhedral angle… which will counteract the keel effect. See my earlier post on dihedral angles to solve this.

If you want to go advanced, another way to help produce the keel effect is to design a new plane from scratch, making sure that more folds are concentrated towards the bottom of the fuselage. I’ll be showing a few ways to do this in future posts.

****END NOTE**** I should add a note here on how the keel effect does NOT operate. Some people think that a low centre of gravity will automatically cause a plane to right itself if it becomes tilted… with the centre of gravity swinging back under the plane like a pendulum. They sometimes say this effect (which doesn’t actually exist) is called the ‘pendulum effect’.

One easy way to understand why this does not happen is to remember that the centre of gravity is the point where the plane balances. This is the case whether the plane is flying the right way up with its wings flat OR if the plane is completely tilted on its side, with the wings on the vertical. Whatever way you spin the plane around the centre of gravity, the weight on each side will always be equal. So, when the plane is titled, it is still balanced.

In a vacuum a plane would be entirely happy to be tilted at any angle. The ONLY forces that cause the plane to return to its ‘correct’ flying position are AERODYNAMIC forces such as the air hitting the plane from the side when it is in side slip and the air hitting it from below when it is in descent.

UPDATE (August 2012): I’ve posted a basic fold for enhanching the keel effect.

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