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.

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…

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.

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

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.

Bingo!

Now lets look at factor number 2!

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.

Apparently a new type of solar cell developed by the Massachusetts Institute of Technology is so flexible that it can be folded up like a paper aeroplane.

I’m not sure if this will be much use for the casual aeroplane builder, but it’s an exciting technological development nonetheless.

http://inhabitat.com/2010/10/18/mit-introduces-paper-thin-solar-cells/

One easy way to give paper aeroplanes lateral stability is to make use of the ‘dihedral effect’.

Now, to some people, the word ‘dihedral’  may sound like something quite complicated, but it’s actually pretty simple. It means that from the root of the wing on the fuselage (the body of the plane), the wing slopes upwards. If the wings slope downwards this is called ‘anhedral’. Here’s a little diagram.

The degree to which the wings slope up from the horizontal is called the dihedral angle.  If the wings are exactly on the horizontal (not sloping either up or down), then the dihedral angle is zero.

So how do dihedral wings stop paper aeroplanes from rolling?

To understand the dihedral effect, it is useful to understand the concept of vectors. The word “vectors” also sounds quite complicated, but is also something pretty simple. It is the idea that a force in a particular direction can be expressed as two or more forces. For example…

Ok, so how do vectors come into this?

Well we can express the forces acting on the wings of a paper aeroplane in terms of vectors. Say a wing is at a dihedral angle, the lift force acting on a paper aeroplane’s wings will look like this…

As you can see, the forces are acting upwards but also a bit inwards. So we can also express the forces like this…

Hopefully, you’re still with me.

Now let’s assume that the paper aeroplane is really well made so the wings are exactly symmetrical. As the paper aeroplane flies, it is kept up in the air by the upward component of the force. The sideways components of the force are in equal and opposite directions, so they simply cancel each other out.

All is well in the world. The plane is flying straight and is perfectly stable.

Unfortunately, that wonderful scene is destroyed when a quick gust of wind comes along and causes the paper aeroplane to tilt to one side. Let’s take a look at the different forces acting on the wings the millisecond AFTER breeze has disappeared…

As you will see, on the force vectors on both wings have changed. The wing on the left (our left) is now sloping even higher. This leads to the upward force on the wing decreasing… but the sideways force increasing. The wing on our right is now almost completely flat, which leads to the upward force increasing, but the sideways force almost disappearing entirely.

So what happens here?

Well the first thing to note is that the plane does not automatically self-right because of the forces on the wings. Although it is tempting to think that the extra upwards force on the right wing will push that wing upwards and level the aeroplane, this is not the case. The reason why is that the sideways force on the left wing is pushing it rightwards, which maintains the tilt.

What actually happens is this: because the opposing sideways forces are now unbalanced, the aeroplane starts to move to one side AS WELL as it’s forward motion. This is  called ‘side slip’.

Once the paper aeroplane starts to move to the side as well as forwards, suddenly the direction that the air is hitting the two wings changes. Let’s look at the aeroplane from the top to see what is happening.

The oncoming air now pushes against the plane with a force with a leftwards component.

The leftward component of the force from the air pushes against the plane’s wings like this…

It is these forces that push the wings back to their original position. The oncoming air hits the underside of the right wing and pushes it up. The air also hits the top side of the left wing and pushes it down.

As the wings return to their original position, the unbalanced sideways force disappears (or, in other words, rebalances)… which means the side slip stops. At this point the plane has righted itself and continues flying straight and level.

The entire process I’ve just described is the ‘dihedral effect’ and I hope you can now see that when you make paper aeroplanes, you should give them dihedral wings if you want your flights to be straight and stable.

To understand the dihedral effect even better, it is useful to look at what might happen if an aeroplane has anhedral wings. As you will see, the result would not be good for your paper aeroplane!

If you want to experiment for yourself, click here to go back to the paperaeroplanes.com main page, then either choose to build ‘The Lion’ or ‘The Merlin’ planes. Both of these designs can be easily modified to have dihedral or anhedral wings. If you make a design and give it dihedral wings, it will tend to fly in a reasonably stable manner and will not roll. If you give the design anhedral wings it will tend to roll rapidly as it flies.

If your experiment doesn’t work, this is usually because your aeroplane doesn’t have enough lift to begin with! The dihedral effect will only work if your wings are producing lift – because without lift, there are no lift vectors to come into play. The easy way to rectify this is to tweak a tiny part of the tail edge of each wing upwards, but only very slightly.