Lateral Stability 1: Paper Aeroplanes & The ‘Dihedral Effect’

In simple terms, ‘lateral stability’ means that a plane will fly the right way up and not roll as it flies.

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

Now, to some people, the word ‘dihedral’Β  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.

Dihedral Vs Anhedral Wings

The degree to which the wings slope up from the horizontal is called the dihedral angle.Β  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…

Understanding Vectors

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…

Forces acting on a paper aeroplane' wings - Diagram 1

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

The forces acting on a paper aeroplane's wings - Diagram 2

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…

Paper Aeroplane hit by breeze

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 isΒ  called ‘side slip’.

Paper Aeroplane in 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.

Paper Aeroplane in Side Slip 2

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…

Sideways air forces on plane during side slip

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!

Anhedral Effect

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.

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14 Responses to Lateral Stability 1: Paper Aeroplanes & The ‘Dihedral Effect’

  1. Pingback: The ‘keel effect’ and paper aeroplanes. | Paper Aeroplanes – The Blog

  2. Kirsten says:

    Thank you. I’m an aeronautical engineering student and that concept had me stumped.

  3. Bhanu Pratap Singh says:

    awesome explanation in a very simple language and with good diagrammatic representation.
    Thank You so much.

  4. Sarah D says:

    Excellent! I am starting to learn about aviation theory and your Wonderful explaination with the diagrams is really really helpful. Thanks a lot!!

  5. StormyFronts says:

    Regarding the lateral stability bit.
    You said it was “the ability of the aircraft to fly the right way up and not roll as it travels through the air”.
    according to the ASA Pilots Handbook for Aeronautical Knowledge p.2-2
    The lateral axis determines the pitch of the aircraft rather than the roll. The roll movement would be along the longitudinal axis.

    Love the site i hope you put some new designs up soon.

    • Peter says:

      There’s a difference between the “lateral axis” and “lateral stability”.

      When people refer to the “lateral axis” they mean drawing a line through the aircraft from wingtip to wingtip. Rotation about this axis is called pitch. However plane that maintains a steady pitch is not referred to as having lateral stability, it is referred to as having longitudinal stability.

      However, “lateral stability” refers to the stability of aircraft’s longitudinal axis – an axis which extends form nose to tail. If an aircraft lacks lateral stability it has a tendency to roll along the longitudinal axis.

      Hope this clarifies!

    • Ahmed ayan says:

      Same here I would really love some more desings as all of the old ones were splendid though the monkey didn’t turn out quite as I expected!!!

  6. Joseph Roake says:

    Required a definition for a talk I am giving and the information you give about dihedral and it’s presentation is the best I have seen. I hope that you cover other topics as you have a gift.

  7. Drithi Shetty says:

    Thank you for the explanation.
    I have a question though.
    If the extra upward force on the right wing does not cause the plane to roll back, then what exactly is its effect on flight?

  8. Alex says:

    Thank you
    πŸ™‚

  9. P. Jeff Wong says:

    I wonder how many of us r here coz were studying Aeronautics. πŸ™‚
    It’s now I realize the site is paperaeroplanes.com lol
    Ur explanations r actually more comprehensible than that in FAA pilot handbook.

    I as well got the answer for why sweep wings contribute to lateral stability.
    Splendid!

  10. Ahmed ayan says:

    I can only say that this is a great website written by a really good and intelligent person thank you very much And the best part is that easy language has been used to explain difficult concepts

  11. Lovenish Agarwal says:

    Excellent explanation..Thanx a lot πŸ™‚

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