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Plane wings come in a huge variety of shapes, sizes and configurations. We have explored
how the aft swept wings of a traditional airliner and the forward swept wings of experimental
planes like the x-29 affect the aerodynamic properties of the plane. We explained why
modern day jet fighters are designed to be aerodynamically unstable, and in one of my
very first videos we investigated why airliner manufacturers like Boeing and Airbus are installing
increasingly complicated winglets at the tips of their wings. However we have never explored
in detail the theory and practice behind wing dihedral angles. Which is simply the angle
the wings make with respect a perfectly horizontal lie through the base of the wing, and planes
throughout history have had a huge variety of variations with this feature.
From the high mounted anhedral wing of the AV-8B Harrier, where the wing angles downwards,
to the low mounted dihedral wings of airliners and WW2 era fighters and everything in between
like modern day F-16s with low mounted straight wings or stranger still the gullwings of seaplanes
and inverted gullwing of the F4U Corsair.
So what’s the purpose behind all these designs? To understand this, we first have to understand
the dynamic lift generated by a wing as it rolls.
Let’s examine a plane with dihedral wings, meaning they point upwards. In straight and
left flight the lift each wing generates does not point directly up. As the lift a wing
generates is perpendicular to the aerofoil of the wing. This means the lift of wings
points inwards at an angle towards the fuselage. [1]
This seems like a strange design choice, as only the vertical component of lift contributes
to getting the plane off the ground, and thus the horizontal component is wasted energy
which results in additional fuel being wasted. So why do they do it? By tilting the wings
upwards we gain roll stability, which we explored briefly in my “Why Jet Fighters Can Be Too
Unstable” video. This means that when the plane rolls it will naturally correct itself
and return to straight and level flight with no input from the pilot. An important safety
feature
This works as a result of a planes tendency to side slip when it rolls. Meaning the plane
begins to move sideways and downwards in the direction of the bank. This introduces a new
air flow to the wing which has both a vertical and sidewise component. As a result of the
dihedral angle, this flow strikes the underside of the lower wing with a great angle of attack
that the higher wing, and thus the lower wing now generates more lift than the upper wing,
providing a restoring force to return the plane to straight and level flight.
The exact opposite occurs with anhedral wings, where the wings point downwards. Here when
sideslip occurs the upper wing achieves more lift due to a greater angle of attack, causing
the plane to roll more.
High mounted wings tend to be anhedral. Some sources will tell you that this due to the
pendulum effect where the weight of the plane itself acts as a restoring force, like how
a pendulum will naturally return to its original position when disturbed, but this is incorrect
and I nearly uploaded this explanation on Saturday before thinking about it a little
harder and realising that that didn't make any sense.
The actual reason high mounted wings are roll stable is a result of how the airflow flows
around the fuselage in sideslip. With high mounted wings it will be deflected into the
underside of the wing, increasing lift on the lower wing and thus providing a restoring
moment, while a low mount wing will have the airflow deflected into the top of the wing
providing a moment which will increase the roll.
So plane designers will use dihedral wings on low mounted wings to counteract the instability
of low mounted wings and use anhedral wings to offset the stability of high mounted wings.
We can see examples of anhedral wings in planes like AV-8B Harrier, where the designers needed
to use a high mounted wing in order to utilize the direct thrust nozzles that would otherwise
strike the top of the wing in a low mounted wing. Perhaps the most impressive example
of high mounted anhedral wings is with the Antonov AN-225. The largest plane in the world.
I could not find a reference to back this up, but I assume they chose this wing configuration
to increase ground clearance for it’s 6 turbofan engines, and thus allow the plane
to have extremely short landing gear. Which would reduce the material needed for them,
and make loading procedures much easier. We also see examples of low mounted wings
with no dihedral angle at all, like the F-16. This made the F-16 slightly unstable in roll,
allowing for better maneuverability. The F-16 was infact one of the first planes in existance
to deliberately introduce instability for the benefit of energy efficient maneuvering.
A technology made possible by fly by wire computers.
Angling the wings like this does come with disadvantages. One of them is its effect on
fuel economy. As stated earlier, only the vertical component of lift contributes to
getting the plane off the ground, and thus the horizontal component is wasted energy
which results in additional fuel being used, but the effect is tiny if we keep the dihedral
angle relatively small. The loss in vertical lift is proportional to the cosine of the
dihedral angle. A wing with a dihedral angle of six degrees, like a Boeing 737, will lose
just 0.55 percent of it’s vertical lift in exchange for roll stability. (Cos (0) - Cos
(6) = 0.005478)[2] [3]
The configurations mentioned above are the most common, but there are configurations
that appear in special circumstances. The F4 Phantom, a fighter created before fly by
wire technology was mainstream, was found to be unstable during the testing phase and
thus they retrofitted a dihedral angle to the wing tips late in the development stage
to increase roll stability. This is called cranked dihedral.
One of my favourite planes. The F4U Corsair features inverted gullwings where the wings
initially protrude out with an anhedral angle before sweeping back to dihedral. This wasn’t
for any fancy aerodynamic reason, but for a similar reason to our AN-255.
When the F4U Corsair was being designed the engineers had some design criteria they had
to hit, namely it was required to be capable of achieving a top speed of 640 kilometres
per hour. [4] This would require not only a large engine to achieve the power needed
to overcome the immense drag at this speed, but a large propeller to provide thrust. This
created ground clearance issues for the plane that would require longer landing gear, but
a longer landing gear would need to be stronger, heavier and would take up more space. Instead
the designers decided to bring the landing gear closer to the ground by curve the wing
downwards where it was located.
The gullwings of seaplanes again use them for clearance reasons, as they try to lift
the wing mounted engines clear of damaging sea water spray.
These are just some examples of how dihedral angles change for different design criteria,
but from here you should be able to look at any plane and understand why it chose a particular
wing dihedral or anhedral angle. Like the Junkers JU-87 another inverted gull-wing world
war 2 era plane flown extensively by the German’s. I will be exploring many of these planes and
other less examined factors that influenced the outcome of World War 2, in my new Logistics
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In my debut episode I explore the reasons Normandy was chosen as the final landing location,
factoring in everything from Allied fighter plane ranges to the geology of Normandy. It’s
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