In aeronautics, dihedral is the angle between the left and right wings (or tail surfaces) of an aircraft. "Dihedral" is also used to describe the effect of
sideslip
A slip is an aerodynamic state where an aircraft is moving ''somewhat'' sideways as well as forward relative to the oncoming airflow or relative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite directio ...
on the
rolling
Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact ...
of the aircraft.
Dihedral angle is the upward angle from horizontal of the wings or tailplane of a
fixed-wing aircraft
A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
. "Anhedral angle" is the name given to negative dihedral angle, that is, when there is a ''downward'' angle from horizontal of the wings or tailplane of a fixed-wing aircraft.
Dihedral angle has a strong influence on dihedral effect, which is named after it. Dihedral effect is the amount of
roll moment
Roll moment is a moment, which is a product of a force and a distance, that tends to cause a vehicle to roll, that is to rotate about its longitudinal axis.
Landcraft
In vehicle dynamics, the roll moment can be calculated as the product of three ...
produced in proportion to the amount of
sideslip
A slip is an aerodynamic state where an aircraft is moving ''somewhat'' sideways as well as forward relative to the oncoming airflow or relative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite directio ...
. Dihedral effect is a critical factor in the stability of an aircraft about the roll axis (the
spiral mode). It is also pertinent to the nature of an aircraft's
Dutch roll
Dutch roll is a type of aircraft motion consisting of an out-of-phase combination of "tail-wagging" (yaw) and rocking from side to side (roll). This yaw-roll coupling is one of the basic flight dynamic modes (others include phugoid, short per ...
oscillation and to maneuverability about the
roll
Roll or Rolls may refer to:
Movement about the longitudinal axis
* Roll angle (or roll rotation), one of the 3 angular degrees of freedom of any stiff body (for example a vehicle), describing motion about the longitudinal axis
** Roll (aviation), ...
axis.
Longitudinal dihedral is a comparatively obscure term related to the
pitch axis of an airplane. It is the angle between the
zero-lift axis
A cambered aerofoil generates no lift when it is moving parallel to an axis called the zero-lift axis (or the zero-lift line.) When the angle of attack on an aerofoil is measured relative to the zero-lift axis it is true to say the lift coefficien ...
of the wing and the zero-lift axis of the horizontal tail. Longitudinal dihedral can influence the nature of controllability about the pitch axis and the nature of an aircraft's
phugoid
In aviation, a phugoid or fugoid is an aircraft motion in which the vehicle pitches up and climbs, and then pitches down and descends, accompanied by speeding up and slowing down as it goes "downhill" and "uphill". This is one of the basic flig ...
-mode oscillation.
When the term "dihedral" (of an aircraft) is used by itself it is usually intended to mean "dihedral ''angle''". However, context may otherwise indicate that "dihedral ''effect''" is the intended meaning.
Dihedral ''angle'' vs. dihedral ''effect''
Dihedral angle is the upward angle from horizontal of the wings of a
fixed-wing aircraft
A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
, or of any paired nominally-horizontal surfaces on any
aircraft
An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines ...
. The term can also apply to the wings of a
bird
Birds are a group of warm-blooded vertebrates constituting the class Aves (), characterised by feathers, toothless beaked jaws, the laying of hard-shelled eggs, a high metabolic rate, a four-chambered heart, and a strong yet lightweigh ...
. Dihedral angle is also used in some types of kites such as box kites. Wings with more than one angle change along the full span are said to be ''polyhedral''.
Dihedral angle has important stabilizing effects on flying bodies because it has a strong influence on the dihedral effect.
Dihedral effect
[ Library of Congress Catalog Card Number: 78-31382] of an aircraft is a rolling moment resulting from the vehicle having a non-zero
angle of sideslip
A slip is an aerodynamic state where an aircraft is moving ''somewhat'' sideways as well as forward relative to the oncoming airflow or relative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite directio ...
. Increasing the dihedral angle of an aircraft increases the dihedral effect on it. However, many other aircraft parameters also have a strong influence on dihedral effect. Some of these important factors are:
wing sweep
A swept wing is a wing that angles either backward or occasionally forward from its root rather than in a straight sideways direction.
Swept wings have been flown since the pioneer days of aviation. Wing sweep at high speeds was first investigat ...
, vertical
center of gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. Thi ...
, and the height and size of anything on an aircraft that changes its sidewards force as
sideslip
A slip is an aerodynamic state where an aircraft is moving ''somewhat'' sideways as well as forward relative to the oncoming airflow or relative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite directio ...
changes.
Longitudinal dihedral
Dihedral angle on an aircraft almost always implies the angle between two ''paired'' surfaces, ''one on each side of the aircraft''. Even then, it is almost always between the left and right ''wings''. However, mathematically
dihedral means the angle between ''any'' two planes. So, in aeronautics, in one case, the term "dihedral" is applied to mean the difference in angles between two ''front-to-back'' surfaces:
Longitudinal dihedral is the difference between the
angle of incidence of the wing
root chord
In music theory, the concept of root is the idea that a chord (music), chord can be represented and named by one of its Musical note, notes. It is linked to Harmony (music), harmonic thinking—the idea that vertical aggregates of notes can form ...
and angle of incidence of the horizontal tail root chord.
Longitudinal dihedral can also mean the angle between the
zero-lift axis
A cambered aerofoil generates no lift when it is moving parallel to an axis called the zero-lift axis (or the zero-lift line.) When the angle of attack on an aerofoil is measured relative to the zero-lift axis it is true to say the lift coefficien ...
of the wing and the zero-lift axis of the horizontal tail instead of between the root chords of the two surfaces. This is the more meaningful usage because the directions of zero-lift are pertinent to longitudinal trim and stability while the directions of the root chords are not.
History
In geometry, dihedral angle is the angle between two planes. Aviation usage differs slightly from usage in geometry. In aviation, the usage "dihedral" evolved to mean the positive, up angle between the left and right wings, while usage with the prefix "an-" (as in "anhedral") evolved to mean the negative, down angle between the wings.
The aerodynamic stabilizing qualities of a dihedral angle were described in an influential 1810 article by
Sir George Cayley
Sir George Cayley, 6th Baronet (27 December 1773 – 15 December 1857) was an English engineer, inventor, and aviator. He is one of the most important people in the history of aeronautics. Many consider him to be the first true scientific aer ...
.
Uses of dihedral angle and dihedral effect
Aircraft stability analysis
In analysis of aircraft stability, the dihedral effect is also a
stability derivative called C
l[Pronounced "See-ell-beta".] meaning the change in rolling moment coefficient (the "C
l")
[A rolling moment ''coefficient'' is a "normalization" of the rolling moment. Rolling moment has units of force times length. The rolling moment coefficient is normalized so it has no units. This is done by dividing the moment by wing area and by wing span and by ]dynamic pressure
In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5
:q = \frac\rho\, u^2
where (in SI units):
* is the dynamic pressure in pascals ( ...
. per degree (or radian) of change in
sideslip angle
A slip is an aerodynamic state where an aircraft is moving ''somewhat'' sideways as well as forward relative to the oncoming airflow or relative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite directio ...
(the "
").
Provision of stability
The purpose of dihedral effect is to contribute to stability in the roll axis. It is an important factor in the stability of the ''
spiral mode'' which is sometimes called "roll stability".
["Roll Stability" is an ambiguous term requiring context to discern the intended meaning of the user. It usually means "Spiral Mode Stability", but it is also often misused to mean dihedral effect or dihedral angle, both of which are not "stability" themselves, though they contribute to spiral mode stability.] The dihedral effect does not contribute directly to the restoring of "wings level", but it indirectly helps restore "wings level" through its effect on the spiral mode of motion described below.
Wing clearance
Aircraft designers may increase dihedral angle to provide greater clearance between the wing tips and the runway. This is of particular concern with
swept-wing
A swept wing is a wing that angles either backward or occasionally forward from its root rather than in a straight sideways direction.
Swept wings have been flown since the pioneer days of aviation. Wing sweep at high speeds was first investigat ...
aircraft, whose wingtips could hit the runway on rotation/touchdown. In military aircraft dihedral angle space may be used for mounting
materiel
Materiel (; ) refers to supplies, equipment, and weapons in military supply-chain management, and typically supplies and equipment in a commercial supply chain context.
In a military context, the term ''materiel'' refers either to the specifi ...
and
drop-tanks on wing hard points, especially in aircraft with low wings. The increased dihedral effect caused by this design choice may need to be compensated for, perhaps by decreasing the dihedral angle on the horizontal tail.
Using dihedral angle to adjust dihedral effect
During design of a
fixed-wing aircraft
A fixed-wing aircraft is a heavier-than-air flying machine, such as an airplane, which is capable of flight using wings that generate lift caused by the aircraft's forward airspeed and the shape of the wings. Fixed-wing aircraft are distinc ...
(or any aircraft with horizontal surfaces), changing dihedral angle is usually a relatively simple way to adjust the overall dihedral effect. This is to compensate for other design elements' influence on the dihedral effect. These other elements (such as wing sweep, vertical mount point of the wing, etc.) may be more difficult to change than the dihedral angle. As a result, differing amounts of dihedral angle can be found on different types of fixed-wing aircraft. For example, the dihedral angle is usually greater on low-wing aircraft than on otherwise-similar high-wing aircraft. This is because "highness" of a wing (or "lowness" of vertical
center of gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. Thi ...
compared to the wing) naturally creates ''more'' dihedral effect itself. This makes it so less dihedral angle is needed to get the amount of dihedral effect needed.
Common confusions
Dihedral effect is defined simply to be the rolling moment caused by sideslip and nothing else. Rolling moments caused by other things that may be related to sideslip have different names.
Dihedral effect is not caused by ''
yaw rate
A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the ...
'', nor by the ''rate of sideslip change''. Since dihedral effect is noticed by pilots when "rudder is applied", many pilots and other near-experts explain that the rolling moment is caused by one wing moving more quickly through the air and one wing less quickly. Indeed, these are actual effects, but they are not the dihedral effect, which is caused by being ''at'' a sideslip angle, not by getting to one. These other effects are called "rolling moment due to yaw rate" and "rolling moment due to sideslip rate" respectively.
Dihedral effect is not
roll stability
Roll or Rolls may refer to:
Movement about the longitudinal axis
* Roll angle (or roll rotation), one of the 3 angular degrees of freedom of any stiff body (for example a vehicle), describing motion about the longitudinal axis
** Roll (aviation), ...
in and of itself. Roll stability is less-ambiguously termed "spiral mode stability" and dihedral effect is a contributing factor to it.
How dihedral angle creates dihedral effect and stabilizes the spiral mode
The dihedral angle contributes to the total dihedral effect of the aircraft. In turn, the dihedral effect contributes to stability of the ''
spiral mode''. A ''stable'' spiral mode will cause the aircraft to eventually return to a nominally "wings level" bank angle when the angle of the wings is disturbed to become off-level.
[In the spiral mode, if it is unstable, the aircraft will slowly, then more rapidly, ''diverge'' from "nominal wings-level" if the pilot makes no control inputs. If the spiral mode is ''stable'' and the pilot makes no inputs, when the aircraft starts from a ''banked'' attitude, it will return close to wings-level by itself.]
If a disturbance causes an aircraft to roll away from its normal wings-level position as in Figure 1, the aircraft will begin to move somewhat sideways toward the lower wing.
In Figure 2, the airplane's flight path has started to move toward its left while the nose of the airplane is still pointing in the original direction. This means that the oncoming air is arriving somewhat from the left of the nose. The airplane now has ''sideslip'' angle in addition to the bank angle. Figure 2 shows the airplane as it presents itself to the oncoming air.
How dihedral angle creates rolling moment from sideslip (dihedral effect)
In Figure 2, the sideslip conditions produce greater
angle of attack
In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is m ...
on the forward-yawed wing and smaller angle of attack on the rearward-yawed wing. This alteration of angle of attack by sideslip is visible in Figure 2. As greater angle of attack produces more lift (in the usual case, when the wing is not near stalling), the forward wing will have more lift and the rearward wing will have less lift. This difference in lift between the wings is a rolling moment, and it is caused by the sideslip. It is a contribution to the total dihedral effect of the aircraft.
How dihedral effect stabilizes the spiral mode
The rolling moment created by the sideslip (labeled as "P") ''tends'' to roll the aircraft back to wings level. More dihedral effect tries to roll the wings in the "leveling" direction more strongly, and less dihedral effect tries to roll the wings in the "leveling" direction less strongly. Dihedral effect helps stabilize the spiral mode by ''tending'' to roll the wings toward level in proportion to the amount of sideslip that builds up. It is not the whole picture however. At the same time that
angle of sideslip
A slip is an aerodynamic state where an aircraft is moving ''somewhat'' sideways as well as forward relative to the oncoming airflow or relative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite directio ...
is building up, the vertical fin is trying to turn the nose back into the wind, much like a weathervane, minimizing the amount of sideslip that can be present. If there is no sideslip, there can be no restoring rolling moment. If there is less sideslip, there is less restoring rolling moment. Yaw stability created by the vertical fin opposes the tendency for dihedral effect to roll the wings back level by limiting sideslip.
The spiral mode is the tendency to slowly diverge from, or the tendency to slowly return to wings level. If the spiral mode is stable, the aircraft will slowly return to wings-level, if it is unstable, the aircraft will slowly diverge from wings-level. Dihedral effect and yaw stability are the two primary factors that affect the stability of the spiral mode, although there are other factors that affect it less strongly.
Other factors contributing to dihedral effect
![TegelbergParaglider gobeirne](https://upload.wikimedia.org/wikipedia/commons/0/06/TegelbergParaglider_gobeirne.jpg)
Factors of design other than dihedral angle also contribute to dihedral effect. Each increases or decreases total aircraft dihedral effect to a greater or lesser degree.
Sweepback
Wing
sweepback
A swept wing is a wing that angles either backward or occasionally forward from its root rather than in a straight sideways direction.
Swept wings have been flown since the pioneer days of aviation. Wing sweep at high speeds was first investigate ...
also increases dihedral effect. This is one reason for anhedral configuration on aircraft with high sweep angle, as well as on some airliners, even on low-wing aircraft such as the
Tu-134
The Tupolev Tu-134 (NATO reporting name: Crusty) is a twin-engined, narrow-body jet airliner built in the Soviet Union for short and medium-haul routes from 1966 to 1989. The original version featured a glazed-nose design and, like certain ot ...
and
Tu-154
The Tupolev Tu-154 (russian: Tyполев Ту-154; NATO reporting name: "Careless") is a three-engined, medium-range, narrow-body airliner designed in the mid-1960s and manufactured by Tupolev. A workhorse of Soviet and (subsequently) Russian ...
, with the small German 1930s – 1945 biplanes of the
Bücker Flugzeugbau
Bücker-Flugzeugbau GmbH was a German aircraft manufacturer founded in 1932. It was most notable for Its highly regarded sports planes which went on to be used as trainers by the Luftwaffe during World War II.
History
The company was founded b ...
, the
Bucker Jungmann two-seat trainer and more famous
Bücker Jungmeister aerobatic competition biplane, both having approximately 11° of wing sweepback giving both designs a degree of dihedral effect, beyond the small amount of dihedral both biplanes' designs also featured.
Vertical position of the center of mass
The
center of mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
, usually called the
center of gravity
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. Thi ...
or "CG", is the balance point of an aircraft. If suspended at this point and allowed to rotate, a body (aircraft) will be balanced. The front-to-back location of the CG is of primary importance for the general stability of the aircraft, but the vertical location has important effects as well.
The vertical location of the CG changes the amount of dihedral effect. As the "vertical CG" moves lower, dihedral effect increases. This is caused by the center of lift and drag being further above the CG and having a longer moment arm. So, the same forces that change as sideslip changes (primarily sideforce, but also lift and drag) produce a larger moment about the CG of the aircraft. This is sometimes referred to as the
pendulum effect.
[The "pendulum effect" is also less commonly called the "keel effect".]
An extreme example of the effect of vertical CG on dihedral effect is a
paraglider
Paragliding is the recreational and competitive adventure sport of flying paragliders: lightweight, free-flying, foot-launched glider aircraft with no rigid primary structure. The pilot sits in a harness or lies supine in a cocoon-like 'po ...
. The dihedral effect created by the very low vertical CG more than compensates for the negative dihedral effect created by the strong anhedral
[The downward curve of a paraglider wing could be termed "continuous polyanhedral".] of the necessarily strongly downward curving wing.
Effects of too much dihedral effect
A side effect of too much dihedral effect, caused by excessive dihedral angle among other things, can be yaw-roll coupling (a tendency for an aircraft to
Dutch roll
Dutch roll is a type of aircraft motion consisting of an out-of-phase combination of "tail-wagging" (yaw) and rocking from side to side (roll). This yaw-roll coupling is one of the basic flight dynamic modes (others include phugoid, short per ...
). This can be unpleasant to experience, or in extreme conditions it can lead to loss of control or can overstress an aircraft.
Anhedral and polyhedral
Anhedral
![An-124 front view](https://upload.wikimedia.org/wikipedia/commons/6/65/An-124_front_view.jpg)
Military
fighter aircraft
Fighter aircraft are fixed-wing military aircraft designed primarily for air-to-air combat. In military conflict, the role of fighter aircraft is to establish air superiority of the battlespace. Domination of the airspace above a battlefield ...
often have near zero or even anhedral angle reducing dihedral effect and hence reducing the stability of the spiral mode. This increases maneuverability which is desirable in fighter-type aircraft.
Anhedral angles are also seen on aircraft with a high mounted wing, such as the very large
Antonov An-124
The Antonov An-124 Ruslan (; russian: Антонов Ан-124 Руслан, , Ruslan; NATO reporting name: Condor) is a large, strategic airlift, four-engined aircraft that was designed in the 1980s by the Antonov design bureau in the Ukrain ...
and
Lockheed C-5 Galaxy
The Lockheed C-5 Galaxy is a large military transport aircraft designed and built by Lockheed, and now maintained and upgraded by its successor, Lockheed Martin. It provides the United States Air Force (USAF) with a heavy intercontinental-rang ...
cargo aircraft. In such designs, the high mounted wing is above the
aircraft's center of gravity which confers extra dihedral effect due to the
pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the ...
effect (also called the
keel effect In aeronautics, the keel effect (also known as the pendulum effect or pendulum stability) is the result of the sideforce-generating surfaces being above (or below) the center of mass (which coincides with the center of gravity (aircraft), center of ...
) and so additional dihedral angle is often not required. Such designs can have excessive dihedral effect and so be excessively stable in the spiral mode, so anhedral angle on the wing is added to cancel out some of the dihedral effect so that the aircraft can be more easily maneuvered.
Polyhedral
![Mc Donnell Douglas F4-F Phantom v](https://upload.wikimedia.org/wikipedia/commons/4/45/Mc_Donnell_Douglas_F4-F_Phantom_v.jpg)
Most aircraft have been designed with planar wings with simple dihedral (or anhedral). Some older aircraft such as the
Beriev Be-12
The Beriev Be-12 ''Chayka'' ("Seagull", NATO reporting name: Mail) is a Soviet turboprop-powered amphibious aircraft designed in the 1950s for anti-submarine and maritime patrol duties.
Design and development
The Beriev Be-12 was a successo ...
were designed with
gull wing
The gull wing is an aircraft wing configuration, known also as ''Pulaski wings'', with a prominent bend in the wing inner section towards the wing root. Its name is derived from the seabirds which it resembles. Numerous aircraft have incorporat ...
s bent near the root. Others, such as the
Vought F4U Corsair
The Vought F4U Corsair is an American fighter aircraft which saw service primarily in World War II and the Korean War. Designed and initially manufactured by Chance Vought, the Corsair was soon in great demand; additional production contracts ...
, used an inverted gull wing design, which allowed for shorter landing struts and extra ground clearance for large propellers and external payloads, such as external fuel tanks or bombs. Modern polyhedral wing designs generally bend upwards near the wingtips (also known as ''tip dihedral''), increasing dihedral effect without increasing the angle the wings meet at the root, which may be restricted to meet other design criteria.
Polyhedral is seen on
glider
Glider may refer to:
Aircraft and transport Aircraft
* Glider (aircraft), heavier-than-air aircraft primarily intended for unpowered flight
** Glider (sailplane), a rigid-winged glider aircraft with an undercarriage, used in the sport of glidin ...
s and some other aircraft. The
McDonnell Douglas F-4 Phantom II
The McDonnell Douglas F-4 Phantom II is an American tandem two-seat, twin-engine, all-weather, long-range supersonic jet interceptor and fighter-bomber originally developed by McDonnell Aircraft for the United States Navy.Swanborough and Bow ...
is one such example, unique among jet fighters for having dihedral wingtips. This was added after flight testing of the flat winged prototype showed the need to correct some unanticipated spiral mode instability – angling the wingtips, which were already designed to fold up for carrier operations, was a more practical solution than re-engineering the entire wing.
[Donald, David and Jon Lake, eds. ''McDonnell F-4 Phantom: Spirit in the Skies''. London: AIRtime Publishing, 2002. .]
References
Footnotes
Notes
External links
* http://www.aeroexperiments.org/washoutbillow.shtml
Demonstration of dihedral effecton
Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields. It is hos ...
Video explanation on Real Engineering
YouTube
YouTube is a global online video platform, online video sharing and social media, social media platform headquartered in San Bruno, California. It was launched on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim. It is owned by ...
channel
{{DEFAULTSORT:Dihedral (Aircraft)
Aerodynamics
Aircraft configurations
Aircraft wing design
Wing configurations