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How gliders could circumnavigate the globe against the jet stream.

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Abstract and Figures

Dynamic soaring could enable perpetual flight by gliders. If albatrosses can soar in flapless flight into a strong wind to gain altitude and airspeed, then gliders and UAVs can as well. Glider pilots just haven’t worked out the mechanics of copying albatrosses by dynamic soaring into a steady wind. Dynamic soaring involves similar airflows and forces to boats sailing and gliders slope soaring. In addition, if sailboats can circumnavigate the globe without engines against the wind, then so can a glider in principle, which has never been done before.
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How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
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How$gliders$can$circumnavigate$the$globe$$
by$soaring$against$the$jet$stream.$$
Dynamic$soaring$enables$perpetual$flight.$
$
$
$
$
Mr.$Nicholas$Landell-Mills$$$
30$$June$$2022$
Pre-Print$DOI:$$$10.13140/RG.2.2.18506.52162/1;$$$$$
CC$License:$CC$BY-SA$4.0$
Keywords:$$Aerodynamics;$flight;$glider;$lift;$Newton;$physics;$UAV.$
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Fig.!1a!!!Circling!the!Earth.!!
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Abstract$$
If albatrosses can soar in flapless flight into a strong wind to gain altitude and airspeed, then gliders and UAVs can as well.
Glider pilots just haven’t worked out the mechanics of copying albatrosses by dynamic soaring into a steady wind. Dynamic
soaring involves similar airflows and forces to boats sailing and gliders slope soaring. In addition, if sailboats can
circumnavigate the globe without engines against the wind, then so can a glider in principle, which has never been done
before. See Fig. 1a.
The argument is supported by a novel explanation of soaring by
Newtonian mechanics (Force = ma) and absolute airflow analysis. The
glider passively re-directs a mass of air (m) from an oncoming airflow
(headwind). The air decelerates (a) and creates turbulence when it
interacts with the undisturbed wind at the trailing edge of the wing.
The reactive equal and opposite forward force generates thrust,
pushing the glider forwards and up. Similar to a boat sailing into a
wind, the glider steals momentum from the air by slowing it down.
This is a new explanation of soaring. See Fig. 1b. Fig. 1b. Newtonian forces soaring.
1. INTRODUCTION
A. Significance.
This analysis is significant because it is the first to use
Newtonian mechanics based on the mass flow rate and absolute
airflow diagrams, to explain how the lift generated (Lift = m/dt *
dv) dynamic soaring into a steady wind is feasible. This
approach differentiates between forces actively generated
gliding, and passively generated soaring. Tis analysis has not
been provided previously.
This analysis challenges the prevailing view that special
conditions such as a wind shear, slope soaring or flying in loops
are required. Dynamic soaring could allow gliders and UAVs to
achieve perpetual flight, increasing their endurance and range.
Lift is of fundamental importance to aviation. The Newtonian
approach is a radically new explanation of lift, which challenges
the prevailing view that fluid mechanics and/or vortices explain
the lift generated by wings.
The Newtonian approach provides new and useful insights
into lift that fluid mechanics (e.g. Navier-Stokes equations) and
other theories have failed to do over the last hundred years. For
example, Navier-Stokes equations cannot explain how a glider
can gain airspeed while slope soaring or how an albatross can
gain airspeed while dynamic soaring.
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B. Benefits.
This simple and easily understood Newtonian explanation of
lift can help glider pilots understand lift and how to achieve
dynamic soaring for the first time.
The possibility to fly by extracting energy from the wind
could produce significant economic benefits to the aviation
industry and the gliding sport. Others have proposed that gliders
could use the jet stream to extract the energy needed for flight,
but based on using a wind shear. [44][45] This is the first paper
to use Newtonian physics to explain how dynamic soaring into a
steady wind is feasible.
The concept of a cargo motor-glider using dynamic soaring in
a wind shear was proposed by the Experimental Soaring
Association (ESA) at least as early as 2018. It could provide an
environmentally friendly, faster and cheaper alternative to
standard transport of goods by ships. [44]
Explaining the physics for how gliders can fly into a wind to
gain altitude and airspeed represents dramatic progress in
aerodynamics. This may well be akin to the Portuguese in the
15th Century working out how to sail large boats into the trade
winds. This development allowed for the first recorded
circumnavigations of the world and a growth of global trade.
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Contents:$
1.$Introduction$..........................................................$1$
2.$Background$...........................................................$3$
$
3.$Newton$$Explains$$Lift$...........................................$4$
4.$Airflow$$Analysis$...................................................$9$
5.$Angle-of-Attack$$(AOA)$.......................................$11$
$
6.$Dynamic$$Soaring$$Explained$...............................$12$
7.$Evidence$$of$$Soaring$...........................................$14$
8.$Example$$Calculation$$of$$Lift$...............................$18$
$
9.$Discussion$$of$$Results$.........................................$21$
10.$Conclusions$.........................................................$23$
11.$Additional$$Information$......................................$23$
12.$References$..........................................................$23$
Appendix$$I$$$$Definitions$..............................................$25$
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2. BACKGROUND
A. Passive vs. Active lift generation.
Fig. 2b-i. Passive and active creation of forces.
Stationary and moving airfoils generate forces differently.
More precisely, an airfoil (e.g. wing, propeller blade or sail) can
passively or actively create forces, calculated based on the same
Newtonian equation for the mass flow rate (Force = m/dt * dv).
See Fig. 2b-i.
1) An oncoming relative airflow (headwind) can be passively
re-directed by a stationary airfoil. The mass of air re-
directed each second (m/dt) decelerates (dv) on contact
with the undisturbed wind, at the trailing edge of the
airfoil. This process produces turbulence and creates a
backward force (Force BACK = m/dt * dv). The inertia of
the air provides resistance, allowing for a reactive equal
and opposite forward force (thrust) to be generated.
2) A moving airfoil can actively accelerate a mass of static
air each second (m/dt) to a velocity (dv) downward and
slightly forwards, creating a downward force (Force DOWN
= m/dt * dv). The inertia of the static air allows for
reactive equal and opposite upward force to be generated.
The key differences of passive and active forces include:
- The reaction to passive forces arises due to the change in
inertia from the decrease in velocity of the relative airflow
(wind) at the trailing edge of the airfoil, which produces
turbulence. In contrast, the reaction to active forces arises
from the inertia of the static air accelerated by the airfoil.
- The direction of the force generated by active force is
almost perpendicular to the alignment of the airfoil, but for
passive forces it is close to the alignment of the airfoil.
- Passively generated forces produce wake turbulence,
with no air being circulated and no vortices. In contrast,
actively generated forces produce spirals of streamlined
laminar wake airflow, which circulates around the two
turbulent wingtip vortices. See Fig. 2b-ii.
Fig. 2b-ii. Turbulent vs. smooth wake airflows.
B. Relative vs. Absolute airflow analysis.
Wing airflow diagrams are of fundamental importance as they
provide the basis of analyzing how airflows create lift. Wing
airflows can be depicted in relative or absolute terms. Both
diagrams show the same airflow but in different ways. See Fig.
2c.
Fig. 2c. Relative and absolute airflows. [55][36]
These two different wing airflow diagrams are compared:
1) Relative wing airflow diagrams have been used for the
last hundred years as the basic template by fluid
mechanics to analyse how wings interact with airflow to
generate forces like lift. For example, relative wing
airflow diagrams accurately reflect how moving air
interacts with a stationary wing in wind tunnels.
However, wingtip vortices and the circulation of the air
behind the aircraft are notably absent from the relative
wing airflow diagrams and any passive force generation
(i.e. thrust or lift generation) by a wing in practice.
According to Newtonian mechanics, relative wing airflow
diagrams are an example of passive force creation. In
addition, it is wrong to use relative wing airflow diagrams
to analyze how a wing actively generates lift.
2) Absolute wing airflow diagrams show a wing or aircraft
moving through stationary air. This is a new type of
diagram derived form the airflows observed behind
airplanes flying through clouds.
The wings push air downwards, which is circulated either
side of the airplane around the two wingtip (wake) vortices
According to Newtonian mechanic, this diagram
accurately describes active force creation by a wing.
Summary
The analysis above demonstrates that the prevailing method
employed by fluid mechanics to analyze how an airplane wing
actively generates lift using relative wing airflow analysis is
wrong, and the absolute airflow analysis based on Newtonian
mechanics is correct.
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3. NEWTON EXPLAINS LIFT
A. Lift = m/dt * dv [3]
Newtonian mechanics based on the mass flow rate (Lift =
m/dt * dv) and a transfer of momentum is used to explain
passive (soaring) and active (flying / gliding) lift generation
using absolute airflow analysis. The argument for Newtonian
mechanics is presented below for each type of flight: See Fig
3a-i.
a) Soaring.
b) Normal flight / gliding.
c) Up-current (thermal).
Fig. 3a-i. Three different methods how
a glider can generate lift.
The three methods of generating a force (lift) summarized:
a) While soaring, the glider wings passively re-direct a
headwind (relative airflow) to decelerate (dv) a mass of air
each second (m/dt) backwards. This action creates
turbulence and a backwards force (Force BACK = ma = m/dt
* dv). The reaction creates forward thrust, similar to how a
boat sails into wind or a albatross soars into a wind.
Momentum is transferred from the air to the glider to
generate the thrust.
b) In flight or glide the wings actively accelerate a mass of
air each second (m/dt) to a velocity (dv) downwards. This
action creates a force (Force DOWN = ma = m/dt * dv). The
reaction generates an upward force that provides lift to
push the glider upward. Momentum is transferred from the
glider to the air to generate the force.
c) In an up-current such as a thermal, the glider is simply
gains altitude as it rises upwards within the a large rising
mass of air. The relative airflow (thermal) is not pushing
the glider upwards to generate lift as there is no equal and
opposite force.
However, As the glider ascends, it trades altitude for
airspeed to maintain forward motion, similar to (b) above.
The glider is flying downwards in a rising mass of air. The
glider gains altitude as long as the speed of the up-current
exceeds the rate of descent (glide).
Abbreviations and formula used:
- m = Mass of air flown through and pushed down.
- m/dt = Mass flow rate.
- dt = Change in time (per second).
- dv = Change in velocity (v) of the air displaced down.
- v = Velocity of the air displaced downwards.
- a = dv/dt = Acceleration.
- Force = ma = m * dv/dt = m/dt * dv [1]
- Force = ma = m * dv/dt = d(m/v)/dt [1]
- Momentum = mv [1]
The Newtonian forces acting on the glider are described in
more detail below:
(a) Soaring explained by Newtonian mechanics
Fig. 3a-ii. Newtonian forces acting on a glider soaring.
‘Soaring’ refers to an aircraft that passively generates lift to
fly from a headwind. e.g. Slope soaring or dynamic soaring. A
glider can soar into a headwind (relative airflow), irrespective of
whether the headwind is rising or horizontal. See Fig. 3a-ii.
Wings with a positive AOA re-direct a mass of air each
second (m/dt) of the apparent wind (relative airflow) against the
undisturbed wind behind the wings to decelerate (dv) and create
turbulence. This action creates a backwards force:
Force BACK = m/dt * dv
The inertia of the air decelerated allows for the creation of a
reactive equal and opposite forward force (Thrust) to be
generated; as summarized by the equation:
Force BACK = m/dt * dv = Thrust
In other words, the turbulence provides the re-directed wind
something to push against. Thrust can be applied by the glider to
gain forward airspeed and/or lift. The stronger the headwind,
then the greater the thrust that the albatross can generate.
This process of thrust generation is possible because the
glider steals momentum from the air by slowing the air down.
Momentum is transferred from the air to the glider.
Evidence of soaring by aircraft includes:
- Slope soaring by remote-controlled gliders at hilltops.
- Airplanes (e.g. super cubs) and hang gliders have been
observed to achieve near-VTOL performance in strong
winds with little or no engine power.
The airflows and resultant forces on a glider (sail-planes)
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soaring are similar to an albatross dynamic soaring and a boat
sailing into wind. See Fig. 3a-iii.
Fig. 3a-iii. Airflows sailing and an albatross soaring.
Slope soaring vs. Dynamic soaring
- In slope soaring, the rising wind pushes the glider up and
backwards. The wings re-direct the airflow to generate a
forward and upward force. See Fig. 3a-iv.
As compared to dynamic soaring, in slope soaring the
glider’s nose is pointed more downwards, to maintain
the same AOA as dynamic soaring.
- In dynamic soaring, the horizontal wind pushes the
glider backwards. A glider’s ability to soar depends on
how well its wings convert the apparent wind into lift.
- In slope and dynamic soaring, the glider alters its AOA
to select the desired mix of airspeed and altitude.
Fig. 3a-iv. Airflows slope soaring v. dynamic soaring.
In addition, gliders slope soaring are observed to benefit from
a rising air mass. For example, an onshore sea breeze that is
pushed up by a hill along a coastline is often used by gliders for
slope soaring. See Fig. 3a-v. In contrast, gliders dynamic soaring
typically face a horizontal relative airflow (headwind).
Fig. 3a-v. Slope soaring along a coastline.
Gliders slope soaring generate so much forward thrust that
they are able to easily fly directly forwards into the wind and
traverse across the wind at high speeds in loops or figure of
eight flight patterns. These observations are consistent with the
description of passive force generation above. See Fig. 3a-v.
(b) Gliding explained by Newtonian mechanics
Fig. 3a-vi. Newtonian forces acting on a glider flying.
‘Gliding’ is the unpowered descent by an aircraft that actively
generates lift to fly. This is what most people commonly
understand as gliding. See Fig. 3a-vi.
A glider can trade altitude for airspeed while flying forwards.
This process is the same principle of dropping an object; as the
object falls it loses altitude and gains velocity due to gravity.
Some of this airspeed gained is then converted into lift by the
wings with a positive AOA. The wings accelerate a mass of air
flown through each second (m/dt) to a velocity (dv) downwards,
to create a downwards force, as summarized by the equation:
Force DOWN = ma = m/dt * dv (1)
The inertia of the air provides resistance to the downward
force. The reactive equal and opposite upward force provides
lift, as summarized by the equation:
Force DOWN = Force UP (Lift) (2)
Lift is the vertical component of the upward force. If induced
drag is negligible, then lift equals the upward force and the
equations (1) and (2) can be combined as follows:
Force DOWN = Force UP (Lift) = m/dt * dv (4)
Or simply: Lift = m/dt * dv (5)
Units: N = kg/s m/s
This process of lift generation is possible because momentum
is transferred from the glider to the air.
Evidence for wings pushing air down in flight is provided by
the downwash from airplanes disrupting dust on the ground and
cloud patterns.
According to absolute airflow analysis in passive and active
force generation there are two separate airflows. One airflow is
above the wing, and the other is below the wing.
‘m/dt’ depends on the volume of air flown through and air
density. The volume of air flown through depends on airspeed,
wingspan, and wing reach (i.e. wing AOA and wing thickness).
‘dv’ depends primarily on aircraft momentum (airspeed and
mass), wing AOA, and wing depth (chord).
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B. Additional considerations.
The time (dt) component of: Lift = m/dt * dv
The thin layer of air flown through by the wings is time
dependent, and therefore, is expressed as the mass flow rate
m/dt’, and not just ‘m’. i.e. The mass of air displaced by the
wing increases with airspeed.
The change in velocity of the air flown through and pushed
downward is expressed as ‘dv’. It is not expressed as
acceleration ‘dv/dt’, because this action is due to a one-off force
(impulse) from the wings against the air. This force is not
continuously applied to the same mass of air (e.g. air
molecules), and therefore, not time dependent.
Absolute wing airflow analysis
Airflows are described according to absolute airflow analysis.
The underside of the wing pushes the air down. A vacuum of
low air pressure on the topside of the wing pulls (sucks) the air
above it downwards, helped by the Coanda effect.
Lift distribution across the wings
‘m/dt’ and ‘dv’ are often presented as a single number. But in
practice ‘m/dt’ and dv’ vary a lot vertically and horizontally
across the wings. See Fig. 3b-i.
Fig. 3b-i. ‘m/dt’ and ‘dv’ created by a wing.
Lift distribution generated by wings varies with airspeed,
aircraft configuration, and flight manoeuvers. The 3D lift
distribution is illustrated in Fig. 3b-ii.
Fig. 3b-ii. ‘m/dt’ and ‘dv’ created by a wing.
Supplementary considerations:
- The lift required to fly depends solely on the aircraft’s
mass. How efficiently wings generate lift varies
- Gliders are unpowered. There are no engines to contribute
to lift.
- This analysis only relates to the wings. It does not include
the affects from the tail or fuselage.
- According to Newtonian mechanics, a wing cannot
generate lift unless it displaces air downwards.
C. The momentum theory of lift.
There is no net gain or loss of momentum, energy and mass
in this process of generating lift.
In flight from active lift generation, wings transfer
momentum and kinetic energy from the aircraft to the air, by
accelerating the air down to generate lift. See Fig. 3c.
Fig. 3c. Newtonian forces (momentum) acting on a glider.
The downward force created by the transfer of momentum is
expressed as the equation:
Force DOWN = ma = d(mv)/dt (6)
Combining equations (2), (3) and (6) allows lift to be
expressed as the change in momentum of the air:
Force DOWN = Force UP (Lift) = d(mv)/dt (7)
Or simply: Lift = d(mv)/dt (8)
Units: N = (kg m/s) /s
Momentum is transferred from the aircraft to the air, to
generate lift in stable flight. At constant power from the engines,
momentum can only be transferred from the aircraft to the air, to
increase lift (e.g. by increasing the wing AOA) at the cost of
lower airspeed. This means that the aircraft trades lower
airspeed for greater altitude.
D. Two Newtonian equations for lift.
The analysis above provides two Newtonian methods and
equations to calculate the lift generated by a wing:
Lift = ma = m/dt * dv (mass flow rate) (5)
Lift = ma = d(mv)/dt (momentum theory) (8)
Both lift equations (5) and (8) are based on Newtons 2nd Law
of motion (Force = ma). Both are correct and produce the same
values, but express the same thing slightly differently.
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E. Free-fall skydiving v. Wingsuits (gliding).
To illustrate the physics involved, a skydiver in free-fall is
compared to a wingsuit flyer. See Fig. 3e-i.
Fig. 3e-i. Skydiving v. Wingsuits
Newtonian physics explains both free-fall skydiving and a
wingsuit gliding. Both fall through a mass of air each second
(m/dt) that they accelerate to a velocity downwards (dv), to
create a downward force (Force DOWN = m/dt * dv). The reaction
generates an equal and opposite upward force (lift).
The direction of the force generated is controlled by adjusting
the angle-of-attack (AOA). See Fig 3e-ii.
Fig 3e-ii. Newtonian forces acting on a skydiver and wingsuit.
The physics of skydiving and wingsuits compared:
- The wingsuit has greater surface area facing downwards
as compared to a skydiver. This increases the ‘m/dt,’ and
therefore, the lift generated.
- The skydiver falls in a near vertical descent and
generates minimal forward airspeed.
- For the skydiver and wingsuit, their underside pushes air
out of their path, and their topside creates a vacuum
above it that pulls air downwards.
The big difference is that the wingsuit has a lower AOA
and benefits, from additional air pulled down due to a
much stronger Coanda effect. This increases ‘m/dt’
significantly, and therefore, boosts the lift generated.
Consequently a wingsuit falls at a slower rate than a
skydiver.
- While the skydiver falls directly downward, the wingsuit
can control the speed and direction of their glide
downwards by adjusting their AOA. This allows the
wingsuit to trade altitude for forward airspeed and/or lift.
- If the wingsuit accelerates the air fallen through
backwards, they generate a forward force, providing
them with forward motion and airspeed.
- ‘dv’ generated by the skydiver is higher due to the
skydiver’s higher descent velocity, and therefore, the
higher momentum.
To help illustrate the physics involved in gliding according to
Newtonian mechanics, a glider in free-fall is compared to a
glider in a glide.
Gliders can control the speed of their glide and descent
downwards by adjusting the AOA. This process allows gliders
to trade altitude for airspeed and/or lift.
According to Newtonian mechanics; The glider’s AOA and
momentum affects the mass of the air displaced each second
(m/dt) and/or the velocity that this air is accelerated downwards
(dv). This controls the downward force (Force = ma = m/dt *
dv) and lift generated. See Fig. 3e-iii.
Compared to a glide trajectory, in a straight-down free-fall a
glider falls at a much higher airspeed:
a) Despite a higher airspeed, ‘m/dt’ falls dramatically as only
the underside of the wing displaces air. The topside of the
wing displaces almost no air. Also, air is displaced
inefficiently due to: increased airflow turbulence and a
reduced Wing Reach and Coanda effect.
b) Whereas, ‘dv’ increases, albeit at angle sideways. But this
is not sufficient to offset the lower ‘m/dt’.
Fig. 3e-iii. Different descents of a glider compared.
The logic of Newtonian mechanics is that the net effect of the
any changes to ‘m/dt’ and ‘dv’ is zero between free-fall and a
glide; irrespective of the trajectory.
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F. Kinetic Energy for lift.
This Newtonian explanation of lift is consistent with the
standard equation for kinetic energy: K.E. = 0.5 mv2 [1]
The kinetic energy for lift depends on the mass of the air
flown through (‘m’) and the square of the velocity (‘v’) to which
it is accelerated downwards.
For example, wings need to use four times the kinetic energy
(K.E. x4) to accelerate the air flown through downwards twice
as fast (‘dv’ x2). See Fig. 3f-i.
Fig. 3f-i. Graph of kinetic energy and velocity.
This calculation and insight was not possible previously using
other theories of lift (such as fluid mechanics).
The kinetic energy transferred to the air depends on a number
of factors such as: the wing AOA, wingspan, wing depth (chord)
and the momentum of the aircraft.
Gliders high aspect ratio wings provide a more energy
efficient form of flight. This is because the glider’s long
wingspan (high aspect ratio wings) maximizes the mass of air
flown through each second (m/dt) rather than the velocity that
this air is accelerated downwards (dv). Also gliders curved
wingspans maximize the Coanda effect. See Fig. 3f-ii.
Fig. 3f-ii. Glider wings.
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4. AIRFLOW ANALYSIS
A. Two airflows. [3]
Airflows need to be laminar (smooth) to generate lift.
Turbulence reduces lift as it reduces both ‘m/dt’ and ‘dv’. There
are two key airflows involved in flight above and below the
wings. See Fig. 4a-i.
Fig. 4a-i. Two airflows on a wing side view
(i) The underside of a wing physically pushes the air flown
through below it downwards and slightly forwards. This creates
high air pressure under the wing based on the standard equation
for pressure (Pressure = Force /Area [1]).
(ii) As the wing moves forwards, the topside pulls air above it
downwards for two reasons:
- First, a vacuum or low air pressure arises on the topside of
the wing, which pulls the air above the wing downwards.
The low air pressure on top of the wing is greatest towards
the trailing edge of the wing, as the upper air mass has the
furthest to travel downwards at this point on the wing. The
faster the wing flies, the stronger the vacuum or low air
pressure is on top of the wing, and the faster the upper mass
is pulled down. See Fig. 4a-ii.
Fig. 4a-ii. 2D diagram of upper wing airflows.
As the air below the wing is being pushed down, it cannot
easily be pulled upwards by the low air pressure above the
wing. Therefore, by default, the low air pressure above the
wing must pull the air mass above the wing downwards.
- Second, any curvature on the topside of the wing can
enhance downward airflows of the air above the wing due
to the Coanda effect; As explained below.
The low and high-pressure patterns created above and below
the wing, are a consequence of the airflows and resultant forces,
not causes of lift.
The two wing airflows are described:
1) The underside of a wing physically pushes the air flown
through below it downwards and slightly forwards. This
creates high pressure on the underside surface of the wing,
based on the standard equation for pressure (Pressure =
Force /Area [1]). See Fig. 4a-iii.
Fig. 4a-iii. Underside of the wing pushes air down
2) On the topside of the wing a zone of low air pressure
arises, due to the forward movement of the wing creating a
relative vacuum (void) behind it. See Fig. 4a-iv.
Fig. 4a-iv. Vacuum behind the topside of the wing.
The upper air mass above the wing is pulled downwards
towards the topside of the wing by the low air pressure
zone, helped by gravity.
In addition:
- After the wing has passed forwards, the upper air mass
continues to descend from the momentum it gained.
- Any curvature on the topside of the wing can enhance
downward airflows of the air above the wing due to
the Coanda effect, as explained below.
- The air above the wing pulled downwards reaches the
trailing edge on the wing, to avoid triggering a stall.
- The low air pressure on top of the wing is typically
described as being greatest towards the leading edge.
- The theoretical path of an air molecule starting above
the wing and travelling downward, as the wing passes
through the air, is illustrated in Fig. 4a-v.
Fig. 4a-v. Theoretical path of an air molecule
starting above the wing.
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B. The Coanda effect Spoon experiment.
Fluid flow naturally follows a curved surface due to the
Coanda effect. For example, water falling from a tap is re-
directed by the curved side of a spoon demonstrating the Coanda
effect, as illustrated in Fig. 4b-i.
Fig. 4b-i. Coanda effect Spoon experiment.
According to Newtonian mechanics, the water flow passively
re-directed by a spoon due to the Coanda effect creates a small
turning force due to the change in momentum of the water flow.
The reactive equal and opposite force pushes the spoon
diagonally to the left sideways and downward. However the
spoon pivots to the left as far as the reactive force allows.
The change in momentum can be calculated using the
standard Newtonian equation based on the mass (m) and
velocity (v) of the water re-directed each second (dt); as
summarized by the equation:
Force = ma = d(mv)/dt
Other explanations of the spoon experiment
A common explanation of this experiment is that the spoon
remains attached to the water flow due to the water’s surface
tension; water is ‘sticky’. However, this explanation not an
accurate depiction of what is observed. Water’s ‘stickiness’ may
explain the Coanda effect, but not the resultant forces arising.
Similar experimentsPing-Pong ball
Similar experiments with curved objects, such as balls and
wings, have produced comparable results. However, researchers
made different explanations and conclusions regarding the
forces involved. See Fig. 4b-ii.
Fig. 4b-ii. Coanda effect ping pong ball experiment.
C. The Coanda effect and laminar airflows.
Wind tunnel experiments
Wind tunnel experiments demonstrate airflows arising due to
the Coanda effect on the topside of a curved airplane wing, as
well as the turbulence that arises on a flat wing. See Fig. 4c-i.
Fig. 4c-i. Airflow on curved and flat wings. [55]
However, wind tunnel experiments are an example of moving
airflows being passively re-directed by a wing,. This is different
to what occurs in practice: a wing actively pushing static air
downwards. Nonetheless these provide a useful demonstration
of the Coanda effect.
The amount of air re-directed by the Coanda effect depends
on the maintenance of laminar (smooth, non-turbulent) airflow
on the topside of the wing to maximize the amount of air
displaced down each second (m/dt). The airflows are shown by
wings in wind tunnel experiments. See Fig. 4c-ii.
Fig. 4c-ii. Smooth vs. turbulent airflows on a wing. [56]
Wings produce a stronger Coanda effect with laminar airflow
at a lower AOA, higher airspeed, and where the wings are
deepest (largest chord, such as near the fuselage). Conversely,
the Coanda effect is weakest at high AOA, slower airspeeds, and
where the wings are narrow (i.e. short chord).
Coanda effect and fighter jet wings
Some fighter jet wing and fuselage designs show pronounced
curvature that maximizes the Coanda effect. See Fig. 4c-iii.
Fig. 4c-iii. Curved fuselage designs of jets.
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11
5. ANGLE-OF-ATTACK (AOA)
A. Angle-of-attack (AOA).
The angle of attack (AOA) is the angle between the zero-lift-
line of the glider’s wing and the relative wind. To put it another
way, this is the angle between the glider’s heading (orientation)
and the direction of its glide. In static air, the relative wind is
provided by the direction of the glide. See Fig. 5a and 5b.
Fig. 5a. Glider AOA.
The angle of attack (AOA) is critical as it directly affects:
‘m/dt’ and ‘dv’, and therefore the lift generated (Lift = m/dt *
dv). The AOA also affects drag from the wings and fuselage, as
well as the additional lift provided by the engines when pointed
downwards.
(i) AOA affects the mass of air flown through and displaced
downwards (m/dt) via how much air the underside of the glider
pushes down, as well as how much air above the glider is pulled
down. In turn this determines the wing reach, which is the
vertical distance that the wings affect the air. This includes the
air directly flown through by the wings. See Fig 5b and 5c.
Fig. 5b. Wing reach.
See definitions in Appendix I.
(ii) AOA affects ‘dv’ via the angle that the air is displaced
downwards and the speed to which this air is accelerated. As lift
is simply the vertical component of the upward force, then lift
only depends on the air pushed directly downwards. Any energy
or force used to push the air flown through sideways, does not
contribute towards lift.
This means that the glider can maximize how efficiently lift is
generated by adjusting the AOA to balance ‘m/dt’ and ‘dv’ for a
given airspeed and drag created.
Fig. 5c. The forces on a glider wing.
B. Changes in the Angle-of Attack (AOA).
AOA has a complicated impact on lift, as many factors are
inter-related. In general, by altering the AOA a glider can trade
altitude for airspeed and/or lift. A complication is that airspeed
also affects lift. Newtonian mechanics can be used to help
understand how changes in AOA impact lift, as shown below.
For example, take an unpowered glider in a typical stable
descent through static air. If the pilot decreases the AOA, by
pushing the control stick forwards. Then the glider adopts a
steeper (‘nose-down’) profile to the direction of travel. The
vertical descent and forward airspeed increase as the glider
adopts a steeper descent. See Fig. 5d.
Fig. 5d. Lower AOA.
Assuming that the airflow remains smooth (laminar) and non-
turbulent, how a lower AOA affects lift depends on the net
impact on airflows of various dynamics:
a) A steeper descent increases airspeed. Higher airspeed then
produces more lift, as lift is proportional to velocity2 (Lift
ó Glider Velocity2). In short, this is because a faster glider
flies through more air each second (m/dt) and accelerates
this air more aggressively downwards (dv) due to its
greater momentum. This produces a greater downward
force and thus greater lift.
b) b) However, the process is not straightforward. A lower
AOA reduces the vertical height of the wing exposed to the
direction of travel, which reduces drag. But it also reduces
the wing reach and therefore ‘m/dt’; which decreases lift.
c) A lower AOA changes the direction and velocity that
‘m/dt’ is accelerated down by the wings. i.e. The angle and
velocity of the ‘dv’ changes; impacting lift.
In summary, lower AOA causes:
a) Less drag : Higher airspeed : More Lift.
b) Wing reach decreases :’m/dt’ falls : Less Lift.
c) Angle and velocity of ‘dv’ changes : Lift changes.
In summary, adopting a lower AOA affects airspeed and lift
depending on the net impact on the wing airflows of ‘m/dt’ and
‘dv’; and therefore the lift generated (Lift = m/dt * dv).
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
12
6. DYNAMIC SOARING EXPLAINED
A. The enigma solved. [11]
The enigma of dynamic soaring is that albatrosses can gain
altitude & airspeed when flying into wind, without flapping its
wings to achieve airspeeds faster than the wind itself. For
example, albatrosses have been observed to soar at about 30
km/hr into a 13 km/hr wind. [50] The stronger the wind, the
better albatrosses can soar. See Fig. 6a-i.
Fig. 6a-i. Albatross flying into wind. [51]
Dynamic soaring faces two unexplained questions:
i. How is a forward force generated from a headwind?
ii. How does an albatross avoid being blown backwards?
The solution according to Newtonian mechanics:
The albatross’ wings passively re-direct a mass of air each
second (m/dt) from the apparent wind back and downward, at a
velocity relative to the albatross (dv), helped by the Coanda
effect. The re-directed airflow decelerates when it interacts with
the undisturbed wind, to create turbulence. The turbulence
provides something for the re-directed air to push against, and
this action creates a backward force (Force BACK = ma = m/dt *
dv). The equal and opposite force (Thrust = m/dt a dv) pushes
the albatross forwards and up, soaring. See Fig. 6a-ii.
Fig. 6a-ii. Coanda effect on an albatross’s wing.
According to Newtonian mechanics, a stronger wind
increases both ‘m/dt’ and ‘dv’, and therefore, increases the
thrust generated (Thrust = m/dt * dv). Similarly, a kite cannot
fly and a boat cannot sail if there is not enough wind.
The albatross can then apply the thrust generated to gain
altitude and or airspeed as needed or desired. The albatross can
maintain a stable altitude if the thrust generated soaring is at
least equal the backward force from the wind. The forces act
simultaneously, allowing the albatross to hover in a wind or fly
in loops.
The role of gravity
In the same way that a sail boat uses its keel to provide
resistance and being blown backwards. An albatross uses gravity
to prevent itself from being blown backwards (downwind). This
is because an albatross can trade altitude for airspeed, in the
same way that any object dropped gains velocity as it loses
altitude.
Trading altitude for airspeed is easily achieved by altering the
wing AOA. The bird’s head is pointed down and it shifts its
center of mass towards the front. The more the albatross points
its body down, the more altitude is lost and the greater the
airspeed that is gained.
The albatross can only achieve this trade-off due to the
existence of gravity and the ability to create turbulence by re-
directing the wind. For instance, this trade-off does not exist in a
zero gravity environment such as outer space.
Additional considerations
- This logic applies to any bird or glider soaring into wind.
Birds with high aspect ratios (long wingspans) like
albatrosses are able to benefit from dynamic soaring as the
can re-direct a larger mass of air each second (m/dt).
- Insect and hummingbird wings are relatively rigid and flat
with little curvature, so benefit little from the Coanda
effect. This limits their ability to achieve dynamic soaring.
- Insects and humming birds are not observed to achieve
dynamic soaring or gliding partly due to the lack of
curvature on their rigid wings. Insect and hummingbird
wing structure, physiology, and kinematics are very
different to most birds who can gliding and achieve
dynamic soaring.
Comparisons to a kite and sailboat
A kite and paraglider are pushed upwards, and a sailboat is
pushed forwards, by the wind, which can be explained by the
same Newtonian physics. See Fig. 6a-iii.
Fig. 6a-iii. Forces acting on a kite and sailboat.
The underside of the kite has a positive AOA, which re-
directs airflow (wind) downwards. The reactive equal and
opposite upwards force pushes the kite up, gaining altitude.
However, a kite cannot replicate dynamic soaring where the kite
gains airspeed and altitude, as its topside of the kite does not re-
direct any wind.
The wind re-directed by the underside is insufficient to
generate dynamic soaring. This aspect explains why a kite is
tethered to the ground to avoid being blown downwind.
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B. Background.
Dynamic soaring defined.
Dynamic soaring is where a bird or glider can increase
airspeed and/or altitude by flying directly into a strong wind.
Dynamic soaring is the reverse of what pilots expect, which is
for the aircraft to be blown backwards by a headwind. See Fig.
6b-i.
Fig. 6b-i. Albatross dynamic soaring.
Dynamic soaring differs to any process in which a rising air
mass pushes a bird or glider upwards, such as thermal soaring
and ridge soaring. Dynamic soaring also differs from a bird or
glider flying in loops being pushed upwards by a wind-shear or
slope gradient.
Increased airspeed v. higher altitude.
A bird or glider could use the force generated by dynamic
soaring to increase airspeed and/or altitude. It is a choice that is
available. A trade-off is available between airspeed and altitude.
When soaring into a wind to gain altitude, a glider may cease
to soar if the AOA increases excessively. At this point the glider
is simply flying upwards and loses airspeed as it gains altitude.
Care needs to be taken to isolate the different processes and
forces that affect a glider in flight. For example, a glider may
gain altitude due to a wind shear, air up-current or slope
gradient. The glider may not be dynamic soaring. The wind may
simply be pushing the glider upwards, similar to how a wind
pushes a kite upwards.
This paper claims that a wind shear is not required for
dynamic soaring. Nor is flying is loops or circles required. The
physics of dynamic soaring is essentially the same as a boat
sailing across an incoming wind (into wind, but not directly into
the wind). Only a strong wind is required, which are plentiful.
Research into UAV dynamic soaring.
Numerous research articles analyse the possibilities for
dynamic soaring. But this tends to be restricted to: (i) Small and
light UAVs, (ii) In particular environmental circumstances, such
as in the presence of a wind shear. (ii) While conducting specific
flight patterns. [28][29]
Research and experiments has not been conducted for soaring
into a steady wind. If UAVs and RC gliders can soar using a
wind shear, then they should be able to soar into a constant
velocity wind.
Vector analysis of slope soaring.
In the examples of slope soaring, a glider can maintain a
stationary position relative to the ground when facing directly
into wind. This means that in a 25 kt wind, a glider is generating
a forward force sufficient to fly forwards at 25 kts,
This was an unresolved enigma. But the explanation is that
the wind and the wings (helped by the Coanda effect) are
generating vertical lift. The glider is then pointing its nose down
to trade altitude gained for forward airspeed. See Fig. 6b-ii.
Fig. 6b-ii. Forces acting on a glider slope soaring.
2006 USAF glider dynamic soaring?
Experiments in a full-sized glider (sailplane) in 2006 by a
USAF pilot, [23][24] may have confirmed that a normal, glider
could use dynamic soaring to gain altitude and airspeed while
flying into a wind.
The tests were conducted flying a glider in a loop in a wind
shear along a hilltop. The experiment was for a Masters thesis in
aeronautical engineering. A major media company (PBS)
documented the event, which is found in a youtube video. [24]
In the experiment the glider’s airspeed slowed as it ascended.
The glider finished the first loop at a airspeed 10 knots (about 19
km/hr) higher than it started. This is a relatively significant
increase in airspeed for one loop, which took less than a minute
to complete. See Fig. 6b-ii.
Fig. 6b-iii. Possible schematic of the glider path,
for one loop, showing the speeds recorded
by USAF glider experiment. [24]
It was not clear if the glider was actually dynamic soaring, or
simply benefitting from a slope gradient or air up-current when
ascending; but not when descending. It was also unclear if the
wind strength increased with altitude. Therefore it is not possible
to conclude if the glider was actually dynamic soaring.
The conclusions by the USAF pilot included: “The first was
that when encountering a wind shear, the sailplane must either
climb while facing a headwind or descend while traveling with a
tailwind in order to realize an energy benefit.”
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
14
7. EVIDENCE OF SOARING
A. Research into UAV dynamic soaring.
Numerous research articles analyse the possibilities for
dynamic soaring. But this tends to be restricted to: (i) Small and
light UAVs, (ii) In particular environmental circumstances, such
as in the presence of a wind shear. (ii) While conducting specific
flight patterns. [28][29]
Research and experiments has not been conducted for soaring
into a steady wind. If UAVs and RC gliders can soar using a
wind shear, then they should be able to soar into a constant
velocity wind.
Below is a summary of examples of aircraft soaring like
albatrosses; gaining altitude and airspeed while fling directly
into wind. The more dramatic and evident examples of soaring
are summarized below in Fig. 7a-i, 7a-ii, 7a-iii, and 7a-iv.
Fig. 7a-i. Unpowered airplane taking-off into wind. [40]
Fig. 7a-ii. Unpowered RC glider launched into wind. [43]
Fig. 7a-iii. Glider taking-off into wind from a hilltop. [53]
Fig. 7a-iv. Super cub landing on a beach. [47]
B. Evidence of airplanes soaring.
Evidence that airplanes can soar is provided by a security
video of an unpowered, unpiloted, small airplane that was
observed to take-off by itself in a strong wind, when parked on
the tarmac, not tied down. In the video the propellers were not
turning. [40] See Fig. 7b-i.
Fig. 7b-i. Unpowered airplane taking off into wind. [40]
On take-off, the airplane initially moved up and slightly
forwards; as shown in image (2) of Fig. 1e above. It was
soaring. The airplane’s trajectory is more evident if the images
from the video are superimposed. See Fig. 7b-ii.
Fig. 7b-ii. Airplane taking off into wind
- images superimposed. [40]
Nonetheless, for the airplane just to maintain its horizontal
position above the ground while airborne, without being blown
backwards by the wind, means that it was generating a forward
force sufficient to offset the force of the wind. See Fig. 7b-iii.
Fig. 7b-iii. Airplane soaring after take-off. [40]
The wing created a forward and upward force, in a manner
similar to how the sail of a boat creates forces and an albatross
soars; by re-directing the airflow from the wind.
A few seconds after becoming airborne, the airplane became
unbalanced and the nose was raised significantly, thereby
exposing more of the underside of the wings and fuselage to the
wind; as shown in image (3) in Fig. 1e above. The airplane
ceased to point into wind. It was then blown rapidly up and
backwards and out of view of the video camera.
A piloted airplane could have maintained the aircraft’s
balance allowing it to continue to gain altitude and airspeed. In
addition, a glider with a higher aspect ratio would have been
able to soar into the same wind with greater ease than the
airplane in the security video; due to a glider’s lower mass and
longer wingspan.
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15
C. Example of RC glider soaring.
It has been demonstrated that remote-controlled (RC) gliders
can increase altitude and airspeed (i.e. dynamic soar) when
flying directly into a strong wind along a wind shear along a
hilltop. These gliders could fly indefinitely
For example, a small RC glider is observed to fly loops into
the wind, and to hold a static position when facing into wind.
This was done in a wind shear along a small hill. The author of
the video incorrectly describes lift due to thermals, instead of a
wind shear. See Fig. 7c-i and ii.
Fig. 7c-i. Unpowered gliders soaring into wind. [41]
Fig. 7c-ii. Unpowered glider looping into wind. [41]
In this example, the glider flew only on the downward side of
the slope on the hill. This indicates that it was constantly
exposed to the same wind. The wind did not appear to increase
strength with altitude.
There are plenty of videos of RC gliders soaring into a wind
shear on youtube. These often show that the RC gliders gain so
much airspeed that it has to traverse from side-to-side along the
hilltop to avoid advancing to far away from the controller.
Another example, RC gliders are observed to exploit the wind
shear on the windward side of a mountain ridges, to gain
airspeed while flying in a circle, similar to the Raleigh Cycle.
[25] See Fig. 7c-iii.
Fig. 7c-iii. RC glider soaring on a hillside.
D. RC glider speed competitions; soaring.
Speeds of over 900 km/hr have been achieved by RC gliders
slope soaring. The gliders fly in loops along a hilltop in a strong
wind.
For example: World's fastest RC aircraft (glider) hits a
stunning 548 mph (882 km/hr) without a motor.” [42] This is
almost as fast as the cruising airspeed of commercial airliners
such as Boeing 787 and Airbus A320 at about 900 km/hr. This
was achieved by flying a RC glider repeated loops into a wind
that was gusting up to 106 km/hr. On each loop the RC glider
gained airspeed and momentum. See Fig. 7d-i.
Fig. 7d-i. RC glider flying loops into wind. [43]
Just to be clear, the RC glider was flown in oblique loops on
its side, not in the standard vertical loops. The RC glider was
travelling so fast that the wings were not critical to generate
enough lift, the tail and the fuselage was sufficient.
YouTube videos of unpowered RC gliders launched into the
wind at hilltops provide ample evidence of gliders soaring. After
launch the gliders gain altitude and airspeed as they advance
forwards into the wind. See Fig. 7d-ii.
Fig. 7d-ii. Unpowered RC glider launched into wind. [43]
Similarly, the landing was conducted into wind, and the
glider descended vertically down with zero forward airspeed.
The RC glider’s nose was pointed down, to limit the lift and
forward airspeed generated by the wings. In other words, the
landing was not conducted like how a power airplane lands,
which is with a forward airspeed. This provides another example
of soaring. See Fig. 7d-iii.
Fig. 7d-iii. RC glider landing into wind. [43]
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16
E. Gliders soaring on take-off and landing.
There is plenty of evidence of gliders, hang gliders, and
paraponts taking-off from hilltops into wind (i.e. a rising air
mass) to immediately gain altitude and airspeed; i.e. soaring.
When soaring, the glider is not simply pushed up and
backwards in the same direction as the wind. But the glider
gains airspeeds as it ascends and continues forwards into the
wind. For example, an image sequence from a video of a glider
taking-off into wind from a hilltop illustrates soaring. The glider
maintains a low AOA into the wind. See Fig. 7e-i.
Fig. 7e-i. Glider taking-off into wind from a hilltop. [53]
In the example above, it is difficult to tell, but there is
probably also a wind shear of slope wind present at the hilltop.
This may provide stronger winds closer to the ground and a
wind rising up the slope. However, these aspects are probably
not enough explain the significant amount of soaring in this
situation.
In addition, hang gliders have been observed to land almost
vertically into a moderate wind, using the wing like a sail to
generate a forward force to offset the wind. Other than the wind,
only altitude provides a source for a forward force. If a hang
glider can soar then so can a glider. See Fig. 7e-ii.
Fig. 7e-ii. Hang glider landing almost vertically. [49]
In these examples of slope soaring, a glider can maintain a
stationary position relative to the ground when facing directly
into wind. For example, in a 25 knot wind, a glider is generating
a forward force sufficient to fly forwards at 25 knots, This was
an unresolved enigma. But the explanation is that the wind and
the wings (helped by the Coanda effect) are generating vertical
lift. The glider is then pointing its nose down to trade altitude
gained for forward airspeed. See Fig. 7e-iii.
Fig. 7e-iii. Forces acting on a glider slope soaring.
F. Gliders soaring into a headwind.
There are plenty of examples of gliders achieving a stationary
position, with a zero ground speed and constant altitude, while
soaring into a headwind. In the example below the glider is at
13,000 ft. and the pilot claims to be benefitting from wave lift.
This is similar to slope soaring. The glider wings generate
enough forward force with a low AOA configuration, from a
rising headwind, to maintain stationary. See Fig. 7e-iii and 7f.
Fig. 7f. Cockpit of a glider soaring into a headwind. [54]
G. 2006 USAF glider dynamic soaring?
Experiments in a full-sized glider (sailplane) in 2006 by a
USAF pilot, [23][24] may have confirmed that a normal, glider
could use dynamic soaring to gain altitude and airspeed while
flying into a wind.
The tests were conducted flying a glider in a loop in a wind
shear along a hill top. The experiment was for a Masters thesis
in aeronautical engineering. A major media company (PBS)
documented the event, which is found in a youtube video. [24]
In the experiment the glider’s airspeed slowed as it ascended.
The glider finished the first loop at a airspeed 10 knots (about 19
km/hr) higher than it started. This is a relatively significant
increase in airspeed for one loop, which took less than a minute
to complete. See Fig. 7g.
Fig. 7g. Possible schematic of the glider path, for one loop,
showing the speeds recorded by USAF glider experiment. [24]
It was not clear if the glider was actually dynamic soaring, or
simply benefitting from a slope gradient or air up-current when
ascending; but not when descending. It was also unclear if the
wind strength increased with altitude. Therefore it is not possible
to conclude if the glider was actually dynamic soaring.
The conclusions by the USAF pilot included: “The first was
that when encountering a wind shear, the sailplane must either
climb while facing a headwind or descend while traveling with a
tailwind in order to realize an energy benefit.”
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
17
H. Super cubs and hang gliders VTOL not STOL.
Super cub pilots compete for shortest landings and take-offs,
which are best achieved by flying into a strong wind. For
example there’s the annual STOL competition in Valdez,
Alaska. However, the landings and take-offs are conducted in
the standard methods, without attempting to use the wings like
the sails of a boat to generate forward thrust and lift.
Videos on youtube provide examples of super cubs landing
almost vertically into a strong wind, i.e. VTOL, not STOL. This
is done at low ground speed and with low engine power (the
propeller turns slowly). In some videos the super cubs are
observed to hover mid-air briefly. The super cubs are soaring,
with the wings acting like a sail to generate a forward force and
some lift. Super cubs have been observed to achieve a
completed stop with almost no ground roll, when landing into a
strong wind. See Fig. 7h-i and 7h-ii.
Fig. 7h-i. Super cub on approach to landing on a beach
into a very strong wind. [47]
In this example, the super cub hovers briefly above the
landing point on the beach (Fig. 7h-ii above). At this point the
super cub is stationary mid-air. The pilot is then heard cutting
the engine while in a hover, after which the aircraft stalls and
descends vertically downwards a short distance (about 1-2
meters) to land without advancing any distance forwards.
The super cub is maintained in the hover, and prevented from
being blown backwards by the wings acting as a sail to generate
a forward force and some lift. See Fig. 7h-iii.
Fig. 7h-iii. Forces acting on a hovering super cub. [47]
It is argued there is little forward force gained from the
propeller and loss of altitude. Therefore, there must be a forward
force being generated by the wings acting as a sail to offset the
backward force from the strong wind. However, a lack of data
means that this aspect cannot be proved.
During the hover landing by the super cub in this example:
- The propeller is barely turning, indicating that it is
providing very little forward force.
- Airspeed is boosted as the aircraft loses altitude. But the
super cub has a low approach trajectory.
- Has a ‘nose-up’ orientation with flaps extended,
providing a high AOA and maximizing the amount of
wing exposed to the wind.
- It conducts a 3-point landing, where the tail and front
wheels touch the ground simultaneously. This is only
possible because the super cub is a ‘tail-dragger’.
Airplanes with tricycle landing gear cannot land with a
high AOA as the lack a tail wheel. See Fig. 7h-iv.
Fig. 7h-iv. Tail-dragger v. Tricycle landing gear.
In summary, tail-draggers with large wings like super cubs
are able to hover mid-air by generating a sufficient force from
the wind, similar to how the sails of a boat generate a force.
Other examples can be found of super cubs landing almost
vertically into wind with little engine power, low ground speed,
and no roll forwards on touching the ground. Even on the
ground the wings continue to produce forward thrust and
prevent the airplane from being blown backwards. See Fig. 7h-v.
Fig. 7h-v Super cub landing almost vertically. [48]
This space was intentionally left blank.
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18
8. EXAMPLE CALCULATION OF LIFT
A. Overview.
Calculations below are only approximate, based on relatively
conservative assumptions and use a methodology for the lift
generated according to Newtonian mechanics based on the mass
flow rate described above. This calculation demonstrates how
the principles discussed in this paper can be applied to what is
observed in practice.
The objective here is to show that it is feasible for a glider to
generate a sufficient lift force to fly. It is not a priority to make
overly precise or detailed estimates. A more accurate calculation
based on empirical evidence is required.
B. Methodology.
Calculations are based on a glider at an optimal glide.
Newtonian mechanics are used to estimate the lift generated by a
glider. See Fig. 8b.
Fig. 8b. Newtonian forces on a glider.
First, the volume of air ‘flown’ thrown and displaced down is
estimated, based on the glider’s velocity, wingspan and the wing
reach.
An important point underlying these calculations is that the
glider generates lift because it pushes and pulls air downwards.
The glider is not treated as a falling object, such as a skydiver,
which simply displaces air out of its way as it falls, without
generating much lift.
Key determinants for ‘m/dt’ and ‘dv’ (and thus lift) is the
wingspan, wing depth (chord) and wing AOA of the glider, not
simply its surface area facing down.
The wing reach is the vertical distance away from the wing
that the glider’s body influences the air; to push and pull the air
downwards. Wing Reach depends on things like the wing shape,
wing depth (chord) and wing AOA. See Fig. 8b.
The average Wing Reach is assumed to be constant across the
glider’s diameter and wingspan (so shown as a box around the
glider in Fig. 8b). Whereas, in practice Wing Reach is more
likely to be elliptical in shape; being greater at the center of the
glider’s wingspan and less at the edges.
Secondly, the air density is used to convert this the volume of
air into the mass of air (m/dt) ‘flown’ thrown and displaced
down each second.
Thirdly, the downward force is calculated based on ‘m/dt’
above and the assumed vertical downward velocity of the air
displaced is accelerated to (dv).
Downward Force = ma = m/dt * dv;
This downward force provides the equal and opposite upward
force (lift). Lift is simply the vertical component of the upward
force.
C. Key assumptions.
The glider in this example is assumed: See Fig. 8c.
- A mass of 800 kg,
- A wingspan of 30 m, with an average wing depth
(chord) of 0.6 m; providing a wing area of 18 m2 (30 *
0.6 = 18); and an aspect ratio of 50 (30/0.6 = 50).
- According to this method of estimating lift, the wing
area of the glider is not directly critical.
- A wing reach of 0.8 m is assumed; this is 0.4 m both
above and 0.4 m below the glider. This is a speculative
assumption based on the Wing Reach demonstrated by
the wings of airplanes. [3]
- Gliding at an airspeed 30 m/s (about 108 km/hr).
- Note: The glide angle and AOA is not included directly
in these calculations.
- Standard density of air is 1.2 kg/m3. [1]
- At the point of calculation, the glider is in a stable,
constant velocity glide through static air. It is not
accelerating.
- Induced drag is minimal; so the upward force equals the
lift generated.
- The glider accelerates air downwards to a velocity (dv)
of only 1.5 m/s.
- All the downward force is converted into lift; and that
there is minimal induced drag or inefficiencies.
Fig. 8c. Key assumptions
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
19
Comment: Downward velocity (dv).
It is assumed that the glider accelerates air downwards to a
velocity (dv) of only 1.5 m/s.
This is a highly speculative assumption given the lack of
empirical evidence in this area. This assumption means that the
glider’s wings traveling at about 108 km/hr (30 m/s), can
accelerate air down at a velocity of about 1.5 m/s, due to the
glider’s momentum and the wig AOA. In turn, this momentum
is derived mostly from the glider’s relatively high airspeed,
given that it has a relatively small mass. (Momentum = mass *
velocity).
To put it another way, Newtonian mechanics requires that the
glider in this example is capable of accelerating the air
downwards at 1.5 m/s, to maintain a stable descent. This feat
appears reasonable.
D. Calculations.
(i) Volume of air flown through.
First, the volume of air around a glider directly flown through
and displaced downwards each second is estimated. See Fig. 8d.
Fig. 8d. Volume of air displaced each second.
Volume of air flown through each second
= ( distance flown in one second * Wingspan
* Wing Reach )
= ( 30 m/s * 30 cm * 0.5 cm )
= 450 m3 /s
The glider in a glide flies through and displace downwards a
volume of about 450 m3/s of air.
(ii) Mass of air flown through each second (m/dt).
The volume of air flown through each second is converted
into mass of air flown through each second using the standard
density of air of 1.2 kg/m3.
Mass/dt = Volume/dt * Air Density
= 450 m3 /s * 1.2 kg/m3
= 540 kg/s (approx.)
The glider flies through and displace downwards a mass of
about 540 kg/s of air (m/dt).
(iii) Downward force.
The lift force that the glider needs to generate to fly is the
equal and opposite upward force to the downward force. As
explained above, the downward force is provided by the
equation:
𝐹𝑜𝑟𝑐𝑒!"#$ = 𝑚𝑎 = 𝑚/𝑑𝑡 𝑥 𝑑𝑣 [1]
= 540 kg/s * 1.5 m/s
= 800 kg m/s2 (approx)
= 800 N
=> Lift = Downward Force = 800 N
=> 800 kg/s total air displaced by this
downward force.
In short, the downward force is sufficient to displace a total
mass of air (directly and indirectly) down each second of 800
kg/s. This mass of air displaced each second is the same mass of
the glider (800 kg). Therefore, it is feasible that the glider is able
to glide based on the assumptions made. [3]
This calculation also implicitly also assumes that the
downward force is sufficient to displace a total mass of air
downwards each second that is equal to the glider’s mass. i.e.
The glider achieves dynamic buoyancy.
Downward Force è Total Mass displaced down /dt.
= Mass of glider
Conclusions of calculations.
This calculation simply demonstrates the methodology and
feasibility of Newtonian mechanics being applied to explain the
lift generated by a glider. This example also demonstrates what
assumptions are required for Newtonian mechanics to explain
the lift experienced by a glider in a downward glide.
This example is not proof as many assumptions are somewhat
speculative and are not based on empirical observations in this
example of gliders. In particular, the wing reach and velocity
that the air is accelerated downwards (dv) are difficult to
observe and are not known for certain. More work needs to be
done to confirm these calculations.
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
20
E. Lift
Mass; not Lift
Weight.
See: ‘Newton explains lift, buoyancy explains flight.’ [3]
These calculations show that in flight it is feasible that: Lift
è Mass; not Lift è Weight. This means that the aircraft
achieves dynamic buoyancy every second. See Fig. 8h.
Fig. 8h. Lift generated by a glider.
Specifically, that the downward force (and consequently lift)
only needs to be sufficient to displace a total mass of air
downwards that equals the aircraft’s mass (Lift è Mass), not its
weight. This can be described in equations:
Flight (dynamic buoyancy):
𝐹𝑜𝑟𝑐𝑒!"#$ = 𝐹𝑜𝑟𝑐𝑒!" (𝐿𝑖𝑓𝑡)
𝑀𝑎𝑠𝑠 !"# !"#$ = 𝑀𝑎𝑠𝑠 !"#$%!&' !"
If lift did equal the aircraft’s weight (Lift è Weight), not its
mass; then given that:
- Weight = Mass * Gravity, and
- Gravity is about 9.8 kg m/s2,
Then the assumptions in the calculations above for the
downward force must be increased by about 9.8x. The only two
assumptions that are somewhat speculative are wing reach and
the velocity downward that the air is accelerated to (dv).
Given the evidence for the assumptions, neither of these
factors is off by such a large factor of 9.8x. It is impossible for
the airplane’s wings to create a lift force that is sufficient to push
a weight of mass downwards equal to its own weight.
This space was intentionally left blank.
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
21
9. DISCUSSION OF RESULTS
A. Newtonian mechanics explains lift and soaring.
It should not be a surprise that Newtonian mechanics based
on the mass flow rate provides a simple and easy explanation of
lift and dynamic soaring by gliders that fits with what is seen
in practice; Given that Newtons laws are universal and apply to
all moving objects. It would be more surprising to claim the
reverse, that Newtons laws do not explain lift (as claimed by
advocates of fluid mechanics). There is no material evidence or
experiment that disproves this Newtonian explanation of lift.
Soaring by RC gliders and UAVs into a wind shear is not
disputed; it is the physics that remains unresolved.
It is worth noting that the theory of flight remains unresolved.
[2][32][33][34] Pundits still debate whether wings create lift by
pushing or pulling (‘sucking’) airplanes upwards. Explanations
of how gliders fly focused on fluid mechanics (e.g. Navier-
Stokes) are considered to be insufficient; particularly due to the
lack of empirical or experimental evidence. [2]
B. Passive thrust generation by sail or wing.
The analysis above indicates that glider wings would
passively generate greatest thrust if shaped like a sail or bird
wing, aligned with a wide AOA (e.g. 45°). See Fig. 9b.
Fig. 9b. Passive force generation by a
Sail and a wing turbine blade.
This conclusion arises because a sail or bird wing should re-
direct a greater mass of air each second (m/dt) against the
undisturbed wind at a higher velocity (dv), and therefore,
generate a greater thrust (Thrust = m/dt * dv). At a wider AOA,
more of this thrust is available to turn the wind turbine blade,
rather than oppose the oncoming wind.
C. Implications of the analysis.
Gliders can airspeed and altitude using a wind shear, the next
step is to see if this is possible while flying across a steady wind,
like a sailboat.
Newtonian mechanics explains both how lift is generated by
gliders and how sails generate a forward force on a boat.
Therefore, if a boat can sail into a steady wind, then a glider
should be able to do so as well (in the same way - by tacking
across the wind).
The RC glider community discovered how gliders could soar
using wind shear in mountains by intuition, trial and error. Post-
event people have rationalized the physics involved. Therefore,
the next step could be establishing if soaring is possible by
flying a glider across a steady wind (if done in the right way)?
Gliders have already proven the capacity to soar across a strong
wind on flat beaches (with a wind shear).
If this concept is correct, that gliders can fly into a wind to
gain altitude and airspeed, it opens up a lot possibilities for
gliders and represents dramatic progress in aerodynamics.
By way of illustration, this concept raises the possibility that
UAVs could fly indefinitely and light commercial airliners could
be designed to save fuel by flying INTO the jet stream. This is
significant can fuel represent a significant proportion of an
airplane’s mass at take-off and cost of operations.
For example, if a Boeing 787 flies its maximum range of
about 14,000 km (e.g. New York to New Zealand); it uses about
100,000 kg of fuel to carry a maximum payload (aircraft and
passengers) of 128,000 kg. The fuel represents about 44% of the
max. take-off weight (MTOW) of the 787 of 228,000 kg. [30]
D. A wind shear is not required for dynamic soaring.
Albatrosses and RC gliders are known to be able to use a
wind shear to gain airspeed and altitude (dynamic soaring) along
hill-tops, among other conditions. However, there is some
dispute whether birds and RC gliders can generate lift in a
constant-velocity wind (laminar airflow).
This paper claims that dynamic soaring is also possible for
birds and gliders while flying into a steady wind, similar to how
a boat sails into a wind. [18] A wind shear is not required for
dynamic soaring.
The evidence for dynamic soaring in constant-velocity
airflow can be found birds of all shapes and sizes that are
observed to hover or fly into strong winds, without circling or
conducting any special manoeuvers, such as a loop nor a circle
(e.g. Rayleigh circle). [31] See Fig. 9d-i.
Fig. 9d-i. Hawk hovering in a wind. [31]
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
22
In addition, sailboats regularly sail at a constant speed across
a constant speed wind. Further supporting the assertion that it is
possible to generate a forward force across a constant velocity
wind (i.e. into wind). A wind shear or wind speed variations are
not necessarily required.
Fig. 9d-ii. Soaring and sailing into wind.
To put it another way; If a RC glider can soar using a wind
shear, a boat can sail into a constant velocity wind; and the
physics involved is similar; Then a glider may be able to soar
into a constant velocity wind. See Fig. 9d-ii.
E. Vortices?
The aerodynamics (airflows) of glider flight due to its
particular shape as well as any consequent vortices affects lift.
Vortices are only significant to lift is they affect the mass of air
displaced downwards, and its velocity. Overall, the impact of
vortices on lift is considered to be of secondary importance.
Detailed analysis of vortices is beyond the scope of this paper.
This space was intentionally left blank.
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
23
10. CONCLUSIONS
Newtonian mechanics based on the mass-flow rate provides
new and useful insight to explain the physics of lift and dynamic
soaring by gliders. If both a heavy boat can sail into a wind and
an albatross can fly into a wind indefinitely; then a glider should
also be able to fly into a wind indefinitely.
This paper predicts that a glider could successfully
circumnavigate the globe against the jet stream. See Fig. 10a.
Fig 10a. A glider circumnavigating the globe.
It is puzzling that UAVs have been built that mimic bird
flight, but none that mimic an albatross soaring into wind;
gaining altitude and airspeed. This demonstrates that soaring
remains explained.
However, given the Newtonian explanation provided n this
paper, it should now be possible to build a UAV that mimics an
albatross soaring into wind. In theory such a UAV could also fly
indefinitely and circumnavigate the globe against the trade
winds or jet stream.
11. ADDITIONAL INFORMATION
Author: Mr. Nicholas Landell-Mills, independent researcher.
Corresponding email: nicklandell66@gmail.com
Funding: This paper was self-funded by the author.
Request for financial support: If you found this research to
be useful, entertaining or worthy, then kindly thank, support and
encourage the author with a financial donation to the author via
the email above on www.PayPal.com or using the direct link:
https://paypal.me/landell66?country.x=FR&locale.x=en_US
This paper could not have been produced through the
established academic and scientific system. Thank you.
Background: The author is British and was born in 1966 in
Botswana. He worked in finance for 25 years in numerous
countries. During this period he qualified as an accountant
(ACA) and obtained a CFA charter. He held a private pilot’s
license (PPL) for 20 years. He flew and maintained a small,
single-engine, home-built airplane (Europa XS monowheel,
registration: G-OSJN).
Academic background: The author is a graduate of The
University of Edinburgh, Edinburgh, UK. He was awarded a
M.A. degree class 2:1 in economics and economic history.
Affiliations: None.
Author Contributions: This paper is entirely the work of
the author, Mr. Nicholas Landell-Mills.
Disclaimer: The author confirms and states that all data in
the manuscript are authentic, there are no conflicts of interest,
and all sources of data used in the paper are acknowledged
where possible.
Acknowledgments: None.
ORCID ID: 0000-0003-4814-0443
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[2] N Landell-Mills (2019), How airplanes generate lift is disputed.
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[3] N Landell-Mills (2019), Newton explains lift; Buoyancy explains
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[5] N Landell-Mills (2019), Why vertical lift on a wing quadruples if
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10.13140/RG.2.2.20536.70409.
How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
24
[6] N Landell-Mills (2019), The diseconomies of scale in lift
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[7] Removed.
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[9] N Landell-Mills (2019), Helicopters achieve buoyancy in a hover;
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[10] N Landell-Mills (2019), How birds fly according to Newtonian
physics; Pre-Print DOI: 10.13140/RG.2.2.19558.98885.
[11] N Landell-Mills (2019), Albatross’s dynamic soaring is explained
by Newtonian physics. Pre-Print DOI:
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[12] N Landell-Mills (2020), How insects fly according to Newtonian
physics. Pre-Print DOI: 10.13140/RG.2.2.13994.98247.
[13] N Landell-Mills (2019), (2019), How frisbees fly according to
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[14] Removed.
[15] N Landell-Mills (2019), Skydivers achieve buoyancy at terminal
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[18] N Landell-Mills (2019), Sailing downwind faster than the wind.
Pre-Print DOI: 10.13140/RG.2.2.33918.33600.
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How$gliders$can$circumnavigate$the$globe$by$soaring$against$the$jet$stream.$$
25
APPENDIX I DEFINITIONS
A. Wing reach.
Wing reach is a new term that includes the vertical distance
facing the direction of travel that the wing directly influences the
air. This includes the air that the wing physically flies through,
and pushes above and below the wing. See Fig. I-a-i and I-a-ii.
Fig. I-a-i. Wing reach diagram absolute airflow.
Fig. I-a-ii. Wing reach diagram relative airflow.
Wing reach includes the air that the wing directly pushes out
of its path due to the volume of space that the wing passes
through. Therefore, wing reach depends on: See Fig. I-a-ii.
- Airfoil’s thickness.
- Wing AOA.
- The air above and below the wing that is directly
affected by the wing’s path through the air.
Fig. I-a-ii. Wing reach in a wing cross-section.
Wing reach does not include the air indirectly affected by the
wing, which is the air displaced by the air that the wing directly
flies through.
Wing reach is a key assumption in the calculation of the air
flown through each second (m/dt) by a wing. The greater the
wing reach, the greater the ‘m/dt’, and therefore, the greater the
lift generated (Lift = m/dt * dv).
This space was intentionally left blank.
ResearchGate has not been able to resolve any citations for this publication.
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This paper examines closed-loop dynamic soaring by small autonomous aircraft. Wind field estimation, trajectory planning, and path-following control are integrated into a system to enable dynamic soaring. The control architecture is described, performance of components of the architecture is assessed in Monte Carlo simulation, and the trajectory constraints imposed by existing hardware are described. Hardware in the loop simulation using a Piccolo SL autopilot module are used to examine the feasibility of dynamic soaring in the shear layer behind a ridge, and the limitations of the system are described. Results show that even with imperfect path following dynamic soaring is possible with currently existing hardware. The effect of turbulence is assessed through the addition of Dryden turbulence in the simulation environment.
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Dynamic soaring uses the gradient of wind velocity (wind shear) to gain energy for energy-neutral flight. Recently, pilots of radio-controlled gliders have exploited the wind shear associated with fast winds blowing over mountain ridges to achieve very fast speeds, reaching a record of 487 mph in January 2012. A relatively simple two-layer model of dynamic soaring was developed to investigate factors that enable such fast speeds. The optimum period and diameter of a glider circling across a thin wind-shear layer predict maximum glider airspeed to be around 10 times the wind speed of the upper layer (assuming a maximum lift/drag of around 30). The optimum circling period can be small ~1.2 seconds in fast dynamic soaring at 500 mph, which is difficult to fly in practice and results in very large load factors ~100 times gravity. Adding ballast increases the optimum circling period toward flyable circling periods of 2-3 seconds. However, adding ballast increases stall speed and the difficulty of landing without damage. The compressibility of air and the decreasing optimum circling period with fast speeds suggest that record glider speeds will probably not increase as fast as they have during the last few years and will probably level out below a speed of 600 mph.
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Flying snakes use a unique method of aerial locomotion: they jump from tree branches, flatten their bodies and undulate through the air to produce a glide. The shape of their body cross-section during the glide plays an important role in generating lift. This paper presents a computational investigation of the aerodynamics of the cross-sectional shape. We performed two-dimensional simulations of incompressible flow past the anatomically correct cross-section of the species Chrysopelea paradisi, showing that a significant enhancement in lift appears at an angle of attack of 35 degrees, above Reynolds numbers 2000. Previous experiments on physical models also obtained an increased lift, at the same angle of attack. The flow is inherently three-dimensional in physical experiments, due to fluid instabilities, and it is thus intriguing that the enhanced lift appears also in the two-dimensional simulations. The simulations point to the lift enhancement arising from the early separation of the boundary layer on the dorsal surface of the snake profile, without stall. The separated shear layer rolls up and interacts with secondary vorticity in the near-wake, inducing the primary vortex to remain closer to the body and thus cause enhanced suction, resulting in higher lift.
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The aerodynamics of horizontal axis wind turbine wakes is studied. The contents is directed towards the physics of power extraction by wind turbines and reviews both the near and the far wake region. For the near wake, the survey is restricted to uniform, steady and parallel flow conditions, thereby excluding wind shear, wind speed and rotor setting changes and yawed conditions. The emphasis is put on measurements in controlled conditions. For the far wake, the survey focusses on both single turbines and wind farm effects, and the experimental and numerical work are reviewed; the main interest is to study how the far wake decays downstream, in order to estimate the effect produced in downstream turbines. The article is further restricted to horizontal axis wind turbines and excludes all other types of turbines.
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See updated paper: Skydivers achieve buoyancy at terminal velocity, according to Newtonian mechanics.
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More than a million insects and approximately 11,000 vertebrates utilize flapping wings to fly. However, flapping flight has only been studied in a few of these species, so many challenges remain in understanding this form of locomotion. Five key aerodynamic mechanisms have been identified for insect flight. Among these is the leading edge vortex, which is a convergent solution to avoid stall for insects, bats and birds. The roles of the other mechanisms - added mass, clap and fling, rotational circulation and wing-wake interactions - have not yet been thoroughly studied in the context of vertebrate flight. Further challenges to understanding bat and bird flight are posed by the complex, dynamic wing morphologies of these species and the more turbulent airflow generated by their wings compared with that observed during insect flight. Nevertheless, three dimensionless numbers that combine key flow, morphological and kinematic parameters - the Reynolds number, Rossby number and advance ratio - govern flapping wing aerodynamics for both insects and vertebrates. These numbers can thus be used to organize an integrative framework for studying and comparing animal flapping flight. Here, we provide a roadmap for developing such a framework, highlighting the aerodynamic mechanisms that remain to be quantified and compared across species. Ultimately, incorporating complex flight maneuvers, environmental effects and developmental stages into this framework will also be essential to advancing our understandingofthe biomechanics, movement ecologyand evolution of animal flight.
The theory of flight remains unresolved
  • N Landell-Mills
N Landell-Mills (2019), The theory of flight remains unresolved, Pre-Print DOI: 10.13140/RG.2.2.16028.33922;
Newton explains lift; Buoyancy explains flight
  • N Landell-Mills
N Landell-Mills (2019), Newton explains lift; Buoyancy explains flight. Pre-Print DOI: 10.13140/RG.2.2.16863.82084.