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Relative airflow analysis is flawed.
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Relative airflow analysis is flawed.
Relative airflow analysis in wind tunnel experiments does not
accurately depict the actual wing airflows and forces seen in flight.
Mr. Nicholas Landell-Mills
19 August 2023
Pre-Print DOI: 10.13140/RG.2.2.19517.38886;
CC License: CC BY-SA 4.0
Keywords: Aerodynamics, relative airflows;
wind tunnel, wing.
Independent Research
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Abstract
The prevailing views in aeronautics assert that all motion is
relative. Therefore, there is no difference between how
airflows around an airplane wing in flight, as compared to a
wind tunnel. It does not matter whether the wing or the air is
moving or stationary, the result is the same. Based on
Galilean relativity, the same force is produced from both
flight and a wind tunnel. This logic means that a boat sailing
into the wind experiences the same airflows and forces as a
moving wing in flight through static air.
However, this is not the case. Observations and analysis
shows that the relative airflows of moving air over a
stationary wing is very different to a moving wing in flight
through static air. See Fig. 1a. A wing in flight produces
airflows and resultant forces that are very different to a boat
sailing into the wind. A sail creates airflows and forces that
are similar to a stationary wing in a wind tunnel.
Fig. 1a. Relative and absolute (actual) wing airflows.
For example, a comparison of wake airflows identifies turbulence behind wings in wind tunnel experiments, which differs to
the laminar airflows seen circulating around the wingtip vortices behind airplanes inflight. See Fig. 1a.
1.
In flight, a moving wing flies through static air. The air flown
through is accelerated downward to actively generate lift,
according to Newtonian mechanics. In contrast, relative airflow
diagrams and wind tunnel experiments show the reverse:
moving air passing around a stationary wing. See Fig. 1b.
INTRODUCTION
A. A critique of relative airflow analysis.
Relative wing airflow diagrams based on wind tunnel
experiments have been used for the last hundred years by fluid
mechanics to analyse how airplane wings interact with airflow
to (actively) generate vertical lift in flight.
Wing airflow diagrams are critical as they provide the basic
model to analyse how wings create airflows and generate forces.
For practical reasons it was easier and cheaper to construct a
small wind tunnel with a stationary wing or airplane, rather than
an airplane that moved through stationary air. However, this
simplicity comes at the cost of a less realistic analysis of lift.
Contrary to the prevailing view, this paper asserts that relative
airflow diagrams and wind tunnel experiments do not accurately
describe how a wing generates lift in flight. This dynamic is
Fig. 1b. Relative and absolute
wing airflow diagrams compared.
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Independent Research – Relative airflow analysis is flawed.
evident when comparing the details of relative airflow diagrams
and wind tunnel experiments to observations of a wing in flight.
Cars are used as a proxy to demonstrate this assertion above,
due to a lack of appropriate images for wings. For example, a
car driving on a dirt road pushes the air passed through in all
directions away from it and produces significant wake
turbulence. This airflow pattern is very different to the neat,
streamlined laminar airflows produced in a wind tunnel. See Fig.
1c.
Contents:
Fig. 1c. A car in a wind tunnel vs. on a dirt road.
The same principle applies to wings; the relative airflows
analysis based on wind tunnel experiments differ significantly
from what occurs in practice. This example is not claiming that
the airflows for cars are similar to those for wings; either in a
wind tunnel or in practice. This paper is only asserting that the
airflows experienced in wind tunnels differ from what is seen in
practice.
The deficiencies of relative airflow analysis and wind tunnel
experiments that render them inadequate to explain the lift
generated by a wing, can be split into several broad sections, as
follows:
-
Problems with relative airflow diagrams.
-
Problems with wind tunnel experiments.
-
Pressure is consequence of lift, and not a cause; as
described in a separate paper. [9]
-
Galilean relativity revisited.
-
Passive vs. Active forces.
1.
Introduction ........................................................ 1
2.
Problems with Relative Airflows ........................ 3
3.
Problems with Wind Tunnels............................. 6
4.
Wake Airflow Analysis...................................... 11
5.
Galilean Relativity Revisited ............................. 13
6.
Passive and Active Forces................................ 14
7.
A Wing is not a Sail ........................................ 15
8.
Airfoil Testing – The Davis Wing .................... 18
9.
Newtonian vs. Fluid Mechanics ....................... 19
10.
Discussion of Results ......................................... 20
11.
Conclusions ........................................................ 21
12.
Additional Information...................................... 21
13.
References ......................................................... 22
Appendix I – Unresolved Theory of Lift .................. 24
Appendix II – Newton Explains Lift........................... 25
Appendix III – Actual Wing Airflows .......................... 27
Appendix IV – Fluid Mechanics Critique .................... 29
B. Significance.
The analysis challenges the prevailing method used by
engineers to assess the forces generated based on fluid
mechanics (Navier-Stokes equations), using relative airflows
analysis of wind tunnel experiments; and/or CFD analysis
(Computational Fluid Dynamics).
Consequently, most design and testing of the forces generated
by wings in aeronautics, is inaccurate and suboptimal. Wind
tunnels are useful for testing how a sailboat performs, not a wing
in flight. This problem applies to the forces generated by wings,
propellers, wind turbine blades, sails, and cars.
This space was intentionally left blank.
Wind tunnels can be large and expensive, especially for
supersonic aircraft. This analysis means that investments in
wind tunnel and CFD analysis are highly unlikely to produce the
benefits expected and may even be misleading.
The importance of these conclusions cannot be overstated as
almost all explanations of how lift is actively generated in the
last 100 years have relied on relative airflow diagrams and fluid
mechanics.
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Independent Research – Relative airflow analysis is flawed.
2.
B.
RELATIVE AIRFLOW DIAGRAMS
Critique in more detail.
1)
A.
Propeller backwash vs. Wing downwash.
One obvious fault is that the relative airflow diagrams present
wing downwash in a similar direction to any engine or propeller
backwash, despite these airflows being at almost perpendicular
directions in practice. See Fig. 2b-1.
Critique summarized.
Relative airflow diagrams and analysis are the prevailing
methods used by fluid mechanics to describe and explain the lift
generated by a wing. This approach is derived from the relative
airflows over a stationary wing seen in wind tunnel experiments.
See Fig. 2a-i.
Fig. 2b-1. Wing downwash
and propeller backwash.
Fig. 2a-i. Wind tunnel experiment
and relative airflow diagram. [13]
2)
Relative airflow diagrams typically fail to show any change
in airflow velocity as the airflows pass across the wing. Also, no
difference in airflow velocity between the upper and lower
airflows is evident. In other words, the upper and lower airflows
appear to maintain a constant velocity relative to each other and
the wing. See Fig. 2a-(i-ii).
The problems with this approach include: See Fig. 2a-ii.
1)
Propeller backwash vs. Wing downwash
2)
No change in airflow velocity is shown.
3)
Moving air vs. Static air.
4)
5)
Two-dimensional and no wingtip vortices.
Turbulent wake airflows?
6)
Limited downwash shown.
7)
Change in airflow and pressure shown separately.
8)
9)
The lower airflow is not high air pressure.
Lack of wing condensation.
10)
Fails to explain the angle of the lift generated.
No change in airflow velocity is shown.
This aspect is inconsistent with claims that the upper airflow
accelerates as it flows over the top of the wing – in absolute
terms, and relative to the lower airflow. This means that wind
relative airflow diagrams fail to accurately replicate supersonic
flight.
3)
Moving air vs. Static air
Relative airflow diagrams and wind tunnel experiments give a
false impression that the air is already flowing, has momentum,
and is simply re-directed downwards by the wing. In practice, a
moving wing flies through stationary air, which is very different
to what the relative airflow diagrams depict. See Fig. 2a-(i-ii).
The relative airflow diagrams are misleading because it gives
an incorrect impression that there is no transfer of momentum
between the air and the wing.
-
If the wings did re-direct airflow, then the airflow would
resemble what is seen on the sails of a boat of wind
turbine blades. But this is not the case. The airflow
behind airplanes is laminar, whereas wind turbine blades
produce turbulent wake airflow.
-
Relative airflow diagrams can exaggerate the importance
of the Coanda effect. As moving and static air behaves
differently, a curved wing in a wind tunnel may provide
a stronger Coanda effect, than a wing moving through
static air.
Fig. 2a-ii. Problems of relative
airflow diagrams summarised.
These problems are described in more detail below.
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Independent Research – Relative airflow analysis is flawed.
4)
Two-dimensional and no wingtip vortices.
6)
The wingtip vortices are notably absent from the relative
wing airflow diagrams, wind tunnel experiments with stationary
wings, and many CFD visualizations. Relative wing airflow
diagrams are often two-dimensional and focused on airflows on
the wing. Therefore, it misses the bigger picture of the wing tip
vortices and the large air mass circulated behind the airplane.
See Fig. 2b-4-(i-ii).
Limited downwash shown.
Relative airflow diagrams incorrectly show limited
downwash and provide no indication of the downwash velocity
generated by a wing. Downwash can be significant close to the
wing. See Fig. 2b-6-i.
Fig. 2b-6-i. Evidence of downwash
Close to the wings [91]
Fig. 2b-4-i. Downwash and wake vortices seen $
in clouds behind an A-380. [85]
IV-d-6-ii. Downwash behind
low-flying jets. [92][93]
Fig. 2b-4-ii. Wingtip vortices. [20][90]
For example, a video of a large blue balloon accelerated
downwards by the downwash from the wing of an A-380 on
approach to landing is referenced below.
5)
The balloon is observed to cross in front of the Airbus’ wing,
and accelerate upwards with the upwash at the leading edge of
the wing. Then the balloon is aggressively accelerated
downwards with the downwash behind the trailing edge of the
wing at an estimated 12.5 m/s. See Fig. 2b-6-iii.
Turbulent wake airflows?
In wind tunnel experiments, wake airflows are turbulent,
which are not shown in relative airflow diagrams. However, in
flight wake airflows are laminar.
If relative airflow diagrams are being used to depict active
force generation by a wing in flight. Then they correctly show
laminar wake airflows behind the trailing edge of the wing,
However, if relative airflow diagrams are being used to
illustrate airflows observed in wind tunnel experiments. Then
they incorrectly fail to show any wake turbulence behind the
trailing edge of the wing. See Fig. 2b-5.
Fig. 2b-6-iii. Image sequence
of a large blue balloon travelling
in the wing airflows of an A-380. [87]
Fig. 2b-5. Turbulence and
relative airflows. [13]
The amount of downwash observed in the video of the A-380
above, is not evident in the corresponding wing relative airflow
diagrams or wind tunnel experiments.
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Independent Research – Relative airflow analysis is flawed.
7)
Change in airflow and pressure shown separately.
10)
Pressure distribution diagrams are often shown separately to
airflow velocities. Relative airflow diagrams typically omit
pressure differences across the wing associated with changes in
the velocities of the airflows. See Fig. 2b-7.
Relative airflow diagrams and wind tunnel experiments fail to
adequately explain why the direction of the aerodynamic upward
force (Force UP) on the wing is angled slightly backwards. See
Fig. 2b-10-i.
Fig. 2b-7. Pressure distribution
visualisation across a wing.
Fig. 2b-10-i. Lift force acting
on a wing. [13]
Relative airflow diagrams fail to adequately explain how or
why the airflow over the topside of the wing is accelerated to
produce low air pressure near the leading edge on the topside of
the wing. It is unclear why the low air pressure is not greatest in
the middle or the trailing edge of the topside of the wing, or
elsewhere.
8)
Fails to explain the angle of the lift generated.
It is unclear exactly how the wing AOA is related to the
direction that the aerodynamic lift generated by relative airflows
for different wing shapes. This point is typically ignored by
explanations of lift. This aspect makes the explanations of lift
incomplete.
In addition, it is unclear why the pattern of low air pressure
near the leading edge of the topside of the wing, would generate
lift in any particular direction or angle. See Fig. 2b-10-ii.
The lower airflow is not high air pressure.
Relative airflow diagrams incorrectly describe the airflow
below the wing as being high air pressure. The underside side of
the wing experiences high pressures due to the force it exerts to
accelerate the lower air mass (Pressure = Force / Area).
However, the lower air mass is accelerated, so has low internal
pressure, not high internal air pressure.
This aspect leads to a misunderstanding that wingtip vortices
are caused by a pressure differential between low air pressure on
top of the wing and high air pressure below the wing. See Fig.
2b-8.
Fig. 2b-10-ii. Low air pressure
distribution on a wing.
Fig. 2b-8. Prevailing explanation of wingtip
vortices due to a pressure differential. [20]
9)
Lack of wing condensation.
There is high-velocity, low-pressure airflow on top of wings
in flight, as evident from wing condensation, which is not
replicated in a any wind tunnel experiment. See Fig. 2b-9.
Fig. 2b-9. Condensation on the top of wings.
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Independent Research – Relative airflow analysis is flawed.
3.
A.
B.
PROBLEMS WITH WIND TUNNELS
Overview.
The problem of applying wind tunnel experiments to
explain the lift generated by a wing, as wind tunnel experiments
do not accurately reflect the conditions observed in flight,
include:
Wind tunnel experiments described.
Wind tunnel experiments can be used to illustrate the
displacement of static air relative to the wing. For example,
wind tunnel experiments with pulsed streamlines of smoke are
shown moving over a stationary wing a positive and significant
wing AOA in Fig. 3a-(i-ii).
-
Airflow separation occurs at low wing AOA.
-
No wing flex is observed in wind tunnels.
-
Fails to adequately explain stalls.
-
No downwash in wind tunnels?
-
Limited upwash in wind tunnels?
-
Ground effect in wind tunnels?
-
No empirical data.
-
No adverse yaw observed in wind tunnels?
These problems are described in more detail below.
Fig. 3a-i. Wind tunnel experiment. [77]
C.
Airflow separation occurs at low wing AOA.
Some wind tunnel experiments show airflow separation on
the topside of the wing at relatively low wing AOA and low
airspeeds and with the flaps extended, which does not occur in
flight. This airflow pattern would trigger a stall for an wing in
cruise flight. See Fig. 3c-(i-ii).
Fig. 3a-ii. Wind tunnel experiment, sequence
of images with pulsed airflows. [77]
In image 5 of Fig. 3a-ii above, when the smoke of the upper
airflow reaches the trailing edge of the wing, the smoke of the
lower airflow is only about halfway along the underside of the
wing. This difference is significant. The lower airflow adjacent
to the wing travels about half the distance of the upper airflow.
Fig. 3c-i. Airflow separation at a
low wing AOA in wind tunnel experiments.
Wind tunnel experiments are extremely well documented and
show consistent observations, depending on the wing design,
wing AOA, relative airspeed, and other experimental conditions.
See Fig. 3a-(iii-iv).
Fig. 3c-ii. Airflow separation at a low and high
wing AOA in a wind tunnel.
Fig. 3a-iii. Wind tunnel experiment. [13]
As the airflow on the topside of the wing is not attached to
the wing, as shown in the images of wind tunnels above, then it
cannot generate any lift.
In addition, the airflow separation observed in wind tunnels
does not correspond to what is observed for a real airplane wing
in flight. Wings in flight require a significantly higher AOA
before airflow separation occurs, given the speed of the relative
airflow.
Fig. 3a-iv. Wind tunnel experiment.
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Independent Research – Relative airflow analysis is flawed.
D.
No wing flex is observed in wind tunnels.
E.
Some modern airliner wings such as the B-787 are designed
to be straight at rest and to flex upwards in flight. See Fig. 3d-i.
Fails to adequately explain stalls.
Relative airflow analysis and the wind tunnel experiments fail
to adequately explain aerodynamic wing stalls, including why:
-
The stall is abrupt and dramatic. See Fig. 3e-i.
Fig. 3d-i. Wing flex by B-787
Significant wing flex is not observed to occur in wind tunnel
experiments. [68] This aspect indicates that the relative airflow
in wind tunnels does not exert an upward force on the wings.
Fig. 3e-i. Airflows pre and post stalls.
However, relative airflow analysis from wind tunnel
experiments indicates that airflow separation and
turbulence on the topside of the wing is gradual, and not
abrupt and dramatic as observed in practice. See Fig.
3e-ii.
For example, to test wing perform in flight at different stages
of wing flex. Wind tunnel experiments have to use small-scale
models for aircraft (eg. B-787) with the wing flex already
established in the airplane model, as there is no wing flex arising
from the relative airflow. See Fig. 3d-ii.
Fig. 3d-ii. Wing flex by B-787
in a wind tunnel. [69]
Fig. 3e-ii. Relative wing airflows in a
wind tunnel, showing an increasing airflow separation
with increased wing AOA. [81]
Similarly, airline manufacturers do not conduct wing loading
/ wing flex tests in a wind tunnel. Instead, a specialised machine
is used. See Fig. 3d-iii.
-
Stalls do not occur at low wing AOA at subsonic speeds,
given that wind tunnel experiments demonstrate that
airflow separation is possible under these conditions.
See Fig. 3e-(i-ii) of wind tunnel experiments on the
previous page.
Fig. 3d-iii. B-787 wing loading test.
-
There is no equation that accurately predicts a stall.
-
Turbulence always arises first at the trailing edge of the
wing, and not at the leading edge. Relative airflow
analysis also fails to explain why shock waves from
supersonic flight start in the middle of the wing. Wing
airflow turbulence always arises first at the trailing edge
of the wing, and not at the leading edge. See Fig. 3e-i
above.
-
In addition, in wind tunnel experiments the observer
controls the speed with which air is blown and wing
AOA. This aspect is the mirror of how a pilot controls
the aircraft’s speed and wing AOA in flight. This aspect
means that the experiment does not necessarily reflect
realistic airspeeds, wing AOA, and airflows that are
actually experienced by a real wing in flight.
Relative and actual airflow diagrams do share similarities:.
Both assert that the wing pushes air downwards, to create
downwash; and that the movement of the air generates lift.
This space was intentionally left blank.
For example, a wing with a high AOA can be exposed to
a high relative speed by the observer, which does not
7
Independent Research – Relative airflow analysis is flawed.
replicate realistic stall conditions in practice. In flight,
the relative airspeed would slow dramatically as the
wing AOA increases and the aircraft enters a stall.
See Fig. 3b-(i-ii) of wind tunnel experiments on the
previous page, and Fig. 3e-iv.
-
Consequently, under these experimental conditions, the
high-speed of the relative airflow prevents the lower
airflow from being pulled upwards to the topside of the
wing, at the trailing and leading edges, which would
cause turbulence.
-
In many wind tunnel experiments, there is insufficient
upward airflow from below the leading edge of the wing
to trigger a standard stall-warning device, located under
the leading edge of the wing. See Fig. 3e-iii.
Fig. 3e-v. Wing airflows in a wind tunnel and
glider wing during a stall compared. [82]
F.
No downwash in wind tunnels?
A common criticism of the Newtonian explanations of lift, is
a wing can be observed to produce lift in a wind tunnel without
generating net downwash a long distance from the wing. The
lack of downwash is assumed to indicate that no Newtonian
forces are present to create the lift observed. The lower the wing
AOA, the less downwash is observed. See Fig. 3f-i.
Fig. 3e-iii. Stall-warning devices located on the
underside of the leading edges of wings. [32]
In other words, the wind tunnel experiment does not
replicate what is observed in flight if not conducted
realistically, which is often the case.
Fig. 3f-i. Wind tunnel experiment
showing no net downwash.
In contrast, the actual airflows can explain how stall
warning devices are triggered at the late stages of the stall
process. See Fig. 3e-iv.
However, this criticism does not distinguish between forces
actively and passively generated by a wing. Consequently, the
observation above of no net downwash in a wind tunnel can be
explained by:
Fig. 3e-iv. Wing airflows sequence in a stall.
See the Newtonian explanation of Stalls. [3][10]
-
The airflow patterns observed in the stall experiments
are not replicated in wind tunnel experiments. See Fig.
3e-v.
-
Relative airflows can be re-directed by a wing to
passively generate turbulence and a force (thrust)
according to Newtonian mechanics.
-
The criticism above of Newtonian solutions does not
account for the turbulence generated by wings in wind
tunnels.
-
A wind tunnel is essentially airflow in a the enclosed
environment of a pipe. Therefore, the downwash created
(by a wing re-directing relative airflow) pushes against
the wind tunnel floor, which simply deflects the
downwash upwards. The airflow naturally returns to an
even distribution some distance behind the wing. The
wind tunnel floor prevents any downwash from
continuing its path downwards.
-
The clear forward airflow pattern at the trailing
edge sown in the glider experiment is NOT
observed in wind tunnel experiments, (which only
demonstrate turbulence at the trailing edge).
-
In wind tunnel experiments, airflow separation on
the topside of a wing indicates little airflow on the
wing.
This fact is so obvious that it is puzzling that anyone
would expect to observe sustained downwash in a wind
tunnel, some distance from the wing.
-
The clear upward airflow pattern at the leading
edge sown in the glider experiment is NOT
observed in wind tunnel experiments, (which only
demonstrate turbulence or backward airflow at the
leading edge).
It is possible to observe this effect by the floor in some
wind tunnel experiments, on the downwash created by
the underside of the wing. See Fig. 3f-ii.
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Independent Research – Relative airflow analysis is flawed.
G.
Limited upwash in wind tunnels?
Wind tunnel experiments appear to produce significantly less
upwash, as compared to aircraft in flight. For example, a wing
in a wind tunnel at a high AOA, shows the airflow in front of the
wing rising only slightly due to the upwash at the leading edge
of the wing. See Fig. 3g-i.
Fig. 3f-ii. Wind tunnel experiment showing
the floor deflecting downwash upwards..
In short, wind tunnels are not a useful or accurate method to
assess the lift generated by a wing.
Fig. 3g-i. Wind tunnel experiment showing
limited upwash at the leading edge of the wing.
Little downward movement is evident in relative airflow
diagrams and wind tunnel experiments. This provides that
impression that little downwash is created by the wings, which
contradicts what is observed in flight. See Fig. 3f-iii.
Upwash is difficult to observe for aircraft in flight, and there
is little reliable data readily available.
Nonetheless, a video of a large blue balloon being accelerated
downwards by the downwash from the wing of an A-380 on
approach to landing with a modest wing AOA (of only 3°
perhaps?), shows significant upwash. [80] The balloon is
observed to cross in front of the Airbus’ wing, accelerate
upwards with the upwash at the leading edge of the wing. Then
the balloon is aggressively accelerated downwards with the
downwash behind the trailing edge of the wing. See Fig. 3g-ii.
Fig. 3f-iii. Downwash behind low-flying jets. [83]
For example, it is estimated that a heavy fighter jet flying at
222 m/s (about 800 km/hr), accelerates the air flown through
downward at a relatively slow speed of 11 m/s (dv) to fly. This
downwash velocity (dv) is so low compared to the airplane’s
airspeed that many observers are prone to conclude that ‘dv’ is
negligible. See Fig. 3f-iv.
Fig. 3g-ii. Image sequence of a large
blue balloon travelling in the upwash
and downwash of an A-380. [80]
H.
Fig. 3f-iv. Speed of a fighter jet
and the downwash.
No ground effect in wind tunnels?
In some experiments, the wind tunnel floor may provide
something solid for the airflow re-directed by a wing
(downwash) to push against. This dynamic could boost the lift
generated by the wing in a manner similar to ground effect if the
wing was close to the wind tunnel floor. See Fig. 3h.
This space was intentionally left blank.
Fig. 3h. Ground effect in wind tunnels?
9
Independent Research – Relative airflow analysis is flawed.
I.
No empirical data.
J.
An internet search of scientific papers and otherwise, failed to
produce a wind tunnel experiment that accurately measured the
velocities of the upper and lower airflows across a wing.
Consequently, it is unclear by how much a wing accelerates the
upper airflow in a wind tunnel experiment; 5% 10% 20%? ….
No adverse yaw in wind tunnels?
The Newtonian explanation of adverse yaw helps to explain
why adverse yaw is not pronounced (not observed?) in wind
tunnel experiments on stationary wings . Although, a lack of
reliable data available on adverse yaws in wind tunnels makes
this point difficult to confirm. See Fig. 3j-i.
The lack of empirical data is puzzling. There is no
experimental data that confirms the prevailing explanation of
wind tunnel experiments that “Airplane wings are shaped to
make air move faster over the top of the wing.” [1]
In flight, the topside of the wing is observed to create low
pressure, which accelerates the air above the wing downwards.
This is evident from vapour condensation on top of the wings.
However, this process and wing condensation is not observed in
wind tunnel experiments. See Fig. 3-(i-ii).
Fig. 3j-i No adverse yaw
in a wind tunnel (?). [13]
To put it another way, if the Newtonian explanation of
adverse yaw is correct. Then adverse yaw is the product of
active force generation from actual airflows; and not the product
of passive force generation from relative airflows (headwind) as
observed in wind tunnel experiments. See Fig. 3j-ii.
Fig. 3i-i. Wing condensation. [32]
Fig. 3i-ii. Wing condensation
observed in flight.
For vapour condensation to occur, sufficient humidity and
low air pressure are needed, as well as a condensation point.
Fig. 3j-ii. Adverse yaw forces acting
on an airplane in a bank. [3]
This space was intentionally left blank.
This space was intentionally left blank.
10
Independent Research – Relative airflow analysis is flawed.
4.
A.
WAKE AIRFLOW ANALYSIS
Turbulent vs. Laminar wake airflows.
Key evidence for the difference between passive and active
force generation is the difference in wake airflows and the
presence or absence of turbulence. Consequently, additional
analysis is provided below.
Fig. 4a-iv. Wind tunnel Flow visualization
results for NACA0025 aerofoil [79]
Wake airflows from sails
Wake airflows from stationary wings
The assertion that relative airflow re-directed by an airfoil
produces wake airflow turbulence is supported by most airflow
analysis of sailing. The computer simulations and visualisations
show sails producing turbulence at the trailing edge of the sail.
See Fig. 4a-iv.
Airflows passively re-directed produce wake airflow
turbulence, as observed in wind tunnel experiments. The
turbulence arises because the re-directed airflows close to the
wing interacts with the undisturbed airflow at the trailing edge.
The further away from the topside of the wing, the airflow
becomes progressively less turbulent. See Fig. 4a-(i-iv).
Fig. 4a-iv. Airflow turbulence behind sails. [71]
Fig. 4a-i. Wind tunnel experiment. [31]
Wake airflows from cars in wind tunnels
The assertion that wake airflow turbulence is caused by the
interaction of the re-directed wing airflows and the undisturbed
airflow, is supported by the analysis of car airflows.
In wind tunnel experiments and for a moving car, there are no
significant airflows under the car. The car primarily affects the
airflows in front of and over the vehicle.
Fig. 4a-ii. More wind tunnel experiments.
Consequently, stationary cars in wind tunnel experiments
display significantly less turbulence than observed in practice
from a moving car. See Fig. 4a-v.
The re-directed airflows over cars in wind tunnel experiments
have little undisturbed airflows to interact with, so produce little
turbulence. Therefore, wind tunnels are not a realistic depiction
of the wake airflow turbulence that arises in practice from a
moving car.
Fig. 4a-iii. Wind tunnel experiment. 3 [78]
For example, a car driving on a dirt road pushes the air passed
through in all directions away from it and produces significant
wake turbulence. This airflow pattern is very different to the
neat, streamlined laminar airflows produced in a wind tunnel.
See Fig. 4a-v and Fig. 5c-ii. The same principle applies to
wings.
Fig. 4a-iv. Airflow around a complex
airfoil in a wind tunnel creates turbulence
at the trailing edge. [72]
Wind tunnel experiments can show wake airflow turbulence
and airflow separation even with low airfoil AOA. Airflow
separation-induced turbulence does not necessarily generate
significant or noticeable force (forward thrust) according to
passive force generation. See Fig. 4a-iv.
Fig. 4a-v. A car in a wind tunnel vs. on a dirt road.
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Independent Research – Relative airflow analysis is flawed.
The laminar airflows behind the car in the wind tunnel in the
image above do not show any wake turbulence, partly because
they do not interact with other airflows. This is different to the
wing airflows in a wind tunnel. Specifically, the upper and lower
airflows collide at the trailing edge of the wing, causing
turbulence.
B.
Wind turbine wake turbulence
Turbulence arises behind wind turbine blades due to the
reduction in wind speed, as the turbine extract power and
momentum from the wind. For example, wind speed can fall by
about 2/3; or from 30 to 10 km/hr.
Wake airflow turbulence is not always visible. Wake
turbulence behind a turbine extends downstream to 3 to 7 blade
diameters. Wake rotation is non-uniform, which impacts the
process of wake mixing. [73][74] See Fig. 4b-v.
Laminar airflows from wings and propellers.
In contrast to the wind tunnel experiments above, significant
turbulence is not observed immediately behind airplane wings in
flight (except at the wingtip vortices), or immediately behind the
propellers/rotors (except at the blade-tips). See Fig. 4b-(i-ii).
Fig. 4b-v. Airflow turbulence from
wind turbine blade. [75]
Fig. 4b-i. Laminar airflow behind wings. [16][13]
Frisbee wake turbulence
Similar to airplane wings, the curved edges of frisbees help to
actively push and passively re-direct air downward to generate
lift, helped by the Coanda effect. In addition, experiments in
wind tunnels show a rotating, static frisbee passively redirecting significantly more relative airflow downward, as
compared to a stationary frisbee. See Fig. 4b-vi.
Fig. 4b--ii. Laminar airflow behind propellers.
In practice and in actual airflow experiments, the wings
accelerated air downwards, which is circulated behind the
aircraft around two counter-rotating wingtip (wake)
vortices. See Fig. 4b-(iii-iv).
Fig. 4b-vi. Downwash from a rotating frisbee.
(The frisbee’s wake airflow is turbulent) [76]
Fig. 4b-iii. Large mass of air circulated and
wake vortices behind an airliner. [66]
This space was intentionally left blank.
Fig. 4b-iv. Downwash and vortices form behind
a model airliner flying through smoke. [1]
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Independent Research – Relative airflow analysis is flawed.
C. Illustration with cars.
5. GALILEAN RELATIVITY REVISITED
The assertion that Galilean relativity is a thought experiment
that only applies to two objects is further illustrated using the
example of moving and stationary cars. The moving car exerts a
force to accelerate air in the atmosphere out of its path and away
from it. Due to the air’s inertia, this action generates drag. The
airflows generated produce turbulence behind the moving car. In
contrast, a stationary car generates no airflows. See Fig. 5c-(i-ii).
A. Background – Galilean relativity defined.
Galilean relativity states that the laws of motion are the same
in all inertial frames of reference. It is also called Galilean
invariance. An often-used illustration of Galilean relativity is
two stationary trains parked next to each other. If one trains
moves, an observer inside one of the trains cannot tell whether
their train or the other train is moving. See Fig. 5a.
Fig. 5c-i. A moving vs. stationary car.
Fig. 5a. Two trains stopped at a station platform.
B. Galilean relativity only applies to two objects.
Fig. 5c-ii. A moving car generates
drag and turbulence.
This paper asserts that Galilean relativity is a thought
experiment that only applies to two objects. If more objects are
considered, such as the ground and the air in the atmosphere,
then it is easily possible to deduce which object is moving and
which is stationary. The wheels of the moving train rotate,
whereas the stationary train’s wheels do not.
A stationary car exposed to relative airflows (wind) in a wind
tunnel generates laminar airflows and little turbulence. These
airflows are very different to those around a car moving through
static air. See Fig. 5c-iii.
In the example above, the observer’s uncertainty as to which
train is stationary and which is moving is easily resolved by
looking out of the window at the station platform. The
observer’s confusion is temporary.
In addition, if the inside of the train was not enclosed
environment, with a large open window, and the observer was
exposed to the atmosphere outside of the train. Then the
observer is less likely to be confused as to which train is
moving, because the observer would feel the wind through the
window if their train was moving.
Fig. 5c-iii. A stationary car in a wind tunnel
exposed to a relative airflow.
By only looking at the airflows around the car it is possible to
judge which car is moving, and which is stationary. This means
that the ground is a fixed reference point, which can be used to
judge whether an object is moving through the atmosphere.
As soon as the observer references a third object, such as the
platform or the atmosphere, then it is clear which train is moving
relative to all objects around it. In the analysis of wings,
airflows, and the generation of forces from these airflows, the
ground is the benchmark to judge whether an object is moving.
The same principle applies to wings; the relative airflows
analysis based on wind tunnel experiments differ significantly
from what occurs in practice. This example is not claiming that
the airflows for cars are similar to those for wings; either in a
wind tunnel or in practice. This paper is only asserting that the
airflows seen in wind tunnels differ from practice.
Contrary to the prevailing views held in aeronautics, this
analysis explains how different airflows, and therefore, forces
(e.g. lift) are generated by:
-
A wing flying through static air to actively accelerate air
downward to generate airflows and forces.
D. Summary.
A stationary wing or a boat sailing into the wind, can
passively re-direct relative airflows to generate a force.
Galilean relativity cannot be applied to the analysis of wing
airflows. More precisely, a stationary wing in a wind tunnel
exposed to the relative airflow (wind), is not the same as a wing
moving through static air. These are different actions that result
in different airflows and forces, as explained below in terms of
passive and active forces.
The analysis above does not establish whether an object is
moving in absolute terms in relation to the universe. This is an
entirely separate consideration that is not relevant to the analysis
of wing airflows. It is beyond the scope of this paper.
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Independent Research – Relative airflow analysis is flawed.
a downward force (Force DOWN = m/dt * dv). The reactive
equal and opposite upward force generated (Force UP)
provides lift. For example, this is how an airplane wing
can generate lift.
6. PASSIVE AND ACTIVE FORCES
This paper describes airflows actively created by a wing in
flight as absolute airflows, to differentiate them from the
relative airflows experienced in wind tunnels.
A. Analysis of actual wing airflows.
Contrary to the prevailing view that favours relative airflow
analysis to explain the forces generated by an airfoil in all
situations. The actual airflows observed from a wing in flight
through static air are significantly different to the airflows seen
from a wing exposed to a relative airflow (headwind) in a wind
tunnel. Consequently, the resultant forces are also different.
Galilean invariance does not apply in this situation. See Fig. 6a(i-ii).
In other words, sailboats and airplane wings generate
different airflows, and therefore, generate different forces. For
example, doubling the number sails doubles the thrust generated
by a sailboat, but doubling the number of wings on an airplane
increases the lift generated only a little.
The key differences between passive and active forces include:
-
The direction of the force generated by an active force is
almost perpendicular to the wing’s alignment. But passive
forces generate thrust in a similar direction as the wing.
-
Momentum is transferred from the relative airflow (wind)
to the wing in passive force generation, and vice versa in
active force generation.
-
The wake airflows produced are different:
The passive forces arising from relative airflow, produces
wake airflow turbulence at the trailing edge of the wing.
In contrast, the active forces arising from the static air
accelerated downwards by a wing in flight, produces
laminar wake airflow, which is only turbulent at the centre
of the two wingtip vortices. See Fig. 6a-iii.
Fig. 6a-i. Actual wing airflows analysed. [13][13]
Fig. 6a-iii. Turbulent vs. smooth
wake airflows. [32][63]
Fig. 6a-ii. The passive and active creation
of forces based on actual airflows.
To put it another way, the prevailing method by fluid
mechanics using relative wing airflow analysis (which is based
on wind tunnel experiments) to analyse how an airplane wing
generates vertical lift in flight, is flawed for the reasons
described below:
In both situations, the resultant forces can be described by the
same Newtonian equation (Force = m/dt * dv) as explained
below. See Fig. 6a-ii.
1)
-
A mass of air each second (m/dt) from oncoming relative
airflow (headwind) can be passively re-directed by a
stationary airfoil. This airflow decelerates (dv) on contact
with the undisturbed wind at the trailing edge of the airfoil
to produce turbulence. This action creates a backward
force (Force BACK = m/dt * dv), and therefore, a reactive
equal and opposite forward thrust is also generated.
In particular, wake airflow turbulence observed in wind
tunnel experiments behind the trailing edge of the wing,
is not observed behind wings in flight.
-
For example, a sailboat, wind turbine blade, and a glider
wing soaring into the wind can passively generate forward
thrust by re-directing a relative airflow (headwind).
2)
Relative wing airflow diagrams and analysis fail to
explain the actual wing airflows observed in flight and
the resultant forces generated.
A re-evaluation of wind tunnel experiments shows that
the prevailing view of how a wing accelerates the upper
and lower airflows is false. [9]
Instead, relative airflows over a wing are shown to passively
generate turbulence and forward thrust according to Newtonian
mechanics.
A moving airfoil can actively accelerate a mass of static
air each second (m/dt) flown through to a velocity (dv)
diagonally down and slightly forwards. This action creates
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Independent Research – Relative airflow analysis is flawed.
7.
A WING IS NOT A SAIL
A. Wing and sail airflows and forces are different.
The physics of sailing is frequently compared to the physics
of how airplane wings generate lift. They have similar (but still
different) curved shapes and designs. Consequently, it is
incorrectly assumed that sails and wings produce similar
airflows and forces. This argument is not supported by evidence.
Fig. 7b-ii. Airplane wing cross-sections. [32]
Thicker wings can boost lift (up to a point). Thin wings
are only beneficial in supersonic flight. In contrast, thicker
sails do not boost the thrust generated.
The airflow generated by an airplane actively accelerating
static air downwards to generate lift, is different to how a sail
passively re-directs a relative airflow (wind) to generate thrust.
However, Newtonian mechanics (Force = m/dt * dv) can be
used to explain the forces generated in both situations.
The main similarity between a wing and sail is the curved
topside of a wing and the curved (convex) leeward side of
a sail. The purpose of this is to maximize the Coanda
effect and airflows on these surfaces.
It would be inconsistent to propose that fluid mechanics can
explain the lift by airplane wings while Newtonian mechanics
explains how boats sail into the wind, or vice versa. Either
Newtonian mechanics explains both, as claimed by this paper, or
fluid mechanics does.
Wings and sails have different purposes. Wings provide
lift to keep the airplane airborne, and do not contribute to
the aircraft’s forward motion. In contrast, sails are the sole
source of energy and power to generate forward motion
for a boat.
In summary, the long list of differences between wings and
sails listed above confirms that they generate forces in a
fundamentally different manner. This is particularly significant
as it confirms that Galilean relativity does not apply in this
situation. i.e. A wing flying through static air is not the same as
a boat sailing into the wind (relative airflow).
Wing and sail designs are incompatible
A thin sail with a hollow leading edge would not generate
optimal lift for an airplane in flight. Thin airfoils are only
found on airplanes built in the early 20th Century.
Similarly, a thick wing with a flat underside does not
generate optimal thrust for a sailboat. Attempts made to
use wing designs as the main sails, called wing-sails,
failed to produce beneficial results. Wing-sails do not alter
the physics of sailing and how a force is generated from a
relative wind. See Fig. 7b-iii.
B. Sails and wings compared.
A sail resembles a thin airplane wing with a deep camber, but
the airflows and forces generate by each are different:
1)
Different shape, design, and function. See Fig. 7b-(i-ii).
Wings are thick and symmetrical with a flat underside and
are made of solid materials designed to fly at high speeds.
Wings are aligned in the horizontal direction, to generate
vertical lift against gravity by accelerating a static air mass
downwards.
In contrast, sails are thin and asymmetrical and have a
hollow or concave windward side made of a flexible fabric
designed to sail at relatively low speeds. A sail is aligned
in the vertical direction and generates horizontal thrust and
forward motion from a moving wind.
Fig. 7b-iii. Wing on a sailboat; and
a sail on an airplane.
These observations confirm that sails and wings are
incompatible, and have different designs and functions.
Different equipment and features
The differences between sails and wings are further
illustrated by the features found on wings but not sails,
including: vortex generators, slats and flaps, Gurney flaps,
and stall warning and AOA sensors.
In contrast, features found on sails but not wings, include:
wind indicators (e.g. tell-tales) and spinnakers.
Fig. 7b-i. Sail and wing compared. [32]
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Independent Research – Relative airflow analysis is flawed.
2)
A wing (airfoil) and hydrofoil have similar designs and
functions that actively generate forces; which is different
to how a sail passively generates a force.
Vectors of forces.
If a sail did generate force similar to a wing, it would
generate a sideways force perpendicular to the sail. This
force would push the boat sideways, not forwards, which
is not a benefit to a sailboat. See Fig. 7b-iv.
4)
Momentum and energy.
An airplane is powered by an engine, and its wings
generate lift by transferring momentum and kinetic energy
from the airplane to the air, by accelerating the air.
In contrast, a sail generates forward motion by transferring
momentum and kinetic energy from the apparent wind to
the sail, by creating turbulence and decelerating the wind.
A sailboat has no engine.
Fig. 7b-iv. Sail = wing? Vector forces.
3)
An aircraft’s momentum affects the optimum wing aspect
ratio. For example, gliders with little momentum favour
high aspect ratio wings. In contrast, a sailboat’s
momentum has no impact on the thrust generated by the
sail from the wind or the optimum sail aspect ratio.
Different forces generated.
According to Newtonian mechanics, airplane wings
actively accelerate a static air mass vertically downwards
to generate lift. Whereas, sails passively re-direct a
moving airflow (wind) horizontally sideways to create
turbulence, and therefore, thrust. See Fig. 7b-v.
5)
Wing AOA.
Decreasing the wing AOA of an airplane in flight,
decreases the vertical lift generated. In contrast, decreasing
the sail AOA typically increases the thrust generated in the
direction of travel, (but not if the boat sails dead into the
wind).
6)
Airplanes circulate the air behind them; sailboats do not.
The air flown through by wings is displaced downwards
with gravity. This action pulls/pushes air elsewhere to
replace the space vacated by the air displaced down. The
result is to circulate the air around two counter-rotating
wingtip vortices.
Airliners flying through clouds provide clear evidence of
air being circulated in flight. The air being circulated looks
like two separate swirls of counter-rotating air. See Fig.
7b-vii.
Fig. 7b-v. Active and passive airflows
and forces of a wing and sail.
The resultant forces generated differ based on whether the
sail/wing is moving or static relative to the wind. Galilean
relativity does not apply in this situation.
However, a glider or albatross wing soaring can passively
generate thrust similar to a sail, by re-directing a relative
airflow (wind). See Fig. 7b-vi.
Fig. 7b-vii. Airliners flying in clouds. [63][16]
Sails create turbulence behind them, and do not circulate
the air. i.e. Sailboats never produce circulating wake
airflow, as seen behind airplanes.
7)
Additional differences include:
-
Multiple sails observed on boats, but few airplanes
fly with multiple wings. See Below.
-
A sail can generate a force by running with the wind,
but a wing cannot.
Fig. 7b-vi. Passive airflows of a sail and wing.
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Independent Research – Relative airflow analysis is flawed.
-
A sail cannot generate thrust when sailing dead into
the wind. Whereas, this problem does not arise for a
wing. Even at a zero wing AOA, the wing can
generate lift.
C. Example: Multiple sails vs. Biplanes.
Fig. 7c-iii. One large sail v. two smaller sails
with the same total sail area.
Additional evidence that sails and wings generate forces
differently is provided by the observation that:
-
Sailing boats are frequently observed with two or more
sails aligned behind each other in the direction of travel.
-
In contrast, airplanes with two or more wings are rare.
By trail and error, multiple sails are found to be efficient and
effective at generating a force, whereas multiple wings are not.
In addition, a catamaran with two parallel sails (twin mast)
sailing into the wind produces different airflows and forces, as
compared to a biplane. This is because the airflows created by
biplanes interfere with each other, whereas the relative airflows
from a double rig do not. See Fig. 7c-(i-ii).
Fig. 7c-iv. Boats with single
and multiple sails. [32]
Fig. 7c-i. Twin mast sailboat and biplane. [32]
This space is intentionally left blank.
Fig. 7c-ii. Airflows and forces acting on
twin mast sailboat and biplane.
Sailboats with multiple sails is common, but biplanes are not.
A boat with multiple sails (e.g. jib and mainsheet) provides a
greater force than a single, large sail with the same total sail
area. Specifically, multiple sails increase the mass flow rate
(m/dt), and therefore, increases the force generated (Thrust =
m/dt * dv).
Multiple sails also increases the air re-directed on the leeward
side of the sail, as well as reducing turbulence and airflow
separation. See Fig. 7c-(iii-iv).
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Independent Research – Relative airflow analysis is flawed.
8.
Subsequently, the Davis wing produced unusual but positive
results in wind tunnel tests. The engineers at the time were
highly skeptical of the positive results and questioned their
validity. It is implied that the wind tunnel results were not
authentic. They were either deliberately adjusted or the test
equipment was faulty.
AIRFOIL TESTING – THE DAVIS WING
A. Passive vs. Active airfoil testing.
Nonetheless, the manufacturer selected the Davis wing for a
flying boat in May 1939. The Davis wing’s performance in
practice validated the predictions of its superior aerodynamic
potential.
For the last hundred years, engineers have used wind tunnel
experiments to test new wing designs prior to aircraft
production. However, according to Newtonian mechanics, wind
tunnels are an inefficient and sub-optimal method to measure the
active lift generation of wings in flight, because wings in wind
tunnels passively generate forces. Consequently, wind tunnel
tests lead to a sub-optimal airfoil selection for aircraft.
Later in 1939, the Davis wing was selected for an aircraft that
became the B-24 bomber; where the Davis wing also delivered
superior aerodynamic performance. The B-24 bomber became
one of the most successful and iconic aircraft of WWII.
For example, thick wings perform poorly in wind tunnel tests,
but perform well in flight; which can be illustrated by the Davis
wing of the B-24 bomber used in WWII. See Fig. 8a.
However, the aerodynamic benefits of the Davis wing are
disputed. It is claimed that the reasons for the B-24’s superior
aerodynamic performance are difficult to precisely identify.
Aspect ratios, surface roughness, and other factors not directly
related to the Davis wing can play a role. [59]
In the 1930’s the causes for how a wing generates lift and
drag were not fully understood. Manufacturers progressed airfoil
designs by a trial and error methodology, as evidenced by the
variety of designs attempted and the long list of aircraft failures.
Fig. 8a. B-24 bomber with the Davis wing.
D. Thick wings are beneficial?
At first glance, it seems logical that a thicker wing would
generate greater parasitic drag, due to the need to push the air
flown through out of the path of the wing. However, thicker
wings were found to produce greater lift. Engineers appear to
reason that there was an optimal middle ground. The ideal wing
was not too thick to avoid excessive drag, but not too thin to
avoid weak lift generation. See Fig. 8d-i.
B. The Davis wing. [59]
The Davis wing had a relatively thick towards the leading
edge with a long wingspan and short wing depth (chord), which
produced a high aspect ratio. The Davis wing produced
significantly lower drag (lower drag coefficient) than other
airfoils at the time and most contemporary designs. The Davis
wing was noted to produce higher airspeeds and greater lift,
particularly at relatively low angles of attack.
Afterwards, the good aerodynamic performance of the Davis
wing was attributed to the maintenance of laminar airflow
further back along the wing from the leading edge, as compared
to other airfoils.
Fig. 8d-i. Parasitic drag?
C. Airfoil testing.
The reasoning above indicates that engineers had not
understood that a wing generates lift by pushing the mass of air
flown each second (m/dt) downwards, and therefore, generates
minimal parasitic drag.
Mr. David Davis, a freelance aeronautical engineer and the
inventor of the Davis wing, lacked funds to test his airfoil
designs in wind tunnels. Therefore, in 1934 Mr. Davis
improvised by placing the test airfoils on top of a car borrowed
from a friend. The car was driven at high speeds to test different
airfoils. Mr. Davis unknowingly tested his airfoils in an optimal
manner for how they would perform on an aircraft. See Fig. 8c.
After WWII the Davis wing stopped being used on aircraft, as
thick wings produced additional drag in transonic flight.
Supersonic flight favors thin wings. See Fig. 8d-ii.
Fig. 8d-ii. B-24 bomber and supersonic Concorde.
Fig. 8c. Passive vs. Active airfoil testing.
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Independent Research – Relative airflow analysis is flawed.
Occam’s Razor, where the simplest explanation with the fewest
assumptions is often correct. It is so simple and straightforward
that some academics and engineers are intellectually offended
by it.
9. NEWTONIAN VS. FLUID MECHANICS
Relative airflow vs. Actual airflow
A. Newtonian vs. Fluid mechanics.
Fluid mechanics and the older Newtonian explanations use
the relative wing airflow diagram to explain lift. However, the
Newtonian explanation based on the mass flow rate proposed by
this paper applies an absolute wing airflow diagram. Diagrams
See Fig. 9a-ii.
Broadly, there are two main competing theories for lift, fluid
mechanics and Newtonian mechanics, [1] as outlined below.
Fluid mechanics
According to fluid mechanics, lift is generated by the
difference in velocity between the solid wing and a fluid.
Specifically, horizontal airflow over the topside of a wing
creates vertical lift due to low air pressure, air viscosity friction
or other atmospheric conditions. The airplane is sucked
upwards. [1]
Fig. 9a-ii. Relative and actual
wing airflow diagrams.
Fluid mechanics use relative wing airflow diagrams and wind
tunnel experiments to illustrate how lift is generated. The wing
is shown as being stationary and exposed to a relative airflow
(wind). See Fig. 9a-(i-ii).
Relative and absolute wing airflow diagrams show the same
airflow in different ways. This paper argues that relative wing
airflows are useful for analysing aerodynamics, whereas analysis
of the actual airflows is needed to understand the lift process.
Acceleration or the air – not airflow
Probably the biggest mistake of the past theories of lift (fluid
mechanics and the old Newtonian theories), was to assume
Galilean invariance applied to wings. This assumed that it was
realistic equate how a wing flies in practice to the relative
airflow over stationary wings, as observed in a wind tunnel
experiments. See Fig. 9a-ii above.
Fig. 9a-i. Wind tunnel experiments
and lift. [29][77]
A detailed critique of existing theories of lift (which are
almost all based on fluid mechanics) is beyond the scope of the
paper. Nonetheless, the limitations of the prevailing approach to
lift are summarized in the appendices:
Relative airflows provide the false impression that the air is
constantly flowing, before and after it passes around a wing.
This incorrect perspective led to a focus on the upper airflow
and low air pressure on top of the wing as a cause of lift. Within
the relative airflow model, there was little else that could be
used to explain how a wing generated lift.
- Wind tunnel experiments. [9]
- Critique of NS Equations. See Appendix IV. [7]
It appears that at no point did physicists or engineers reconsider the relative airflow model used to explain lift in the last
100 years. There seems to have been no serious debate on the
basic model used to explain lift, even though it was the opposite
of what a moving wing experienced in flight.
Newtonian mechanics
According to Newtonian mechanics, the wing accelerates (a)
a mass of air (m) downward to create a force (Force = ma). The
reaction generates an equal and opposite upward force that
pushes the aircraft up (lift). This explanation is preferred by
pilots as it is based on what is observed in flight.
This approach by past theories of lift is fundamentally wrong,
because both the top and bottom sides of a wing in flight
accelerate the air it flies through downwards. The critical part of
the lift process is the acceleration of the air, not the air pressure
differences within an existing airflow. Air pressure is a
consequence of the process that generates a lift force, and not
the cause of lift.
There are rival Newtonian explanations of exactly how this
occurs. The old Newtonian theories of lift include ‘flow turning’
or a change in airflow momentum. These are very different to
the Newtonian approach proposed in this paper based on the
mass flow rate.
For example, the past literature on the physics of lift
overwhelming refers to airflow as a cause of lift and not
acceleration of static air. This difference creates a preference for
fluid mechanics to explain lift, not Newtonian mechanics.
Complex vs.. Simple
In general, the theories of lift based on fluid mechanics
(Navier-Stokes equations) tend to be mathematically focused
and extremely complex, but lack empirical validation.
However, once the acceleration of the static air flown through
by the wings is identified as the key part of the lift process. Then
only Newtonian mechanics can be used to explain how a wing
generates lift, not fluid mechanics.
In contrast, Newtonian explanations of lift tend to be
relatively simple. The Newtonian approach is consistent with
19
Independent Research – Relative airflow analysis is flawed.
10.
C. The example of the Davis wing.
DISCUSSION OF RESULTS
The Davis wing was originally designed and inadvertently
tested in the 1930’s by driving a wing forwards on top of a
moving car through static air, which is consistent with how a
wing actively generates lift in practice. The test methodology
produced an airfoil with superior aerodynamic performance.
However, wind tunnel testing of the Davis wing provided
ambiguous results. See Fig. 10c.
A. The wrong approach.
In practice, airplanes in flight pass through stationary air, and
wings do not experience oncoming airflows (headwind).
However, engineers decided to analyse airflows the other way
around; studying how moving air interacts with a stationary
wing, incorrectly assuming that this approach is accurate.
In other words, engineers wrongly assumed that Galilean
relativity applies in this situation. No doubt engineers preferred
relative airflow analysis in part because wind tunnels built on
this basis are significantly cheaper, as compared to wind tunnels
built for an airplane to move through stationary air.
Fig. 10c. Wind tunnel vs. Car
testing of airfoils. [15]
B. Insights.
The contrast in results between the test process using a car
and wind tunnel tests provides additional evidence for the claims
that wings passively and actively generate forces differently.
Even with the crude and simple tests, Mr. Davis was able to
design a superior airfoil in the 1930’s.
Key insights from the analysis above on passive and active
forces include:
-
-
There are two ways in which a wing, sail, or propeller
blade can create forces; actively or passively, which
involve very different airflows and resultant forces.
For example, the prevailing views assert that a sail and a
wing generate a force in the same way, as explained by
fluid mechanics. In contrast, this paper asserts that
Newtonian mechanics can be applied to explain how a sail
passively generates a force by re-directing airflow, and a
wing actively generates a force by accelerating air
downwards.
It is puzzling that no one investigated the discrepancy
between the superior aerodynamic performance of the Davis
wing in practice, and the unusual wind tunnel test results. They
might have discovered the original tests done with a car by Mr.
Davis and then questioned whether wind tunnels produce
optimal results. It appears that it was beyond the capacity of
engineers to question the methodology of testing wings using
wind tunnels. This was a significant missed opportunity.
The difference between passive and actively created forces
is confirmed by analysis of wake airflows and wind tunnel
experiments.
D. Implications for the use of fluid mechanics.
-
Passive and active forces can be explained by the same
Newtonian equation based on the mass flow rate (Force =
m/dt * dv).
-
Relative airflow analysis is only applicable where airflow
is moving against a stationary airfoil to passively create a
force. For example paraglider (or glider) wing soaring, an
albatross dynamic soaring, wind turbine blade, or sailboat.
-
Conventional wind tunnel experiments that blow air
(relative airflow) over a stationary wing or aircraft, do not
provide an accurate method to analyse the active lift
generation by airplane wings. See Fig. 10b.
Relative airflow diagrams may be useful to analyse the
aerodynamics of a wing and how efficiently a wing moves
through the air. But relative airflow analysis does not allow an
accurate analysis of the lift force generated by a wing in flight.
Relative airflow analysis is only applicable to passive force
creation; such as a wind turbine blade or sail.
This means that fluid mechanics (Navier-Stokes equations)
cannot be used to explain active lift generation by an airplane
wing in flight, as it relies on relative airflow analysis. This
assertion that fluid mechanics provides an inaccurate
explanation of lift is supported by other analysis an
observations, including:
Fig. 10b. Wind tunnel experiments
and lift. [13]
20
-
For over 100 years of aviation, engineers have failed to
adequately explain lift using relative wing airflow
diagrams. See Appendix I. [2]
-
Additional problems of relative airflow analysis in wind
tunnels highlighted in a separate paper titled “Is low air
pressure on top of a wing a consequence or a cause of
lift?” [9]
-
A critique of the Navier-Stokes equations used by fluid
mechanics to calculate lift is provided in Appendix IV.
Independent Research – Relative airflow analysis is flawed.
11.
A.
CONCLUSIONS
12. ADDITIONAL INFORMATION
Author: Mr. Nicholas Landell-Mills, independent researcher.
Résumé.
Corresponding email: nicklandell66@gmail.com
The key insight is that there are two ways in which a wing,
sail, or propeller blade can create forces; actively or passively,
which involve very different airflows and resultant forces.
Consequently, Galilean relativity does not apply to wings in the
analysis of airflows and lift. It does matter to the forces
generated whether the wing or the air is moving or stationary.
See Fig. 11a.
Personal background: The author is British, currently living
in France, and was born in 1966 in Botswana. The author is
dyslexic. The author held a private pilot’s license (PPL) for 18
years. He flew and maintained a small, single-engine, homebuilt airplane (Europa XS monowheel, registration: G-OSJN).
Academic qualifications: 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 in
1989.
Professional background: The author qualified as an
accountant (ACA) in England & Wales, as well as a Chartered
Financial Analyst (CFA). He worked in finance for 24 years in
numerous countries for different companies.
Author Contributions: This paper is entirely the work of
the author, Mr. Nicholas Landell-Mills.
Affiliations: None.
Acknowledgements: None.
Fig. 11a. Relative and absolute
wing airflow diagrams.
Disclaimer: All data in the manuscript is authentic, there are
no conflicts of interest, and all sources of data used in the paper
are identified where possible.
The differences between active and passive force creation
have been overlooked or ignored by pilots, academics, and
engineers. Consequently, explaining this argument to people
who have studied lift (engineers), is akin to telling a group of
athletes playing basketball that they are in a football game,
which is subject to completely different rules. They have
fundamentally misunderstood what has been going on and the
rules that apply.
Project duration: This paper is one of the products of nine
years research in applied physics (2014 – 2023) into how objects
fly, sail, fall, and swim.
The continued use of relative airflow analysis and fluid
mechanics to explain how lift is generated by a wing, is unlikely
to provide any significant progress.
Project costs: The direct expenses used to write this paper
were minimal and included things like a computer, internet
access, and living expenses. However, the opportunity cost of
the salary forgone by not being employed while conducting the
research for over eight years, was substantial.
ORCID ID: 0000-0003-4814-0443
Funding: This paper was self-funded by the author.
Request for financial support: This paper could not have
been produced through the established academic and scientific
systems. There is no intention to publish this paper or its
contents in an academic journal, as then it would no longer be
available for free to all. If you found this research to be useful,
valuable, informative, entertaining, or otherwise worthy. Then
kindly thank, support, and encourage the author with a financial
donation via:
-
PayPal.com at: https://paypal.me/landell66
Or buy me a coffee: https://bmc.link/zhJIg4zRCW
Thank you!
21
Independent Research – Relative airflow analysis is flawed.
[33]
13.
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This space is intentionally left blank.
23
Independent Research – Relative airflow analysis is flawed.
C. Academics, engineers, pilots, pundits, …..
APPENDIX I – UNRESOLVED THEORY OF LIFT
Various groups promote at least twelve radically different
theories of flight, which include:
A. The theory of lift remains unresolved.
The physics of lift is disputed.
There is no scientific experiment on a
real aircraft in realistic conditions that
conclusively proves any theory or
equation for how a wing generates lift
to be true.
-
Academics and engineers prefer complex models based
on fluid mechanics (e.g. Bernoulli, Navier-Stokes, Euler,
….). They frequently confuse mathematical proof, wind
tunnel experiments or computer simulations (e.g. CFD) for
scientific evidence.
-
Aircraft manufacturers and designers (e.g. Burt
Rutand) design wings by intuition, trial and error, rather
than by any particular theory or equation for lift.
[43][48][49][50] This aspect is evident from the long list
of failed wing designs as well as the unresolved debate on
how wing design affects lift performance.
Fig. I-a. Unknown.
Experts still cannot agree whether aircraft generate lift by
being pulled upwards according to fluid mechanics, or pushed
upwards according to Newtonian mechanics; nor exactly what
role vortices play. This is surprising given airplanes have been
flying for over a hundred years.
Similarly, micro unmanned vehicles (drones) are simply
built to mimic bird and insect flight, without the
designers fully understanding the physics involved.
Academics, engineers, aircraft manufacturers, pilots, aviation
authorities, and other pundits (e.g. NASA) promote over twelve
diverse theories of lift. New theories are occasionally proposed.
Worse, there is no accepted universal theory for how lift is
generated that applies to all objects that fly. Airplanes,
helicopters, birds and insects each have their own unique
explanations. Different theories are used to explain lift in
different insects. This aspect is highly inconsistent.
-
Pilots prefer Newtonian-based theories of lift, which
correlate to what they experience in practice. Wings push
air downward and the reactive equal and opposite force
pushes the airplane upwards. Momentum is transferred
from the airplane to the air.
-
NASA sits on the fence in this debate and supports both
explanations of lift. “So both Bernoulli and Newton are
correct.” [1] NASA fails to state what proportion of lift
is explained by Bernoulli and Newton; 50/50? Or 70/30?
However, both Newtonian and fluid mechanics cannot be
true as they provide very different and incompatible
explanations of lift. How can NASA not know which
theory of flight is correct?
B. Media and academic commentary.
The media occasionally comment on the ongoing debate
about the mysterious, unproven and unknown causes of lift:

“Staying Aloft; What Does Keep Them Up There?” in
New York Times, 2003. [39]

“How Do Airplanes Fly?” in Live Science, 2006. [40]

“Why the true nature of lift continues to elude us.”
Flying magazine 2012. [88]

“Bernoulli Or Newton: Who’s Right About Lift?” In
Plane & Pilot Magazine, 2016, [89]

“The secret to airplane flight. No one really knows.”
in the National Newspaper, 2012. [41]

“There's No One Way to Explain How Flying Works,”
in Wired Magazine, 2018. [42]

“No One Can Explain Why Planes Stay in the Air.” in
the Scientific American magazine, 2020. [43]

“….there are still myriad open questions about how
animals fly with flapping wings,” [46]
Other groups promote a mixture of different theories of
lift based on vortices, the Magnus effect, the Coanda
effect, …..
-
Some experts advocate that the pressure differential on a
wing explains lift. However, the correlation of pressure
and lift on a wing does not prove causality. Pressure is the
result of a force (Pressure = Force/Area), not a cause.
-
The key factors that affect lift in practice have been
observed and measured; as summarized by the empirical
equation for lift: [1]
However, this equation only describes the factors that
affect lift; it does not explain why these factors affect lift.
The physics of how birds fly is also debated:
“….to date, flapping flight is not fully understood.”
[45]
-
* Wing Area * Lift Coefficient)
“Quest for an Improved Explanation of Lift,” in the
AIAA journal, 2012. [44];

Aviation authorities (e.g. FAA, CAA, EAA; …)
recommend that pilots are taught a theory of flight based
on the Venturi effect and Bernoulli’s principles of fluid
dynamics. NASA describes this theory to be incorrect’ [1]
and academics discredited Bernoulli’s theorem as an
explanation for lift at least as early as 1972. [51]
Lift = 0.5 (Aircraft Velocity2 * Air Density
Academic journals occasionally address this issue as well:

-
In particular, fluid mechanics fails to explain the physics of
the empirical equation for lift, but Newtonian mechanics
can. For example, only Newtonian mechanics can explain
why lift quadruples if aircraft velocity doubles.
24
Independent Research – Relative airflow analysis is flawed.
B. The simple Newtonian explanation (Lift = ma).
APPENDIX II – NEWTON EXPLAINS LIFT
According to Newtonian mechanics, wings with a positive
angle-of-attack (AOA) fly through a mass of air (m) in flight.
This thin slice of air is accelerated (a) downwards, to create a
downward force (Force DOWN = ma). The reactive equal and
opposite upward force generated (Force UP) provides lift; as
summarised by the equations: See Fig. II-b.
A. Newtonian mechanics explains lift. [3]
Newtons Laws of Motion describe the relationship between
the motion of an object (airplane wing) and the forces acting on
it. Newtonian mechanics can be applied in three ways to explain
the lift generated by a wing: See Fig. II-a-i.
1)
Lift = ma
2)
Lift = ma = d(mv)/dt
(momentum theory)
3)
Lift = ma = m/dt * dv
(mass flow rate)
Force DOWN = ma = Force UP (Lift)
(simple explanation)
Fig. II-b Newtonian forces
acting on a wing.
C. Momentum theory: Lift = d(mv)/dt
Fig. II-a-i Newtonian forces acting on
a wing shown by three equations.
There is no net gain or loss of momentum, energy and mass
in this process of generating lift. In flight, wings transfer
momentum and kinetic energy from the aircraft to the air, by
accelerating the air flown through downwards to a velocity (v)
to generate lift, which can be expressed by the equations: See
Fig. II-c.
All three equations above are based on Newtons 2nd Law of
motion (Force = ma). All equations are correct, complimentary,
and produce the same values for lift. The equations describe the
same process of a wing generating lift in different ways.
Force DOWN = ma = m * dv/dt = d(mv)/dt [1]
Other equations:
- Kinetic Energy = K.E. = 0.5 mv2 [1]
- Momentum = mv [1]
K.E. = 0.5 mv2
[1]
The momentum and kinetic energy used to generate lift are
calculated using the same factors; ‘m’ and ‘v’.
Definitions:
- m = Mass of air the wings fly through.
- m/dt = Mass per unit time. The mass flow rate.
- dt = Change in time (i.e. per second).
- dv and v = Change in velocity of the air; and the
velocity that the air flown through is accelerated to in
one second (downwash velocity). i.e. ‘dv = v’.
- a = dv/dt (acceleration).
The downward force generates a reactive equal and opposite
upward force, which provides lift. Combining the equations
above allows lift to be expressed as the change in momentum of
the air accelerated downwards:
Force DOWN = Force UP (Lift) = d(mv)/dt
The wing airflow diagrams and analysis used by the
Newtonian approach depict a moving wing passing through
static air; i.e. Actual wing airflows. In contrast, the relative
airflow analysis used by fluid mechanics (Navier-Stokes
equations) and the flow-turning theories for lift depict the wing
as stationary with relative airflows moving around the wing.
See Fig. II-a-ii.
Or simply:
Lift = d(mv)/dt
Units:
N = (kg m/s) /s
Fig. II-c. Lift generated by transferring
momentum and K.E. to the air.
Fig. II-a-ii. Relative and absolute
airflow diagrams.
25
Independent Research – Relative airflow analysis is flawed.
D. Mass flow rate: Lift = m/dt * dv.
Mass flow rate (m/dt)
Newtonian mechanics based on the mass flow rate is used to
explain active lift generation using actual airflow analysis.
Simply put, the wings fly through a thin layer of air that is
accelerated downward. The reactive equal and opposite force
pushes the wings and aircraft upward. See Fig. II-d-i.
‘m/dt’ is a product of the volume of air flown through each
second by the wings and air density. The volume of air flown
through depends on airspeed, wingspan, and wing reach (i.e.
wing AOA and wing thickness). ‘m/dt’ is also the downwash
created by the wings.
For an airplane in stable flight through static air. Wings with
a positive angle-of-attack (AOA) fly through a mass of air each
second (m/dt), which is accelerated to a velocity (dv) downward.
This action creates downwash and a downward force (Force
DOWN), as summarised by the equation:
‘m/dt’ increases with airspeed. Therefore, lift is expressed as
the mass flow rate ‘m/dt’, and not ‘m’, because this factor of lift
is time-dependent. i.e. Lift depends on the amount of air flown
through by the wings each second.
Force DOWN = ma = m * dv/dt = m/dt * dv [1]
Downwash velocity (dv)
The inertia of the air provides resistance to the downward
force, producing a reactive equal and opposite upward force
(Force UP) that provides lift, as shown by the equation:
‘dv’ depends primarily on aircraft momentum (airspeed and
mass), wing AOA, and wing depth (chord). Slower and lighter
aircraft have less momentum. Their wings strike each air
molecule in their path with less force, which accelerates the air
to a lower velocity (lower dv).
Force DOWN = Force UP (Lift)
‘dv’ is caused by a one-off force (impulse) from the wings,
which accelerates the air. Therefore, ‘dv’ is not time-dependent;
and not expressed as acceleration ‘dv/dt’. ‘dv’ does not change
if the time period is altered.
Evidence of downwash
A wing can only generate lift if it accelerates a mass of air
downward, which creates downwash and a pressure impulse as
observed behind airplanes. The evidence is more evident from
heavier and faster aircraft, which need to accelerate air down
aggressively in order to generate the significant lift needed to
fly. See Fig. II-d-(iii-v).
Fig. II-d-i. Newtonian forces
acting on an airplane.
Lift is defined as the vertical component of the upward force,
in the opposite direction to gravity. See Fig. II-d-ii.
Fig. II-d-ii. Forces acting on a wing.
Fig. II-d-iii. Downwash evident behind airplanes.
For simplicity, it is assumed that an airplane in flight at a very
low wing AOA, the upward force is close to the vertical
direction. Therefore induced drag is negligible, and lift equals
the upward force, as shown by the equation:
Force UP = Lift
The equations above for the momentum transferred from the
wings to the air (i.e. the change in momentum of the air) are
combined as follows:
Fig. II-d-iv. A-380 flying through clouds. [63]
Force DOWN = Force UP (Lift) = m/dt * dv
Simplified to:
Units:
Lift = m/dt * dv
N = kg/s * m/s
The Newtonian approach based on the mass flow rate is a
different approach to the old Newtonian explanations of lift
based on a change in momentum or flow turning.
Fig. II-d-v. Pressure impulse below jets. [61]
26
Independent Research – Relative airflow analysis is flawed.
APPENDIX III – ACTUAL WING AIRFLOWS
The two wing airflows are described in more detail below:
1)
The underside of the wing directly pushes air down. See
Fig. III-a-iv.
The force exerted by the wing on the air creates high
pressure on the underside surface of the wing, as described
by the equation for pressure (Pressure = Force /Area).
A. Two wing airflows.
Analysis of the actual wing airflows that actively generate a
force is described below. This approach differs to analysis of
relative wing airflows that passively generate a force.
The topside and underside of a wing with a positive AOA,
accelerates the static air flown through downwards and slightly
forwards, creating two separate airflows. See Fig. III-a-(i-ii).
1)
The underside of the wing directly exerts a force against
the air flown through that pushes the air downward.
2)
Low pressure on the topside of the wing indirectly pulls
air down, helped by the Coanda effect and gravity.
Fig. III-a-iv. The underside of the wing
directly pushes air down.
2)
U p p er ai r m as s PU L L E D do w n
The forward movement of the wing creates a zone of low
pressure (vacuum) behind it on the topside of the wing.
See Fig. III-a-v.
The low-pressure zone indirectly pulls air above the wing
downwards, helped by:
Wing
L o w er ai r m as s PU S H E D d o w n
Fig. III-a-i. Two actual airflows
on a wing.
Direction
of flight
m/dt
HIGH
pressure
-
Any wing curvature due to the Coanda effect.
-
The weight of the atmosphere (i.e. gravity) pulls the
air above the wing downwards, into the area of low
pressure on top of the wing created by the forward
movement of the wing.
Upper air mass
PULLED down
Upwash
Win
g
LOW
pressure
Lower air mass
PUSHED d own
Fig. III-a-v. The topside of the wing
indirectly pulls air down.
Fig. III-a-ii. 2D diagram of
actual wing airflows.
Additional considerations include:
The wing airflows generated can be illustrated by the path of
air molecules above and below the wing. See Fig. III-a-iii.
-
The leading edge of the wing initially pushes the air up and
forwards, creating upwash.
-
If the air above the wing pulled down does not reach the
trailing edge of the wing by the time that the wing has
moved forwards. Then turbulence can arise, triggering
airflow separation and a stall. This dynamic explains why
stalls always arise at the trailing edge of the wing.
-
After the wing has passed forwards, the lower and upper air
masses accelerated by the wing continue to descend due to
the momentum gained.
-
The generation of lift produces a pressure difference on the
wing; Low pressure on the topside of the wing and high
pressure on the underside of the wing.
Contrary to the prevailing view, this paper argues that wing
the pressure patterns observed are a consequence of the
airflows and resultant process that generates lift, and not a
direct cause of lift.
As the airflows have been accelerated, they both have low
internal air pressure.
Fig. III-a-iii. Actual path of air molecules
as the wing moves forwards in flight.
27
Independent Research – Relative airflow analysis is flawed.
B. The Coanda effect.
C. The topside of the wing is critical for lift.
Fluid flow naturally follows a curved surface due to the
Coanda effect.
The optimum wing AOA maximizes the combined airflow redirected or accelerated downwards by the underside and topside
of the wing, and therefore, the generated force.
For example, water falling from a tap is passively re-directed
to the right (and slightly up) by the curved side of a spoon due to
the Coanda effect. According to Newtonian mechanics, this
action creates a small turning force, due to the change in
momentum of the water flow. The reactive equal and opposite
force pushes the spoon sideways to the left (and slightly
downwards). See Fig. III-b-i.
The top airflow is sensitive to changes in wing AOA due to
the Coanda effect. Whereas, the lower airflow does not rely on
the Coanda effect, which makes it more stable and less sensitive
to changes in the wing AOA. Stalls arising due to disrupted
airflow on the topside of wings provide evidence of this
difference in airflow sensitivity.
Consequently, attention is focused on the upper airflow when
analysing how changes in AOA or other wing characteristics
affect lift. The implication is that the topside of the wing can
displace a much greater airflow under ideal conditions, as
compared to the underside of the wing.
In other words, the lift generation of the topside of the wing is
considered to be a lot more variable, as compared to the
underside of the wing. However, experiments need to be done
to confirm this assertion.
For example, as the wing AOA increases (at a constant
airspeed), more air is displaced down by both sides of the wing.
But the increase is greater on the topside of the wing, due to the
Coanda effect; until a stall is triggered. See Fig. III-c.
Fig. III-b-i. Spoon experiment
demonstrating the Coanda effect.
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 turbulence that can arise.. See Fig. III-b--ii.
Fig. III-b--ii. Airflow on curved and flat wings. [15][28]
Fig. III-c. Upper wing airflow is highly sensitive
to changes in wing AOA.
In general, wings produce a stronger Coanda effect with
laminar (smooth/non-turbulent) 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
(small chord, such as at the wing tips). See Fig. III-b--iii.
The bar graph in the image above (See Fig. 7k) represents the
mass of air flown through and accelerated down each second
(m/dt); for each wing configuration. Consequently, it is a key
factor that directly affects the amount of lift generated.
Fig. III-b--iii. Smooth vs. turbulent wing airflows. [15]
The flat undersides of wings are typically designed to push air
down without inducing any Coanda effect.
28
Independent Research – Relative airflow analysis is flawed.
APPENDIX IV – FLUID MECHANICS CRITIQUE
The criticisms of Navier-Stokes equations (NS equations)
fall into the following broad categories: [7]
A.
A. Navier-Stokes equations (NS equations). [7]
The long list of material criticisms shown below makes it is
extremely puzzling that anyone would use NS equations or fluid
mechanics to explain lift. NS equations are limited as they are
simplifications of reality. Therefore, they are only as good as
how well the model reflects reality. The NS equations are based
on a number of false assumptions, theoretically faults, and
(unsurprisingly) fail to adequately explain what is observed in
practice. See Fig. IV-a
General criticisms.
A.1.
NS equations are unproven.
A.2.
Multiple NS used to explain lift.
A.3.
No agreement on the physics that explain lift.
A.4.
No general theory of lift for all objects.
A.5.
No universal theory or equation of lift.
A.6.
NS equations focus on fluid flow.
A.7.
The existence and smoothness problem.
A.8.
Excessively complex.
A.9.
Little practical benefit to pilots or manufacturers.
A.10.
Excessively abstract.
A.11.
Cannot compare efficiency of lift generation.
B.
False assumptions.
Fig. IV-a. Part of the Navier-Stokes equations.
B.1.
Low air pressure explains lift.
NS equations are widely critiqued in publications such as the
Quanta magazine, for their theoretical problems and limitations
in explaining lift. [57][55][56]
B.2.
B.3.
2D models are sufficient.
Fluid mechanics can explain lift.
B.4.
Fluids can be described by a Reynolds number.
B.5.
Airflow accelerates due to wing curvature.
B.6.
The fuselage is excluded from lift calculations.
The criticisms are particularly significant given that NS
equations have been applied to airplanes for over a hundred
years. It is reasonable to expect that solutions and proof should
have been found by now.
C.
The high degree of uncertainty surrounding the theoretical
basis for NS equations is highlighted by the $1 million award
offered by the Clay Mathematical Institute since the year 2000.
The award is for anyone who can prove that Navier-Stokes
equations explain fluid flow and turbulence. [55]
“Since we don’t even know whether these (Navier-Stokes)
solutions exist, our understanding is at a very primitive level.
Standard methods from PDE appear inadequate to settle the
problem. Instead, we probably need some deep, new ideas.” [55]
This paper asserts that there is no solution to the Navier-Stokes
problem identified by the Clay Mathematical Institute.
Despite the criticisms, fluid mechanics (NS equations) is the
prevailing method used to model airflows and explain lift by
engineers, academics, and pundits.
Description vs. Explanation
There is a subtle but critical difference between being able to
describe the dynamics of the lift observed in practice and
explaining the physics for why and how lift occurs. For
example, the empirical equation for lift:
C.1.
Logic contrary to how other things move.
C.2.
Inconsistent logic with rotors and fan blades.
C.3.
Inconsistent logic for thrust, drag, weight, and lift.
C.4.
C.5.
Why the aerodynamic force has a backward angle.
Exclude wing AOA, induced drag, and stalls.
C.6.
Relative wing airflow diagrams.
C.7.
Focus on immediate wing airflows.
C.8.
Bernoulli and the Venturi effect.
D.
NS equations fail to adequately explain:
D.1.
Flight manoeuvers. e.g. Inverted flight, ...
D.2.
Practical aspects of lift. e.g. Ground effect, …
D.3.
Stalls, turbulence, and supersonic shock waves.
D.4.
D.5.
How aircraft momentum can affect lift.
Dynamic soaring by gliders and albatrosses.
D.6.
How bees can fly.
D.7.
Prandtl’s lifting line theory.
D.8.
The empirical equation for lift.
Lift = 0.5 (Aircraft Velocity2 * Air Density
D.9.
Optimal wing design – Aspect ratios, wing shape
and the energy used to generate lift.
D.10.
Aircraft performance data.
D.11.
The lift paradox – How airplanes fly with a thrustto-weight ratio as low as 0.3.
D.12.
How vortices affect lift.
D.13.
Other enigmas NS equations fail to solve.
* Wing Area * Lift Coefficient)
Lift = 0.5 (Aircraft Velocity2 * Air Density
* Wing Area * Lift Coefficient )
For example, this empirical equation for lift above describes
the relationship between lift and aircraft velocity; where lift is
related to the square of aircraft velocity. But the equation does
not explain the physics for why lift quadruples if aircraft
velocity doubles. Similarly, a significant criticism of NS
equations is their failure to explain what is observed in practice.
29
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Faulty logic.