- World View Outreach

Download Report

Transcript - World View Outreach

Created to Fly
Bio-Aerodynamics –
Biological Inspiration for Advanced Aircraft
Presented to
Arizona Origin Science Association
Village Meadows Baptist Church
Sierra Vista, Arizona
September 20, 2014
Larry Kisner, M.S., Physics
Retired Adjunct , Physics, Arizona Christian University
AzOSA Secretary, Board Member
Founder, Director, World View Outreach
Member, Creation Research Society
Created to Fly
Bio-Aerodynamics –
Biological Inspiration for Advanced Aircraft
•bird design has inspired the designers of flying machines for over a century
•Irreducible complexity of nature’s flying creatures reveals God’s creation
•Advances in robotics, computer simulation, aviation have produced amazing
designs of flying machines…but they can not come close to what God created.
Larry Kisner, AzOSA speaker spent 25 years in the aerospace industry as a
research engineer and engineering scientist. He designed and tested
advanced aerodynamic concepts for NASA and the Air Force.
Created to Fly
The Marvels of God’s Creation of Flying Creatures
and Man’s Attempt to Fly
•Man has always looked to the heavens and aspired to fly
•Since the Beginning of Creation on Day 5, Birds have Flown
•Birds were Created fully functional to Fly
•Man has taken about 6000 years to Design a Flying Machine
•Modern Man is Looking to Nature to Design Advanced Aircraft
Which is the More Advanced Flying Machine?
Created to Fly
The Marvels of God’s Creation of Flying Creatures
and Man’s Attempt to Fly
•Man has always looked to the heavens and aspired to fly
•Since the Beginning of Creation on Day 5, Birds have Flown
•Birds were Created fully functional to Fly
•Man has taken about 6000 years to Design a Flying Machine
•Modern Man is Looking to Nature to Design Advanced Aircraft
Which is the More Advanced Flying Machine?
Birds are Designed With Four Basic Wing Types
Each Has Different Aerodynamic Advantages
Long Narrow
Elliptical
Long Pointed
Broad Slotted
High Speed Take-off and Level Flight Specialists
Elliptical or short, rounded wings. This wing
shape allows for fast take-off speeds, sprinting
ability, and great manoeuvrability. These are
found in forest and ground-living birds, especially
pheasants, doves, woodpeckers, perching birds
(passerines), and the true hawks or accipiters.
Gray Hawk shown
Long pointed wings without slots. These wings
give high speed and fast, level flight.
These wings are found on birds that rely on high
speed to feed in the air,
such as swifts, swallows, and falcons.
Lagger Falcon shown
High Speed Gliding and Soaring Birds
Long, narrow wings. These allow high-speed
gliding in the strong winds and help birds take
advantage of short spurts of updrafts. These
high-aspect-ratio wings are characteristic of
soaring sea birds such as gulls and albatrosses.
Ring-billed Gull shown
Broad, slotted wings. These wings are best for
soaring and gliding because they can use warm
air updrafts to fly using almost no energy. Birds
with these types of wings include hawks,
eagles, and vultures. Golden Eagle shown
Light Chaser Birds Gallery
Photographer Rick Furmanek
http://www.lightchaserphotography.com
Light Chaser Birds Gallery
Photographer Rick Furmanek
http://www.lightchaserphotography.com
Light Chaser Birds Gallery
Photographer Rick Furmanek
http://www.lightchaserphotography.com
Light Chaser Gallery
Photographer Rick Furmanek
http://www.lightchaserphotography.com
Light Chaser Gallery
Photographer Rick Furmanek
http://www.lightchaserphotography.com
Basic Aerodynamic Forces
Lift
• Defined as the component of
aerodynamic force
perpendicular to the relative
wind
• Lift Coefficient (CL )
– Indicate capacity of an airfoil to
generate lift
Drag
• Defined as the component of
the aerodynamic force
parallel to the relative wind
• Drag Coefficient (CD )
– Indicate capacity of an airfoil to
generate drag
Stall
• High pressure on
under surface and low
pressure on upper
surface
• Drag increases greatly
and there is no lift
• Instead of smooth
flow, air separates
How Birds Maneuver
• Pitch
– Rotation about the
transverse axis, running
horizontally & transversely
through the center of
gravity
– Related to control of speed
• Roll
– Rotation about the median
axis running horizontally &
longitudinally
– Used to change direction,
usually precedes a turn
• Yaw
– Rotation about the vertical
axis
– Steering
Flight Methods
•
•
•
•
•
Active Flight
Hovering Flight
Migration
Soaring
Gliding Flight
• Active Flight
– Basic requirements: average
lift balances weight & average
thrust balances drag
– Wings do not produce
constant lift and thrust
throughout the wing stroke
• Hovering Flight
– Production of a vertical force
to balance the weight of the
bird
– Symmetrical hovering
– Asymmetrical hovering
• Migration
– Birds have well
developed vision, a wide
hearing range, can
detect air pressure
changes, and have a
magnetic sense that aid
in migration
– Line formations & cluster
formations
– A bird diagonally behind
the leading bird exploits
the upwash created by The routes of satellite tagged Bar-tailed
migrating north from New Zealand. This
the flight of the leading Godwits
species has the longest known non-stop migration
bird
of any species, up to 10,200 km (6,300 mi).
The V formation greatly boosts the efficiency and
range of flying birds, particularly over
long migratory routes. All the birds except the first
fly in the upwash from the wingtip vortices of the
bird ahead. The upwash assists each bird in
supporting its own weight in flight, in the same way
a glider can climb or maintain height indefinitely in
rising air. In a V formation of 25 members, each bird
can achieve a reduction of induced drag by up to
65% and as a result increase their range by 71%. The
birds flying at the tips and at the front are rotated in
a timely cyclical fashion to spread
flight fatigue equally among the flock members.
The V formation greatly boosts the efficiency and
range of flying birds, particularly over
long migratory routes. All the birds except the first
fly in the upwash from the wingtip vortices of the
bird ahead. The upwash assists each bird in
supporting its own weight in flight, in the same way
a glider can climb or maintain height indefinitely in
rising air. In a V formation of 25 members, each bird
can achieve a reduction of induced drag by up to
65% and as a result increase their range by 71%. The
birds flying at the tips and at the front are rotated in
a timely cyclical fashion to spread
flight fatigue equally among the flock members.
• Soaring Flight
– Static soaring
• Slope soaring
• Thermal soaring
Source: Birds in Flight, John Kaufmann, 1970
• Soaring Flight
– Dynamic soaring
Some seabirds dynamically soar by repeatedly diving into the
valleys of ocean waves, and then wheeling back up into the
air. Albatrosses are particularly adept at exploiting the technique
and they use it to travel many thousands of miles using very little
energy from flapping. When the bird pulls up into the wind out of
the still air in the lee of a wave, it suddenly becomes exposed to a
head wind, so the speed of the air over its wings increases. It then
turns in the other direction and, with the wind behind it, dives back
into the shelter of a wave. This also results in an increase in its airspeed. So by repeating this "wheeling" pattern, the bird can
continue flying almost indefinitely without having to put in much
effort besides steering. In effect it is harvesting energy from the
wind gradient.
• Gliding Flight
– Main component in
soaring flight
– Muscles do no
mechanical work
– Flap-gliding
Among birds, flap-gliding is
commonly used by
medium to large species,
where it is regarded to
have a lower energetic
cost than continuously
flapping flight
Features That Affect Flight
• Geometry of wing
– A.R.= wing span / mean wing chord
– Wing loading = weight / area
• Gliding speed proportional to wing loading
•
•
•
•
Tail
Feet
Feathers
Alula
Features That Affect Flight
• Flight feathers
The long, stiff, asymmetrically shaped, but
symmetrically paired feathers on
the wings or tail of a bird; those on the
wings are called remiges (singular remex)
while those on the tail are
called rectrices (singular rectrix). Their
primary function is to aid in the generation
of both thrust and lift, thereby
enabling flight.
The Alula
• Basically a thumb
• Automatic action
• Prevents stall at low
speed
• Spread wing tips
Starling
Mute Swan
Raised
alula
Raised
alula
Source: The Miracle of Flight , Stephen Dalton, 1977
The Alula
• The Alula is a design
feature of a bird that
allows it to fly at high
angles of attack without
stalling. This feature is
used on aircraft that
need to take-off and land
on short runways (STOL)
Wind Tunnel Testing of Bird Wings
• Wind tunnel set up takes a lot of design
• Dynamometer
– Measures lift and drag
Black Scoter Wing
Redhead Wing
C L vs. Angle
2.0
1.5
CL
1.0
0.5
0.0
-15
0
15
30
45
-1.0
B.Scoter(3)7-15
Angle (degrees)
CD vs. Angle
0.7
0.6
CD
-45
-0.5
-30
B.ScoterAlula HeldDown
B.ScoterActual AlulaUp
Redhead(2)7-16
0.5
RedhaedAlulaUp
0.4
Airfoil
0.3
PIV Results for Redhead Wing
Design Features That Affect Stealth
• Tiny serrations on the
leading edge of their
remiges help owls to fly
silently and therefore
hunt more successfully.
Design Features of Feathers
for Support
• The extra-stiff rectrices
of woodpeckers help them to
brace against tree trunks as
they hammer.
A Matter of Life and Breath
Birds breathe differently from
both mammals and reptiles, and
even from dinosaurs. The
respiratory system of a bird
enables oxygen to be fed straight
into air sacs which are connected
directly to the heart, lungs and
stomach. This system keeps air
flowing in one direction through
special tubes (parabronchi) in the
lung, and blood moves through
the lung’s blood vessels in the
opposite direction for efficient
oxygen uptake, an excellent
engineering design.
Biomimicry or Bionics Applications
Insects – spy robots that can cover varied terrain, climb walls,
panoramic vision, morphing wings for stealthy manovering.
Butterfly scales reflect light – Qualcomm developed displays for
hand held smart devices that use almost zero power when static.
Shark skin – reduced drag by manipulating boundary layer while
swimming. Applied to submarines, aircraft fuselages (Airbus),
Speedo Fastskin swimsuits.
Diatoms – valve feature applied to nanodevices, used to deliver
drugs to specific targets in the body.
Dolphin nose – improved efficiency of oceanic vessels
Lotus effect – windshield wipers and water repellent metal
Biomimicry or Bionics Applications
Plant photosynthesis – applied to more efficient fuel cells
Humpback whale flipper – next generation wind turbine blades
Rodents teeth – sharp tool design
Healing power of body – self healing plastics
Gecko tape – microscopic fibers on tape mimic gecko design
Streamlining Principle – sea shell spiral design applied to fans,
impellers, mixers…PAX scientific design 15% more efficient
The nighttime twinkling of fireflies has inspired scientists to
modify a light-emitting diode (LED) so it is more than one and a
half times as efficient as the original. Researchers from
Belgium, France, and Canada studied the internal structure of
firefly lanterns, the organs on the bioluminescent insects'
abdomens that flash to attract mates. The scientists identified
an unexpected pattern of jagged scales that enhanced the
lanterns' glow, and applied that knowledge to LED design to
create an LED overlayer that mimicked the natural structure.
The overlayer, which increased LED light extraction by up to 55
percent, could be easily tailored to existing diode designs to
help humans light up the night while using less energy.
Biomimicry good bad?
DaimlerChrysler Research
department have for the first time
looked for a specific example in
nature which not only
approximates to the idea of an
aerodynamic, safe, comfortable
and environmentally compatible
car in terms of details, but as a
formal and structural whole. The
example arrived at was the
boxfish.
Does this fish remind you of some
of the new car designs?
Bat Sonar Design
Finding with frequencies
Bats send out harmonic pairs of
frequencies to sense where
things are. The strength
differences in the high and low
frequencies in the pair (minimal
in red, greater in blue) help the
bat focus on the target front
Bats demonstrate remarkable skill in
and center.Image: James
tracking targets such as bugs through
Simmons/Brown University
trees in the dark of night. Simmons
Claims the bat’s ability comes from the physics of the echolocation
sound waves and how bat brains have evolved to process their signal.
“This is a better way to design a radar or sonar system if you need it to
perform well in real-time for a small vehicle in complicated tasks,”
Bat sonar design is supported by the Office of Naval Research
A recent study by Nir Nesher and his team at the
Hebrew University of Jerusalem, Israel, published in
Current Biology, reveals how a self-recognition mechanism
prevents octopuses from getting in a twist.
A self-avoidance mechanism of this sort could have
major implications for the design of robots and for use
in artificial intelligence. In particular, creating a
bio-inspired robot whose limbs can react to changes in
terrain, for example, without needing instructions
from central processors can have implications for
advancing technologies in search and rescue operations.
Portugal S J Exp Biol 2014;217:2987-2988
©2014 by The Company of Biologists Ltd
The strong, flapping flight of bats offers
great possibilities for the design of
small aircraft, among other applications.
By building a robotic bat wing, Brown
researchers have uncovered flight secrets of real bats:
the function of ligaments, the elasticity of skin,
the structural support of musculature, skeletal
flexibility, upstroke, and downstroke.
Describing the robot and presenting results
from preliminary experiments is published in
the journal Bioinspiration and Biomimetics.
The work was done in labs of Brown professors
Kenneth Breuer and Sharon Swartz.
Biomimicry in not New
Since the beginning of creation man has dreamed of being able to fly
The first successful flight by the Wright Brothers was aided by insight
from observing birds “warp” their wings to achieve stability
To maximize a plane's efficiency
over a broader range of flight
speeds, Penn State engineers have
developed a concept for morphing
airplane wings that change shape
like a bird's and are covered with a
segmented outer skin like the
scales of a fish.
The Wright brothers gained
insight by studying how birds
change the angle of their
wings in order to roll to the
left or right. They figured that
an aircraft could be controlled
in the same manner by "wing
warping". After proving this
theory or wing warping by
attaching control lines to twist
the sides of a box-kite while in
flight, they decided to build a
glider that incorporated wing
warping.
Man’s Design vs. God’s Design
Engineers working on futuristic spy planes are taking
flight lessons from seagulls.
Robotic drones developed in a military-funded project
change their wing shape to navigate urban areas. The
goal: to soar down a boulevard and swoop between
buildings.
Man’s Design vs. God’s Design
Nature is inspiring the design of the next generation of
drones, or flying robots, that will be used for everything
from military surveillance to search and rescue.
In the journal Bioinspiration and Biomimetics, 14
research teams reveal their latest experimental drones.
The designs are inspired by birds, bats, and insects.
Aerial robotics expert Prof David Lentink, from Stanford
University, says that bio-inspiration is pushing drone
technology forward, because evolution has solved
challenges that drone engineers are just beginning to
address."There is no drone that can avoid a wind
turbine,"And it is very difficult for drones to fly in urban
environments," where there are obstacles to navigate,
Beyond Our Design Capabilities
"If you fly in the urban canyon, through
alleys, around parking garages and between
buildings, you need to do sharp turns, spins
and dives," said project leader Rick Lind, an
aerospace engineer at the University of
Florida. "That means you need to change
the shape of the aircraft during flight."
Lind previously worked at NASA and helped develop
shape-changing wings for the F-18 fighter jet. Since
then, he has re-examined how the
Wright Brothers controlled their early planes by
twisting wings instead of using flaps. Then he pondered
the true masters of flight.
"Birds morph all the time, and they're very agile," Lind
said. "There's no reason we can't achieve the same
control that birds achieve."
Lind's colleague, doctoral student Mujahid Abdulrahim,
photographed agile seagulls in action, then developed a
prototype drone based on the gulls' ability to flex at the
shoulder and elbow. Elbows straight, the plane glides well.
Elbows down, it loses stability but is highly maneuverable.
Elbows up, control is maximized for landing.
Tiny motors move the wings through the full range of motion
in 12 seconds, "fast enough to use in a city landscape,"
Abdulrahim said. The drone can execute three 360-degree
rolls in one second, the engineers say. An F-16 fighter, they
note, can manage at least one roll in a second, but three rolls
would produce excessive g's, killing the pilot.
Beyond Our Design Capabilities
Flapping flight is inherently unsteady, but that’s why it works
so well. Birds, bats and insects fly in a messy environment
full of gusts traveling at speeds similar to their own. Yet they
can react almost instantaneously and adapt with their
flexible wings.
Shyy and his colleagues at U of M have several grants from
the Air Force totaling more than $1 million a year to research
small flapping wing aircraft. Such aircraft would fly slower
than their fixed wing counterparts, and more importantly,
they would be able to hover and possibly perch in order to
monitor the environment or a hostile area.
A more reasonable explanation: God designed the dragonfly
Beyond Our Design Capabilities
Shyy’s current focus is on the aerodynamics of flexible wings
related to micro air vehicles with wingspans between 1 and 3
inches.
“These days, if you want to design a flapping wing vehicle,
you could build one with trial and error, but in a controlled
environment with no wind gusts,” Shyy said. “We are trying
to figure out how to design a vehicle that can perform a
mission in an uncertain environment. When the wind blows,
how do they stay on course?” A dragonfly, Shyy says, has
remarkable resilience to wind, considering how light it is.
The professor chalks that up to its wing structure and flight
control. But the details are still questions.
“We’re really just at the beginning of this,” Shyy said.
A more reasonable explanation: God designed the dragonfly
Man’s Design vs. God’s Design
A Blackbird jet flying nearly 2,000 miles per hour covers 32 body
lengths per second. But a common pigeon flying at 50 miles per
hour covers 75. The roll rate of the aerobatic A-4 Skyhawk plane
is about 720 degrees per second. The roll rate of a barn swallow
exceeds 5,000 degrees per second. Select military aircraft can
withstand gravitational forces of 8-10 G. Birds routinely
experience positive G-forces greater than 10 to 14 G.
“Natural flyers have some highly varied mechanical properties
that we really have not incorporated in engineering,” Wei Shyy,
chair of Aerospace Engineering, U of Michigan.
“They’re not only lighter, but also have much more adaptive
structures as well as capabilities of integrating aerodynamics
with wing and body shapes, which change all the time,”
“Natural flyers have outstanding capabilities to remain airborne
through wind gusts, rain, and snow.” Shyy photographs birds to
help him understand their aerodynamics.
Australian Defense Science and Technology
Australian National University Research
A joint DSTO-ANU team traveled to the United States to
demonstrate a small unmanned delta-wing aircraft featuring
information-processing technology drawn from insects at a NASA
test range in the Mojave Desert northeast of Los Angeles. The
demonstration was intended to show that small aircraft equipped
with an array of simple sensors, including cameras, can avoid
collision with the ground even over rough terrain, says project
leader Javaan Chahl, of DSTO. Chahl and colleagues analyzed the
ocelli, an obscure sensor organ in dragonfly heads, and found a
complex optical and neural arrangement that helps the insects
maintain level flight under adverse conditions.
Australian Defense Science and Technology (cont)
Chahl's team has developed electronic ocelli based on those found
in dragonflies, according to DSTO, to measure the distribution of
ultraviolet and green light to maintain level flight. They also have
borrowed from the insect world to develop a sun compass that
uses the polarization pattern of skylight. The success of the US
forces' Global Hawk and Predator unmanned aircrafts during the
Afghanistan and Gulf conflicts enhanced their standings as
significant battle-zone assets for surveillance roles and remoteweapons platforms.
But these craft are vulnerable, because they depend on several
technologies, including radar, (GPS), which can be used to compute
position, velocity, and time; other active devices for navigation;
and radio links to pilot controllers. Their transmissions can expose
the aircraft and controllers to counter-attack, compromising their
role in covert surveillance.
Biomimicry or Bionics and Evolution
Bionics research does not mean copying nature. The aim is rather
to understand its principles and use them as a stimulus for
innovations. The inventions of nature, which have been developed
and continuously improved over millions of years, provide an
inexhaustible reservoir of ideas and inspirations from which not
only technology can benefit. More than ever before, bionics can
also further the cause of environmental protection. Many of the
innovative concepts which engineers and scientists are adopting
from nature correspond to the principle of sustainability. Nature
always achieves its objectives economically, with the minimum
energy, conserves its resources and completely recycles its waste –
an example which is well worth following.
Biomimicry or Bionics and Evolution
The comparatively recent research area of bionics is actually an
inter-disciplinary subject which combines engineering science,
architecture and mathematics. The basic principle is to make
nature's ideas and problem solutions, which have stood the test of
time over millions of years of evolution, usable for man.
There is no doubt that nature is the best engineer and most
ingenious designer of all.
University of Cambridge Research and Evolution
Industry, commerce and the military are all interested in
developing 'micro-air vehicles' (MAVs), tiny aircraft for
reconnaissance inside buildings and other confined spaces.
Charles Ellington of the University of Cambridge, UK, says
designers will take a leaf out of nature's book: insects are great
little MAVs, perfected by an R&D programme stretching back
350 million years.
In the Journal of Experimental Biology, Ellington looks at the
principles of insect flight that could be emulated by MAV
designers. Engineers will have to throw away their textbooks "insects cannot fly according to the conventional laws of
aerodynamics", says Ellington. By the usual rules of
aerodynamics, the tiny wings of bumble-bees would should
never get them off the ground - let alone allow them to be the
exquisitely manoeuvrable aeronauts they evidently are.
University of Cambridge Research and Evolution
Insects get around their handicaps in two ways. First, they
exert precise control over their attitude in flight, minutely
changing the profile and shape of their wings and bodies
from moment to moment according to their circumstances.
MAV design will have to abandon fixed wings and
incorporate this concept of flexible, 'intelligent' aerofoils.
Second, insects use what Ellington calls 'unsteady high-lift
mechanisms' - tricks to generate more lift than you might
expect from conventional aerodynamics. One such trick is
found in the very tiniest insects, with wingspans of the
order of a millimetre or so, to which the air seems much
more viscous than it does to us - more like water than air.
This has lead some to suggest that such insects might
abandon aerodynamics altogether and swim, rather than
fly through the air.
University of Cambridge Research
More recent study shows, in contrast, that tiny insects
use lift in an ingenious way. The wasp Encarsia formosa,
for example, beats its minute wings (spanning 1.5 mm)
400 times a second. Their wing motion is similar to that
of most insects except that at the top of the
upstroke, Encarsia formosa 's wings clap together and
are then flung apart. Air moving into the vacuum created
by the 'fling' sets up vortices circulating around the
wings that increase lift more than you might expect from
the shapes of the wings alone. A MAV that clapped its
wings together hundreds of times a second, however,
might soon bash itself to pieces.
University of Cambridge Research
Larger insects employ what is called 'dynamic stall': their
mode of flight also generates vortices of air around the wing
margins, and hence lift, so that the insects get caught up in
their own slipstreams. But this mode of flight is inherently
unstable, and insects must constantly manoeuvre themselves
out of the stall before gravity forces them to earth.
So what can engineers learn from insects? The first insectinspired MAVs, thinks Ellington, will be able to independently
adjust the flapping rate and angle of each wing. Initially, such
'intelligent' wings will be like tiny sails, with a stiff leading
edge supporting a membrane, additionally supported by a
boom at the base.
MAVs with short, fast-flapping wings would be able to fly
much faster than MAVs with longer, slower wings - but at the
price of greatly increased power consumption.
Flying Dinosaurs?
Dinosaurs evolved into birds
History of Evolution and Birds
National Geographic Society and the feathered
dinosaur “Archaeoraptor” October 15, 1999
The story exposed
History of Evolution and Birds
R. Monastersky, “All mixed up over birds and
dinosaurs,” Science News, January 15, 2000
“Red-faced and downhearted, paleontologists
are growing convinced that they have been
snookered by a bit of fossil fakery from China.
The ‘feathered dinosaur’ specimen that they
recently unveiled to much fanfare apparently
combines the tail of a dinosaur with the body of
a bird.”
Bird Evolution?
2008 Article on Microraptor
Evolution of Flight?
Man’s Idea
God’s Creation
Bird Evolution is Impossible
For a bird to be able to fly, many components must
work together. Suppose we have an ‘almost’ bird
with all the above structures—viz. feathers, preening
gland, hollow bones, direct respiration (unique lung),
warm blood, swivel joint and forward-facing elbow
joint, but no tail! Controlled flight would still be
impossible. Pitch or longitudinal stability (i.e. along
the direction of flight) can be achieved only with a tail
structure, which most children soon realize when
making paper airplanes!
Bird Evolution is Impossible
The tail is essential, but also needs muscles to vary its
small, but all-important wing surface—for instance,
holding the plumage spread out and downwards
when coming in to land. In other words the tail is
little use as a static ‘add-on’. It must have the means
of altering its shape in flight.
All these mechanisms are controlled by a nervous
system connected to the on-board computer in the
bird’s brain, preprogrammed to allow a wide
envelope of complicated aerodynamic maneuvers.
Bird Evolution is Impossible
Modern airplanes are an example of man’s creativity
and intelligence. This should not be surprising, since
man was created in the image of God, who was the
first to make flying machines. God’s flying machines
are far more complicated than man’s—they can even
repair and reproduce themselves. So how much more
do they declare ‘his eternal power and divine nature’
(Romans 1:20)!