supplies¡¡the¡¡true¡¡answer¡£¡¡The¡¡answer¡¡lies¡¡in¡¡the
angle¡¡of¡¡movement¡¡of¡¡every¡¡wing¡¡motion£»¡¡which
is¡¡at¡¡the¡¡control¡¡of¡¡the¡¡bird£»¡¡and¡¡if¡¡this¡¡is¡¡examined
it¡¡will¡¡be¡¡found¡¡that¡¡it¡¡supplies¡¡the¡¡correct
answer¡¡to¡¡every¡¡type¡¡of¡¡wing¡¡which¡¡nature¡¡has
made¡£
AN¡¡INITIAL¡¡IMPULSE¡¡OR¡¡MOVEMENT¡¡NECESSARY¡£
Let¡¡A£»¡¡Fig¡£¡¡9£»¡¡represent¡¡the¡¡section¡¡of¡¡a¡¡bird's
wing¡£¡¡All¡¡birds£»¡¡whether¡¡of¡¡the¡¡soaring¡¡or¡¡the
flapping¡¡kind£»¡¡must¡¡have¡¡an¡¡initial¡¡forward¡¡movement
in¡¡order¡¡to¡¡attain¡¡flight¡£¡¡This¡¡impulse¡¡is
acquired¡¡either¡¡by¡¡running¡¡along¡¡the¡¡ground£»¡¡or
by¡¡a¡¡leap£»¡¡or¡¡in¡¡dropping¡¡from¡¡a¡¡perch¡£¡¡Soaring
birds¡¡cannot£»¡¡by¡¡any¡¡possibility£»¡¡begin¡¡flight£»
unless¡¡there¡¡is¡¡such¡¡a¡¡movement¡¡to¡¡change¡¡from¡¡a
position¡¡of¡¡rest¡¡to¡¡one¡¡of¡¡motion¡£
_Fig¡£¡¡9¡£¡¡Wing¡¡Movement¡¡in¡¡Flight¡£_
In¡¡the¡¡diagram£»¡¡therefore£»¡¡the¡¡bird£»¡¡in¡¡moving
forwardly£»¡¡while¡¡raising¡¡the¡¡wing¡¡upwardly£»¡¡depresses
the¡¡rear¡¡edge¡¡of¡¡the¡¡wing£»¡¡as¡¡in¡¡position
1£»¡¡and¡¡when¡¡the¡¡wing¡¡beats¡¡downwardly¡¡the¡¡rear
margin¡¡is¡¡raised£»¡¡in¡¡relation¡¡to¡¡its¡¡front¡¡margin£»
as¡¡shown¡¡in¡¡position¡¡2¡£
A¡¡WEDGING¡¡MOTION¡£Thus¡¡the¡¡bird£»¡¡by¡¡a
wedge¡like¡¡motion£»¡¡gives¡¡a¡¡forwardly¡propelling
action£»¡¡and¡¡as¡¡the¡¡rear¡¡margin¡¡has¡¡more¡¡or¡¡less
flexure£»¡¡its¡¡action¡¡against¡¡the¡¡air¡¡is¡¡less¡¡during¡¡its
upward¡¡beat£»¡¡and¡¡this¡¡also¡¡adds¡¡to¡¡the¡¡upward¡¡lift
of¡¡the¡¡body¡¡of¡¡the¡¡bird¡£
NO¡¡MYSTERY¡¡IN¡¡THE¡¡WAVE¡¡MOTION¡£There¡¡is
no¡¡mystery¡¡in¡¡the¡¡effect¡¡of¡¡such¡¡a¡¡wave¡like¡¡motion£»
and¡¡it¡¡must¡¡be¡¡obvious¡¡that¡¡the¡¡humming
bird£»¡¡and¡¡like¡¡flyers£»¡¡which¡¡poise¡¡at¡¡one¡¡spot£»¡¡are
able¡¡to¡¡do¡¡so¡¡because£»¡¡instead¡¡of¡¡moving¡¡forwardly£»
or¡¡changing¡¡the¡¡position¡¡of¡¡its¡¡body¡¡horizontally£»
in¡¡performing¡¡the¡¡undulatory¡¡motion¡¡of
the¡¡wing£»¡¡it¡¡causes¡¡the¡¡body¡¡to¡¡rock£»¡¡so¡¡that¡¡at¡¡the
point¡¡where¡¡the¡¡wing¡¡joins¡¡the¡¡body£»¡¡an¡¡elliptical
motion¡¡is¡¡produced¡£
_Fig¡£¡¡10¡£¡¡Evolution¡¡of¡¡Humming¡Bird's¡¡Wing¡£_
HOW¡¡BIRDS¡¡POISE¡¡WITH¡¡FLAPPING¡¡WINGS¡£This
is¡¡shown¡¡in¡¡Fig¡£¡¡10£»¡¡in¡¡which¡¡eight¡¡successive¡¡positions
of¡¡the¡¡wing¡¡are¡¡shown£»¡¡and¡¡wherein¡¡four
of¡¡the¡¡position£»¡¡namely£»¡¡1£»¡¡2£»¡¡3£»¡¡and¡¡4£»¡¡represent
the¡¡downward¡¡movement£»¡¡and¡¡6£»¡¡7£»¡¡8£»¡¡and¡¡9£»¡¡the
upward¡¡beat¡£
All¡¡the¡¡wing¡¡angles¡¡are¡¡such¡¡that¡¡whether¡¡the
suspension¡¡point¡¡of¡¡each¡¡wing¡¡is¡¡moving¡¡downwardly£»
or¡¡upwardly£»¡¡a¡¡support¡¡is¡¡found¡¡in¡¡some
part¡¡of¡¡the¡¡wing¡£
NARROW¡WINGED¡¡BIRDS¡£Birds¡¡with¡¡rapid¡¡flapping
motions¡¡have¡¡comparatively¡¡narrow¡¡wings£»
fore¡¡and¡¡aft¡£¡¡Those¡¡which¡¡flap¡¡slowly£»¡¡and¡¡are
not¡¡swift¡¡flyers£»¡¡have¡¡correspondingly¡¡broader
wings¡£¡¡The¡¡broad¡¡wing¡¡is¡¡also¡¡typical¡¡of¡¡the
soaring¡¡birds¡£
But¡¡how¡¡do¡¡the¡¡latter¡¡overcome¡¡gravitation
without¡¡exercising¡¡some¡¡sort¡¡of¡¡wing¡¡movement£¿
INITIAL¡¡MOVEMENT¡¡OF¡¡SOARING¡¡BIRDS¡£Acute
observations¡¡show¡¡that¡¡during¡¡the¡¡early¡¡stages
of¡¡flight£»¡¡before¡¡speed¡¡is¡¡acquired£»¡¡they¡¡depend
on¡¡the¡¡undulating¡¡movement¡¡of¡¡the¡¡wings£»¡¡and
some¡¡of¡¡them¡¡acquire¡¡the¡¡initial¡¡motion¡¡by¡¡flapping¡£
When¡¡speed¡¡is¡¡finally¡¡attained¡¡it¡¡is¡¡difficult
for¡¡the¡¡eye¡¡to¡¡note¡¡the¡¡motion¡¡of¡¡the¡¡wings¡£
SOARING¡¡BIRDS¡¡MOVE¡¡SWIFTLY¡£Now£»¡¡the¡¡first
observation¡¡is£»¡¡that¡¡soaring¡¡birds¡¡are¡¡swiftly¡
moving¡¡creatures¡£¡¡As¡¡they¡¡sail¡¡overhead
majestically¡¡they¡¡seem¡¡to¡¡be¡¡moving¡¡slowly¡£¡¡But
distance¡¡is¡¡deceptive¡£¡¡The¡¡soaring¡¡bird¡¡travels
at¡¡great¡¡speeds£»¡¡and¡¡this¡¡in¡¡itself¡¡should¡¡be¡¡sufficient
to¡¡enable¡¡us¡¡to¡¡cease¡¡wondering£»¡¡when¡¡it¡¡is
remembered¡¡that¡¡swift¡¡translation¡¡decreases
weight£»¡¡so¡¡that¡¡this¡¡factor¡¡does¡¡not£»¡¡under¡¡those
conditions£»¡¡operate¡¡against¡¡flight¡£
MUSCULAR¡¡ENERGY¡¡EXERTED¡¡BY¡¡SOARING¡¡BIRDS¡£
It¡¡is¡¡not¡¡conceivable¡¡that¡¡the¡¡mere¡¡will¡¡of¡¡the
bird¡¡would¡¡impel¡¡it¡¡forwardly£»¡¡without¡¡it¡¡exerted
some¡¡muscular¡¡energy¡¡to¡¡keep¡¡up¡¡its¡¡speed¡£¡¡The
distance¡¡at¡¡which¡¡the¡¡bird¡¡performs¡¡this¡¡wonderful
evolution¡¡is¡¡at¡¡such¡¡heights¡¡from¡¡the¡¡observer
that¡¡the¡¡eye¡¡cannot¡¡detect¡¡a¡¡movement¡£
WINGS¡¡NOT¡¡MOTIONLESS¡£While¡¡the¡¡wings¡¡appear
to¡¡be¡¡absolutely¡¡motionless£»¡¡it¡¡is¡¡more¡¡reasonable
to¡¡assume¡¡that¡¡a¡¡slight¡¡sinuous¡¡movement£»
or¡¡a¡¡rocking¡¡motion¡¡is¡¡constantly¡¡kept¡¡up£»¡¡which
wedges¡¡forwardly¡¡with¡¡sufficient¡¡speed¡¡to¡¡compel
momentum¡¡to¡¡maintain¡¡it¡¡in¡¡flight¡£¡¡To¡¡do¡¡so¡¡requires
but¡¡a¡¡small¡¡amount¡¡of¡¡energy¡£¡¡The¡¡head
resistance¡¡of¡¡the¡¡bird¡¡formation¡¡is¡¡reduced¡¡to¡¡a
minimum£»¡¡and¡¡at¡¡such¡¡high¡¡speeds¡¡the¡¡angle¡¡of
incidence¡¡of¡¡the¡¡wings¡¡is¡¡very¡¡small£»¡¡requiring¡¡but
little¡¡aid¡¡to¡¡maintain¡¡it¡¡in¡¡horizontal¡¡flight¡£
CHAPTER¡¡II
PRINCIPLES¡¡OF¡¡AEROPLANE¡¡FLIGHT
FROM¡¡the¡¡foregoing¡¡chapter£»¡¡while¡¡it¡¡may¡¡be
rightly¡¡inferred¡¡that¡¡power¡¡is¡¡the¡¡true¡¡secret¡¡of
aeroplane¡¡flight£»¡¡it¡¡is¡¡desirable¡¡to¡¡point¡¡out¡¡certain
other¡¡things¡¡which¡¡must¡¡be¡¡considered¡£
SPEED¡¡AS¡¡ONE¡¡OF¡¡THE¡¡ELEMENTSEvery¡¡boy£»
probably£»¡¡has¡¡at¡¡some¡¡time¡¡or¡¡other¡¡thrown¡¡small
flat¡¡stones£»¡¡called¡¡¡¨skippers¡£¡¨¡¡He¡¡has¡¡noticed
that¡¡if¡¡they¡¡are¡¡particularly¡¡thin£»¡¡and¡¡large¡¡in
diameter£»¡¡that¡¡there¡¡is¡¡a¡¡peculiar¡¡sailing¡¡motion£»
and¡¡that¡¡they¡¡move¡¡through¡¡the¡¡air¡¡in¡¡an¡¡undulating
or¡¡wave¡like¡¡path¡£
Two¡¡things¡¡contribute¡¡to¡¡this¡¡motion£»¡¡one¡¡is¡¡the
size¡¡of¡¡the¡¡skipper£»¡¡relative¡¡to¡¡its¡¡weight£»¡¡and¡¡the
other¡¡is¡¡its¡¡speed¡£¡¡If¡¡the¡¡speed¡¡is¡¡slow¡¡it¡¡will
quickly¡¡wend¡¡its¡¡way¡¡to¡¡the¡¡earth¡¡in¡¡a¡¡gradual
curve¡£¡¡This¡¡curved¡¡line¡¡is¡¡called¡¡its¡¡trajectory¡£
If¡¡it¡¡is¡¡not¡¡very¡¡large¡¡diametrically£»¡¡in¡¡proportion
to¡¡its¡¡weight£»¡¡it¡¡will¡¡also¡¡make¡¡a¡¡gradual¡¡curve¡¡in
descending£»¡¡without¡¡¡¨skimming¡¨¡¡up¡¡and¡¡down
in¡¡its¡¡flight¡£
SHAPE¡¡AND¡¡SPEED¡£It¡¡has¡¡been¡¡observed£»¡¡also£»
that¡¡a¡¡round¡¡ball£»¡¡or¡¡an¡¡object¡¡not¡¡flattened¡¡out£»
will¡¡make¡¡a¡¡regular¡¡curved¡¡path£»¡¡whatever¡¡the
speed¡¡may¡¡be¡£
It¡¡may¡¡be¡¡assumed£»¡¡therefore£»¡¡that¡¡the¡¡shape
alone¡¡does¡¡not¡¡account¡¡for¡¡this¡¡sinuous¡¡motion£»
but¡¡that¡¡speed¡¡is¡¡the¡¡element¡¡which¡¡accounts¡¡for
it¡£¡¡Such¡¡being¡¡the¡¡case¡¡it¡¡may¡¡be¡¡well¡¡to¡¡inquire
into¡¡the¡¡peculiar¡¡action¡¡which¡¡causes¡¡a¡¡skipper
to¡¡dart¡¡up¡¡and¡¡down£»¡¡and¡¡why¡¡the¡¡path¡¡thus
formed¡¡grows¡¡more¡¡and¡¡more¡¡accentuated¡¡as¡¡the
speed¡¡increases¡£
As¡¡will¡¡be¡¡more¡¡fully¡¡described¡¡in¡¡a¡¡later¡¡chapter£»
the¡¡impact¡¡of¡¡air¡¡against¡¡a¡¡moving¡¡body¡¡does
not¡¡increase¡¡in¡¡proportion¡¡to¡¡its¡¡speed£»¡¡but¡¡in¡¡the
ratio¡¡of¡¡the¡¡square¡¡of¡¡the¡¡speed¡£
WHAT¡¡SQUARE¡¡OF¡¡THE¡¡SPEED¡¡MEANS¡£In¡¡mathematics
a¡¡figure¡¡is¡¡squared¡¡when¡¡it¡¡is¡¡multiplied
by¡¡itself¡£¡¡Thus£»¡¡4¡¡X¡¡4=¡¡16£»¡¡5¡¡X¡¡5¡¡=¡¡25£»¡¡and¡¡so
on£»¡¡so¡¡that¡¡16¡¡is¡¡the¡¡square¡¡of¡¡4£»¡¡and¡¡25¡¡the¡¡square
of¡¡5¡£¡¡It¡¡has¡¡been¡¡found¡¡that¡¡a¡¡wind¡¡moving¡¡at¡¡the
speed¡¡of¡¡20¡¡miles¡¡an¡¡hour¡¡has¡¡a¡¡striking¡¡or¡¡pushing
force¡¡of¡¡2¡¡pounds¡¡on¡¡every¡¡square¡¡foot¡¡of¡¡surface¡£
If¡¡the¡¡wind¡¡travels¡¡twice¡¡as¡¡fast£»¡¡or¡¡40¡¡miles
an¡¡hour£»¡¡the¡¡pushing¡¡force¡¡is¡¡not¡¡4¡¡pounds£»¡¡but
8¡¡pounds¡£¡¡If¡¡the¡¡speed¡¡is¡¡60¡¡miles¡¡an¡¡hour¡¡the
pushing¡¡force¡¡increases¡¡to¡¡18¡¡pounds¡£
ACTION¡¡OF¡¡A¡¡SKIPPER¡£When¡¡the¡¡skipper¡¡leaves
the¡¡hands¡¡of¡¡the¡¡thrower¡¡it¡¡goes¡¡through¡¡the¡¡air
in¡¡such¡¡a¡¡way¡¡that¡¡its¡¡fiat¡¡surface¡¡is¡¡absolutely
on¡¡a¡¡line¡¡with¡¡the¡¡direction¡¡in¡¡which¡¡it¡¡is¡¡projected¡£
At¡¡first¡¡it¡¡moves¡¡through¡¡the¡¡air¡¡solely¡¡by¡¡force
of¡¡the¡¡power¡¡which¡¡impels¡¡it£»¡¡and¡¡does¡¡not¡¡in¡¡any
way¡¡depend¡¡on¡¡the¡¡air¡¡to¡¡hold¡¡it¡¡up¡£¡¡See¡¡Fig¡£
1£»¡¡in¡¡which¡¡A¡¡represents¡¡the¡¡line¡¡of¡¡projection£»
and¡¡B¡¡the¡¡disk¡¡in¡¡its¡¡flight¡£
_Fig¡£¡¡11¡£¡¡A¡¡Skipper¡¡in¡¡Flight¡£_
After¡¡it¡¡has¡¡traveled¡¡a¡¡certain¡¡distance£»¡¡and
the¡¡force¡¡decreases£»¡¡it¡¡begins¡¡to¡¡descend£»¡¡thus¡¡describing
the¡¡line¡¡C£»¡¡Fig¡£¡¡1£»¡¡the¡¡disk¡¡B£»¡¡in¡¡this¡¡case
descending£»¡¡without¡¡changing¡¡its¡¡position£»¡¡which
might¡¡be¡¡described¡¡by¡¡saying¡¡that¡¡it¡¡merely¡¡settles
down¡¡to¡¡the¡¡earth¡¡without¡¡changing¡¡its¡¡plane¡£
The¡¡skipper¡¡still¡¡remains¡¡horizontal£»¡¡so¡¡that¡¡as
it¡¡moves¡¡toward¡¡the¡¡earth¡¡its¡¡flat¡¡surface£»¡¡which
is¡¡now¡¡exposed¡¡to¡¡the¡¡action¡¡of¡¡the¡¡air£»¡¡meets
with¡¡a¡¡resistance£»¡¡and¡¡this¡¡changes¡¡the¡¡angle¡¡of
the¡¡disk£»¡¡so¡¡that¡¡it¡¡will¡¡not¡¡be¡¡horizontal¡£¡¡Instead
it¡¡assumes¡¡the¡¡position¡¡as¡¡indicated¡¡at¡¡D£»
and¡¡this¡¡impinging¡¡effect¡¡against¡¡the¡¡air¡¡causes
the¡¡skipper¡¡to¡¡move¡¡upwardly¡¡along¡¡the¡¡line¡¡E£»
and¡¡having¡¡reached¡¡a¡¡certain¡¡limit£»¡¡as¡¡at£»¡¡say¡¡E£»
it¡¡automatically¡¡again¡¡changes¡¡its¡¡angle¡¡and¡¡moves
downwardly¡¡along¡¡the¡¡path¡¡F£»¡¡and¡¡thus¡¡continues
to¡¡undulate£»¡¡more¡¡or¡¡less£»¡¡dependent¡¡on¡¡the¡¡combined
action¡¡of¡¡the¡¡power¡¡and¡¡weight£»¡¡or¡¡momentum£»
until¡¡it¡¡reaches¡¡the¡¡earth¡£
It¡¡is£»¡¡therefore£»¡¡clear¡¡that¡¡the¡¡atmosphere¡¡has
an¡¡action¡¡on¡¡a¡¡plane¡¡surface£»¡¡and¡¡that¡¡the¡¡extent
of¡¡the¡¡action£»¡¡to¡¡sustain¡¡it¡¡in¡¡flight£»¡¡depends¡¡on¡¡two
things£»¡¡surface¡¡and¡¡speed¡£
Furthermore£»¡¡the¡¡greater¡¡the¡¡speed¡¡the¡¡less¡¡the
necessity¡¡for¡¡surface£»¡¡and¡¡that¡¡for¡¡gliding¡¡purposes
speed¡¡may¡¡be¡¡sacrificed£»¡¡in¡¡a¡¡large¡¡measure£»
where¡¡there¡¡is¡¡a¡¡large¡¡surface¡£
This¡¡very¡¡action¡¡of¡¡the¡¡skipper¡¡is¡¡utilized¡¡by
the¡¡aviator¡¡in¡¡volplaning£»that¡¡is£»¡¡where¡¡the
power¡¡of¡¡the¡¡engine¡¡is¡¡cut¡¡off£»¡¡either¡¡by¡¡accident£»
or¡¡designedly£»¡¡and¡¡the¡¡machine¡¡descends¡¡to¡¡the
earth£»¡¡whether¡¡in¡¡a¡¡long¡¡straight¡¡glide£»¡¡or¡¡in¡¡a
great¡¡circle¡£
As¡¡the¡¡machine¡¡nears¡¡the¡¡earth¡¡it¡¡is¡¡caused¡¡to
change¡¡the¡¡angle¡¡of¡¡flight¡¡by¡¡the¡¡control¡¡mechanism
so¡¡that¡¡it¡¡will¡¡dart¡¡upwardly¡¡at¡¡an¡¡angle£»¡¡or¡¡downwardly£»
and¡¡thus¡¡enable¡¡the¡¡pilot¡¡to¡¡sail¡¡to¡¡another
point¡¡beyond¡¡where¡¡he¡¡may¡¡safely¡¡land¡£
This¡¡changing¡¡the¡¡course¡¡of¡¡the¡¡machine¡¡so¡¡that
it¡¡will¡¡glide¡¡upwardly£»¡¡means¡¡that¡¡the¡¡incidence
of¡¡the¡¡planes¡¡has¡¡been¡¡changed¡¡to¡¡a¡¡positive
angle¡£
ANGLE¡¡OF¡¡INCIDENCE¡£In¡¡aviation¡¡this¡¡is¡¡a¡¡term
given¡¡to¡¡the¡¡position¡¡of¡¡a¡¡plane£»¡¡relative¡¡to¡¡the
air¡¡against¡¡which¡¡it¡¡impinges¡£¡¡If£»¡¡for¡¡instance£»
an¡¡aeroplane¡¡is¡¡moving¡¡through¡¡the¡¡air¡¡with¡¡the
front¡¡margin¡¡of¡¡the¡¡planes¡¡higher¡¡than¡¡their¡¡rear
margins£»¡¡it¡¡is¡¡said¡¡to¡¡have¡¡the¡¡planes¡¡at¡¡a¡¡positive
angle¡¡of¡¡incidence¡£¡¡If¡¡the¡¡rear¡¡margins¡¡are
higher¡¡than¡¡the¡¡front£»¡¡then¡¡the¡¡planes¡¡have¡¡a¡¡negative
angle¡¡of¡¡incidence¡£
The¡¡word¡¡incidence¡¡really¡¡means£»¡¡a¡¡falling
upon£»¡¡or¡¡against£»¡¡and¡¡it¡¡will¡¡be¡¡seen£»¡¡therefore£»
that¡¡the¡¡angle¡¡of¡¡incidence¡¡means¡¡the¡¡tilt¡¡of¡¡the
planes¡¡in¡¡relation¡¡to¡¡the¡¡air¡¡which¡¡strikes¡¡it¡£
Having¡¡in¡¡view£»¡¡therefore£»¡¡that¡¡the¡¡two¡¡qualities£»
namely£»¡¡speed¡¡and¡¡surface£»¡¡bear¡¡an¡¡intimate
relation¡¡with¡¡each¡¡other£»¡¡it¡¡may¡¡be¡¡understood
wherein¡¡mechanical¡¡flight¡¡is¡¡supposed¡¡to¡¡be¡¡analogous
to¡¡bird¡¡flight¡£
SPEED¡¡AND¡¡SUR
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