aeroplanes-第3章

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THE　LAW　OF　GRAVITY。As　the　effort　to　fly

may　be　considered　in　the　light　of　a　struggle　to

avoid　the　laws　of　nature　with　respect　to　matter；

it　may　be　well　to　consider　this　great　force　as　a

fitting　prelude　to　the　study　of　our　subject。



Proper　understanding；　and　use　of　terms　is　very

desirable；　so　that　we　must　not　confuse　them。

Thus；　weight　and　mass　are　not　the　same。　Weight

varies　with　the　latitude；　and　it　is　different　at　various

altitudes；　but　mass　is　always　the　same。



If　projected　through　space；　a　certain　mass

would　move　so　as　to　produce　momentum；　which

would　be　equal　at　all　places　on　the　earth's　surface；

or　at　any　altitude。



Gravity　has　been　called　weight；　and　weight

gravity。　The　real　difference　is　plain　if　gravity

is　considered　as　the　attraction　of　mass　for　mass。

Gravity　is　generally　known　and　considered　as　a

force　which　seeks　to　draw　things　to　the　earth。

This　is　too　narrow。



Gravity　acts　in　all　directions。　Two　balls　suspended

from　strings　and　hung　in　close　proximity

to　each　other　will　mutually　attract　each　other。

If　one　has　double　the　mass　it　will　have　twice　the

attractive　power。　If　one　is　doubled　and　the　other

tripled；　the　attraction　would　be　increased　six

times。　But　if　the　distance　should　be　doubled　the

attraction　would　be　reduced　to　one…fourth；　and

if　the　distance　should　be　tripled　then　the　pull

would　be　only　one…ninth。



The　foregoing　is　the　substance　of　the　law；

namely；　that　all　bodies　attract　all　other　bodies

with　a　force　directly　in　proportion　to　their　mass；

and　inversely　as　the　square　of　their　distance　from

one　another。



To　explain　this　we　cite　the　following　illustration：

Two　bodies；　each　having　a　mass　of　4

pounds；　and　one　inch　apart；　are　attracted　toward

each　other；　so　they　touch。　If　one　has　twice　the

mass　of　the　other；　the　smaller　will　draw　the　larger

only　one…quarter　of　an　inch；　and　the　large　one

will　draw　the　other　three…quarters　of　an　inch；

thus　confirming　the　law　that　two　bodies　will　attract

each　other　in　proportion　to　their　mass。



Suppose；　now；　that　these　balls　are　placed　two

inches　apart；that　is；　twice　the　distance。　As

each　is；　we　shall　say；　four　pounds　in　weight；　the

square　of　each　would　be　16。　This　does　not　mean

that　there　would　be　sixteen　times　the　attraction；

but；　as　the　law　says；　inversely　as　the　square　of

the　distance；　so　that　at　two　inches　there　is　only

one…sixteenth　the　attraction　as　at　one　inch。



If　the　cord　of　one　of　the　balls　should　be　cut；　it

would　fall　to　the　earth；　for　the　reason　that　the

attractive　force　of　the　great　mass　of　the　earth　is

so　much　greater　than　the　force　of　attraction　in

its　companion　ball。



INDESTRUCTIBILITY　OF　GRAVITATION。Gravity

cannot　be　produced　or　destroyed。　It　acts　between

all　parts　of　bodies　equally；　the　force　being

proportioned　to　their　mass。　It　is　not　affected　by

any　intervening　substance；　and　is　transmitted

instantaneously；　whatever　the　distance　may　be。



While；　therefore；　it　is　impossible　to　divest　matter

of　this　property；　there　are　two　conditions

which　neutralize　its　effect。　The　first　of　these　is

position。　Let　us　take　two　balls；　one　solid　and

the　other　hollow；　but　of　the　same　mass；　or　density。

If　the　cavity　of　the　one　is　large　enough　to　receive

the　other；　it　is　obvious　that　while　gravity　is　still

present　the　lines　of　attraction　being　equal　at

all　points；　and　radially；　there　can　be　no　pull　which

moves　them　together。



DISTANCE　REDUCES　GRAVITATIONAL　PULL。Or

the　balls　may　be　such　distance　apart　that　the　attractive

force　ceases。　At　the　center　of　the　earth

an　object　would　not　weigh　anything。　A　pound

of　iron　and　an　ounce　of　wood；　one　sixteen　times

the　mass　of　the　other；　would　be　the　same；absolutely

without　weight。



If　the　object　should　be　far　away　in　space　it

would　not　be　influenced　by　the　earth's　gravity；

so　it　will　be　understood　that　position　plays　an

important　part　in　the　attraction　of　mass　for　mass。



HOW　MOTION　ANTAGONIZES　GRAVITY。The　second

way　to　neutralize　gravity；　is　by　motion。　A

ball　thrown　upwardly；　antagonizes　the　force　of

gravity　during　the　period　of　its　ascent。　In　like

manner；　when　an　object　is　projected　horizontally；

while　its　mass　is　still　the　same；　its　weight　is　less。



Motion　is　that　which　is　constantly　combating

the　action　of　gravity。　A　body　moving　in　a　circle

must　be　acted　upon　by　two　forces；　one　which　tends

to　draw　it　inwardly；　and　the　other　which　seeks　to

throw　it　outwardly。



The　former　is　called　centripetal；　and　the　latter

centrifugal　motion。　Gravity；　therefore；　represents

centripetal；　and　motion　centrifugal　force。



If　the　rotative　speed　of　the　earth　should　be　retarded；

all　objects　on　the　earth　would　be　increased

in　weight；　and　if　the　motion　should　be　accelerated

objects　would　become　lighter；　and　if　sufficient

speed　should　be　attained　all　matter　would　fly　off

the　surface；　just　as　dirt　dies　off　the　rim　of　a

wheel　at　certain　speeds。



A　TANGENT。When　an　object　is　thrown　horizontally

the　line　of　flight　is　tangential　to　the　earth；

or　at　right　angles　to　the　force　of　gravity。　Such

a　course　in　a　flying　machine　finds　less　resistance

than　if　it　should　be　projected　upwardly；　or　directly

opposite　the　centripetal　pull。



_Fig　1。　Tangential　Flight_



TANGENTIAL　MOTION　REPRESENTS　CENTRIFUGAL

PULL。A　tangential　motion；　or　a　horizontal

movement；　seeks　to　move　matter　away　from　the

center　of　the　earth；　and　any　force　which　imparts

a　horizontal　motion　to　an　object　exerts　a　centrifugal

pull　for　that　reason。



In　Fig。　1；　let　A　represent　the　surface　of　the

earth；　B　the　starting　point　of　the　flight　of　an　object；

and　C　the　line　of　flight。　That　represents　a

tangential　line。　For　the　purpose　of　explaining

the　phenomena　of　tangential　flight；　we　will　assume

that　the　missile　was　projected　with　a　sufficient

force　to　reach　the　vertical　point　D；　which

is　4000　miles　from　the　starting　point　B。



In　such　a　case　it　would　now　be　over　5500　miles

from　the　center　of　the　earth；　and　the　centrifugal

pull　would　be　decreased　to　such　an　extent　that　the

ball　would　go　on　and　on　until　it　came　within　the

sphere　of　influence　from　some　other　celestial

body。



EQUALIZING　THE　TWO　MOTIONS。But　now　let　us

assume　that　the　line　of　flight　is　like　that　shown

at　E；　in　Fig。　2；　where　it　travels　along　parallel

with　the　surface　of　the　earth。　In　this　case　the

force　of　the　ball　equals　the　centripetal　pull；or；

to　put　it　differently；　the　centrifugal　equals　the

gravitational　pull。



The　constant　tendency　of　the　ball　to　fly　off　at

a　tangent；　and　the　equally　powerful　pull　of

gravity　acting　against　each　other；　produce　a

motion　which　is　like　that　of　the　earth；　revolving

around　the　sun　once　every　three　hundred　and

sixty…five　days。



It　is　a　curious　thing　that　neither　Langley；　nor

any　of　the　scientists；　in　treating　of　the　matter　of

flight；　have　taken　into　consideration　this　quality

of　momentum；　in　their　calculations　of　the　elements

of　flight。



_Fig。　2　Horizontal　Flight_



All　have　treated　the　subject　as　though　the

whole　problem　rested　on　the　angle　at　which　the

planes　were　placed。　At　45　degrees　the　lift　and

drift　are　assumed　to　be　equal。



LIFT　AND　DRIFT。The　terms　should　be　explained；

in　view　of　the　frequent　allusion　which

will　be　made　to　the　terms　hereinafter。　Lift

is　the　word　employed　to　indicate　the　amount

which　a　plane　surface　will　support　while　in　flight。

Drift　is　the　term　used　to　indicate　the　resistance

which　is　offered　to　a　plane　moving　forwardly

against　the　atmosphere。



_Fig。　3。　Lift　and　Drift_



In　Fig。　3　the　plane　A　is　assumed　to　be　moving

forwardly　in　the　direction　of　the　arrow　B。　This

indicates　the　resistance。　The　vertical　arrow　C

shows　the　direction　of　lift；　which　is　the　weight

held　up　by　the　plane。



NORMAL　PRESSURE。Now　there　is　another　term

much　used　which　needs　explanation；　and　that　is

normal　pressure。　A　pressure　of　this　kind

against　a　plane　is　where　the　wind　strikes　it　at

right　angles。　This　is　illustrated　in　Fig。　4；　in

which　the　plane　is　shown　with　the　wind　striking

it　squarely。



It　is　obvious　that　the　wind　will　exert　a　greater

force　against　a　plane　when　at　its　normal。　On　the

other　hand；　the　least　pressure　against　a　plane　is

when　it　is　in　a　horizontal　position；　because　then

the　wind　has　no　force　against　the　surfaces；　and

the　only　effect　on　the　drift　is　that　which　takes

place　when　the　wind　strikes　its　forward　edge。



_Fig。　4。　Normal　Air　Pressure_



_Fig。　5。　Edge　Resistance_





HEAD　RESISTANCE。Fig。　5　shows　such　a　plane；

the　only　resistance　being　the　thickness　of　the

plane　as　at　A。　This　is　called　head　resistance；

and　on　this　subject　there　has　been　much　controversy；

and　many　theories；　which　will　be　considered

under　the　proper　headings。



If　a　plane　is　placed　at　an　angle　of　45　degrees

the　lift　and　the　drift　are　the　same；　assumedly；　because；

if　we　were　to　measure　the　power　required

to　drive　it　forwardly；　it　would　be　found　to　equal

the　weight　necessary　to　lift　it。　That　is；　suppose

we　should　hold　a　plane　at　that　angle　with　a　heavy

wind　blowing　against　it；　and　attach　two　pairs　of

scales　to　the　plane；　both　would　show　the　same

pull。



_Fig。　6。　Measuring　Lift　and　Drift_



MEASURING　LIFT　AND　DRIFT。In　Fig。　6；　A　is　the

plane；　B　the　horizontal　line　which　attaches　the

plane　to　a　scale　C；　and　D　the　line　attaching　it　to

the　scale　E。　When　the　wind　is　of　sufficient　force

to　hold　up　the　plane；　the　scales　will　show　the　same

pull；　neglecting；　of　course；　the　weight　of　the

plane　itself。



PRESSURE　AT　DIFFERENT　ANGLES。What　every

one　wants　to　know；　and　a　subject　on　which　a

great　deal　of　experiment　and　time　have　been　expended；

is　to　determine　what　the　pressures　are　at

the　different　angles　between　the　horizontal；　and

laws　have　been　formulated　which　enable　the　pressures

to　be　calculated。



DIFFERENCE　BETWEEN　LIFT　AND　DRIFT　IN　MOTION。The

first　observation　is　directed　to　the　differences

that　exist　between　the　lift　and　drift；

when　the　plane　is　placed　at　an　angle　of　less　than

45　degrees。　A　machine　weighing　1000　pounds

has　always　the　same　lift。　Its　mass　does　not

change。　Remember；　now；　we　allude　to　its　mass；

or　density。



We　are　not　now　referring　to　weight；　because

that　must　be　taken　into　consideration；　in　the

problem。　As　heretofore　stated；　when　an　object

moves　horizontally；　it　has　less　weight　than　when

at　rest。　If　it　had　the　same　weight　it　would　not

move　forwardly；　but　come　to　rest。



When　in　motion；　therefore；　while　the　lift；　so

far　as　its　mass　is　concerned；　does　not　change；　the

drift　does　decrease；　or　the　forward　pull　is　less

than　when　at　45　degrees；　and　the　decrease　is　less

and　less　until　the　plane　assumes　a　horizontal　position；

where　it　is　absolutely　nil；　if　we　do　not　consider

head　resistance。



TABLES　OF　LIFT　AND　DRIFT。All　tables　of　Lift

and　Drift　consider　only　the