basic aspects of the theory of jet propulsion - Department of ...
basic aspects of the theory of jet propulsion - Department of ...
basic aspects of the theory of jet propulsion - Department of ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
)81'$0(17$/6 2) 7+(<br />
7+(25< 2) 52&.(7 $1'<br />
63$&(&5$)7 )/,*+7<br />
352)(6625<br />
'U 2/(;$1'5 3(75(1.2<br />
,167,787( 2) 3+
,1752'8&7,21<br />
7KH ,167,787( 2) 3+
,1752'8&7,21<br />
7KH ,QVWLWXWH FRQVLVWV QRZ RI PDLQ<br />
GHSDUWPHQWV<br />
'HVLJQLQJ DQG FRQVWUXFWLRQ RI<br />
IOLJKW YHKLFOHV<br />
(QJLQH EXLOGLQJV<br />
6\VWHPV RI DXWRPDWLF FRQWURO<br />
5DGLR HOHFWURQLF DXWRPDWLRQ<br />
7HFKQRORJ\ RI SURGXFWLRQ
,1752'8&7,21<br />
,Q WKLV FRXUVH FDQ EH GLVWLQJXLVKHG VXFK<br />
SDUWV<br />
z %DVLF DVSHFWV RI WKH WKHRU\ RI MHW<br />
SURSXOVLRQ<br />
z &RRUGLQDWHV DQG DQJOHV V\VWHPV )RUFHV<br />
DQG PRPHQWV WKDW DUH RSHUDWH RQ D URFNHW LQ<br />
IOLJKW<br />
z )OLJKW WUDMHFWRU\ RI D EDOOLVWLF PLVVLOH<br />
z %DVLF SULQFLSOHV RI WKH URFNHWV FRQWURO<br />
z 2UELWDO IOLJKW RI D VSDFHFUDIW
3$57<br />
%$6,& $63(&76 2) 7+(<br />
7+(25< 2) -(7 35238/6,21
&217(176<br />
0DLQ FRPSRQHQW SDUWV RI D EDOOLVWLF PLVVLOH<br />
DQG ODXQFKHU<br />
3ULQFLSOH RI MHW PRWLRQ<br />
&ODVVLILFDWLRQ RI URFNHW HQJLQHV<br />
(TXDWLRQ RI D SRLQW PRWLRQ ZLWK YDULDEOH PDVV<br />
7KUXVW DQG VSHFLILF LPSXOVH RI D WKUXVW RI D<br />
URFNHW HQJLQH<br />
)RUPXOD =LRONRYVN\ IRU LGHDO YHORFLW\ RI D<br />
URFNHW<br />
7HVWLQJ TXHVWLRQV
%$6,& $63(&76 2) 7+( 7+(25< 2) -(7<br />
35238/6,21<br />
0$,1 &20321(17 3$576 2) $ %$//,67,&<br />
0,66,/(<br />
)LJ 7KH VFKHPH RI D VLQJOH VWDJH<br />
URFNHW<br />
SD\ORDG R[LGL]HU WDQN IXHO<br />
WDQN WXUER SXPS XQLWV RI WKH<br />
HQJLQH FRPEXVWLRQ FKDPEHU RI<br />
WKH HQJLQH VWDELOL]HUV FRQWURO<br />
HQJLQHV QR]]OH RI WKH HQJLQH<br />
, QRVH FRQH ,, LQVWUXPHQW PRGXOH<br />
,,, IXHO ED\ ,9 ² DIW ED\
0$,1 &20321(17 3$576 2) $ %$//,67,&<br />
0,66,/(<br />
)LJ 7KH VFKHPH RI D<br />
XQJXLGHG URFNHW ZLWK WKH<br />
HQJLQH RQ VROLG SURSHOODQW<br />
± EDWWOH SDUW<br />
FRPEXVWLRQ FKDPEHU RI<br />
WKH HQJLQH<br />
± VROLG IXHO<br />
QR]]OH<br />
VWDELOL]HUV
0$,1 &20321(17 3$576 2) $ %$//,67,&<br />
0,66,/(<br />
)LJ 7KH VFKHPH<br />
RI D PXOWLVWDJH URFNHW<br />
± SURSHOODQW ED\V<br />
HQJLQHV<br />
SD\ORDG<br />
QRVH FRQH<br />
LQVWUXPHQW PRGXOH<br />
KDUG SRLQWV RI VWDJHV<br />
FRQQHFWLRQ
)LJ )RU DQ H[SODQDWLRQ<br />
RI D SULQFLSOH RI MHW PRWLRQ<br />
35,1&,3/( 2) -(7 027,21<br />
D<br />
E<br />
Z FRPEXVWLRQ FKDPEHU<br />
ZLWKRXW WKH QR]]OH<br />
7HUPLQRORJ\<br />
MHW IORZ<br />
MHW IRUFH<br />
SURSXOVLYH PDWWHU<br />
SULPDU\ HQHUJ\<br />
URFNHW HQJLQH<br />
E VDPH WKH FRPEXVWLRQ<br />
FKDPEHU ZLWK WKH QR]]OH
7+( 52&.(7 (1*,1(6 :,7+ /$5*(<br />
7+5867<br />
/LTXLG URFNHW HQJLQHV<br />
5RFNHW HQJLQHV ZLWK VROLG SURSHOODQW<br />
7KH K\EULG URFNHW HQJLQHV<br />
7+( 52&.(7 (1*,1(6 :,7+ 60$//<br />
7+5867<br />
&/$66,),&$7,21 2) 52&.(7<br />
(1*,1(6<br />
(OHFWUR WKHUPDO URFNHW HQJLQH<br />
(OHFWURPDJQHWLF URFNHW HQJLQH<br />
(OHFWURVWDWLF LRQLF URFNHW HQJLQH
'W<br />
o P W o P 'P<br />
o<br />
P<br />
PY<br />
'P<br />
Y<br />
) 'W<br />
(48$7,21 2) $ 32,17 027,21<br />
:,7+ 9$5,$%/( 0$66<br />
'Y<br />
X<br />
'PX<br />
GY<br />
P<br />
GW<br />
GP<br />
GW<br />
X Y )<br />
X Y ZD<br />
GP<br />
P<br />
GW<br />
)RU<br />
o<br />
GY<br />
o P<br />
GW<br />
GY<br />
P<br />
GW<br />
GP<br />
)<br />
)<br />
GW<br />
3<br />
3<br />
o<br />
PZD<br />
)RU DQ\ LQVWDQW W DW PRWLRQ RI D<br />
SRLQW ZLWK YDULDEOH PDVV WKH<br />
SURGXFW RI SRLQW PDVV RQ LWV<br />
DFFHOHUDWLRQ LV HTXDO WR WKH<br />
JHRPHWULFDO VXP RI UHVXOWDQW DOO<br />
H[WHUQDO IRUFHV ) DQG DGGLWLRQDO<br />
MHW IRUFH 3
3<br />
3<br />
RXW<br />
3<br />
7+5867 $1' 63(&,),& ,038/6( 2)<br />
$ 7+5867 2) $ 52&.(7 (1*,1(<br />
RXW LQ 3<br />
3<br />
K<br />
6<br />
D<br />
3 K H[WHUQDO VWDWLF SUHVVXUH<br />
6 D VTXDUH RI RXWSXW VHFWLRQ RI<br />
WKH QR]]OH<br />
D D 6 3 3D<br />
6D<br />
3RXW<br />
'P<br />
˜ 'P<br />
˜ Z 'P<br />
˜<br />
'P<br />
˜ ZD<br />
3D<br />
6D<br />
3RXW<br />
D<br />
Z<br />
D<br />
'W<br />
3<br />
D<br />
6<br />
D
'P<br />
'W<br />
˜<br />
Z<br />
7+5867 $1' 63(&,),& ,038/6( 2)<br />
$ 7+5867 2) $ 52&.(7 (1*,1(<br />
D<br />
'P<br />
3RXW ˜<br />
'W<br />
'P<br />
'W<br />
3<br />
P<br />
PZ<br />
D<br />
3<br />
Z<br />
D<br />
D<br />
6<br />
FRQVW<br />
6<br />
D<br />
3<br />
D<br />
D<br />
3 PZD<br />
6D<br />
3D<br />
3<br />
D<br />
3<br />
6<br />
3<br />
RXW<br />
D<br />
K<br />
3<br />
3 DWPRVSKHULF SUHVVXUH<br />
IRU WKH VHD OHYHO<br />
3<br />
3<br />
3<br />
K<br />
Y<br />
3<br />
o<br />
PZ<br />
D<br />
3<br />
6<br />
Y<br />
D<br />
6<br />
3<br />
D<br />
3<br />
D<br />
PZ<br />
YH<br />
3<br />
K<br />
3<br />
6<br />
D<br />
3<br />
Z YH DQ HIIHFWLYH IORZ YHORFLW\<br />
LQ YDFXXP<br />
D
7+5867 $1' 63(&,),& ,038/6( 2)<br />
$ 7+5867 2) $ 52&.(7 (1*,1(<br />
$V PDVV VSHFLILF LPSXOVH , 6 FDOO D LPSXOVH WKDW FRPHV<br />
SHU XQLW PDVV NJ RI D SURSHOODQW PDVV , 6 , P<br />
,I WKH HQJLQH WKUXVW LV FRQVWDQW GXULQJ DOO WKUXVWHU RQ<br />
WLPH DQ LPSXOVH GHYHORSHG E\ WKH HQJLQH , 3 W<br />
7KHUHIRUH PDVV VSHFLILF LPSXOVH<br />
, 6<br />
3W<br />
P<br />
><br />
, 6<br />
@<br />
3<br />
P<br />
> 3@<br />
> P@<br />
,<br />
6Y<br />
3<br />
Y<br />
P<br />
> 1 @<br />
> NJ VHF@<br />
Z<br />
D<br />
3<br />
D<br />
6<br />
P<br />
> 1 ˜VHF@<br />
> NJ@<br />
D<br />
Z<br />
YH
)2508/$ =,2/.296.< )25 ,'($/<br />
9(/2&,7< 2) $ 52&.(7<br />
7KH VSHHG RI D EDOOLVWLF PLVVLOH WKDW LV PRYHV LQ YDFXXP<br />
VSDFH ZLWKRXW IRUFHV RI JUDYLWDWLRQDO ILHOGV LV FDOOHG DV<br />
LGHDO VSHHG 9 ,<br />
P9,<br />
G9<br />
P<br />
GW<br />
G9<br />
Z<br />
9<br />
,<br />
,<br />
YH<br />
,<br />
PZ<br />
Z<br />
GP<br />
ZYH<br />
P<br />
FRQVW<br />
Z OQ P OQ&<br />
YH<br />
YH<br />
YH<br />
GP<br />
GW<br />
9,<br />
P P<br />
9,<br />
P<br />
ZYH<br />
OQ<br />
P<br />
P<br />
P<br />
o9,<br />
P<br />
ZYH<br />
OQ<br />
d P<br />
d<br />
P
9<br />
9<br />
9<br />
,<br />
,<br />
,Q<br />
)2508/$ =,2/.296.< )25<br />
,'($/ 9(/2&,7< 2) $ 52&.(7<br />
,GHDO YHORFLW\ IRU PXOWLVWDJH URFNHW FRQVLVWV RI Q<br />
VWDJHV<br />
P<br />
P<br />
Z<br />
Z<br />
Z<br />
YH<br />
YH<br />
YHQ<br />
PQ<br />
OQ P<br />
OQ P<br />
OQ<br />
P<br />
Q<br />
9<br />
,<br />
9,<br />
9<br />
ZYH<br />
OQ P<br />
Z OQ P<br />
YH<br />
,<br />
Z<br />
ZYHL FRQVW PL<br />
9 Q ˜<br />
,<br />
Z<br />
YH<br />
OQ<br />
YH<br />
9,Q<br />
OQ P<br />
Z OQ P<br />
P<br />
YH<br />
FRQVW<br />
6SHHG RI D ILQDO VWDJH LQ Q WLPH ODUJH WKDQ IRU D<br />
VLQJOH VWDJH URFNHW<br />
Q
7HVWLQJ TXHVWLRQV<br />
:KDW LV DVVLJQLQJ WKH PDLQ SDUWV RI D OLTXLG<br />
SURSHOODQW PLVVLOH"<br />
:KDW DUH VWUXFWXUDO GLIIHUHQFHV RI D VROLG PLVVLOH<br />
IURP OLTXLG"<br />
7KH PDLQ SULQFLSOH RI RSHUDWLQJ RI D PXOWLVWDJH<br />
URFNHW<br />
3ULQFLSOH RI MHW PRWLRQ :KDW EDVLF ODZV RI SK\VLFV<br />
DUH XVHG LQ WKH EDVLV RI WKLV SULQFLSOH"<br />
+RZ WKH URFNHW HQJLQHV DUH FODVVHG"<br />
'HGXFH DQ HTXDWLRQ RI PRWLRQ RI D ERG\ ZLWK<br />
YDULDEOH PDVV<br />
'R GHGXFH RI DQ HTXDWLRQ RI WKUXVW IRUFH<br />
:KDW LV VSHFLILF LPSXOVH RI D WKUXVW" :KDW LW<br />
FKDUDFWHUL]HV"
7HVWLQJ TXHVWLRQV<br />
+RZ VSHFLILF LPSXOVH RI D WKUXVW RQ DQ DOWLWXGH RI<br />
IOLJKW GHSHQGV"<br />
$W ZKDW DVVXPSWLRQV WKH IRUPXOD RI WKH =LRONRYVN\<br />
IRU LGHDO VSHHG RI D URFNHW LV GHGXFHG"<br />
7R WKDW WKH LGHDO VSHHG RI D URFNHW LV HTXDO"<br />
:KDW EDVLF ZD\V RI LQFUHDVH RI VSHHG RI D URFNHW"<br />
&DOFXODWH LGHDO VSHHG RI D URFNHW IRU ZKLFK RQH<br />
WKH PHDQ HIIHFWLYH H[KDXVW YHORFLW\ RI JDVHV LV HTXDO<br />
P?V DQG UHODWLYH ILQDO PDVV LV HTXDO<br />
&DOFXODWH LGHDO VSHHG RI D WZR VWDJH URFNHW KDYLQJ<br />
IROORZLQJ YDOXH Z HY DQG µ d<br />
)RU , VWDJH Z HY P?V µ d<br />
)RU ,, VWDJH Z HY P?V µ d