The most important factors in evaluating performance of gliders are minimum sinking speed and minimum gliding angle. To assure their optimum value the energy necessary for flight, that is, the energy of lift and friction must be kept very low, or in other words, weight and total drag which have a decisive effect on the sinking speed and on the gliding angle, must be kept to a minimum. How great the effect of a reduction of these two quantities will be shown in the following

Kosin, R

English

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“’”6’&&d>.-g... 4t~_TE CHNI CAL MEMORANDUMS #-;~2
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
.--— —. --—
3T0. 759
--.——.-—-
THE EF1’ECT OF WEIGHT AND DRAG ON THE SINKING SPEED
AND LIFT/DRAG RATI() OF GLIDERS
By R. Kosin
vol.
Verlag Ton
Luftfahrtforschung
11, No. 5, Octoh~r 25, 1934
R. Oldenbourg, Iiunchen und Berlin
Washington
December 1924
—..
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https://ntrs.nasa.gov/search.jsp?R=19930094658 2020-06-17T00:41:50+00:00Z
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3117601441 1467* __.. ..————-—-–
NATIONAL ADVISORY COMMITTEE
——— ——...—--
TECHNICAL ~~EMORANDUM
-.,.-
-——, _______
TJOR AER()~AuTI(’js
NO. 759
THE EFFECT OF WEIGHT AND 12RAG ON THE SINKING SPEED
AND LIFT/DRAG RATIO Ol? GLIDERS*
Cw ,
R
Cf$
c,
FR,
c,
cmin’
~z’
Vz
min ‘
v~
rein’
c
‘z rein’
Vv z rein’
T~
rein’
Cv
z rein’
By R. lZosin
1. NOTATION
coefficient of residual drag.
coefficient of frictional drag.
mean wing chord, m.
equivalent residual drag, ~2a
- [;
ltft/d&g ratio. x [.
minimum lift/drag ratio.
sinking speed,
mitiimum sinking speed,
flight speed for
‘mih,
lift/drag ratio for Vz
rein’
flight speed for Vz
rein’
wing chord for cmin ‘
wing chord for v
‘rein’
In/s.
m/s.
m/s.
m/s.
r~.
m.
-——————_____________________________ ___________________ ,. ______
*tlEinfluss von Gewicht und Widerstand auf Sinkgeschwindig-
keit und Gleitzah% bei Segelflugzeugen.11 Luftfahrt-
forschung, October 25, Z934, pp. 128-130.
. ... . . ‘.,. ,”.! .“: ’.- .“, ? “
,,.
2 ‘~.A,C. A. Technical Memorandum No. ‘759”-
. . . . ..- ., :.. ...
2. APPRAISAL OF GLIDER PEilFORMANCE
,-- -.,
.. .. .
. .
The factors for evaluating the performance of gliders
are: minimum sinking speed, rni.nirnti”nl’gliding angle, cruis-
ing speed, cruising speed gliding anglej and smallest pos-
sible radius of turn. The most itiportant of these are min-
imum sinking speed and minim-m gliding angle. To assure
their optimum value the energy necessary for flight, that
is, the energy of lift and fr~ction must be kept very low,
or in other words, weight and total drag which have a de-
cisive effect on the sinking speed and on the gliding an-
gle, must be kept .at a r.linimun.
Hovv great the effect of “a”reductidr.. of these two ,
quantities is, shall be shown in the followiilg.
“j2uGG/$l,FT
----
yf3. WING DESIGITED FOR MININUMLI’- DRAG RATIO
.
.
We first treat the wings which Bake the lift/drag ra-
tio a minimum. Itis :
Cp,. :r
-. t (.
Cw. . (p.’.
~ = ––k + :~~ -1-;:. “
Ca Ca c—i .
,.
With
we have
K Caa F F~ c+.;]’ ‘:[ ‘:
Cwi = ————— _— and cm
nb R = i–i
~.::”(7,/,,’,
1
,
.,
K Ca I FR
Cw ,
c= ––--–- + –-:––--+’ –--~.
n b btca Ca
The wing chord Fe corresponding to crnin follows
nin
fron the differentiation of c according to t and equat-
ing the differential quotients
f
dc Yi Ca
/
FR
——-— - .. —
~~ = nb
_z–...–= ();
btCa
—. k“.JG’.”,FC = —.-.-—.—.— 0 zero:
r.1in Ca
I?.A. C.A. Technical Memorandum No. ‘75’9
I 1111
3
With this t
cmin
the minimum
.,.,. ,,. ..
. .
r,.,2., ‘F’R -
c.”=
““ ~E b +
‘c is
.
Cw
P
—- .,.
Ca ,”’
and the flight speed corresponding to .crnin ‘s:’
According to the equation” for cmin an improvement
in effect of FR on % in occurs only in 0.5th power,
and then only on one summand which for very ~ood gliders
amounts to 1/2 to 3/5 of the total c. A’nd even then this
improvement is contingent upon FE becoming smaller, ;
min
—.
corresponding to the reduction of~PR. Unless T is suit-
ably reduced the improvement of l?R is effective only o,n
one surmland of the equation:
Cwi CWR Cw
c = ‘––– -1-–--– + -“–Q
Ca Ca Ca
cw~An improvement of –__=. is in both cases identically
Ca
effective.
The sinking speed Vz for ~~]in is:
=
‘z c min cr~in ‘Enin;
‘is dependent on ~~ and >z~, and v.<, on
cm in JIin
vf-G and –.–>=.,
~ FR
that is, the sinking speed of a glider
designed according to cmin is influenced by Z and
~~. Thisreadily discloses theprepbnderate effect of
the weight over the residual draG on the sinking speed of
a glider designed for Gnin.
4“
,.
. . .
N.’A.C.A. “Technical ldemorandum “No.’“7”69
4. WING DESIGNED I’OR MINIMUM SINKING SPEED
Its best wing chord is:
I?R FR
.:
~. = -________ __________ .____+ _________ =
‘z min
———— .
~
r——— ———— -1 Ca b [x]
Cw 2 PR cm
()
U
c~ I) —._*_6ca + “-–-––~–– - ~;~3nb K
a .1
With this value, the lift/drag ratio becomes:
~R Cw
~v “
=
––––-~-–––-–. + [x] -1-;i~o
z min 3’rrb K[x]
As this term does not lend itself very.readily to dis-
cussion because of its complicity, we have compiled the
values for cw Cwi, and cwR for a num%er of very satis-P’
factory gliders designed for
‘Z~in which are shown in
figure 1. It reveals the smallness of the residual drag
in proportion to the total drag. A change in residual
drag without a corresponding reduction in wing chord does
not afford much change in total drag; and> because of tk.e
relationship between Vz and e , the sinking speed is
likewise affected very little. The effect of the weight
is F
In order to gain an insight into the conditions, we
computed the aspect ratio, flight speed, lift/drag rat?o,
sinking speed, and Cw for a series of gliders with span
increasing from 12 to 24 m (39.35 to 68.9 ft.), which were
designed for ~min and vzmin (see fig. 1).
The Emin shown herein is referred to the gliders
with wing area designed according to cmin $ the v
‘rein
for gliders with wing area designed for
‘Z~i~”
../
The figures serving as basis are those of a glider of
12 n (39.36 ft.) spa~, for wiich the l,lostaccurate data
were available. It was assu~.ed that the’weight of fuselage
and equipment + useful load remains N constant, while the
wing weight rises as the 1.5th power of the span. This is
slightly unfavorable, but it should be borne in mind that
, .,...- —
N. A. C.A. Technical Memorandum No. 759 5
the aspect ratio increases considerably, so that the rela-
tive structural height becomes less. -l-he.r.esidual drag ‘--
‘co”nsi-stsof fuselage andzcontrol-surfac e drag. With a
surface assumed at 6.5 m (69.97 sq. ft.) , its equivalent
flat-plate area is surface CWF.
,,The coefficient of friction according to V7ieselsber-
ger!s measurements is CWF N 0.004.
The control-surface drag increases proportional to the
control;surface dimensions. We assumed it to increase pro-
portional to “the weight ”with increasing span, which is
equivalent to an increase in span with unchanging wing
loading.
‘rL = 0.009 l?L, FL = 2 mz (21.53 sq.ft.) for
———————————————.., —--———.
Span
—.-————————. .————____.-.
Weight of fuse-
lage + useful
load + control
surface ......’....0
--—-
kg
Wing weight ........~kg
I
Equivalent resid- i
ual drag-plate 1
area of fuselage. ..m 2
Equivalent resid-
ual drag-plate
area of control
surfaces . . . . . .. . . . m2
Total. equivalent
residual drag-
plate area ........m2
I—————_________________..
TABLE I
..-——.—
12
.——--—
120
35
0.03
.016
,.046
.—.———
.————
14
————
120
44
).03
.017
.047
-———
The figures given in table I
designed according -to emin , may
————
16
————
120
54
0.03
.018
.048
———.-
————.
18
————
120
64
O*O3
.019
.049
———— .
——--—
20
————
120
’75
).03
.021
.051
-———
b= 12.
-———
22
-———.
120
87
).03
.022
.052
-———
—_-.-_—
24
120
99
J.Q3
.023
.053
with respect to’gliders
be excee~ed with respect
to residual drag by gliders .dqsigned for Vzmin.
However, one is not apt to build a glider defined by
one of these minimum calculations, but rather to keep the
6 ‘N.A.C.A. Technical Memorandum No. 759
.
chord always within the two extreme figures. The reasons
fo,~::t.@i.s.areseveral, viz: TO build the “~ptimum”t ?ing
impli.els.an estimation relative to any quantity wherein both
Vz and c may become less satisfactory, while for a wing
whose chofd lies between the extreme figures, it simply
means that sinking speed is gained at. the expense of glid-
ing angle or vice versa.. The results of the optimum cal-
culation are illustrated in figure 1: aspect ratio, opti-
mum flight speed, gliding angle~ and sinking speed. The
wings for
~min are seen to exceed by far the possible
a“s-pecti5tio,s of the wifig”s$especially when bearing”in
tii’ndthat for reasons of flight performances the taper is
not to exce’ed a.-ce’rta’in’amount.
Using the quoted weights and the stipulation Vmin =
25 m.p.h. for Ca = 1.6 to develop a glider series, give
the data shdw~ in figure 2.
5. DESIGN OF GLIDER WITH STIPULATED CRUISING SPEED
Here the problem is, how to design the glider so
that the performances at this speed are as godd as possi-
ble, or in other words, to assure an optimum c with a
certain speed~
The wing chord should .be reduced up to near &
min ‘
since a smaller c-nerd gives a higher speed and a better
gliding angle, whereas a higher G gives only a higher
speed.. If ~~ is reached, then G would have to be
,min
raised to raise the speed because any further reduction
in E would vitiate the gliding angle againo
Now F: min is not obtainable in wood design on ac-
count of the high aerodynamic quality of modern aircraft;
in fact, our -present structurally attainable wing chords
very closely approach TV Therefore,
z rein” given a wing
of stated. chord, a certain flight speed can only be ob-
tained by an increase in G or with flight at low Ca l
Up, to a certain dynamic pressure q (an? thereby Ca)
flight at low ,Ca improves the gliding.angle..
,.
..- ..
IN.A.C.A. Technical Memorandum No. ’759 7
K Ca ~ CWR Cw
c% ..——-— +,___ + __2; ,, ‘
Ill) Ca Ca
,.., .—
.. .. . .. . ...
dc
‘P
———— .
de Ca dca
Cw
K r CWK P
---
dca = i–; - ;~- +
--——- --—-—— ..—= o
Ca
,.
gives the Ca for the best c.
To raise the flight speed. beyond that of the best c
without vitiating the gliding angle, calls for an increase
in G. But this increases the minimum sinking speed, and
it would be a question of experience in practical flying
as to whether or not a slightly poorer gliding angle in
cruising flight is preferable in favor of a substantial
improvement in minimum ~j~.king speed. The extent to which
the speed may be raised without vitiating the gliding an-
gle depends altogether on the employed airfoil. Then the
choice of airfoil would have to be made from the point of
view of good lift/drag ratio at low ca; that is, perhaps
Cw
??
.-—————.-——- .
Cacruisir.g
I?igure 3 shows the velocity polars of tv?o airplanes
of 20 m (65.62 ft.) span, with 4,410 lb. and 4,58~.4 lb-
flight weight. They differ in wing area only (aspect ratio
h= 1:20 and 1:30). Here it is shown very definitely how
the “flight perforuancest$ Cail be raised by reducing t’he
wing chord, especially with concurrent light design.
The increase in weight alone affords but a minor improve-
ment in gliding angle (and thereby in sinking speed) at
high speeds, while, as stated before~ it vitiates the mini-
mum sinking speed substantially, which may cause the in- ‘
terruption of flight (in long-distance flight).
In figures the cited examples disclose: with ~ =
1:20 and G = 4,410 lb., a 40 percent increase in flight
weight means an 18 percent poorer minimum sinking speed,
while the gliding angle does not improve below w 37.2
m.p.h. l?or h = 1:30 and G = 4,410 lb., a 40 percent
raise in flight weight denotes a 20 percent poorer ~inimu.m
gliding speed, w-nile the gliding angle begins to improve
only at - 41 m.p.”r..
Translation by J. Vanier,
National Advisory Conmittee
for Aeronautics.
—N.A.C.A.
60
~-1
j 40
d’h
*
Technical.Memorandum No. 759
QCD
@
4
OE!.IZII
12 16 20 24
Span b, m
“12 16 2G 24
Span b, m
“04r__!-rl
d-a)(D
g
I?ig.1
30 ““
! ~min
!
20 > ~“ -
In/ s~
I
10 }
v /
‘rein’
o
12 16 20 24
Span b, m
+
,,- m Is
al
(i)
% .40 \1
v
——————
Zmi~’
.:
“2!.!+rn 012 16 2C 24
Span b, m
u i2 16 20 24
Span b, m
“ 12 15 20 24
S@n b, -m
Figure l.- - = 120.+;5 (&)1”5 w;Airplane series: b= 12 to 24m; ti
Gx
%R.r= 0.03+ 0.016 —“ ~ = 0.012
-. G12’
Il. .
IT.A.C.A. Technical Manorandum No. 759 i?ig.2
————60
?/
-P
4
Cmin\ ._ ./\\
..—.
/ I Aspect..ratio needed -for,. “>’ v min /’= A() ~fl .’-—
,~~
.G-:’4:
-.
-Structurally possible
<.4
~~pCct ratio
//_—
~–2@) –
I
Span b, m
~ At 50 km/h flight speed (ca= 1)
.64
.Oz
%
.02
.01
r>
u lZJ 16 20 ~1$
Span b, m
l.(j-——-— —
N
P
‘w;
.8 ——— —...
—
V= 80 km/h-’
jrni s \ “——
T:
.—..
m
~
.4 “——
‘Y / “—v= 50 km h---
~
—.—
.rl
m
n“
“ 1.2 16 20 24
Span b, m
.G2
%’
.C1
o
12 16 x 24
Sym b, m
IEEEl
12 16 20 24
Snan b, m
-b 1.5
Figure 2.- Ai~plane series: b=12 to 24”m; G=l.20+ 35(~) ‘kg;
vminca=~.~ = z3,0km/h
1— “—-
-.
I?.A.C.A. Technical Memorandum ITo. 759
1
1
m
-2-
.
d
(i)
al
$.4
.F’ig.3
,.
CD J
‘rf“~=~om 3’r=O.05
‘Airfoil interpolated between200 kg flight weight)
280 11 ‘1 ,, ~f N Afl.A. 441.2and,4409_—— ——— .
[ C~i~ = 0.012
.2’
.0
.8
.6
.4‘-
.2—
0
.. I
I ,:
I
.—
Lj’, Z(jmz1==1:2
—— - _–+.._._+_ _
“‘?! /’.—— ..=—- =%=””“’i—.—-. ..——.— .—.
1=13., n12A=,1:X3A—..—. /I/ i, /
IN\
#d ‘
,/
\, /
—.,
/
/
.
JI/’/
‘f— “–l—
3
—— —..— .—
10 12 1.4 16 18 20 22 24 26 28 30
Flight s~eed, m/s
FiLgure 3.. Effect of G and h on the velocity pclars of a monoplane
of 20m (65.6 ft.) span.
111l“fl’~-(”~[l11I ‘“
3117601441 1467 :.’”
---- -— J
,,
,.. .
7/ , , ,..&
*! . .
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.


The effect of weight and drag on the sinking speed and lift/drag ratio of gliders

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