The publication of the following details is due to the desire of the editor to have the problems of soaring flight treated on the occasion of the Rhone Soaring Flight Contest

Prandtl, L

English

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TECHNICAL MEMORAND~S
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““N~T~,ONALADVISORY COMMITTEE FOR AERONAUTICS
.,:SOME R3MARKS
No. 47
CONCERNING SOARING FLIGHT
By L. Prandtl
From “Flight, “ September 22, 1921
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October; 1921
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SOME ~lMRKS—rONC~----SOXRtNG FLIGHT.*
By.
L. Prandtl.
-—..,...
.-. .,,...
-,.
.
.
The publication of the following details is due to the de-
sire of the editor to have the problems
ed on the occasion of the Rhone Soaring
main,.these problems are only connected
.,
more or less known. For anything wtiich
of soaring flight treat-
~light Contest. In the
with matters which are
nay be new, I am indebt-
ed to frequent talks with G,”Madelung and A. Betz, who have giv-
......
en me their permissiori to publish these remarks.
By soaring flight - in contrast with gliding flight - is
meant motorless flight without 10S8 of height. According to the
laws of the mechanics of flight, two sources of energy are avail-
able for soaring flight. One is, air cuzrents having an upward
trend; and the other is, irregularities in.the natural wind,
Under the iatter head we can dis,tin~isk between two effective
forms: (1) Great fluctuations in the strength (and also direc-
tion) of the wind, lasting several seconds; (2) The rapid fluctu-
e.tion in wind direction which is commonly described as “turbulent
wind, “ The fluctuations of long duration can only be utilized by
effecting considerable changes in the velocity and height of the
machine. For instance, by, in one single =mst, climbing at the
expense of relative velocity., and theg~ in the calm which followsj
,,,. ,,
gliding with a dofiward acceleration. The procedure to follow in
~,
,’
order to efiract energy from the wind can be condensed into a sim-
* From “Zeitschrift fur Flugtechni~ und Motorluftschiffahrt, ?I
July 30, 1921.
.,
-2”
ple rule: One must a.t.tempt to equalize the fluctuations in the
wind. In so doing,
——
the energy in the wind fluctuations is obvi-
,-.
otis’ly>edi~ced,”‘and “the‘energy of the machine increased by a cor-
reSFonding amount. Thus, for instance, one i?.1’USt present great
resistance against a gust, sfiallresistance against a .lu1l; in an
upward cu~rent the machine ii~ust be gradually elevated to increase
the pressure on the wings, in a downward current depressed to de-
crease the pressure.
The fluctuations of short duration, on the other hand, can be
utilized without any substantial change in velocity of the e.g.
of the machine. As A. i3etzhas shown in a very instructive arti-
cle in this journal in 1912,* useful effect is available in suf-
ficiently great fluctuations in i~inddirection even with rigid
and non-warped aeroplane nings. With elastically mounted or flex-
ible wings, the force obtained from changes tn wind direction, if
these be sufficiently great, may assume perceptible proportions.
The effect may be imagined as resembling that of the so-called
fish-tail propellers. This name has been used to designate an ar-
range~lent by which the waves of the sea have been’utilized for
the production of power.
flexible plates, rigidly
sides of a ship. As the
The arrangement consists of a number of
attached with their leading edge to the
waves rise and fall the plates bend like
~~the tai-l-of+.,a-.fish.,and.produg.e.power
when bent upwards.
When we now come to the question
both when bent downwards and
., .... ,.
of which of these sources of
-gauxgy do soaring birds make use, the answer can - at least as re-
* A, Betz: ““A contritiution to the Explanation of Soaring Flightj~r
Z.F.M. , 1912, p,269.
-3-
gards our domestic birds - only be tha,t,if ‘notexclusively at ahy
.,,,. rate-mainly, they *take ad~-antage of risirigai~ currents. Rising
—.
,.., ,,.
air currents are always to be found in uneven country when a wind ~
is ?o].owing.Tileyare also caused over the plains by meteorologi-
cal influences. For
rising air currents,
exten~...i_s~acece, the
their flying practice birds naturally seek the
and as these are frequently not of very ~~eat
birds hav~ to circie in orde~ to rsiflainin
the rising air currents. By observing the soaring of birds of
prey one may frequei~tly see that they suddenly lose height and
then conmlenceto fiap their wings, continuing in flapping flight
until they are seen suddenly to rise. From this moment onwards
they recoilmenceto soar. They have again found their rising cur-
rent which they had previously lost. The soaring seagulls near a
steamer make use of the air deflected by the steamer and comii~ence
to flap as soon as, for soriereason or otk.er,they have to leave
.
their favorable position.
That a bird intentionally r:lakesuse of gusts does not appear
to occur generally. In order to do so it would kave constaiitly
to inake jumps up and down, which, .SOfar as I am aware, it has not
been observed to do. On the other hand, it does not
Iy that many birds utilize the rapid.fluctuations in
~ides, after the manner of the fish-tail principle.W..t”,. .. -, T,,.*..,,.
...
appear unlike-
the wind be-
Probably, ho’n-
ever, these forces suffice-in no case to cov”er~fie’&fi”%i2e’work of
“no soarirlgwithout a wind with an up-flying, so that the axiom .
ward trend*lcan probably be accepted as correct. It might be nen- ~
-4--
tidned that in regard to sea birds, each”individual wave gives the
wind .anupward deflection, of which the birds take advantage.*
..-...,.. ...
. . .-,. ..... ..
In the case of human soaring flight, all the previously men-
tioned possibilities of making-use of the energy in the air hold
good in principle. The fish-tail effect, as I will call it for
the Sake of brevity, may ‘possibly be utilized by a suitable form
of flexible ~ving-sectionsj although I should”advise experiments
with crewless (unbemannten) models. It is quite probable that the
wind flu~.tuations, which such wings vmuld be designed. to utilize,
might frequently not be of such magnitude as to have a perceptible
effect, In view of the probably inconsiderable gain to be expect-
ed one would not like to risk the uncertainty of the flying quali-
ties of such a flexible aerofoil, which might easily lead to a use-
less, or even dangerous, machine. A crewless model, on the other
hand, could more easily be sacrificed.
The utilization of great mind fluctuations is a“question of
the skill of individual fliers. It is conceivable”now and then to
extract a slight gain from these, but too much should not be ex-
pected from this source. There then remains, as the most important
help to human soaring flight, air currents with an upward trend.
If it is desired to utilize to the fullest extent rising air
currents, one must strive to build machines with a slo~ rate of
,..
desc&t (kink&&~h:~~~indi”~k’&~t)”.‘ O“ne’’’”is%henin’a P
\
osition to util-
‘<since~~’iting this article I find in Physikalischen Berichten,-
1S21, some notes by Everling on a work on soaring flight by E. H.
20 (1921), pp. 219-227), accordingHankin (Proc. Cambr. Phil. SOC.,
to which soaring by turbulent mind only is said to be possible when
the earth is strongly heated, as occurs in the trop$cs, Dr. Hankin
describes observations of birds, dragon-flies and flying fish.
ize all rising air currents
.- than the rate of descent of
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whose vertical component ‘“is:‘ greater
the machine, provided that, at the same
time, the upwazd slope of the mind is greater than the best glid-
ing angle of the machine. On a slope which is steeper than the
best gliding angle of the machine, it is moreover possible to soar
in winds whose velocity is smaller than that of the lowest gliding
speed of the machine,
greater than the rate
in this case soar out
viously rise in doing
provided the rate of ascent of the wind is
of descen”tof the nachine.
horizontally into the free
so. It would, however, in
The machine will
air and will ob-
time get outside
the region of the ascending wind, but if the slope has sufficient
breadth the machine can be pointed diagonally to the slope and pass
across it at the same height or climbing slowly, the sideways dis-
placement giving sufficient speed for soaring. This method of fly-
ing can often be observed on seagulls over the beach. Under simi-
lar conditions the method should be possible of execution by human
beings.
The conditions for the smallest possible rate”of descent can
be formulated. To begin with, the gliding angle c is given by the
well known relation
-.
tan c =
~
c& (1)
. .;. . Further, the.rate’of descent, Vz = v sin e . If we observe
that the weight G . Ca F~P@ , that is
v ‘m
(2)
l
1 11
-6-
.
and that.,owing to the fact that the sm.gle is small, sin c and tan
.. .. .. .
e can “be-exchcji~e”d,’tie”“find’ ‘“ ~~~ ~~ ~~-
(3)
Therefore, for ~.given wing loading, the rate of descent is
smallest when the well-known efficiency ratio Cas/ctTz is a maxi-
muiil . We must therefore aim at the smallest possible Cli with a.
large Ca, This is obtained on the one hand by a large aspect ra-
tio, or~the other by avoiding all sources of extra resistance.
“Inorder to obtain a large Ca one would have to choose a deeply
cambered wing s“ection,as is “wual with fast motor-driven aeroplanes.
If a polar diagram is available the maximum Ca3/Cw2 is easily
found by trial. But if one wishes to obtain the zesults by calcu-
lation - which has t’headva~.tage that one is not obliged to start
with a previously giver.aspect
to do so as follows: - Fo~ the
ered it is frequently possible
ratio --one may for instance proceed
range of aii.glesof incidence consid-
to express the change of Cw with
chemge of Ca by an equation of the following forzn:-
0
*W ‘ACa2+B (4)
The coefficient A is mainly dependent wpon the “induced drag,~’
which in turn depends upon the aspect ratio. As, however, the
,..!.,,,,..”.
It”section’dra-g-tl’‘also’fisu~ll~~’ti~bw’san iri5r”ea&#ttitllgreater ‘angles
of incidence$ this earlbe inciuded in t’hecoefficient A by writing
A=L+A?Tb2 (5)
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in which, as usual, b indicates span. B in equation (4) then
‘indi”d’~te’sthe constant ~~ortion of the ‘!seotiondr~.gjtlincluding
all detriinent.alresistance of the nachin&. The second factor of
equation (3) nb~.~becorles C~iCa 3/2 =A G’al’2 -t.B Ca-3’~ A simple
calculation gives for the minirnur.1of this expression the relation
A GaA =33,
‘dlience
. c~=m
As will be seen, the iziniuu.nof 3/2Cm/Ca occurs when the
first portion”of the resistance in equation (4) is Vnree times as
(6)
great as the second. The total
consequently
Cw then becomes equal to 4 B, and
(’i) ‘
that
In making this calculation one rmst, of course, make certain:
one obtains frofilequation (6) a value of Ca which, lies with-
in the limits for which form.la (4) is valid. Should this not be
possibl~ the greatest value of Ca for which formula (4) is valid
ma37 be taken. It might be of interest to elucidate~hese cal~la-
tions by a numerical example, the figures for which are taken from
model tests- Assuming an aspect ratio F/b2 of 1/10-, and further,
Al=O.01, and E= 0.025 we obtain A ~ 0.0318 + 0,01 = 0.0418.
.. Thus ,..
r
---–,-. .
Ca =~~~ 0.025 = i.34,<
0.0418
,..
r
I Imlll I Hllllll 1111111111I 111111111111111 11 I ,,.,,.,,,,,, , .,
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wh.ichfigure is attainable with deeply-cambered aerofoils. Cm be-
... .=... ,, ..,- ,,
c Onles ~ 4 B = !).1,’””T-hisgives C~”/Cwz “z 240.’ If we assume a wing
loading of S kghr~ (1.85 lbs/sq.ft.) we get
/
—
f
a’”x”~ = “-~6 ~ 9 z 12
p ~ ~“4
Thus the rate of descent becomes 12//%---= 0.’775m/s2.
If a value of Ca of 1,.2 only were attainable, the other constants
remaining as before, CM would become
cw = 0.0418 x 1.22 ; 0.025 = 0.0855,
giving. Ca3/ClT2= 236. As Ca z 1.2 is still coiiparativelynear
the optimum value of 1.34, Ca3/CVt2 is thus but little smaller
than the maximum value of 240. One can therefore also in cases
like that
For
(2) to be
1.2 =1:
by a wind
just dealt with ccnfidently use formulae (6) and (7).
Ca =1.2 the gliding speed v is found ‘from equation
approximately 11 m/s and the gliding angle is 0.0855 :
14. On a wide slope of 1 : 5 the rate of descent would
of 4 ‘m/s,be smalier than the rate of,ascent of the air.
Soaring across the slope would, of cmurse, require a transverse
f
velocity of ~ 112 - 42 E 10.25 meters per second.
E In order to assist those English xeadexs who are not familiar
with the Qerman system of expressing lift, resistance, etc. , it1.. ..a.~.,-...,,.
. .. ,.,,
might be mentioned that in th; “equations‘~rintet aboVe Cw is-the
drag coefficient, and Ca the lift coefficient. .They are converted
into the ‘labsolute’[units efilployedby the N. P. L. by being divided
by two. Thus when Professo% Prandtl speaks of a lift coefficient
. . ...
_$)-
of 1.2, this eoriesponds to “an ‘~absolute”lift coefficient of 0..6.
..
The velocity is, of course, stated in meters per second, and the
—,. ,, —.. . .
letter F is
G the weigh+
&ed ~o’cie-note‘tiifigaf”ea”.b denotes wing spaliatid
a
- .5,.. ,,, .


Some remarks concerning soaring flight

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