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Tail
Rotor Design
Part
I:
Aerodynamics
R.
R. Lynn
Chief of Research an d D evelopment
F.
D. Robinson
Senior Research and Development Engineer*
N N
Batra
Research and Development Engineer
J.
M.
Duhon
Group Engineer. A erodynamics
Bell Helicopter Company
Fort Worth, Texas
This paper discusses the various aerodynamic conside~.ationr
involved in tail rotor design. Sizing criteria aye given, and the
contribu tion of gyroscopic precession in caw ing b lade st,nll dur-
ing fa d turn s is explained. Th e stall boundariex fo r severnl Bell
helicnpters are shown s a function of yaw rate and acceleration.
These acceleration an d r ate values are suggested ns n minimum
reqniremont
for
fu tur e designs.
T h e
effects
of
fin
inlerferencc for both the Lrectur and p11sI1c1.
configurations are disc~lssed n d t,he app aren t effects of direction
of rotation are noted. Considerat,ions ~ 1 c iscussed which in-
volve selecting a tail rotor's d h c loading, ti p speed, airfoil
s
tion, and design torque. I u e h ~ d e d re noise, efficiency, and str11r:-
tura l loading.
T h e direction al conLrn1 requ irem ents of n helicopter and simpli-
fied equations for yaw an d gust sensitivity, and yam damp ing a1 e
discussed. Some
o
the directional control prohlems encountered
by the indmtry a1.e descrihed along with steps taken
to
c o l ~ e e t
them.
NOTATION
lift curve slope a 5.73/wdian)
B tip loss factor; blade elements outboard of
radius BR are assumed to have profile
drag but no lift,
b
number of blades
C
damping coefficient,( - M / ) ft-lb/rad/scc
c blade chord,
ft
cl section lift coefficient
l rcsenre,l HL tlra 25th
A n n ~ t t l
utiamal lic~r11111f ~ I I B ~ ~ ~ r r i v i k l t
I lc li co p tc r S or ie tv , A l ~ sIRO
N o w Senior Stnif I.:ncito* er, Huaht\i 'l'ool Cnm,ral.s, Aircrtxft
Division, Cu lver City, Caiifornis
l
average lift coefficient of rotor aftefter trip los
correction h fiT/bp~ BR)~n~)
CT/a thrust coefficient/solidit,y C,/v T/bpcR3n
Fti fin force, lb
I
polar moment of inertia per blade for :I. t.a
rotor), slug ft2
I
helicopter yaw moment of inertia, slug ft.2
M moment, Ib-ft
R rotor radius, f t
S A
ratio of bloclced disc area t,o t,otal disc area
T tail rotor thrust, lb
T,
tail rotor thrust requircd t,o compeusate fo
main rotor torque, lb
V velocity, fps
X
distance bet.nreen maiu rotor axis and ta
rotor, ft
first harmonic flappiug augle bet,ween t,h
rotor disc and the control plane), radians
-y
Lock number; ratio of air forccs to mass force
Y
pR4ac/I,)
63
pitch-flap coupling positive a produccs nose
down pitch with up flapping)
0 blade pitch, rad
p air density, slugs/fta3
yaw rate, rad/sec
3; yaw acceleration, rad/sec2
rotor speed, rad/sec
Direction of rotation-Main rotor direction of rota
t.ion is assumed to be counterclockwise when viewe
from above.
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OCTOBER 1970 TAIL ROTOR DESIGN PART I : 9EROOYNhMlCS 3
THE
LOW
DISC loading tail rotor is by far the most,
efficient approach t,o torque compensatio~land direc-
tional control for the single rotor helicopter. Experience
on a wide vaxiety of helicopters has shown that it is
fa r from a simple task t o develop a tail rotor installation
t,liat has completely acceptable co~itrol, tability, and
structural characteristics. In view of the tail rotor's
know11 advautages as a coutml and alltitorque device,
it is considered highly desirable t.o develop
it
thorougll
uuderstanding of its operating e~lviroilmetitand tlie
important co~~sidcratiotisor its design. This kuowledgc
is essential if successful, long life tail rotors are to be
designed wit.h conlideoce for future high performance
helicopters.
A tail rotor is often thought of, incorrectly, as a
propeller or a small main rotor. Unlike a propeller, t,he
tail rotor must produce thrust with t,he free air corniug
from all directions. Unlilce a main rotor, a tail rotor is
not trimmed for wind or flight velocities with cyclic
pitch.
It
operates in an extremely adverse aerodynamic
aud dynamic environme~it and must produce hot11
positive and negative t,l~rust.Despite the difficulty of
tlie design task, tail rotors have operated successfully
for the most part, which at,tests to t he fact that they
are very forgiving. However, as wit11 the design of
all mechanical equipment, concentrated effort and
attention can produce an improved product, aud i t is t,o
t,hat, ud tha t this two-part paper is dedicated.
111
tlie succeeding Part I1 of this paper, the struc-
tural dynamics aspects of stiff-inplane tai l rotor de-
signs are co~widered. this Part
I
the major aero-
dynamic aspect,sof tail rotor design are discussed.
Ef i IGN
CRITERIA
Critical Ambient Co?iditi o?~
A tail rotor should be desigried for one of the follow-
ing ambient conditions: ( a ) the aircraft's critical
hovering altitude and temperature, or
(b )
the engi~lc
critical altitude. Usually the most severe of those
c~ndit~ionshould be used; however, in certai~icases
where the rotorcraft has extreme altitude capability,
such as a crane-type machine at light gross weight, a
less severe hovering altitude-temperahre design condi-
t,ion \r.ould be adequate.
The use of eugine crit,ical altitude as the tail rotor
design condition covers the normal situation for rotor-
craft wit,h supercharged or flat-rated engines. Tlie
use of tlie aircraft's critical liover condition provides
for the spccial cases noted above and for rotorcraft
designed with sea level engines.
Tlie first step in designiiig a tail rotor is to establish
t,he required t,hrust and the conditions under which it
must be generated. In all fliglit regimes, the tail rotor
must produce sufficient net thrust to couuteract residual
main rotor torque and simultaneously maneuver the
aircraft in yaw and/or correct for disturbances. The
term net thrust is used to account for the effect of fin-
tail rot,or and other such interferences which are dis-
cussed in a later section. Residual main rotor torque is
used because of the ~iow ommon practice to unload the
tail rotor io forward flight with a cambered or canted
fin. Also, in sideward flight, static stability of t,he air-
frame affects the tail rotor thrust required.
There are no special high-speed tail rotor thrust
requirements. Experience lias shown that if the lom-
speed trail rotor thrust rcquirements discussed below are
met, the forward flight requiremeuts will be satisfied.
The tail rotor t,lirust capability should be checked,
however, for various forward flight maneuvers. This is
especially so when higli advance ratios or high ivlacl~
numbers are used.
In liover aud low-speed flight there are two condi-
t.ions which need to be evaluated to establish the maxi-
mum required tai l rotor thrust. These are:
1
thc critical
maximum sideward flight velocity, and
2
near zero
velocity yawing maneuvers.
It
is one of these condi-
tions in combination with maximum maiu rotor torque
that results in the maximum required tail rotor thrust.
In all cases investigated, the yawiug maneuver require-
ment lias been found to be critical.
During a low-speed yawing maneuver, tail rotor
thrust capability is required to:
1
compensate for main
rotor torque,
2
accelerate the aircraft in yaw, and
3
accommodate tail rotor precession effects at the yaw-
ing rate of the aircraft. For most tail rotors, these re-
quirements are of comparable magnitude. The first
two are usually well understood; the third require-
ment is not, and its origiu is explained in the following
section.
effe ts o Precession.
A tail rotor is a gyroscope
which must be precessed wlie~lever he helicopter has a
yawing rate. The moment required to precess a gyro-
scope is equal to
I,
and is applied
90
ahead of the
direction of precession. For a fan or propeller this
moment is carried structurally, but for a flapping tail
rotor it must be produced aerodynamically. As the air-
craft yaws, the tail rotor tip path plane axis lags the
tail rotor mast or co~ltrol xis. This produces an equiv-
alerlt cyclic feathering or differential blade angle of
:l,t,taclc from one side of tlie rotor to the other. As
IL
couscquence, olie side of the disc will be loaded more
highly than the other. If stall is encountered, tlie addi-
t,ioual precessional moment must be produced by t,lie
u~wtalled ide of the disc \vIiere it subtracts from the
basic thrust.. This significa~ltly reduces the thrust
capability of the tail rotor.
After subt,racting the tail rotor thrust required for
main rotor torque compensation, tlie stall boundary of
the tail rotor call be plotted as a function of yaw ac-
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4
I,YNN, ROBINSON,
B A T I t l l
A N 0 DUHOS
Y W
RATE
Y W RATE
Tr~oun~. Tail
rotor
stall hountla13 n a ho~cl.ing u~ n
celeration and yaw rate as sliomn in Fig. 1.The limiting
rate and acceleration values indicated on Fig. 1 are de-
rived in tlie appendix.
When stall due to precession is encou~ltered, arge
flapping angles occur as the unstallcd side of tlie disc
attempts t,o create all of the required precessional
moment. This pl~euomenon s the principal reason for
the excessive hover and high speed maneuver flapping
mliich has been encountered during the development of
many helicopters.
Stall due t o precession is most likely to occur when-
ever there is a combinatio~l f high tail rotor thrust and
high yaw rate. This occurs when stopping a uose-
right hovering turn. The trail rotor thrust required for
main rotor torque compensat,ion s cssent,ially the same
in steady turns to the riglit or left as it. is in steady
hover. Therefore, changes in tail rotor thrust are pri-
marily dependent, on wliet,her or not the aircraft is being
accelerated in yaw. A nose-left yaw acceleration in-
creases the tail rotor thrust rcquired and occurs either
at the beginning of a lcf t tu rn or when stopping a rigbt
tunl. Thus, stall is most liicely to occur in stopping
:I
right turn when bot.11 t,he t,lirust,and yaw rate are maxi-
mum.
In forvard flight, thc situation is somewhat altered.
Although yam rates are generally lower than in liover-
ing maneuvers, the effect of precession is to increase thc
angle of attacli of the tail rotor s ret,reating blade when
the aircraft is turning lcft. This is dependent on tlie
JOURNAL 01 THE
A M E R I C A N
HELICOPTER SOCIETY
main rotor s direction of rotation and is independent o
the direction of rotmationf the t,ail rotor. Consequently
in fol ~vard flight, helicopters with main rotors tha
rotat,e counterclocliwise when viewed from above wil
be susceptible to precessional stall of t.he tail rotor when
turning or yawing left.
Precessional stall can be delayed by increasing th
airfoil
el
the blade Lock number, or the tail roto
tip speed. Pitch-flap coupling,
fig
does not affect stal
due to precession. It only increases the amount o
equivalent cyclic feathering produced by the blad
flapping, and thereby changes the magnitude and aei
muth of the resultant blade flapping.
Suggesled
Criteria
Figure 2 shows the tail roto
st,all boundaries for t l~ree ell helicopters calculated a
indicated in the appendix. In each case, the boundarjz
was determined for the critical altitude condition
noted. Two-dimensional NACA airfoil data were used
to determine el . and t.he tip loss factorB mas assume
to be (1-c/2R).
The st.all boundary sllown for the UH-1D is believed
to represent an acceptable minimum for future designs
Based on the UH-1D capability, the follomi~~griteri
are suggested: A rotorcraft should be able to perform
the following maneuvers at its critical ambient desig
condition:
(1)
Start a left hovering turn wit11 a
initial yaw acceleration of 1.0 rad/sec2, (2) Stop a righ
hovering turn ratme f 0.75 md/sec with an initia
deceleration of 0.4 rad/sec2.
The first of the above maneuvers is critical from tb
thrust standpoint. The second is critical due to tb
gyroscopic moment, required for high inertia, low 1,ock
number blades.
In the next seet,ion the major considerations involve
in
designing
a, ail rotor to meet these requirements a.r
discussed.
AT OGE HOVER
C E I L I N G S OR
E N G I N E
C R I T I C A L ALTITUDE
2 0 6 A @
2900 LB
UH-LD @ 8500 LB
47 G 38 @ 10,000 FT
0
5
1.0
YAW RATE, , RAD/SEC
F I O U ~ ~ ETypical caleulat~d
tall
boundaries at
nltitudc
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5
LYNN, ROBINSONJ, BATRA A N D OUHON
JOURNAL OF THE A A IERICA N HElrlCOPTEH S O C I E T Y
AH 1G
S/A=.264
UH C
15
10
AH 1G
TRACTOR PUSHER
P I G ~ EENerl
of
fin-tail
ro tor
s l~nmtion
a significant increase in comparison to tlic model and
zero wind flight dat.a. Furthermore, the adverse
pressures extended over a la,rgcr portiou of the tai l
boom. Thus, wit,li an aft and left wind, a higher t,ail
rot,or tlirust is required to overcome the larger adverse
fin and boom forces. This increase in tail rotor tlirust
required can become significant under crit~icaloper-
ating condit,ions.
It is believed that tlic wind effect on the pusher fin
intcrference is related to the main rotor malce. Al-
though tlie exact mechanism has not becn dcfined,
model t,ests show that. when a tail rotor is operat,ing,
t,hc main rot,or wvalce is drawn toward the t.ail mtor and
fin. Thus, t,he main rotor walce affects the fin and tail
boom pressures. The changes duc to wind direct,ionseen
in tlic flight dat a suggest tallat he effect,s of main rotor
wake are sensitive to the wind. In addition, the main
rot,or flow field may determine tlie best tail rotor direc-
tion of rot,at.ion as discussed later. The individual
effect,s of fin-tail rotor, and maill rotor male-tail rotor,
are extremely difficult to isolatc.
The UH 1C pusher flight tests, with the longer t,ail
rotor mast mentioncd earlier, shon, that the wind sen-
sitivity effect persists even when the fin-tail rot,or sep-
aration distance is doubled. This gives rise to t,lie possi-
bility that tlie principal wind effect is related to the
main rotor wake and tail rotor's direction of mtat.ion
since thc effccts have not beenseparated. For reference,
t,he rotation of the UH 1C trail rotor is blade forward
nt t.he top of tlie disc. This mill be disc~ascd ater.
Because of this uncert,ainty, t,he puslrer should be ap-
proached ~vit,haut.ion.
The tractor configuration with the hladc moving aft,
has becn sho~vno be free from t,he adverse wind effects,
so it, can be used wwrith confidcncc. Thc inhcrent high fin
sidcload losses associated ~w~it~l~he t.ract,or are severe,
and efforts t o eliminate t,hc pushcr problems could well
be worthwhile.
Engine Ezlraust. It has bccn theorized t8hat n hover
and low-speed flight,, condit.ions might exist where tlie
hot exhaust from the powcr plant can flow through the
tail rotor, reducing the air density and thus the tail
rotor thrust. This possibility
was
invest,igated with a
UH 1 helicopter instrumented wit11 thermocouples ontlie
fin, boom, and tail rotor blade. It was found t,hat hot
gases from the engine are indecd in tlic vicinity of thc
tail rotor and pass through it. under certain conditions
while tlre aircraft is tied down. However, in '11 hover
or lowv-speed flight conditions invehgated, including a
long interval IGE t,ail rotor blade and fin tempera-
t,ures did not rise appreciably above ambient . Thus, for
t,his aircraft t.he exhaust gases do not pass through the
tail rot,or or affect its performance for t.lie crit,ical lev-
speed maneuvers. i\lot.ion pict,ures of a hovering UH 1
\vit,h a tail pipe smol\-egenerator, shown by the photo-
graph in Fig. 6 confirm this. In high-spccd flight, ex-
haust. gas impingement on the tail rotor has been ell-
countcred and is belicved to hnve caused mild yaw
oscillat,ions ~vliichwere corrected by a tail pipe changc.
Whether or not the engine exhaust effects on the
UH 1 t,ail rot,or represent the general case is not lcnown.
It
is believed that tlie abovc theorized low-speed
phenomenon could occur and that it call be investi-
gated qualitatively by smolce flow dies of models.
Sucli t,ests, and tlle provisio~i or exhaust angle change
by t,ail pipe design, are recommended approxches to
avoid possible interference due to enginc exhaust,.
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O C T O B E R 1970
TAIL
ROTOR
DESIGN
Pf
LRT
I: AE R ODYNi IAI IC S
Rotor Pa7.aateters
Diameter and Disc Loading. Principal consider-
ations in establishing the tail rotor diameter, moment
arm, and disc loading are: 1) the overall size of t he air-
craft as limited by such requiremeuts a air trans-
portability or carrier operation; 2) ground clearance,
particularly for rotorcraft with low-mounted tail rotors;
and 3) t.he effect of tail rotor power required and weight
(including balance) on tlie overall performance of th e
helicopter.
To make t,he tradeoffs suggested by item 3, it is
necessary to estimate the weiglit changes in the air-
frame, drive syst.em, and tail rotor, as the tail rotor di-
ameter is varied. Both weight and power required can
be expressed in terms of payload to find the optimum
diameter (or disc loading) for a give11 design. I such a
study the tail rotor power considered should be bascd
on the critical hovering condition for the aircraft.
System weight should be based on tail rotor thrust and
torque resulting from the most critical paw strwt.ura1
requirement.
The t, rade study suggested here has often been
neglected because tlie effects are small. Under certain
critical hover condit,ions,ho~vever, mall changes in t,otal
power required, which might be obt,ained with proper
attention given t,o he tail rot,or, can result in significant
payload increments. For example, th e UH-1H at GOO0
ft, 95'F day, has a payload of 767 lb. If tlie total power
required were reduced by 2 , tlle payload would in-
crease to 887 Ib, or 14.7 . I n many cases a 2 total
power reduct,io~lmay be obt,ained by careful at,tent.ion
to the tail rotor design.
The performance aspects of such an approach are
easily shown by considering disc loading. Typical tail
rotor disc loadings for present-day helicopters are
to 12 psf for main rotor torque compensation. Tliesc
values can easily double momeut,arily during a critical
maneuver. Fig. 7 shows th e effect of disc loading 11 t,he
rot,or power, expressed in terms of percent total power
required.
T i p Speed; N ~ n b e r f Blatles.
Factors which must,
be considered in select,ing t,lie t,ail rotor t,ip speed in-
clude noise, profile power, blade stall a t high advance
ratio, drive system torque, weight, and control forces.
I n comparison to a low-tip-speed design, biglier-tip-
speed tail rotors are relatively light, permit a lomer-
torque drive system, are less suscept,ible to blade stall
at high advance ratio and yawing maneuvers, and are
less sensitive to gusts. However, higher t, ip speeds
result in illcreased profile power, compreesibility
effects, and noise. In the past, noise was [lot considered
of primary importauce. This is no longer true.
For nearly all flight condit,ions, t,he tail rotor is the
predominant noise source for single rotor iielicopters.
Tlle perceived noise occurs at discrete harmonics which
are multiples of the blade passnge frequency. The
T A I L ROTOR D I S C L O A D I N G
(PSP)
FIGURE Effect of tail rotor disc loading an nntitorque powcr
required
sound pressure energy levels of a tail rotor are usually
slightly lower t,hau those of a main rotor; however, due
to their frequencies being more within the audible
range, they sound louder to the observer.
Tail rotor rotational uoise is a funct,ion of t,he total
aerodynamic forces ac ti~ ig n the blades, the number
of blades, and th e tip speed. Of these, t ip speed is t.he
most important. Lower thrust, per blade reduces noise,
and this is frequently the primary aerodynamic con-
sideration in selecting the number of blades. Compressi-
bility increases the noise directly by its effect on the
related forces, and indirectly by increasing the more
easily perceived Irigher frequency components.
A great deal of effort is being made to reduce rotor
noise. Recent i~~vestigationsy Bell and o t l~ e rs ~ , ~ave
shown that significant reductions are possible 4 t.o 8
db) by altering th e blade tip loading and/or by reduc-
iug the compressibility effects. In any eveut, future
rotorcraft designed with noise as a primary consider-
ation will probably feat,ure mult,ibladed designs 1vit11
tip speeds be be en 575 and 650 fps.
Some degradation of performance will have to be
accepted to achieve a significant reduction in noise
level. Since there is a laclc of valid noise criteria, or even
definition, it is hoped that both the customer and the
regulatory agencies mill exercise caution in est,ablishing
rest,rictive noise limitations.
I ,tuist.
Negative values of blade twist have been
used for the tail rotor, as for the main rotor, t o improve
the spanmise load distribution. In hover and low specd
flight, twist is helpful in reducing the tail rot,or torque
required at. lhigh t,hrusts. In high-speed flight, the in-
flow can be from either side of the disc so negative twist
is not advautageous. This is especially true when the
tail rotor is unloaded by a fixed surface. Increases in
oscillatory blade moments have bee11 observed ~vhich
were attributed to increased twist,. However, for low-
speed lielicopt,ers, t~ vi st liould be considered because
of t,he higlrcr hovcring efficiency.
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JOURNAL
O F
THE
A M E R I C A N
HELICOPTER
SOCIETY
T I G I ~ ~ E1Jppel.
sul face
of IJH-l tail ro tor
a1
hi h tl>l.,nstin
flight.
Airfoil
Section
A primary parametcr in tail rotor
design is the blade airfoil section. This is generally
realized, but has often bccn neglected due to conccnt,ra-
tion in other areas. Many t,imes airfoil shape has beell
i~d uc nced sig11ificant.ly by structural, dynamic, or
manufacturing considerat,ions.
A
good airfoil section
has often been degraded acrodynamicallg by a thick
abrasion &rip placed around the leading edge. Such
considerations am important,, but tlic so lutio~~so de-
sign problems should not violate the basic aerodynamic
requirements. Airfoil selection is important because the
blade airfoil section is one of only three means available
to the designer to minimize the adverse characteristics
of a tail rotor that is designed for high thrust (i.e.,
increased gust sensitivity, high design torque, added
weight). The other two means available to the designer
are to make the blade as light as possible (delays pre-
cessional stall) and to increase the t ip speed.
The principal feature desired of
a
tail rotor blade
airfoil section is a high maximum lift coefficient at t11e
operating Mach and Reynolds numbers. Low minimum
drag cocfficients are desircd but. are secondary in im-
portance to t,he stalling characteristics. Zero or Ion.
pitching moment,s in thc past have been tliougl~t csir-
able; ho~vever, t is believed that the design can be
such that section pitching moments are not a problem.
Compressibilit,y effects, of course, me significant for
all of the parameters associated witah the airfoil. For
example, the cl . of a n NACA
15
airfoil at a Mach
number of
0.6
is only about
2 s
of its CI,,,, a t low Mach
nu mb ers .TT s effect, plus th e fact th at inflo , reduces
the angle of attack a t the tip less than it does inboard,
makes the typical untwisted tail rotor quit,e suscept,ible
to tip st,all. The id ight photograph in Fig.
8
sho~vs
11
examplc of this. Radial locations for the calculated
critical, drag divergence, and shock stall R4acb num-
bers are indicated. Compressibility also produces
pitching moments and t,orquc increases due to drag
divergence.
t
is expccted tha t a great dcal more attenti011will be
givcn tail rotor airfoil
selection
in the future and opti-
mum airfoils, including those nrit,h camber, will be
used. The results of recent BHC experiment,alwork~vith
tail rot,or airfoil sect,ions support this. Recent,l.v, a lavge
increase in maximum thrust was achieved by adding
leading edge camber to a symmetric~l ect.ion and
eliminatting t,he abrasion strip discontinuit,y. For this
case, the helicopter flight envelope and t,ai1 rotor t,ip
speed allowed the use of a large amount of fo~~var
camber. Figure
9
illustrates the combined effect. of
droop and elimination
of
the abrasion strip.
Ch o ~ d
Wit11 the other dcsign parameters defined,
the blade chord required can bc calculated using the
following expressioli which is derived in t.he appendix
To satisfy the maneuver criteria suggest,ed in n pre-
vious section,
= 0.75
and
II
0.4
can be substituted
into the above for the critical ambient condition. For
helicopters with large fins, an additional margin should
be allowed for interfercnce.
In deriving the foregoing expression, and in t, I~eol-
Ionring control section, linear theory has been em-
ployed for clarity and simplicity. In somc cases, more
det,a.iled analyses would be appropriate.
FORWARD
CAMBER
SYMMETRICAL WITH
A B R A S I O N S T R I P
COL L E CT IVE P IT CH DE G)
FIGURE
Effect of
leading
e ge
camber
and
abrasion strip elimi-
nation
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OCTOBER
1970
TAIL
HOTOR
DESIGN PART :
AE R ODYNAMIC S
9
Pitcl~.
ange.
Select,ion of the correct t,a.il otor pitch
range as controlled by the rudder pedals has impo~-tant
effects on directional handling qualities. Maximum
posit,ive tai l rotor collective pitch is required a t the
maximum right sideward flight speed for the critical
combination of power, design altitude, and tempera-
ture. This condition requires the higllest pitch travel
due primarily to the inflow velocity in sideward flight,.
The maximum negat,ive pitch is usually based on the
negative t,hrust required to trim and maneuver the
rotorcraft in autorotation. This requiremeut is strongly
influenced by a canted or cambercd fin uscd to unload
the tail rotor in forwad flight. In certain cascs, side-
ward fliglit to the left may define this value.
Convelitio~lal are applicable in esti-
mat.ing the required tail rotor collective pitch values.
Some of the problems and peculiarities associated with
tail rotor control in sideward flight are discussed in a
later sect,ion.
I'atu
Acceleration Se~rsitiuitu. Reference 7 defines
the acceptable pedal travel for aircraft design as 3 n.
Wit,h the control travel fixed at the cockpit and a t the
tail rotor, the pitch change per inch of pedal travel is
established. With t,he tail rotor sized to prevent blade
stall, t,his determines the minimum y a ~cceleration
per inch of pedal travel. Neglecting the change in ill-
duced velocity, and letting (Acl)/in. = a(AO)/in., the
instanta~ieous a ~cceleration sensitivit,y ( /in.) of t,he
aircraft is:
1
M,,,/in.
=
abcp(BRJ3S12
e)
6
m.
I
Actually, the change in induced velocity is not negli-
gible. For severe maneuvers, it can reduce the yaw ac-
celeration per inch by 50% or more. Therefore, the
preceding expression should be used for comparat,ive
purposes only and not t o correlate with flight test data.
I'azu
Dampiny; Rate Sensitivity.
When a rotorcraft
has a yaw rate, the airflow through the tail rotor changes
the elemental angle of attack on the blades. This alters
the tail rotor thrust so as to oppose the yax7 rate.
Neglecting the change in induced velocity and 1ett.ing:
X a 1
atl
= nd AT = J- ~p(rSl)~(AC~)cZr,
1 n 2
an approximate expression for tail rotor damping, ref-
erenced to the aircraft's yaw inertia, is:
As with the y a ~cceleration sensitivity, meeting the
maneuver criteria tends t o establish the minimum yaw
damping for a given design. For small and medium size
F r o u n ~
10
Typical test
vnlucs of
yaw dnmping acceleration.
and rate
sensitivities.
helicopters, the valuc of the inherent damping will only
be about one-half tha t required by Rcf.
8
By combining the damping expressioll rnit.11 that. for
control se~isitivity rom t,he preceding paragraph, the
steady (final) rate of yaw per inch of pedal call be ex-
pressed as:
It
can be sho~vnhat about
2 3
of this rate is obtained
after a time equal to I,,/C, following an abrupt pedal
displacement. Figure 10 gives typical flight tes t values
of yaw damping, acceleration sensitivity, and rate
sensitivity for several helicopters.
The pitch change per inch of pedal is dictated by the
sideward flight and human factors requirements; the
tail arm, X by geometric considerations; and the tip
speed by the considerations listed earlier. Therefore,
the designer is not left with a great deal of freedom to
alter the yaw rate sensitivity.
Gust
Response.
In th e expression for yaw damping,
S
is the sideward velocity of the tail rotor due to a
given yaw rate. If the velocity of a side gust,
V...
is
substituted into the expression in place of
S ,
the
following expression for gust response is obtained:
This means that there are no basic parameters, other
than tail length, which the designer can usc to change
the ratio of the gust. response to yaw damping. This
ratio, which is important mith respect to the aircraft's
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10 LYNN,
ROBINSON
BA TH A
A N D
DUHON
JOURNAL O F THE A n I E R I C A N HELICOPTER SOCIETY
WITH VORTEX
R I N G E F F E C T S
WINDMILL
BRAKE
STATE
L E F T 0 RIGHT
SIDEWARD FLIGHT VEIDCITY
FIGURE1. Tail rotor pitch in
sideward
flight.
flying qualities, can only be varied for a given machine
by adding artificial damping.
Tho consequences of t,his are that as the inherent
damping
C/I,,)
of the tail rotor is increased, the ma-
chine will become more susceptible to gusts. In-
creasing the inherent damping of tlie tail rotor will im-
prove a helicopter's no mind handling characteristics
in a hovcr, but it will make it more gust sensitive and
less accept,able to the pilot.
Thc consequences of a gust are largely dcpcndent on
tlie reaction timc available to the pilot for corrective
action. This can be altered favorably if the damping,
and
therefore
the gust sensitivit,~,nn be reduced for a
given maximum thrust capability. The lower the gust
sensit,ivit,y, he slower and less severe will be the yaw
resulting from a gust,. The gust response is redefined
below in terms of the maneuver thrust requirement and
related parameters:
t is seen that the gust response can be reduced by in-
creasing the t ip speed or maximum lift coefficient of th e
blade or by lowering the maximum tbrust/inertia ratio.
To explain this physically, increasing the
cl ..
or
lowering the maximum thrust/inertia ratio allows the
required maximum thrust to be produced with less
blade area. Thus, a given gust will produce the same
change in blade anglc of attack but less change in
thrust. Increasing the tip speed also reduces gust re-
sponse, but not by its reduction in blade area required,
since this is accompanied by a corresponding increase in
dynamic pressure. For this case a given gust velocity
combined with the higher t.angentia1velocity produces
a smaller change in thc blade angle of attack and hence,
less change in tlirust.
For a given configuration, with a required maneuver
capability and normal restrictions on tip speed, the
only variable left that will reduce gust response is an
increase in
C
Yaw gust response effccts are also
discussed in Ref. 9
Sideward
Flight
The major aerodynamic tail rotor problems en-
countered have occurred in left, sideward flight. As
noted earlicr, thc problems
generally
relat,e primarily to
the aircraft's yaw control charact,eristics.
In
the
following paragraphs, the principal peculiarities as-
sociated with sideward flight are discussed.
T ortex Rin g Sla te. Tlic Bell i\~Iodel47 and many
ot,her helicopters experieiice a not.iceable difficulty in
establishing pedal trim in left sideward flight from 5
to 15 knots. Trim pedal posit,ion vs sideward flight
speed is extremely difficult to define in flight test. The
pedal-speed gradient appears to be flat or with a slight
reversal. When flight under these conditions must be
maintained, the characteristic is annoying; if possible,
pilots change heading t,o avoid it,. This is caused by
operation in the vortex ring state.
I sideward flight to the left, the vortex ring state is
entered at 5-10 knots and extends up to 15-35 knots
depending on tail rotor disc loading. This flow state
produces strong vortex formations which increase t.he
rotor power and effective induced velocity at. the rotor
plane and produce nonuniform flow through tlie rotor
disc. In the higher speed range of the vortex ring sta te
there is a tendency for the f l o ~o be unstable as tlie
voltices are carried away from the blades.
References 10 and 11, for example, give experimeutal
data ~ h i c han be used in calculating the steady state
power and control angles throughout the sideward
flight speed range, including the vortex ring state. This
has been done for several cases for a free tail rotor and
tlie effects of t,he vortex ring statc are illustrated in
Fig. 11. Test data for the Bell Model 47 and other
helicopters substant,iate these trends.
The vortex ring state causes a reversal tendency in
the steady-statc tail rotor blade pitch vs sideward
flight velocit,y plot. For higher thrust,s and disc load-
ings, the vortex ring state, and consequently the re-
versal, occurs at a higher speed due to the increase in
tail rotor induced velocity.
Main Rotor Torque T ariation. When in ground
effect during steady-st,ate sideward flight, just as the
LEFT
0
RIGHT
SIDEWARD
FLIGHT VELOCITY
FIGURE2.
Effcct
of main ro tor
torque
Q,,,,)variation
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helicopter "loses its ground cusl~ion," llcrc is an in-
crease in main rotor power required.
This requires
addit,ional t,ail rotor thrust,, and hence, more left pedal.
This effect increases t.lie pedal reversal in left sideward
flight as shown by Fig.
12,
which is based on Model 47
flight data.
Other phenomena affect the pedal reversal ttendency,
but are usually of minor impo~l.ance. Under certain
condit,ions, liowevcr, such effects as t,lie aircraft's
weathervaning characteristics a.nd sideload produced by
the main rotor wake act,ing on t,he boom must be con-
sidered in evaluat,ing t,lie pedal reversal.
Stall a71rl Con~bi~iedf e e t s .
Any phenomenon that
causes a dissymmetry of angle of
attack across the tail
rotor disc reduces the maximum thrust capabilit,~ f
the rotor. The vortex ring state a ~ idin and main rotor
\ralce interferences are examples.
If a tail rotor is operated at its maximum thrust
capability a~idhen subjected to one of the above, its
thrust \\rill be reduced due to the stall produced by the
dissymmet,ry. Under such a condition, t,lie applica-
tion of additional pitch will aggravate the situation.
3Ianifestations of this t,ype of plienome~lon re loss of
control, high torque, and reduced thrust. Also, n.lien
operat,io~~s at full engine power available, the incre-
ment in t,ail rotor power can cause loss of Rlt,it,udeor
"settling."
A
similar situat.ion might occur mit,liout t,he stall and
h i ~ l iorque if the phenomenon produci~ig ,he dissym-
met,ry were more effect,ive
ii
reducing t,ail rotor t,hrust
t,han the pitcli is in increasing it,.
hIai11rot,or wake and
vortex effects may be t,11ispowerful.
When problems such as described here occur, usually
they result fromacombinat,ion of effects.
It
is not surpris-
ing to find many explanations as to the cause. In t,he
follo~ving aragraphs, several problems of this t,ypc are
recorded.
Pa vtic t~l av Pvobleins E ncout~tererl.
During informal
discussions with representatives of several helicopter
manufacturcrs from this connt,~ynd abroad, a problem
in left sideward flight was noted. As far as can be de-
tcrmincd, all aircraft, were of the pusher tail rotor con-
figuration with tlie direction of the tail rot,or rotat,ion
such that tlie blades moved forward at the top of tlie
disc.
With each of the aircraft, yaw control cliaracterist,ics
became unsatisfactory to the pilot in low spccd, left,
sideward flight. Some describe tlie phenomenon as a
static instability, where the ship feels to the pilot as
thougli the tail rotor were "falling in a hole to the left
Others emphasize the inability to stabilize or control
t,he heading, more like an accentuat,ion of t,he yaw trim
difficult,^
experienced by the 3Iodcl 47. In one case,
the control difficult,^, mas rcpoitcd as follows: "At a
speed range between 8 and 8 knots when passing
tlirough the vortex ring st,at,eof tlie tail rot,or, t, l~ere as
a dist,inct shudder of the tail, causi~ig iolent reaction of
the pilot's pedal movement^. For one of the aircraft,
it is stated tha t t,he problem occurred only in t,rue left
side~va,rdlight. I t disappeared when a small component
of forward or aft speed was present. Details are missing;
however, it is uilderstood that tlie instability was not
accompa.nied by excessive flapping or tail rot,or ttorqne.
Comments mit,h respect t,o t,he cause indicate that the
Row aroillid the hi1 fin or pylon, t,he t.ail rotor speed,
and the direction of tail rotor rotation were significant.
In most cases, multiple changes to t,he aircraft were
made simultaneously i n an cffol-t to correct t,he problem.
However, in three cases t,he reversal of direction of rot,a-
tion of the tail rotor (from moving formard to aft at
tlie top of the disc) is credited with changing the un-
acceptable characterist.ics to a~cept~able,ven though
ot,her changes were made a t tlie same timc. In tlie fourth
case, the problem is said to have been eliminated by
only the clii~ngen direction of rotation.
A similar problem was e~lcountercdwit.11 t,he AH-1G
Cobra helicopter when configured with a pusher tail
rotor, rotating blade for\va.rd at the top of the disc.
With a118-15 knot,1vi11d coming from the aft left quarter
a left pedal input would have little or no effect,. The
characterist,ics were similar to a static divergence in
yaw to the riglit. The most adverse situatio~iwas when
tlie aircra.ft was heavily loaded, on a hot day or a t
alt.itude. Under such conditions, ~vhen eft pcda.1 was
applied to a.rrest a right turn for instance, the ship
somet,imes would swing around to the right momen-
tarily. As left pedal was applied, a rise in tail rotor
torque occnrrcd, sugge~t~ivef blade stall. 17lapping
cha~iges ere not noted. Tests showed tha t t,he problem
was diminatfed by repositioning the t,ail rotor to the
opposite side of tho fin (from pusher to t,metor) and
simultaneously, cl~anginghe direction of rot,at,ionof t,he
tail rotor t,o blade t.ip moving aft a t the top of the disc.
Diveclio~a f R olatio t~.
The above problems and their
reported solutions have resulted in considerable coli-
jecture as to the combined effects of direction of rota-
t,ion of the tail rotor, main mtor wake, and ~vind. n
an attempt to define these effects, some simple model
and flight tests were conducted at Bell. To this point,
t,he cause-effect relationships have not been est,ablislied;
l~owever, some pertinent informati011 has been ob-
tained and is reported.
The testsinvolved hoverand sideward flightwith a Bell
47-G. The tests were then repeated with the tail rotor
rotating in the opposite direction. Since this liclicoptcr
s
no fin in t,lie tail rotor flow field, the fill-tail rotor
interference discussed earlier is avoided. The tail rot,or
blade surface was instrumented to mcasure local air-
flow velocitjr at 86% radius and 37 chord. Additional
qualitative smolte tests of t he main rotor flow in t,hc
vicinity of a thrust,ing tail rotor were carried out with a
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12
TIYNN,ROBINSOT B A T R A AN11 DUHOK JOUHShIl OF THE AAIE HICAN HElrlCOFTER S O C I E T Y
VELO ITY
90
FIGURE
3. Airflow rrelocity variation
over
tail rotor
blade
model.
Wind-tunnel tests of tlie
main and tail rotor
combination are needed.t
Figure 13 shows typical airflow velocity over the
blade as measured during the flight tests. During these
tests the wind velocity was measured at about 4 knots.
The data indicate that tlie local velocity is a function
of tail rotor azimuth, main rotor height above ground,
and tail rotor direction of rotation. These variations of
air-flow velocity are also present, in varying degrees,
during sideward flight, botli in- and out-of-ground
effect. To date the effect of these local flow variations on
tail rotor thrust lias not been show conclusively.
Figure 14 shows a typical model smoke flow test.
Notc thc position of thc main rotor t ip vol%ices. Thc
observed patterns of these tip vortices are given by
Fig. 15. They are shown with and without tail rotor
t,lirust and for tlie casc with a ground plane. It is seen
that the main rotor walce is drawn toward the t.lirust,ing
t.ail rotor, and as expected, the main rotor ~valce s
marlccdly altered in thc presence of
a
ground plane.
Because of this, ground tests are not considered 60 be
conclusive in est~ablishing he effect of tail rotor direc-
tion of rot,ation.
From tlle work to dat,e, many I~ppot,hescs r specula-
tions can be developed to explain tlie observed effccts.
At, this point, it can only be concluded positively that
there are main rotor walce-tail rotor interactions; and,
that t,hey are a function of rotor height above t,hc
ground, t,ail rot,or position, and relative mind.
Work is bcing conti~~uedo define t,he causal re-
lationships. Until these have been cstablished, it is
See paper by Huston and Morris in
t his
irw
of the Journal
suggested,
based on the experie~lces escribcd in the
prior section, that the direction of t.ail rot,or rot.ation,
blade aft at. the top of t,he disc, be uscd.
A tail rotor drive system is different from most
others becanse there is no rest,riction on the available
po\vcr or torque. It is a demand system in that whatcver
torque it requires mill be supplied by the power plant
or main rotor. As a consequence, either the system
must be designed for the maximum torque that can be
encountered, within reasonable flight restrictions, or
means must be found to limit tlie ability of the pilot or
aircraft, to enter situations wlicre excessive torque can
be obtained.
If tlie approacll is talcen to limit tlie pilot or aircra.ft,
then the design of tlie trailrotor geaxing and antifriction
bearings should be based on fatigue considerations at
the maximum steady state torque. That torque will
usually occur a t the maximum sideward fight speed at
the critical ambient design condit,ion. Use of tlie maxi-
mum torque is justified since structural loading cycles in
the tail rotor drive build up rapidly. With contemporary
gear design and technology, this approach should result
in gear tooth scuffing and st.at,ic orque limit,s of about
2 or
3
times tlie fatigue design value.
If it is elected t,o design tlie system for the maxinrum
torque tha t can be
encountered,
in addition to the above
fat,igue crit,eria, the structural loads must
be established and the system designed statically to
t.hat value. Yor aircraft designs using flat-rated engines,
the static design condition is the application of full
tail rotor pitch
11
the ground or in flight at sea level.
This is justified by the recent experience with botli
the Bell Model 47 and UH-1 helicopters. Flight mall-
euver and ti cd ow ~tatic evaluation of tail rotor pomer,
thrust., and blade pitch show that for all practical pur-
F l o m r ~ 4 Typical n l n i t ~ olol. make
in
the vicinity
of
the tml
mlor
OGE).
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OCTOBER
1970 *TAIL H O TO R DESIGN~PART
I : AERODYNAMICS
13
poses, near zero airspeed, maximum tail rotor torque is
defined by the maximum blade pitch.
The impact of the static requirement can be quite
adverse from the weight and balance standpoint, not
only for the drive system, but also for the tail boom.
If the pitch is available, homever, it probably mill be
used by the pilot a t some point during th e life of the air-
craft. Since the consequence of not providing for this
can be static failure, the system must be designed to
withstand full pedal input, or the pedal must be re-
stricted.
Pedal rate limiting has been used but this approach
is not considered satisfactory because with it, the yam
maneuver capability is reduced. Other approaches
should be developed. Presently, altitude-compensated
pedal stops and rate limiting are being investigated.
Plapping
Magnitude
The tail rotor flapping range and boom
clearance are establislied by the detail design of the
rotor and the configuration of the aircraft. Early in the
design, maximum flapping values should be estimated to
assure tha t tbe flap stops \\,ill not be contacted in flight.
Excessive blade-hub structural loading has occurred due
to bitting the stops in hover and high-speed maneuvers.
If the tail rotor is designed to the maneuver criteria
suggested to prevent stall during hovering turns, then
maximum flapping will most probably occur at high
speed and thrust with a yawing rate to the left. During
structural demonstrations, and also during normal
operation, rapid pedal inputs are occasionally required
at high forward flight speeds. When the helicopter is
turning or yawing in fornrard flight, the precessional
flapping (derived in the appendix) adds to the forward
flight flapping.
Normal flapping does not significantly affect the
pcrfolmance of a tail rotor but t can be an important
parameter in determining structural loads. Fuselage,
fin, engine exhaust, and main rotor effects reduce the
accuracy \\.it11 which flapping can be estimated. Addi-
VORTEX
CORES
W I TH O U T TA I L
/
ROTOR THRUST
WITH
Z ab
ITH TAIL ROTOR
THRUST OGE
TAIL ROTOR
THRUST IGE
~ouno
15
Main rotor
make
distortion due to thrusting tail
rotor and ground plane.
-ROTOR
PLANE
BLADE SPAN
\
A X I S
ONTROL
FIGUR 6 Eff~ct f on tail
mtor
flapping
tional work is needed to develop an understanding and
representation of these effects.
Delta Three Efects Pitch-flap coupling, a 8 , is used
in many tail rotor designs to reduce the first harmonic
flapping. First harmonic flapping is the tilt of the rotor
plaue relative to the control plane.
Various analytical methods have been used in the
literature to account for the effects of
63
on flapping.
These methods seem unnecessarily complex and un-
wieldy when trying to visualize or calculate the result-
ing magnitude and phase lag of forward figh t or pre-
cessional flapping. It is believed tha t an easier and more
direct method is to considcr only the maximum equiva-
lent cyclic feathering required, the resultant flapping
produced, and the phase angle between them.
This can be visualized by considering the blades to be
whirling in the rotor plane ~vllile he ends of their pitch
horns are whirling in the control plane (plane of no
feathering), With first harmonic flapping, the ends of
the pitch horns are moving back and foi-th relative to
the rotor plaue (see Fig. 16) thus producing an equiva-
lent cyclic feathering of the blades. This is true witb or
without
a3
(Equivalent cyclic feathering is uscd here to
denote a cyclic change in the blade angle of attack and
not necessarily a rotation of t he pitch change bearings.)
The equivalent cyclic feathering produced is maximum
when the end of the pitch born is a t that azimuth posi-
tion ~vhere he separation between the rotor plane and
the control planc is greatest. The relative travel of the
pitch horn end is equal to tho flap angle times the
arm (y). The equivalent feathering produced is equal to
this travel divided by the pitch horn arm about the
blade span axis (u cos a 3 . Letting t,he equivalent feath-
ering required equal the flap angle without
83
results in
the following:
Thus, the flap angle with
8a
present cquals the flap angle
reauired without
8 .
multi~liedby cos
S3.
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14 LYNN, OBINSON,ATRA AND DUAON
Since the maximum
feathering
occurs when the pitch
horn end is at the 'zimuth positioii where the separation
between the rotor plane and cont,rol plane is greatest,
it then follows that thc phasc augle between maximum
feathering and maximum flapping is tlie angle between
t,he blade span axis and the pitch horn end, or (90 3)
degrecs.
The aa shown in Fig. 16 is defiued as positive (up
flapping produces anose down change in angle of attack).
If negative a8 (trailing edge pitch liorns) is used, i t can
be seen from the figure tha t the magnitude of the flap-
ping would still be reduced by cos 8%; o~vever,he phase
angle between the maximum flapping and the maximum
feathering rvould be (90
+
J3) degrees.
An interesting difference bet.n.een positive and negac
tive 83 is tha t with positive aa the addit,ion of flap hinge
offset further reduces first harmoilic flapping. Con-
versely, with negative present, the addition of flap-
lringe offset actually increases flapping.
To visualize this, consider a rotor in forward flight
where the higher relat,ive velocity of the advancing
blade produces a moment on the rotor disc, causing it to
tilt aft, thus producing the necessary feathering for
equilibrium. With positive
a3,
this til t of the rotor plane
occurs less than 90 past
the advancing side. With flap
hinge offset, the tilt of the rotor plane produces a cen-
trifugal couple on the rotor hub; t,he rotor hub in turn
prnduces an opposite reaction moment on the rotor disc.
Since the reaction moment on the disc is less than 90'
past the advancing side and is in the opposite direction,
it has a component which subtracts from the aero-
dynamic moment produced by the advancing blade aild
thus, reduces the flapping required. With negative as
the phase lag is greatcr than 90 ; therefore, the offset
hinge reaction moment increases the flapping required.
This is also true for precessional flapping and for hubs
with other types of hinge restraint.
Two-bladed tai l rotors frequent.1~ ave their flap
hinge axes coclced by the same angle as the
as
of their
pitch liorns. Tliis prevent,^ l/rev cycling of the pitch
change bearings as the tail rotor flaps. Cocking tlie flap
hinge does not affect the pitch-flap coupling described
above, and the S3angle is still the angle between the end
of the pitch horn and a line normal to tlie blade span
axis. With this arrangement,, t,he angular travel about
the cocked hinge is increased over the t,rue flapping by
l/(cosine of cocked hinge angle). In flight testing, flap-
ping is usually measured about the coclced hinge; there-
fore, the correction to obtain true flapping should not be
overlooked.
APPENDIX
Deriwation of Tail Rotor Thrust and Precession Capability
The aerodynamic moment required to precess a tail
rotor during a turn can be derived as follo~vs:
JOURNAL OF
THE AMERICAN
HELICOPTER
SOCIETY
For any gyroscope, the precessioiial moment equals:
J I 01,. For a tiail rotor this becomes: OI,b.
As the tail mtor flaps, an equivalent cyclic feathering
is produced. This provides t,he cliange in lift from one
side of tlie disc to the other required to precess the
rotor.
Letting
Acl
ap
thc aerodynamic moment. produced
equals:
The /, in front of thc integral is because a blade is
producing moment only /, of the t,ime as it rotates.
Setting the aerodynamic momeilt equal to tlic preces-
sional moment, required gives:
The flap a.ugle required to precess the rotor is:
For rotors with
by referring to the section on Delta
Three Effects, t,he flap angle required for precessioii is:
To determine the tail rotor's susceptibility to stall
in a hovering tunl , i t is necessary to find the maximum
combined c . The combined cl is the sum of t.he follonr-
ing :
AZ for main rotor torque
compensation
(TQ)
AZI for yaw acceleration (6)
AZI for precession (4)
Letting the combined
CI
= c~ . for determining the
stall boundary and noting that:
G =
GT
b ~ p ( B R ) ~ 0 ~
ndI,,6 = XT,
the follon~ing xpression is obtained:
To determine and plot the stall boundaiy for a given
tail rotor on a graph of vs 6:
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O C T O R E R 1 J T O
T. I I L H O T O R D E S I G N P A R T I : A E R O D Y N h l l l C S 15
-
YAW
RATE
T h c t e r m s c a n b e a r r a n ge d t o s o lv e d i re c tl y f o r t h e
n u n i m u n ~ h o rt l r e q u ir e d a t a g i v en an d :
REFEREN ES
1. McI