C.P. No. 93 I
MINISTRY
OF
AERONAUTICAL
TECHNOLOGY
RESEARCH
CURRENT
COUNCIL
PAPERS
“Zero Rate of Climb
Speed”
as a Low Speed Limitation
for the Stall-Free Aircraft
bY
W. 1. G. Pinsker
LONDON:
HER MAJESTY’S STATIONERY
1967
PRICE 4s 6d NET
OFFICE
U.D.C. No. 533.5.013.66 : 533.6.015.32
533.693.3 : 533.6.013.61
:
: 656.7.08
C.P. No.931 *
by 1966
"ZXRO l?A!?E OF CLI1SE3SPEED" AS A LOV SPhBD
L3XI11ATION FOR TIE3 Sm&-F~
AIRCRAFT
17. J. G. Pinsker
An attempt
is made to assess the significance
to flight
safety
of a
oondition
at low speeds where drag exceeds the available
engine thrust.
For the low aspect ratio aircraft
and especially
with slender wing designs
the "zero rate of climb speed" define6 by the
having practically
no stall,
condition
may constitute
the lowest limit
of the practical
speed range,
Methods are suggested to assess the necessary margins to protect
airoraft
of this general dass against the accidental,
possibly
catastrophic,
loss of
performance below this speed,
*Replaces
R.A.C.
Technical
Report
No,66144- - A,R,C, 28297
2
CONTENTS
1
2
3
4
5
6
7
8
Page
1rvTR0DUCT10N
RIXOVERY FROMFLIGXT BELOWZERO RAT% OF CLIh23 SPEED
!&E POTENTIAL RISK OF STALLING
THE POTENTIAL RISK OF CATASTROPHIC LOSS OP PFXFOilMANCE
CALCULATIONS AND PWIJ~TS~
DISCUSSION
GENER4L CONSIDERATIONS
CONCLUSIONS
Table 1
Symbols
Illustrations
Detachable
3
5
8
Figures
abstract
cards
3
3
-:
12
-l3
14
15
16
.
l-8
3
ratio
stall
The low speed potential
of the clnssioal
aircraft
with its high aspect
In non-manoeuvring
Plight the
wing is sharply limited
by the stall.
defines a speed below which flight
cannot be sustained and furthermore
it is a condition
of height even if
from which recovery
the pilot
can avoid
is only possible with a substantial.
entry into a spin.
These unique
10s~
charscteristics
made the stall a compulsive datum from which to define speed
It is not
and manoeuvring margins to provide
safety in low speed flying.
surprising
therefore
that in the formulation
of airworthiness
requirements
the stalling
speed vs plays a dominant role.
Xowever , as wing aspect ratio is decreased the stsll is delayed to
larger
angles of incidence and in the extreme case of a slender
wing, say if
the aspect ratio is below 2, it would occur at an incidence which is
completely
outside the practical
flight
range.
With such aircraft
low speed
flying
must be limited
by considerations
other than the stall,
such as for
instance general deterioration
of lateral
or longitudinal
control,
pitch
tendencies or difficulties
in speed holding in flight
below minimum drag
&peed.
up
Tith the possible
exception
of pitch up, if and when it occur3,
these
graaually
cith dccrcasing
spa ma it
characteristics
will deteriorate
fairly
certainly
in the design stage, to use them for the
generally
impossible,
definition
of a sharply and uniquely determined
absolute low speed limit.
As an alternative
it has been proposed that the nsnufacturer
sha.L?. select
operational
sFeeds, such as for instance the initial
climb out speed, and
demonstrate that at these speeds and at speeds a specified
number of knots
below these, the aircraft
satisfies
certain
stand~&s of controllability.
!i!his procedure api>ears generally
satisfactory,
since the use of autostabilisation
is permitted
to achieve these handling
characteristics
provided
it is designed to an acceptable
skndard
of reliability
- and
these regulations
give the designer good scope to exploit
the low speed
potential
of a design.
requirements
for the
hIore recently,
however, in an attempt to formulate
tie British
and French airworthiness
supersonic trensprt
aircraft,
authorities
have suggested new minimum speeds to take the place of the stalling
speed of the conventional
These are the "zero rate
aircraft
of climb
in the take off
speeds", defined
performance
requirements.
as the lowest speeds at
is
which with either full power or with one engine inoperative
level flight
can
just be maintained.
Fig.1 shows how these conditions
are defined by the
thrust and drag-characteristics
of an aircraft.
For the legislator
these speeds are clearly
attractive
as they share
at least two of the outstanding
features
of the stalling
speed:
(i)
they are sharply
precision
in flight
(ii)
they define
and they therefore
defined
and can be established
with
adequate
speeds below which level flight
cannot be maintained
set a limit to the practical
speed range*
It should be noted, however, that whereas the 5tall is uniquely
determined by a purely aerodynamic phenomenon and is usually preceded
by symptoms
indicating
to the pilot
the imminence of flow breakdown, no such warning will
signal the approach to zero rate of climb speed, which is entirely
governed
by performance
and thus a direct function
of weight, drag, configuration,
and
parameters influencing
engine power such as air temperature
and altitude.
As the term zero rate of climb speed implies,
it considers the ability
of an aircraft
to maintain level flight.
It may be more appropriate
for take
off for instance,
to consider instead the speed at which a given minimum
Such a speed
climb gradient
can be maintained,
rather
than level flight.
would of course be higher than zero rate of climb speed, as the available
/T - sin \ .
propulsive
force is now reduced ,to \,f
Honever these are matters
';;
for the certification
authorities
to consider and will not be further
discu3sed here.
We shall only investigate
the nature of the hazard - in
relation
to the flight
condition
to be maintained
- when an aircraft
drops
below this minimum speed and the nature of the protection
afforded
by speed
1
margins.
Quite clearly
it is of interest
to know whether zero rate of climb
speed has a practical
significance
to flight
sef'ety similar
to that of the
Equally it is necessary to consider
stalling
speed of conventional
aircraft.
if the speed margins required
to protect an aircraft
against the consequences
of a stall
would be also appropriate
The drag characteristics
typical
high
speed aircraft
with
respect
of the low aspect
of the foreseeable
to zero rate
ratio
future,
of climb
speed.
wing and thus of the
are such as to bring
the speed below which drag is greater than the available
engine thrust
In certain
cases this
near to the speed range considered for take off.
1
5
condition
might even be relevant
in the landing
realistic
safety margins against the occurrence
speed is therefore
an important
task.
The establishment
of
phase,
of catastrophic
fall
off in
The airworthiness
authorities
argue that since the existing
speed
margins have beeneffective
in preventing
stalls in civil
operations,
similar
m,argins will safeguard drcraf't
equally well against the exceedence of zero
On the other hand such a requirement
n‘ay appear unduly
rate of climb speed.
The
severe as a safeguard a,gainst an essentially
less sovcre phenomenon.
contribution
towards a possible resolution
present paper is written
as a first
of this problem although,
and this must be clearly
stated, it considers only
some aspects
which may well
of the problems,
In particular
of climb speed (V,)
V. is compared with
The first
study
question
which arises
In the case of the stall
of climb
with
we require
the stall shall be essentially
not more than a specified
loss
As zero rate
basis.
Z3RO R.X!E OP CLIEB SPlG3D
en aircraft
of climb speed rather than by the stall is the nature
to the pilot in the region below this speed.
entering
require
on a broader
below zero rate
the height loss in recovering
from flight
below
is calculated
and also the probability
OP falling
the probability
of stalling
a conventional
aeroplane.
RECCNERYFROM FLIGHT ~3'J
2
require
limited
hy zero rate
of the hazard presented
tJlat the motion
symmetric
of height.
and that
speed i s not necessarily
of the aircraft
recovery
associated
with
shall
a change
of flow behaviour
on the aircraft,
control
difficulties
need not be expected,
although they may of course appear in about the same sptied rogine for separate
The only flying
hazard directly
associated with the phenomenon
reasons.
This is perhaps best expressed as
under discussion
is loss of performmanoo.
the height loss incurred
in recovery to a condition
from xh-ich love1 flight
can be maintained.
This recovery manoeuvre can of course bc demonstrated
in flight,
where
one would expect the height loss to incrcasc progrcssivcly
with the anlount the
speed has been allowed to drop initially
bclom zero rate of climb speed.
The certification
of climb speeds,
but one engine.
iS
authorities
are interested
mainly in tno specific
zero rate
that with full engine poyrer and one with full power on all
These arc of special
One may have to consider,
Operated
with partial
power,
interest
for
take off.
however, also a condition
where the aircraft
e.C. in the approach.
If in such a condition
6
due to gross mishandling,
speed is allowed
to drop
to a certain
value
still
above the zero rate of climb speed appropriate
to full power, imbalance of
drag aver thrust canreduce
speed at so fast a rate that as a consequence drag
This
increeaoa faster than it is possible for the engines to increase t‘nrust.
pflenomenon would then mean that in this situation
a speed exists slightly
above
zero rate of climb speed proper, from which recovery without loss of height is
impossible.
Returning
now to the basic case with engines operating
at full power,
it is clear that once speed has dropped below zero rate of climb speed
Soma broad indications
of the recovery
recovery must involve
loss of height.
penalties
can be obtained from simple energy considerations.
If V. is zero rate
of climb
speed and AV is an increment in speed with
The minimum height AH, required
for the
respect to V. we get V = V. + AV.
aircraft
to recover from a negative
diversion
in speed AV to V. can be
calculated
by considering
the exchange of potential
and kinetic
energy as
AH,
q &
(2 v. AV + 21')
(1)
.
For
For negative values of AV, AH, will be negative,
i.e. a loss in hoight.
has been plotted
a representative
range of v'alues for Vo and AV this function
in Pig.2.
however, presents an optimistic
picture,
as it does
This energy equation,
In fact during
not allow for loss of energy during the recovery manoeuvre.
this manoeuvre the aircraft
flies below zero rate of climb speed where arag is
in excess of thrust.
Consequently
the work done against this excess drag
during the duration
tR of the recovery manoeuvre,
It R
(D-T)V
requires
the e-xpenditure
of additioilal
AH2 mg
at
potential
energy
= - I tR Orngv
Vdt
.
69
:0
Thus the total height loss for
adding equations
(1)
end (2).
recovery
from (V. + AVo) to ‘I, is obtained
by
.
7
t
AH = AH, + AH2 = &
(2Vo AV + AV') - / R 7
V a t.
(3)
'0
The terms under the integral
are of course functions
of time i.e. function
A
proper
solution
would therefore
the nature of the recovery manoeuvre.
As hero only a vory crude
require
the specification
of pilots
control.
estimate of the orders of magnitude is required,
it is proIjosod
!The
drag
the integral
by making suitably
simple assumptions.
characteristics
are assumed linear
within the range of interest
Of
to evaluate
versus
speed
as
It is firther
assumed that V(t) can be replaced by
where K is a constant.
during
the mean speed V = (V, + 5) = const and that AV varies symmetrically
the recovery
so that it can be represented
again by a mean AVm = $f if AV is
the initial
speed error.
J?indly
mean vertical
the duration
of the recovery manoeuvre can be related
velocity
grn and the total recovery height AH as
to the
tn = F .
(4)
Hm
Thus we obtain
zv, AV + AV2
AH = &
(5)
This expression
has been computed to cover a representative
range of
conditions
with the results
shown in Fig.3.
nvo values of K = a (+-3/+
ai-e
considered,
K = 0*25 as more representative
of a high aspeot ratio wing and.
It is seen that the height
K = 0.5 as more appropriato
for a slender
wing.
loss resulting
from this more realistic
analysis is generally
much greater
than that predicted
in Fig.2.
It is also seen that the height loss can be
minimised by using the fastest
possible rooovory technique,
i.e. by using a
It should bo noted that
large mean descent
rate
irn
during the manoeuvre.
these sums do not consider the practicability
of the implied manoeuvre, c.g*
no account is taken of the pitch response characteristics
of the aircraft.
However, this can be roughly assessed
by reference
to the given values of the
8
manoeuvre
duration
requiring
completion
the
curves
in
t
Fig.3
arc
The results
In
practice
to
less
must
speed
in
all
in
this
and overshoots.
itself
event.
is
THE POTENTIM,
An aircraft
that
this
ignoring
the
fact
values
of
flight
other
words
to
a combination
W
in
and
if
portions
of
be noted
zero
rate
of
height
loss.
etc.
arc bound
that
to be effective
climb
to lead
and this
requires
must
clear
that
a deviation
be treated
shows the
below
Cth
an engine
is
of
lift
off,
TJill
climb
caution
a serious
restricting
failed
rate
as much
only
after
more
zero
almost
speed
height
as
hazsrd
during
landings
condition
on a
situation
is
and this
OF STN,LIMG
stall
if
st,alling
that
substantial
a certain
incidence
in
dynamic
the
incidence,
critical
is
independent
manoeuvres
mfargin
incidence
in
the
of
stall
norm,?l
is
speed
esceeded.
and also
may be delayed
acceleration
to
available
in
is
In
(Fig.4)
is
from
An,
An,
also
above
it
V. witn
RISK
will
Assuming
level
account
as Fig.1
Also,
aircraft
higher
into
condition
multi-engined
3
minimum
However I zero rate of climb
immediately
to the ground,
i.e.
close
a rare
a theoretical
turbulcncc
should
a value
an aircraft
this
sp2a.
flight
to
corresponding
those
of height.
recovering
and that
stalling
speed
the
technique,
It
ca;?s,
lines.
represent
recoveries.
impracticable
4 seconds,
as dashed
piloting
expenditure
Taking
some obviously
than
Fig.3
of
return
an additional
less
in
variations
recovery
To exclude
shovm
given
favourable
be lost
R'
within
an aircraft
v&l1
of pilot
is
the
reached
the
level
of
stall
induced
or
exceeded.
to
speed
manoeuvre
one assumes
that
and gust
these
two
I.
at
a given
and verticsl
one
of
speed
gusts
the
V,
if
due
associated
Can specify
speed
errors
reaching
or
occuring
operationally
VT and
1:robability
statistical
-
when flying
If
distribution
a target
Lq2
vsi
manoeuvre
statistical
relation
(ii)
=
of
induced
distributions
normal
execoding
a given
acceleration,
are
independent,
(i.e.
that
9
the pilot will not simply cancel the gust idm?d
loads by scting as a gust
alleviator)
the total probability
of stalling
anywhere over the full
speed
range say during the approach or some other specific
flight
phase, can be
calculated.
Evidently
neither
are these assumptions absolutely
true nor can
we specify the statistical
distribution
of the two relevant
quantities
V and hn
with any degree of confidence
at least
exposure.
However, even using rather
that
4
such analysis
,$
may be able
to reveal
at the extremes constituting
accident
arbitrary
assumptions,
it is thought
some typical
qualitative
trends.
POTENTIAL RISK OF CATASTROPHIC LOSS OF PE?~GRkWCE
When an aircraft
flies below minimum drag speed, the available
margin
of thrust over drag will decrease progressively
with decreasing
speed until
a
point is reached at which level flight
can just be sustained with the
available
engine power (Fig.1).
Below this speed (Vo) the excess drag will
lead to a speed divergence
from which recovery is only possible by increasing
It has been shown earlier
in
the rate of descent, i.e. by losing height.
Section 2 that at least during approach and landing,
flight
in tnis regime is
However, a short term drop below this critical
speed, the
not permissible.
zero rate
of climb
speed, due to a brief exposure to a tail gust, will not
neither mill speed divergence
be of
necessarily
lead to speed divergence,
necessity fatal at the final
stages of an approach provided
that the aircraft
has enough elevator
po;ver and tail clearance for a safe touch d~~,n at the
required
large incidence.
Although these conditions
may well be claimed to provide further
relief
the results
of tho analysis
in Section 2 suggest that any drop of speed below
zero rate of climb speed close to the ground is almost as impermissible
as is
reaching the stall.
The probability
of experiencing
an impermissible
speed divergence
can
-thUS
conservatively
be stated to be equivalent
to the probability
of flying
at a speed V c v. when in close proximity
to the ground.
.
5
CALCULATIOXS ANI RESbL!i'S
As was said before the prodiction
bjr statistical
analysis
of the
potential
exposure to such flying
hazards as the stall or speed divcrgcnco,
leans heavily
on a series of assumptions.
For instance the awareness of the
existence of these hazards will obviously
rostrain
the pilot,
although it
will not affect
the gust-induced
variations.
Tnerc will also be a strong
correlation
between
the occurrence
of gust induced
speed variations
and non;lal
IO
acceleration
peaks, but here the corresponding
probability
speed and normal acceleration
are treated as independent;
detail
The principal
the following
distributions
of
variables,
are assumed to have a normal distribution,
assumptions are made:
In
(i)
Speed variability
is described by a normal distribution
round a
chosen mean speed V .
This mean speed represents
a speed target
m
selected by the pilot and available
statistical
data suggests that in
practice
it lies above the corresponding
target speed (VT) recommended
in the flight
manuals. : Two values are considered Vm/VS = I-35 corresponding to a 3@ speed margin and Vm/vS = I.25 corresponding
to a 2q:
margin.
In both casesthe pilot is assumed to allom himself a 5$margin
above the recommended target speed.
The statistical
variability
of
speed is described by the standard deviation;
two values are considered,
= 0.07 Ifs and GV =: 0005 '\TS, to represent
conditions
typical
for
OV
flight
in severe and moderate turbulence
respectively.
(ii)
Normal acceleration
is assumed to contain
two independent
contri-
butions,
one resulting
from piloted
manoeuvres, the other being gust
Considering
lift
off or approach as relevant
flight
phases
induced.
it is necessary to account for the required
pull up in the flare and
for this reason the mean normal acceleration
is taken as 1*05g or
1*03g respectively,
the incremental
variations
being normally
distributed
about this mean.
Pilot induced manoeuvring
is assumed to produce normal accelerations
constant
proportional
to V2, i.e. the Pilot is assumed to use approximately
Gust induced normal accelerations
control movement irrespective'of
speed.*
are varied in proportion
to V, as corresponds
to real conditions.
In order to cover a plausible
environments"
are considered.
range
three
distinct
"acceleration
* It is not suggested that +&is relationship
is a correct representation
of
Other laws may
real flying
practice
or even a particularly
plausible
one.
be more appropriate
but for the present purpose such subtleties
are irrelevant.
St~~dzrd
Flight
environment
Pilot
i$iuccd
P
Smooth
/q2
0.03 ‘r
is/
Moderate
0*04
0v
Ps/
"g"
deviation
of
Gust in$xed
G
O*O2 (11
g
i’s/
"g"
g
Moan "g"
nm
1*ogg
2
~*Wg
g
Severe
The
sum
of the two contributions
normal distribution
quantity
is plotted
The probability
with a standard
against V/vs for
of
experiencing
to the normal
act 1 r tion is again
2
This
deviation
of cn = r +.
G
the three cases conzidcrcd in Fig.5.
a
stall.
is
now
deterk.ned
a
by the
combination
of the probabilities
of finding
oneself at a givon sped and at
the
same
time
of experiencing
a normal
acceleration
equal to or greater
than
Mathematically
.lhi3 mean3
multithat defining
the stall at that speed.
plying the probability
of flying
at a given spsed (as dcfincd by the assumed
variability
cv) by the probability
of at each speed sxcocding the corresThis
product i3 a distriponding stalling
incidence
(plotLed
in Fig.6).
Exn~ples of
bution n\nction
of the probability
of stalling
against aped.
such distribution
functions
for the case of a moderate Plight environment
It can be seen that that maximum stalling
risk is
are shown in Fig.-/.
Integrating
these
associated tith speeds well above the stalling
sped.
functions
from 0 < V c CJ gives then the total probabiliLy
of stalling
for an
The30 integrals
were computed
aircraft
flying
in the particular
environment.
for all combinations
of the above liisted assumptions and are presented in
Table
1 and plotted
in Fig.8.
In the case of an sircraft
being limited
by zero rate of climb speed
the O&J danger to be considered
is that of speed
rathor than by a stall,
The probability
of this happening is then simply the
falling
below V,.
speed distribution
function.
integral
between 0 < V < V. of the appropriate
This integral
defines the probability
of encountering
a speed divergence
Substituting
which recovery is only possible at the expense of height.
from
V.
12
for
VS used as a data3
speed in the stall
analysis,
these integrals
have been
evaluated
for the same conditiong
as treated above.
The results
are also given
in TaUe 1 and Fig.8.
To make The comparison between the stalling
case and the
performance
limited
aircraft
absolutely
fair,
the zero rate of climb speed
should be computed not for
for
the stall
the lg colidition
but for
the mean "g" > 100 assumed
analysis.
The probabilities
derived %y this procedure rind shonn in Pig.8 appear
rather high in the more adverse con&i tions, in fact in some cases they appear
to be in obvious contradiction
to, the known very low incidence
of stalling
observed in real life.
Before any interpretation
is attempted of these
results,
the following
reservations
must be noted:
W
The calculations
do not claim to predict
absolute figures,
they
are clearly
based on a series of arbitrary
assumptions,
which are not
Nevertheless
they should be
derived from operational
statistics.
adequate
to allow
relative
comparison
between
the various
cases.
(ii)
The quoted probabilities
refer to particukz
onvironmentd
To obtain from these an overall
probability
of
conditions
(weather),
one would have to multipa
experiencing
the specific
incident
considered,
the results
again with the probability
ta exist.
This will obviously
give
those shown in Fig.8.
for
total.
thcsc environment
c&ditions
probabilities
much lower than
(iii)
The cases cvdustcd
for a mean speea V, = 1.25 VS ap:>ropriate
to
an assumed recommended target speed of 205; above stalling
speed, are not
realistic
when applied to the stalling
case itself,
since such low
These are only
margins are not permitted
by airworthiness
regulation.
shown as a basis for comparison with the zero rate of climb speed case.
6
DISCUSSION
The results
of these
namely that the probabilitjr
calcuistions
show of course the expected
- other things being equal - of stalling
craft due to a combination
of low speed and the application
acceleration
is much greater thari the probability
of flying
Also it is seen that a reduction
of the speed margin of the
the vulncrabili.kJ
to
operational
speed by 1% Vs increases
factor
of bektiecn IO2 to 104.
'
If
of just
one compares the potential
falling
below Vs = V,,
it
danger
of stdling
is seen that
- except
of normal
at V < Vs alone.
sclrctca
target
either
an aircraft
for
trends,
an air-
hazard by a
with
the extreme
that
case
13
(o?V = 0*05 V ) and in a smooth environment
S
instance a 25:; margin olffcrs better protection
against speed diver,-ence
Vo than does the 35’: margin against stalling.
with
small
It
speed variability
would appear
that,
if
present
margins
provide
adoquatc
stall
- for
below
protect-
ion, zero rate of climb speed could be equally protected
by a margin I&
It can be argued that when V. is only critical
after
smaller than these.
engine failure
which itself
is a rare event,
the overall
probability
of
dropping belo& V. is substantially
reduced and an even smaller V. - margin
might be acceptable.
Gl3'NERALCOKSID-XlL~TIOXS .
7
The above process of attempting
to arrive
at a safety margin against
novel flight
hazard by statistical
analysis is based essentially
on the
customary approach of applying past experience to a new design.
In this
approach the operative
word is always:
"other things being equal".
condition
t!lat other things are equal is of course not automatically
and further
regulations
are needed to ensure handling
characteristics
make the avoidance of a given hazardous condition
equally easy,
an
a
The
satisfied
which
With the conventionel.
aircraft,
for instance,
safety from stalling
rests
not only on the choice of suitable
low speed margins but moreover on the aircraft
possessing clearly
distinguishable
stall warning,
either natural
or synthetic.
If szo rate of climb speed or indeed any other phenomenon replaces the stall
as the primary lam speed hazard it may be necessary
to warn the pilot of the
approach to this condition
by an equivalent
vmrning.
Physically
"&is may
well take the form of the well proven stick-shake*.
If take-off
directors
are used the warning may be incorporated
into this instrumenta
The sensing
sign&
however,
is rather
complex as zero rate
of climb
speed is a function
of aircraft
weight
as well as those parameters
affecting
engine power such as air temperature
and altitude.
Yrequently
zero rate of
climb speed will only bc a practical
hazard during take off and in this case
a simple pracomputed setting may be adequate,
Another
the fact that
aspect affecting
in the approach
the aircraft
limited
by zero rate
to this hazard it will in addition
of climb
be f&ing
below minimum drag speed.
It is generally
recognised
that in this regime
speed control
is more difficult
and there appears to be a possibility
therefore,
that speed errors become larger and more frequent
and as a
consequence the potential
cxponure to zero rate of climb speed is sharply
increased.
essential
However,
to consider
in practice,
this is not nocessariljr
so and it
the two primary low speed regimes separately.
is
is
(i)
In take off full poxer is used at least until
a height is reached
at which zero rate of climb speed ceases to be a hazard.
In this
configuration
the aircraft
flies
with excess poxer, usually converted
into rate of climb and the speed instability
associated
with flight
below minimum drag speed a0Os not arise, unless the pilot attempts to
fly a constant climb gradient.
(ii)
In the approach where the constraint
to the glide path can lead to
temporary speed divergenccj
zero rate of climb speed is usually well
In any case it
outside the practical
range of even gross speed errors,
is now generally
accepted that aircraft
approaching
below minimum drag
speed require
automatic throttle
control and this should in fact lead
to improved speed holding when compared vtith conventional
aircraft.
In
this case there is, hoxvor,
still
one aspect that nec&s consideration.
If the authority
of th.e automatic throttle
control
is too limited,
from _
time to time speed may fall below the operating
range of the system and
from then on, if the pilot is unaware of this situation
speea will be
lost rather rapidly.
Since automatic throttle
control may develop a
habit in pilots
to pay less attention
to speed, it is imperative
to
ensure that the autothrottle
authority
to cope with all
is not only reliable
but also has enough
likely
extremes.
It may be advisable
to
warn the pilot
of a condition
thrust under its command for
8
when the autothrottle
applies
more than a brief moment.
all
the
COMcLUSIONS
The high induced drag of the modern low aspect ratio aircraft
is capable
of generating
a condition
at very low speed below which drag exceeds the
If a0pm
available
engine thrust so that level flight
cannot be maintained.
to this
speed no stall
or other
prohibitive
control
problem
arises,
this
"zero
flight
rate of climb speed" may then constitute
the extreme limit of safe
and operational
speeds must be chosen to provide adequate margins
loss of pcrf'ormance below
against the accidental
exposure to irrecoverable
this
speed.
Statistical
considerations
indicate
however,
that
such margins
could be
significantly
lower than those rk@red
to protect more conventional
aircraft
against the stall.
It may be desirable,
nevertheless,
to provide
the aircraft limited
by zero rate of climb speed xith a warning device similar
to
those developed
for
stall
protection.
Table
Standard
deviation
of speed
%
0*07
vs
~
Standard
Manoeuvre
deviation
g
UP
o*04 (v/$) 2
0*03
(v/Q2
of
Gust g
uG
r Probability
idean
manoeuvre
n
m
0*05 v&
1905
O-04 v/v,
I.05
O-02
I.03
v&
I
with Vm = I.35 VS 7 Probability
ivith V, = I-25
I
of being at
of stalling
of being at
of stalling
v d vs = v.
v < vs = v.
I
g
O-2
x IO
t
-6
_
0.05
I
vs
o*g (v/fq2
0.04 (v/+q2
@03 (v&T2
0.05 vfis
I*05
o*Q4 v&
1.05
0=02
I.03
v/vs
i
i
10*000003
1
i
x 10
-6
440 x IO
-6
110 x IO'"
3looo
15 x 10
-6
x loo6
-6
1~0x10
12 x 10 -6
6700 x
13 x IO -6
3600 x IO -6
0*16
0~0000&
x 10 -6
x 10
-6
0.2
x IO
-6
630 x
IO
IO
39 x IO
-6
-6
-6
VS
16
s-YNBOLS
D
K =
H
AH
m
n
m
'k
v
v.
Vm
vs
AV
Avo
cG
o-n
"h
%
height
recovery height
aircraft
mass
normal acceleration
mean normal acceleration
thrust
duration
of manoeuvre
speed
zero rate of climb speed
mean speed
stslling
speed
incremental
speed
initial
speed excursion from either Vs or V.
rms gust induced normal acceleration
ms normal accelera'tion
33x3 pilot induced normal acceleration
rms speed variability
.
t
FIG.1
DRAG
DEFINITION
FULL
THRUSr
ALL
ONE
ENGINE
FAILED
AND THRUST
OF ZERO
VERSUS
ENGINES
/
SPEED
RATE OF CLIMB
AND
THE
SPEED
I
RECOVERY
FIG. 2 POTENTIAL
HEIGHT LOSS FOR RECOVERY FROM
FLIGHT AV KNOTS BELOW ZERO RATE OF CLIMB
SPEED V, ASSUMING NO ENERGY LOSSES
K * 025
K =o-so
400
MEAN
Vf RTICAL
VELOCITY
ft
AH
AH
t,’
200
I
(j m :sb&oc
400p
400 Ft
AH
‘AH
40sec.
LR
200
20 sec.
400ft
I?,:
AH
ZOf VS&C
AH
200fL
-20
-10
AV
KNOTS
0
-20
I
-IO
AV
0
KNOTS
FIG .3. HEIGHT AH AND TIME tR LOST IN
RECOVERY
FROM SPEED
AV KNOTS BELOW
ZERO
RATE OF CLIMB SPEED V. FOR A
RANGE OF AIRCRAFT AND RECOVERY
MANOEUVRES-
tR
I.0
I@3
Is2
FIG.4
NORMAL
ACCELERATION
ABOVE STALLING
01
I-0
v/vs
MARGIN
SPEED
I
I.3
I.1
Iv2
AVAILABLE
Vs
I
I*4
vvs
FIG. 5 ASSUMED
STANDARD
DEVIATION
OF NORM AL
ACCELERATION
AS A FUNCTION
OF SPEED
l-4
180
101
I-2 v/v,
l-3
PROBAB
FIG.6
PROBABILITY
OF EXCEEDING
STALLING
INCIDENCE
WHEN FLYING AT A GIVEN SPEED V AS A FUNCTION
OF
V/V,
AND OF THE SEVERITY OF FLIGHT ENVIRONMENT
I*3
0.3
f”lOCE:RATE
FLIGHT
OIVIRONMENT
FIG. 7 TYPICAL EXAMPLES
FOR PROBABILITY
DISTRIBUTION
FUNCTIONS
OF g - STALLING
OVER THE SPEED RANGE
SPEED VARIABILITY
Ov=Oe07 Vs NORMALLY
DISTRIBUTED
ABOUT Vm
FLlf+fT
CALM
ENWRONMENT
ROUGH
MOOERATE
I
.
1
I
,,I,;
‘PROBABILf
TY
/OF
STALLING
PRUBAB/LITY
-4
IO
lO-6
--I
FIG.8
---m--
(al
FLIGHT
CALM
OF FALLING
-J6ELOW
VsV
Pm = ‘-35 “0
C”
= 0.07
0
vs (if())
E:NVlROWMEtdT
MOOERATf
ROUGH
I
lO-2
PROBABILITY
lO-4
F STALLING
PROBABILITY
1O-6
PR06ABlLlTY
IO
OF FALLING
BELOW vs v.
- (0
I O"z
FIG. 8 09
r,
= o*o5
vs (vo)
FIG.8
COMPARISON
OF PROBABILITY
OF STALLING
AGAINST PROBABILITY
OF DROPPING
BELOW V.
FOR A RANGE Of ASSUMED FLIGHT
ENVIRONMENTS
Printed
in figland
the Royal Aircraft
for Her Najesty’s
Stationery
BstabIishment,
Farnborough.
Office by
Dd.125875.KY.
I
A.R.C. C.P.931
thy 1966
Pinsker,
W. J. G.
~3.4013.66:
533.4015.32:
533.6433:
533.4013.61:
656.7.08
533.4013.66:
533.&o\ 5.32:
Y3.693.3:
533.6.ol3.61:
656.7.08
C.P.%l
my 1966
AJLC.
Plnsker, W. J. 0.
“ZERO RAlC DF CLI?lE!SPEED AS A Low SPEL;DLIHITAtI@4
FOR THE STALLAIRCRAFT
w=O ItAlE OF (ZIMB w
AS A LM SPEED
LMITATICN
FURTHESTAU-FREEAImAFT
m amapt
An attempt is 1~48 t0 assess the signirito night
safety or a
condition at low speedstire drag exceeds the available engine thrust.
For the low aspect ratio elicraft and especially with slenbr wing designs
having practically no stall, ths azero rate or climb speedr derined by the
condition imy constitute the lovwst limit of the practical speed i%nge.
Methodsare suggested to assess the necessary nmrgins to plPtoct aitcrart
of this general class against the accidental, posslbly oatastrophic, loss
or prronsence below this speed.
is 1~48 t0 assess the signiri0m0e
to riight sarety or a
at low speeds where drag exceeds the available engine thrust.
For the low aspect ratio
aircrart and especially with slender wing designs
having practically no stall, the “zero rate or climb speed defined by the
condition amy constitute the lorrcst limit or the practical speedrange.
Methodsare suggestedto assessthe necessary margins to protect aircraft
of this general class against the accidental, possibly catastrophic, loss
0r perrormancebelow this speed
condition
A&C.
C.P.931
MSY 1966
T~3.6.013.66:
533.6.~ 5.32:
533.693.3:
533.6.013.6r :
656.7.08
Pinsker. W. J. G.
“ZERORATEOFCLIHB SPED” AS A Low SPEEDLIMITATION
FCRTHESTALL-FREE
AIiVXAFT
An attempt is madeto assess the signiticance to flight safety of a
condition at low speedswhere drag exceeds the available engine thrust.
For the low aspect ratio aircraft and especially with slender wing designs
having practically no stall, the ItzerO rate of climb speed@defined by the
condition may constitute the lowest limit of the Practical speed range.
Methodsare aggested to assessthe necessary margins to protect airc!%rt
or thls general class against the accidental, possibly catastrophic, loss
0r perroncance below this speed.
-
_.
.-
-
-
--
I
C.P. No. 93 I
C.P. No. 93 I
S.O. CODE No. 23-9017-31