REPORT OF PRELIMINARY PITCH AXIS ANALYSIS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP67B00945R000200040001-4
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 89
• Document Creation Date: December 27, 2016
• Document Release Date: May 29, 2014
• Sequence Number: 1
• Publication Date: August 18, 1960
• Content Type: REPORT

1,
: .
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c7f-c_
? e) 9 0 0
-Copy
?SF 3
IN REPLY
REFER TO; I1L9-72-60 Copy
DATE: 18 August 1960
TO: A. C. Angel
SUBJECT: Report of Preliminary Pitch Axis Analysis
Enclosure: Report of Preliminary Pitch Axis Analysis
Gentlemen:
Page 1 of 1
Results of preliminary analyses of the pitch axis control system are presented
?
in the enclosure. These results are subject to changes as dictated by simulator
and aeroelastic studies now in progress. Additional analysis results are
available at WLO if desired, however, the enclosed report covers the significant
results.
JP14:d11,-
Project Engineer
STAT
STAT
Senior Account dministrator
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W10-72,60
Report of Preliminary Pitch Analysis
SECTION 1
ABSTRACT
This document contains results of preliminary analyses to determine
suitable configurations for
and autopilot.
Results are
o A completely linear
the pitch axis stability augmentation
included for studies covering:
airplane - damper system.
system
Pagel
o A linear damper controlling an airplane with non-linear static
stability and non-linear manual control system.
o An autopilot with pitch attitude hold and Mach hold modes and
automatic trim.
* Failsafety through redundant damper mechanization.
In each of these areas, configurations have been established which
meet or exceed performance requirements with minimum complexity. Failsafety
studies verify satisfactory vehicle protection for stability augmentation
servo, gyro, or electronics ramp type failures. Preliminary estimates
indicate adequate protection against autopilot failures except in the low
altitude, high q region.
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SECTION 2
WLO-72-60 Page 2
INTRODUCTION
Objectives
Preliminary analysis and design have been conducted to meet three basic
design objectives:
1. Failsafety - Design the system such that one failure known to the
pilot plus a second unknown failure will not result in a maneuver
from, which the pilot cannot recover.
Primary effort toward this objective has been design and analysis
of the redundant stability augmentation system. Continuing
analysis of the autopilot and auto-trim systems will verify
compliance with the objective or delineate action necessary to :
meet the objective.
2. Scheduling Complexity - Endeavor to achieve satisfactory performance
with a minimum of air data scheduling in order to enhance system
reliability.
Due to the wide variations in aircraft dynamics, some system
parameter scheduling has been necessary to meet the minimum
performance requirements outlined in objective Number 3. At the
same time however, the parameter scheduling has allowed the
minimum performance requirements to be exceeded without additional
complexity. Presently a total of 7 scheduling potentiometers
and three altitude switches are required in the pitch axis,
(includes damper redundancy). This represents a considerable
reduction over similar systems with narrower aircraft dynamic
variations.
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NZO-72-60
Sco e
Page 3
3. Performance - Optimize performance at the design flight conditions;
augment static stability during the approach and landing condition.
Vehicle must possess reasonable handling qualities at all other
flight conditions but need not possess optimum performance.
As stated in Item 21 this objective has been reached and exceeded
for the rigid vehicle. Most of the significant variations in
performance which remain are due to large variations in weight
and C.G. location which cannot be easily compensated for by
scheduling.
The scope of analytical work at WIL has thus far been restricted mostly
to small perturbation studies including only the rigid body aircraft
equations of motion. In view of these restrictions, the configurations
and results included herein are subject to changes delineated by aeroelastic
studies and simulator results.
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1,J10-72-60 Page 4
SECTION 3
SYSTEM CONFIGURATION
The pitch axis automatic control System consists of a redundant stability
augmentation system waidpg through series servos, and a single 'channel autopilot
Working through a parallel servo. Each available, mode of the system will be
discussed in terms of single channel operation, with aspects of cmultiple channel
operation being discussed separately.
(a) Modes
(1) Stability Augmentation
The free airplane frequency and damping are augmented by a qte
(pitot differential pressure) scheduled proportional pitch rate
feedback to the series servo.
At high altitudes (above 62,000 feet) the static stability is
further augmented by a lagged pitch rate signal, The gain and
time constant of this term are fixed,
The above two terms are sufficient to provide good handling
qualities throughout the flight envelope. However, the pitch
attitude loop requires better inner loop damping at high altitudes
than these two terms provide, This additional damping is obtained
by adding more proportional pitch rate at high altitudes, This is
easily accomplished by adding a lead term to the lagged pitch rate
feedback, Thus, the damper equation is:
[IS (1 + s)1 where: ? = q c)
= 9 66 1 4. 12s J ha 62,000
The damper block diagram is shown in Figure 30l,
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W10-7260 Page 5
(2) Attitude Hold
The Pitch Attitude Hold mode configuration is illustrated by a portion
of the block diagram in Figure 3.1. The system consists of the
stability augmentation system discussed above and a proportional
parallel servo driven by lagged pitch attitude error. As noted,
the low-pass time constant is scheduled with log Ps as shown in
Figure 3.2. The gain of the pitch attitude loop, SQL, is scheduled
with both log qlc and log Ps as shown in Figure 3.3. The control
equation for the mode is
(3)
g e = gg + 6
1 + TS
4. [5 (1 +
1 + 12s J h 62,0001
Mach Hold
Mach hold mode, described by the block diagram in Figure 3.1,
utilizes the pitch attitude hold mode as an inner loop and two
signals, nog (R-1) and
provided by the air data
computer. The air data quantities are proportional to Mach error,
AM, and Mach rate, M, respectively. The quantity R is the ratio
of total pressure to static pressure, The ratio Alog (R-1) (in
AM
effect a variable gain in the Mach loop) is a function of Mach number
which decreases as Mach increases.
The Mach signals are summed into the autopilot bridge such that they
command lagged pitch attitude changes. An electromechanical integrator
is used to provide an integrated Mach error signal necessary for
accurate control of Mach number regardless of varying trim requirements.
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WW-72-60 Page 6
Mach error and integral gains OR and gril are scheduled with log Ps
as shown in Figure 3.4.
Mach rate gain is constant at 50 degrees pitch attitude
unit of log (R-1)
sec
The control equation for Mach hold is2
e Eg
Alog (R-1) (?pt QSR)
- R-1) 911
+ (1 + 5s)_1
1 + 12s 1.1?. 622000'
(4) Automatic Trim
The auto-trim system represented in the block diagram of Figure 3.1
consists principally of a switch sensing parallel servo position,
an electrical trim actuator and a stability compensator. The switch
is represented in the diagram as having a deadSpot and hysteresis.
A nominal switch deadspot of -?0.25 degrees of equivalent elevator
deflection is recommended together with -?0.050 hysteresis. While on
duty, the trim actuator will drive at a rate of 0.1 deg equivalent
sec
surface rate. The function of the auto trim system is,to provide
changes in trim elevator angle necessary to maintain 1 g flight and
at the same time have negligible effect on dynamic response of the
other automatic control modes.
(b) Redundant System
A redundant monitoring system was devised for the pitch damper mode to
provide failsafe operation throughout the mission profile. The system
Consists of duplicate channels, A,and 13, each containing a pitch rate gyro,
damper parameters (56 and 66L and asSociated electronic circuitry, and
the right and left series servos. In addition, the system includes a monitor
channel, M, containing a pitch rate gyro, scheduling parameters and electronic
circuitry, to monitor the gyro and electronics for Channels A and B. Initial
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na-72-60
Page?
plane for a servo analog to monitor the redundant series servo channels
were discarded because of the difficulty of designing an analog to duplicate
the servo characteristics over the entire operative temperature range of
the profile. The block diagram of the redundant channels is shown in
Figure 3.5.
The redundant monitoring system detects and disengages a faulty channel
,whenever the following events occurs
(1) The Voltage proportional to the displacement from center of
a series servo differs from that of its mate in the same channel
by the allowable difference E= 2.18? = (ER
(2) The voltage proportional to the output of the rate gyro and the
gain scheduling electronics of one channel differs from that of
another Channel by the allowable difference E = 2.18? = (SR + 6L).
The redundant pitch damper configuration was analyzed on an analog
computer at fourteen flight conditions which were selected to yield a
representative coverage of the mission profile. Series servo malfunctions
and gyro and electronic malfunctions were simulated at series servo rates
varying from the maximum servo rate of 150/s down to 0.3?/8 (slow,
? preeping failure), Inlboth single and multiple channel malfunctions, the
largest incremental gos resulted from the slow, creeping type of failures,
The incremental peak gos obtained at the critical flight conditions 72 82
and 10 - all high surface effeCtittnessAonditions are aumgarizo below
tor failures in straight and level flight at a series servo rate of 0.3Vs:
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WLO-72-60
Page 8
1st Failure
2nd Failure
Malfunction:
,
Servo
XAR
Gyro
XA
Servo
XBL
Gyro
XB
Condition 7
.85 g s
.57 g's
1.0 g's
?
.75 g's
, Condition 8
.87 g's
,
.55 gts
1.1 g's
.7 g's
.?Condition 10
.85 ggs
,
.6 g's
.95 g's
.78 gt s
In the first failure condition, one of the redundant operating channels
fails due to a servo or gyro failure while the second channel continues
operating., In the second failure condition, an operating channel has
failed and been disengaged and a servo or gyro failure then occurs in the
remaining operating channel.
Nominal values of E = 2.18? = (ccR 6-0 for servo malfunctions and
E= 2.18? S'Et + EL) for gyro malfunctions; system dead time of
35 milliseconds, and servo recentering lag time of 50 milliseconds were
used. The effect of varying the nominal values was also checked.
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AIRFRAME
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4
AIR MITA
7?7?
74-*5
+ 125
?
hs
619L1-9/?
h< 175
SERIES
SERVO
5
orHER
? Am HOLD
MACH HOLD
Alo90?-1)
?
R-I
A7T. HOLD
tlfCH HOW
onIER
OTHER
+? .
Wm./ ? oniER?
PARequi..
SERVO
CoMPEAl 54TOR
All
HoLD
4 0.2C? PEAOSPor
? 100 ourPvr
? OTHER
I.
RsuRE3.1 .sws-LE CH,4 A/ME L 0/4M 75 R A/VL) Al/TOPI Zor 8L OCK D/A 6R4
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10
TR/ll
Acrehlroi?
9
AIRFRAME
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4
AIR MITA
7?7?
74-*5
+ 125
?
hs
619L1-9/?
h< 175
SERIES
SERVO
5
orHER
? Am HOLD
MACH HOLD
Alo90?-1)
?
R-I
A7T. HOLD
tlfCH HOW
onIER
OTHER
+? .
Wm./ ? oniER?
PARequi..
SERVO
CoMPEAl 54TOR
All
HoLD
4 0.2C? PEAOSPor
? 100 ourPvr
? OTHER
I.
RsuRE3.1 .sws-LE CH,4 A/ME L 0/4M 75 R A/VL) Al/TOPI Zor 8L OCK D/A 6R4
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10
TR/ll
Acrehlroi?
9
AIRFRAME
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4
AIR MITA
7?7?
74-*5
+ 125
?
hs
619L1-9/?
h< 175
SERIES
SERVO
5
orHER
? Am HOLD
MACH HOLD
Alo90?-1)
?
R-I
A7T. HOLD
tlfCH HOW
onIER
OTHER
+? .
Wm./ ? oniER?
PARequi..
SERVO
CoMPEAl 54TOR
All
HoLD
4 0.2C? PEAOSPor
? 100 ourPvr
? OTHER
I.
RsuRE3.1 .sws-LE CH,4 A/ME L 0/4M 75 R A/VL) Al/TOPI Zor 8L OCK D/A 6R4
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10
TR/ll
Acrehlroi?
9
AIRFRAME
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4
AIR MITA
7?7?
74-*5
+ 125
?
hs
619L1-9/?
h< 175
SERIES
SERVO
5
orHER
? Am HOLD
MACH HOLD
Alo90?-1)
?
R-I
A7T. HOLD
tlfCH HOW
onIER
OTHER
+? .
Wm./ ? oniER?
PARequi..
SERVO
CoMPEAl 54TOR
All
HoLD
4 0.2C? PEAOSPor
? 100 ourPvr
? OTHER
I.
RsuRE3.1 .sws-LE CH,4 A/ME L 0/4M 75 R A/VL) Al/TOPI Zor 8L OCK D/A 6R4
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10
TR/ll
Acrehlroi?
9
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?,-
ZDZIA/L),/lAi ;7- /1")/ 7677/ L17-71/// -/2f-
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WIL-72-60
SECTION 4
PROBLEM AREAS
Three major problem areas are known to exist with this vehicle -
pitch-up, speed instability, and aeroelasticity.
(a) Pitch-Up
The aircraft C curves taken from wind tunnel data reverse slope
indicating static instability at high altitudes and high lift
coefficients. For this reason static stability is augmented With
a lagged pitch rate feedback at altitudes above 62,000 feet. The
choice of gain and time constant on this term is based on the
assumption that the aircraft will never exceed 1% F negative
static margin.
If future data shows that a negative static margin of more than 1%
c can exist, or, that violent static instability can exist at
?
lower altitudes then a damper change may be required.
(b) Speed Instability
Page 1)4
The trim elevator versus Mach number curves show a speed instability
problem at Mach numbers between 0.5 and 1.1 for altitudes below
36,000 feet. In this region the pilot would be required to pull
_
back on the stick after an increase in speed. This is opposite
to normal stick feel.
The problem is common to most high speed aircraft. However, it is
accentuated in this case, because it occurs during refueling when
the pilot is attempting to maintain precise control.
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W10-72-60
(b) (Cont,d)
Several schemes are available for providing an elevator trim angle
as a function of Mach number.
The seriousness of the problem together with the schemes for
alleviating it are currently being studied on a moving cab
simulator.
(c) Aeroelasticity
Early structural analyses have shown that the vehicle will have
five symmetric bending modes below 10 cps. The lowest frequency
(or fundamental) will be in the neighborhood of 2 cps. The
highest vehicle short period frequencies will be in the neighbor-
hood of 1 cps. Thus, allowable low frequency phase margin will
not permit extensive filtering, and, as a result, selection of a
favorable gyro location becomes a necessity.
The analyses shown in this report are based on the assumption of a
rigid vehicle and hence the gyro has no structural pickup. As a
result the damper is likely to require some modifications once the
aeroelastic problems are fully known.
Page 15
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WL0-72-60 SECTION 5 page 16
ANALOG COMPUTER SIMULATIONS
Analog computer wiring diagrams used in the various pitch axis studies
are included in this section. Separate diagrams are included for the
linear damper and autopilot studies, for the non-linear damper study and
for the failsafety study. A single list of airfrahle potentiometer settings,
applicable to all of the diagrams is given in Table 5.1.
(a)
Linear Damper and Autopilot
The computer simulation is shown in Figure 5.1. For the linear
damper studies, only the lift and pitching moment equations were
used to describe the aircraft. The series servo was simulated as
a second order system with natural frequency of 14.2 cps and damping
ratio of 0.7. Early damper studies used a frequency of 30 cps,
but traces included in this report are based on 14.2 ep . Serve
authority was set at ?4 5? equivalent surface deflection. Unity
gyro dynamics were used and the power actuator was represented
by a first order lag of 0.03 seconds.
Pitch? attitude hold studies were also conducted with a two degree-
of-freedom airplane. The parallel servo used in the attitude
hold mode was simulated as a second order system with a natural
frequency of 10 cps and a damping ratio of 0.9.
A third degree of freedom provided by the airspeed equation was
included in the Mach hold studies to provide a computation of Mach
error. Altitude rate was also computed to provide an additional
term in the Mach error computation accounting for the effect of
temperature lapse rate on Mach number. Dynamics of the air data
cbmputer have thusfar been simulated as a linear second order
equation. The ADC has two separate channels, one driven by a (ale
signal and the other by a Ps signal. Although both loops affect
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WI0-72-60
(a) (Contld)
Mach error computation, separate simulation of both channels is not
justified in a preliminary analysis. The slower of the two channels,
the Ps channel was simulated to be conservative. The natural
frequency varies from 2.3 radians/sec0 at maximum altitude to
23 radians/sec0 at sea level. A damping ratio of 0.8 was used.
Page 17
Each of the air data pressure sources PT and Ps has a tubing lag
associated with it. It was agreed that this lag should not exceed
3 seconds if good Mach hold performance is to be maintained at max-
imum altitude. A single lag, Tss, was simulated with a linear
variation on a semi-log plot from 3 seconds at maximum altitude
through 0.1 seconds at 30,000 feet. Both the pressure source,
lag and the ADC dynamics were applied to the sum of all of the
Mach signals to avoid multiple simulation.
Simulation of the auto-trim switch is accomplished with a pair of
relay amplifiers which are biased to energize when parallel servo
displacement exceeds the bias. One relay simulates each side of
the switch. When a relay is energized, a second bias signal is
switched into the circuit to provide switch hysteresis. When
either relay is energized it also provides a step input to the
trim actuator and the stability compensating lag network.
(b) Non-Linear Damper
The non-linear damper simulation consisted of the linear short
period pitch aircraft characteristics at flight conditions 17 and
below. At flight conditions 18 and above, the non-linear slope
of the variable NyCe? (the pitching moment due to angle of attack
changes times the angle of attack change,) was simulated on a
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W10-72-60 Page. 18
(b) (Cont'd)
(c)
non-linear function generator. The dynamics of the series servo
were mechanized as a second order loop with natural frequency of
6,) . 30 cps and damping ratio of lf . 0.8. The servo rate
limits of 15?/sec and displacement limits of ?4.5? were included.
A first order lag of 1 represents the actuator dynamics,
1 + 003S
and the rate gyro dynamics were neglected. The manual control
system breakout force of 2.5# stick force was simulated by a
deadspot circuit. The coulomb friction of 2.5# stickforce was
approximated by a hysteresis circuit. The effect of the bobweight
was included in the simulation by feeding a normal acceleration
signal at 5#/g into the stick force circuit. A second order
loop was used to simulate a spring rate of 3.9#/1n. and a viacous
damping term sufficient to make 2; . 0.7. A control system mass
Sc/
of 0.3 slugs was used. The non-linear gearing of the stick, /A 9
was simulated on the non-linear function generator.
The computer diagram is shown in Figures 5.2 and 5.2 b.
Failsafety? Redundant System
The pitch aircraft equations of motion for angle of attack and
pitching moment variations were uSed. At flight conditions 17 and
below, the variations were linear. At flight conditions 18 and
above, the non-linear slope of the variable Modewas simulatedlon
function generators.
The redundant channels Ay B, and M were simulated with identical
circuitry on analog computers. The pitch rate gyro, the series
servo, and the hydraulic and linkage thresholds were simulated
as one lumped system threshold of 0.052 degrees of surface in
channel A and in channel B to conserve amplifiers. The gyro
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1410-7-60 (c)
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(Contld) Page 19
threshold in channel M was neglected. The gyro dynamics were
neglected in all channels. The servo dynamics of (.') . 30 cps
and 25 . .8 were simulated in a second order loop for each
redundant servo. The servo rate limit of 15 ?/s was included.
A first order lag of I was used to approximate the
1+ .033
actuator dynamics. The actuator rate limits of 30 ?/s were not
simulated. Since the manual control system was not simulated,
and no manual elevator commands were used in the analysis the
elevator sunning amplifier was limited to the series servo
authority limits of ?4.5?.
The hardware mechanization of the redundant series servos utilizes
a series hook-up between the A and B channel servos in each right
and left actuator linkage (Reference Figure 3.5). Here, the two
servos track together to drive the associated actuator in normal
system operation. The servo output authority is 15?/s and ?4.5?.
of actuator motion whether one or both servos are operating. The
electrical analog of the mechanical system utilized a parallel
hook-up between the A and B channel servos in each right and left
actuator simulation to achieve the same servo behavior effect in
both normal and malfunctioning operation. Here, each servo shared
the load of driving the right and left actuators in normal operation.
During malfunctioning operation, the gain of the servo output is
doubled to provide full authority to each servo in the malfunctioning
channel. The analog computer diagrams are shown in Figure 5.3.a
and 5.3.b.
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V10-72-60 Page 20
(c) (Contld)
The detection and disengagement of a faulty channel was simulated
with relay logic. The voltage difference between two servos
outputs ( for example: XAR and XAL in channelA) was f d to a biased
relay amplifier. In the event that a malfunction occurred, this
difference exceeded the bias, and the relay energized and fed a
fixed voltage into an integrator. After a predetermined time delay
or system dead time elapsed, the integrator output exceeded the
bias of a second relay amplifier. The second relay then energized
and its contacts disengaged the malfunctioning channel by removing
the input and recentered the servos in that channel with a first
order lag network in the servo simulation. A similar process
occurred for gyro and electronic malfunction simulations. In this
analysis, a 5:1 time scale (machine time is 5 x real time) was used
to minimize the inherent relay lags.
The servo and gyro malfunctions were simulated by feeding ramps
of varying rates into the appropriate amplifiers.
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Pot
Al
Value
A2
A3
AU
A5
A6
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Declassified in Part - Sanitized Copy Approved for Release 2014/05/29 CIA-RDP67B00945R00020004000.1-4
TABLES.! CORRECTED ANALOG COMPUTER POT SETTINGS FOR
LINEAR DAMPER AND AUTOPILOT STUDIES
2
3%-
7
9
10
11*
12*
.126
.158
.782
.012
.012
.230
.108
0
0
0
.036
.052
.133
.165
.524
.018
.018
.217
.103
.051
0
0
.070
.503
.553
.526
.030
.030
.773
.364
o
O
0
.124
.343
.324
.347
.526
.030
.030
.597
.279
o
o
0
.227
.264
.231
.243
.526
.030
.030
.374
.175
o
.147
0
0
.165
.681
.772
.386
.0141
.0143.
1.0
.514
o
o
0
.053
.670
.437
.484
.386
.041
.041
.835
.394
0
0
.360
.517
.323
.341
.386
.041
.041
.530
.247
o
.325
0
0
.326
.367
.293
.283
.o56
.o56
.715
.145
.489
0
0
.574
.164
.175
.36o
.044
.044
.264
.123
.218
0
.1814
.238
.259
.377
.0142
.042
.365
.169
0.
.758
.241
0
.292
0
.018
.7140
1.099
0
.198
0
..028
.371
.861
.056
.123
0
.013
.117
.301
.056
.122
0
.020
.102
.454
.056
.124
0
.089
.136
.46o
.056
.099
.021
o
.131
.154
.056
.097
.021
o
.092
.224
.098
.010
o
.082
.265
.114
.135
.504
.472
.054
.108
.096
.048
0
.0913
.1480
.118
.097
.061
0
.083
.371
1.14140
.036
o
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.960
.053
o
o
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.576
.090
.250
.500
.o5o
.576
.090
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.050
.576
.090
.250
.500
.050
.424
.123
.250
.500
.05o
.424
.123
.250
.500
.050
.424
.123
.250
.500
.050
.310
.183
.250
.50o
.00
1396
.145
.250
.500
.00
.1413
.145
.250
.5oo
.o o
.0
0
.100
1.00
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0
.100
.726
.0
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.100
.465
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.100
.465
0
.100
.465
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0
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0
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.357
.0
0
.025
.357
.087
o
.025
.256
.o83
o
.098
.312
.o72
.10
.312
13
.120
.14o
.585
.027
.027
.214
.101
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.076
.o92
.074.
.136
0
.034
.192
130
. 41
.090
250
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.465
114
15
16
17
18
19
.234
.315
.091
.120
.127
.133
.261
.180
.094
.065
.052
.0147
.352
.245
.336
.253
.189
.151
.049
.065
.047
-463
.08/4
.108
.049
:1065
.047
.063
.0814
.108
.447
.661
.161
.240
.219
.210
.2-513
0
.o76
0
0
0
0
.1494
o
.180
.029
.041
.310
.865
O
.287-
.403
.473
349
.396
0
0
.832
0
1:7-
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o
o
0
0
0
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.121
.1414
.161
.1814
.054
490
0
0
0?
0
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-.-042
.096
.054
.028
.022
:151
.099
.157
.105
.0
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056
T209
? 0
.095
o
.106
o
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.380
.049
.377
.0148
418
.327
.610
.1514
.123
4
J267
.369
!277
.208
.166
42.63
.221
.161
.fff
.297
.3714
.250
i250
.250
.250
.250
.250
.500
.500
.475
.1475
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.052
.052
.652
.o9q
:125
.014
1
.213
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.084
.282
0
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Y:215
0
.10
.282
0
.10
.215
0
.040
.161
0
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.1214
20
.051
.017
.138
.119
.119
.079
0
.021
.136
.068
O
.083
o
.021
.646
.033
:
vel
.1412
.250
: 093200
.287
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.o72
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21
22
23
214*
5
26*
27
28*
29
30
.0514
.056
.0149
.0214
.020
.0214
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.027
.017
.018
.017
.016
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.007
.006
.007
.006
.008
.005
.004
.112
.095
.086
.094
,.095
.o85
.on
.091
:083
.150
.1148
.1714
.192
.177
.179
.195
.181
.182
.201
.1148
.174
.192
.177
.150
.179
.195
.181
.182
.201
.078
.078
.070
.035
.029
.033
.035
.030
.023
.0214
0
0
0
0
0
0
024
.o114
.011
.006
.009
.006
.005
.006
.0014
.004
.1140
.1314
.092
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.076
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.073
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.t65
.093
.545
.497
.424
.1496
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.1492
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0
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0
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-15
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.034
.023
.032
.035
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.080
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.039
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-=
0314
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0
0
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.216
.179
.212.
.232
.207
.2014
.027
.222
.0114
0
.011
0 '
.013
0
.012
.014
0
.011
0
.011
0
4'012
.011
0
.012
.665
.676
.620
.763
.969
.755
.779
.3147
.531
.532
.023
.017
.022
.022
.014
.022
.013
.022
.031
.016
.103
.9.26
.072
. 090
.106
.089
.085
.083
.088
.074
.123
.104
.095
.103
.121
.102
.093,
.101
.100
.091
.5o8
.599
.652
.599
.508
.599
.599
.599
.652
.25o
.250
.250
.250
.250
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:250
.250
.250
.25o
.320
.320
.3o6
.300
.300
.300
.300
.300
.300
.300
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.349
.000
.090
.408
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.100
.436
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.100
.373
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.357
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.554
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.025
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.064
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.069
.100
.100
.100
.804
.664
.575
.6614
.8014
.664
'.574
.6614
.6614
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Declassified in Part - Sanitized Copy Approved for Release 2014/05/29: CIA-RDP67B00945R000200040001-4
NLO-72 -60
SECTION 6
PRESENTATION AND DISCUSSION OF RESULTS
Representative results of the various pitch axis design studies are
Page 27
presented here together with discussions of significant points of interest.
(a) Linear Damper
Figure 6 A shows the free aircraft characteristics for normal acceleration
(at the cog.) response to elevator deflection. Lines of desirable
characteristics are superimposed on this plot (dotted lines). The
desirable lines are tempered by:
a0
b.
the low fundamental structural frequency (which sets
an upper limit on augmented frequency)
a compromise between system performance and system simplicity.
The resulting modified desirable characteristics for the 129 are plotted
as solid lines on Figure 6 A.
When the damper loop is closed with a proportional pitch rate feedback
both the natural frequency and damping are
the pitching moment due to elevator (Ms.e )
time constant (Ts) is low the frequency is
increased.
In regions where
is high and the aerodynamic
rapidly increased while the
damping ratio is in comparison, slowly increased. In regions where Mse
is small and Ta large the reverse is true, i.e0 damping ratio is rapidly
increased in comparison to frequency. If static instability should occur
in this second region (imaginary natural frequency) then it sometimes
becomes necessary to augment the frequency separately from the damping.
Separate frequency augmentation can be obtained from:
a0 a lagged pitch rate feedback
b0 a normal acceleration feedback
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4 Declassified in Part - Sanitized Copy Approved for Release 2014/05/29: CIA-RDP67B00945R000200040001-4
WL0-72-60 Page 28
In the case of this vehicle, Ne is small and Ta very large for conditions
20 through 30. In addition static instability can occur at several of
these flight conditions when the vehicle is pulling normal acceleration
Abelow the limit load factor. Thus separate static stability augmentation
is required at high altitudes.
Since pitch rate is readily available in the system lagged pitch rate is
used for separate frequency augmentation at altitudes above 62,000 feet.
The results for a fixed gain and time constant on this term are shown in
Figure 6 B. The proportional gain) 66, is scheduled with clic. The
schedule is shown in the inset,
Many of the flight conditions fall outside of the desired region. However,
improving these conditions would require a much more complicated schedule.
For example, conditions 4 and 5 are the same Mach number and altitude thus
they have the same gain. Since condition 4 has a lower weight than 51 Ms-e
is larger and the gain is much more effective than at condition 5. The same
is true of tonditions 7, 8, and 90
With the lagged pitch rate term the high altitude conditions fall within
the desired region. However, the low damping ratios, while sufficient
for manual operation, will not provide an adequate inner loop for autopilot
modes. Thus it is desirable to have more proportional pitch rate at the
higher altitudes during autopilot operation. A fixed gain of 1 degree
per degree per second of pitch rate will provide sufficient additional
damping for autopilot operation at altitudes above 62,000 feet. Since
the lagged term and the additional pitch rate are fixed and both switched
in at the same altitude they are combined into a single term;
1+ 5 6 (1 + 2s)
.:- 1 + 12s = 1 + 12s
which converts the lagged term to a lag-lead term.
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Declassified in Part - Sanitized Copy Approved for Release 2014/05/29: CIA-RDP67B00945R000200040001-4
W10-72-60 Page 29
? The results of this configuration are shown in Figure 6 C. The
hexagonal boxes show the characteristics of perturbations from trimmed
2g ( An = 1 g) flight for the conditions where Mcw is non-linear.
(Conditions 18-30)
Figures 6.1 through 6.12 show the transient responses for 0!gusts and S.
steps. .The free and augmented aircraft are shown together for the
purpose of direct comparison. For brevity, only the landing, takeoff,
refueling, and design flight conditions are shown. Data on other flight
conditions are availableAlpon request.
Since the landing and takeoff characteristics are of extreme importance
the pitch rate response to an elevator step for conditions 1, 2 and 3
are shown separately in Figure 6 D.
The analog computer studies (both damper and autopilot) show that the
lag-lead term can be reduced to 5 (1 + s) without noticeable effects.
1 + 12s
The results shown in Figures 61. through 6.12 include this modification.
The damper control equation then becomeS:
= [64 + rs(1 + s)
1 + 12s h?62,0001]
r
where: c) = f (q',.)
The damper gain schedule,EA = f (q,0)5, is shown in Figure 6 E. Transient
results for both 1 g ad 2 g (primed conditions) at high altitudes are
shown in Figures 6.5 through 6.12.
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Declassified in Part - Sanitized Copy Approved for Release 2014/05/29: CIA-RDP67B00945R000200040001-4
M10.-72.-60 Page 30
A better evaluation of the damper is obtained by studying the acceleration
response due to stick force. This type of study can include the, effects of
non-linear gearing, bobweight, and fuel system. In addition the non-linear
characteristic: of Ma at high altitudes can also be simulated more exactly.
This type of study has been done. The, results are given in Section 6 46
(b) Pitch Attitude Hold
The principal objective of attitude hold analysis was to define scheduling
curves for the pitch attitude gain 64L and the filter time constant Tg,
and at the same tiMei Minimize any damper changes. The selected criteria
for pitch attitude response to step commands were a response time to 90% .
t90, of 3 to 5 seconds 'anda maximum overshoot of 25%. It was soon
apparent that sufficient damping was not available to meet these criteria
at the higher altitude flight conditions. As a result an additional
1 deg/deg/sec of straight-through pitch rate gain was added to the pitch
damper (discussed in Item a.of this section), Resulting performance,
with the 6 and TQ schedules of Figures 3.2 anci3.3, gave response times
of from 1.5 to 6 seconds and overshoots of less than 20%. At a constant
altitude, both response time and overshoot tend to be larger for the lower
Mach.numbers. Some representative time histories Of attitude hold responses
are shown in Figures 6.13 through 6.18 These responses for the "starred"
design flight conditions only. Responses to both attitude step commands and
vertical gusts are shown, In computing these responses, ?2 degree
displacement limits were placed on the parallel servo. Figures 6.17. ahd. 6.23
show the effect of these limits if inputs are large enough to "bottom" the
servo. In practice, the parallel servo will be force limited rather than
displacement limited. Further analysis will determine a safe level of force
limiting.'
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Declassified in Part - Sanitized Copy Approved for Release 2014/05/29: CIA-RDP67B00945R000200040001-4
WLO-72 60 Page 31
Figures 6.1 through 6.12 include responses of the dampered airplane with the
revised pitch rate network 5 (1 + s) . Although the autopilot responses
1 + 12s
shown here do not include this network, sufficient analysis has been conducted
to determine that the change does not seriously harm autopilot performance.
(c) Mach Hold
Determination of suitable Mach displacement, integral, and rate gains
has been based upon the following criteria:
"Following a step input command of pitch attitude, the
resulting Mach error Should decrease from its maximum
? value to 10% of that value in from 5 to 25 seconds and
reduce each overshoot by at least 60%."
Experience has shown that the longer response time is more desirable
from the pilot's viewpoint and that zero overshoot should be an objective
if not a requirement,
It was found that the Mach gains most suitable for the high altitude
conditions resulted in responses at lower altitude which were too fast
and exhibited too much overshoot, After applying the gain schedules
as shown in Figure 3.4, response times over the flight envelope varied
from 15 to 28 seconds and overshoots were less than 30%. Mach rate gain
was included primarily for its effect On conditions in the left half of
the flight envelope, Transient responses for the "starred" flight conditions
are given in Figures 6.19 through 6424.
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Declassified in Part - Sanitized Copy Approved for Release 2014/05/29: CIA-RDP67B00945R000200040001-4
W10-72-60 Page 32
(d) Automatic Trim
The configuration of the auto-trim system is based on the capability of
the vehicle to change flight condition and on the stability requirements
of the auto-trim loop. Maximum rates of change of altitude and Mach number
dictate that a trim rate of 0.1 deg/sec is necessary. Since the trim
actuator and the parallel servo displacements sum in parallel to drive the
power actuator, recentering of the parallel servo during the trimming
process would be accomplished entirely by feedback through the airplane
pitch axis if a stability compensator was not employed. Without
compensation, the phase lag through the airplane and back to the parallel
servcAs such that the stability of the attitude and Mach hold modes
is significantly altered by the auto-trim loop.
The compensator, however, begins to recenter the servo immediately upon
activation
of the trim actuator. As a result the net perturbed surface
motion during the trimming process is greatly reduced together with sub-
sequent aircraft motion, It can be seen from the block diagram (Figure 3.1)
that, once the parallel servo stabilizes within the switch deadband, the
compensator output decays to zero and has no effect on steady-state trim.
The effects of the auto-trim loop on attitude and Mach hold responses to
disturbances are illustrated by Figures 6.13 through 6.24. It will be
noted in Figures 6.13 through 6.18 that the commanded value of 9 is not
always attained with auto-trim operation. These static errors result
because integral control is not used on attitude hold. The maximum error
is proportional to the auto-trim switch deadspot and inversely proportional
to pitch attitude gain. At the design flight conditions, where attitude
gain is high, the maximum attitude error is less than 0,1 degree with a
0,25 degree switch deadspot. Selection of the deadspot size was affected
to some extent by parallel servo motion during a disturbance0 Smaller
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values of deadspot (more desirable from an accuracy viewpoint) resulted
in higher frequency on-off cycling of the trim system as the trim
condition was approached. It was reasoned that less frequent stick
mOtions of somewhat larger amplitude would be more desirable.
(e) Non-Linear Damper Study
Th h results of the non-linear damper study, utilizing a non-linear slope
for the variable Moz at conditions 18 and above, and including the non-linear
effect of the manual control system, indicated that
(1) Rescheduling of the pitch rate parameter, S, to break at
800 clic instead of 750 qlc had little, if any, effect on the
damper performance. This change makes all (1'0 scheduling
potentiometers in the damper identical and thus interchangeable.
(2) The fixed lagged pitch rate term, 5 (1 + s) , could be switched
(1 .4; 12s)
into the damper configuration at an altitude between 50,000 feet
and 70,000 feet.
The transient normal acceleration responses to stick force commands with
the bobweight iet at 5 #/g were very similar to those obtained with the
fl
linear damper simulation at conditions 17 and below. At conditions 18 and
above, the transient normal acceleration responses to large stick force
coMmands with the bobweight set at 5 #/g did differ from that of the
linear damper primarily as a reault of the non-linear slope of IvIce
Representative responses at conditions 26 and 27 are shown for stick
force commands near one g in Figure 6.25. A pilot lag of 0.5 seconds waa
used. Here, stable g commands can be held to the limit of the series servo
authority at condition 26. However, lack of adequate stability augmentation
allows pitch up to occur at condition 27 although the series servo is
not saturated prior to pitch up. Additiprial responses in Figure 6.26
indicate the effect of changing the lagged pitch rate term at these
conditions.
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The bawl& will _add a normal acceleration feedback (destabilizing)
to the damper configuration. The effects of this feedback vary with
the bobweight size, the force deadspots in the control system, and the
amount of damping provided by the pilot.
If the bobweight is held within the force deadspots of the control system
then the destabilizing feedback to the damper will only be "seen" at
conditions where the incremental load factor exceeds lg. Analog computer
runs were made with the bobweight set at 5 lbs/g and 10 lbs/g. The loss
of damping resulting from the 10 Vi bobweight is quite noticeable with
pilot lags up to 0.2 sec. The 5 #/g bobweight shows no detrimental
performance with "g" commands up to the limit load factor and no pilot
lag. Since it is very difficult to evaluate the bobweight without a
pilot in the loop, it is recommended that the bobweight be held to
5 #/g until the final value can be determined through simulator tests.
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(f) Failsafety, Redundant System
The results of the analog computer analysis of the redundant pitch damper
system hidicate that automatic failsafe protection is provided for the first
damper failure throughout the mission profile, In addition, automatic
failsafe 'protection is provided for the second damper failure at all
inherently statically stable conditions in the profile? At statically
unstable flight conditions, such as condition 13, the vehicle will slowly
pitch up upon disengagement of the damper system? Since the incremental
load factor resulting from the damper failure does not exceed the maximum
allowable load factor of 1.5 g/s until 14 seconds have elapsed at condition
131 recovery by the pilot is possible? The term "damper failure" is defined
as ramp type failures in the series servo, pitch rate gyro or electronic
? circuitry? In 'this study, only failures occurring in straight and level
? flight were considered. Thus, the second damper failures simulated at
conditions in the non-linear Ploc0C region were failsafe because the low
surface effectiveness yielded small angle of attack changes from trim
within the statically stable portion of the M slope?
The logic equations used in the failsafe analysis to detect and disengage a
malfunctioning channel are described below:
Let 6 = allowable difference between channel displacements?
A/ represents IXAR XAL I Normal operation in Channel A
A represents XAR XAL I 9 either right servo, XAR,
or left servoXAL, failed in
channel A
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BI represents IXBR XBIJE E normal operation in channel B
B represents IXBR XBIJ2 either right servo, XBB, or
left servo, XBL, failed in
channel B
CI represents 1XA XB j E normal operation in gyro
channels A and B
represents IXA XBI E 9 gyro and electronics of either
channel A or B failed
EI represents XA E normal operation in channels
A and M
? represents IXA - Xml>' E gyro and electronics of either
channel A or M failed
FI represents XB - XM/ E 9 normal operation in channels
B and M
? represents XB - Xm I 9 gyro and electronics of either
channel B or M failed
The malfunctioning channel is detected and disengaged by the following
discrimination.;
FA A or C and E, channel A failed
FB B or C and F, channel B failed
Fm E and F, channel M failed
In the event of multiple failures, the combination of one gyro channel
failure plus a monitor failure will disengage the remaining good
channel. However, the combination of one channel servo failure plus
a monitor failure will not disengage the remaining good channel,
The remaining channel will continue operating until a third failure
disengages that channel,
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The failure types considered in the failsafe analysis are described below:
a. First Failure: servo
E = 2.18 degrees = ER' differential
L
Here three servos can oppose the malfunctioning servo. The
malfunctioning servo can drive the right actuator, ER, (or the
left, EL) up to the full authority of 15 degrees/s and ?14.5 degrees
as commanded by the ramp failure. The mating servo in the ER
channel (or the 61, channel) can oppose the malfunctioning servo up
to the full authority as commanded by the feedback parameters
and The 6 The two servos in the opposite 61 (or 6-R) channel track
together to drive that actuator at full authority as commanded by the
feedback parameters E 6 and E When the error sinal is.
exceeded, condition A or B exists and the malfunctioning channel A
(or B) servos are disengaged and recentered. The remaining channel B
(or A) servos continue to drive ER andL at full authority as
commanded by the damper feedback parameters.
b. Second Failure: servo
= 2.18 degrees = 6-R - EL, differential
Here, one servo can oppose the malfunctioning servo as one operating
channel has been previously disengaged. The malfunctioning servo can
drive its actuator at full authority as commanded by the ramp failure
and the remaining good servo can oppose it by driving its actuator at
full authority as commanded by the damper feedback parameters. When
the error signal E is exceeded, condition A or B exists, the damper
servos are disengaged and recentered., and the unaugmented vehicle
remains0
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First Failure: Gyro
= 1.09 degrees = SR -
Here, a gyro or electronic failure drives one servo in each
right and left actuator channel at full authority as commanded
by the ramp failure. The remaining servo in each ER and EL
channel can oppose the gyro malfunction at up to full authority
as commanded by the damper feedback parameters. When the error
signal E is exceeded, condition C and E or F exists; the
faulty gyro channel is disengaged, and the servos are recentered.
The remaining channel carries on at full authority.
d. Second Failure: GyroJ
E.= 1.09 degrees a 7
Here, one channel is disengaged and a
function in the remaining channel can
gyro or electronic mal-
drive each surface .
actuator as commanded by the ramp failure with no opposition.
The gyro monitor, M,
although not an operative channel, does
emit a voltage proportional to the damper feedback parameters
times the pitch rate generated by the failure. Thus the
error signal c is exceeded and conditions C, E and F exist,
before the surface moves the full error amount. The damper
is disengaged and only the unaugmented vehicle remains
Operative.
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Various failure combinations, such as a servo failure in one
channel followed by a monitor failure which is then followed
by a gyro failure in the remaining channel, are covered by
the preceding failure conditions. Here, the gyro and electronics
of the first channel (servo failure) would still be available
to serve as a monitor for the third channel gyro failure.
The failsafe analysis used the nominal values of
= 2.18 degrees . ER - 6i, for servo failures,
m 1.09 degrees- ER 0 EL for gyro and electronic
failures, servo recentering time of t63% 50 milliseconds
and system dead time of 35 milliseconds. An increased dead
time of 115 milliseconds was used on slow, creeping failures.
Variations in the nominal values were checked at three
critical flight conditions.
The transient responses to a series of ramp inputs to the four
failure types previously described are shown at flight
conditions 7, 8 and 10 in figures 6.27 through 6.32. Peak
failure load factors up to 1.1 incremental are obtained at
these flight conditions because of the high surface effective-
ness. The peak failure load factors are plotted against pitot
differential pressure, (4101 at the flight conditions checked
for ramp inputs of 15 degrees/s, the maximum series servo
rate, and 0.3 degrees/s, a typical slow creeping type of
failure, for four failure types in figures 6.33 through 6.36.
These figures indicate that peak failure load factors are
predicted in the pitot differential pressure region of 800
to 1000 psf.
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The peak failure load factors at the critical conditions 7,
8 and 10 are plotted against the ramp inputs for four failure
types in figure 6.37. For servo failures, the ramp input is
the rate at which either the right or left surface would
be driven if no pitch rate feedbacks were present. For gyro
or electronic failures, the ramp input is the rate at which
the right and left surfaces would be driven if no pitch rate
feedbacks were present. Thus, it can be seen that the gyro
failures produce a surface rate roughly twice that of the
servo failures. In addition, the allowable error signal
for servo failures is 2.18 degrees = - That is,
if no pitch rate feedbacks are considered, one surface would
have to move a full 2.18 degrees displacement before the
relay logic would disengage the channel. In the case of
gyro failures, the allowable error is 1.09 degrees . 6'11
Here, if no pitch rate feedbacks are considered, each surface
would move 1.09 degrees displacement before the relay logic
would disengage the channel. As a result, a gyro failure at
a ramp of 0.3 degrees/s would cause a total surface motion
nearly equivalent to that of a servo failure atf four times
0.3 degrees/s or 1.25 degrees/s. This can be checked by
referring to figure 6.37. Since the peak failure load
factors occur at the slow, creeping failure rates, the servo
failures naturally would produce the highest load factors
for a given slow ramp input.
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The peak failure load factors at the critical flight conditions
7, 8 and 10 are plotted in figures 6.38 through 6.40.for
variations in E for four types of failures. The maximum
allowable 6 caused by tolerance deviations can be 3 degrees
g R 6L for servo'failurep and 1.5 degrees . 6-R 41., for gyro
failures without,dxceeding the peak load factor of 1.5 g incremental.
The effect of varying the system dead time and the servo
recentering time on the peak gyro failure load factors at
condition 7 is plotted in figure 6.41. As would be expected,
large system dead times greatly increase the peak load factors
at the fast failure rates; whereas the effect is negligible
at the slow, creeping failure rates. The mitigating effect
of the pitch rate feedback on the surface motion can be seen
by comparing the peak Os obtained with a 200 millisecond dead
time on the first gyro channel failure with that of the second
gyro channel failure. Variations in servo recentering time
have far less effect on the peak g's than system dead time
variations.
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