GUDDANCE AND NAVIGATION - ibiblio Analysis...errors that would result from gyro performance...

.. 4 I DECLASSIFI

GUDDANCE AND NAVIGATION

Approved: a. * Date: ;/+q Mil ton B. Trageser, Mrector Apollo Guidance & Navigation Program

Approved ate:- ector

(Unclassified Title) E- 1473

ANALYSIS OF LEM MISS ION INERT I AL UNCERTAINTIES

by John M. Dahlen

Malcolm W. Johnston December 1963

I I I N ST R l J M E N TAT I 0 N

LAElORATORV CAMBRIDGE 39, MASSACHUSETTS

COPY# 7 OF W C O P I E S THIS DOCUMENT CONTAINS 7& PAGES

1 -

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1

ACKNOWLEDGMENT

Helpful cooperation throughout this study was obtained f rom F. Grant, R. Brown, and R. Goss, all of the M . I . T . Instru- mentation Labor at o r y .

This report was prepared under DSR Project 55-191, spon-

sored by the Manned Spacecraft Center of the National Aero- nautics and Space Administration through Contract NAS 9- 153 .

This document the national defe States within the meaning of th Laws, Ti t le 18,

U. S. C . , Sections 793 e t ransmission or the revelation of nner to an unauthorized pe

The publication of this report does not constitute approval by the National Aeronautics and Space Administration of the

findings or the conclusions contained therein.

for the exchange and stimulation of ideas.

It is published only

2

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E-1473

ANALYSIS OF LEM MISSION INERTIAL UNCERTAINTIES

ABSTRA.CT

The major sources contributing to LEM position and velocity uncertainties at perilune, hover, and burn-out are in- dividually investigated. ponent uncertainty through these phases a lso se rves as a common

basis upon which the following alternate inertial schemes a r e compared:

The format utilized to t r ace each com-

1. Gimballed v s gimballess iner t ia l measurement unit,

2 . Crude vs precision gyros,

3. Inertial realignment between injection and perilune vs no realignment.

by John M. Dahlen Malcolm W. Johnston

December 1963

3

TABLEOFCONTENTS Page

I LISTOFSYMBOLS. , , , , . . . . . , . . . . . . . 7

I1 INTRODUCTION , . , , . . , e . , : . , , . . 9

111 DISCUSSION , . , . , I . e . . . , . . , . . . - . 13 Orbital Navigation Uncertainties . , . . . . . . 1 3

LEM Inertial Uncertainties . o , a . . I . . . . 1 3

Illustrative Example . , . , . . . . . . . 13

IV CONCLUSIONS. , . . . I , . a , , . . . . + , . . 1 7

V REFERENCES. , . . , . I . , . . . . . , . 1 9

VI APPENDICES , . , . . , , . . , ._ - . . . . . . . 2 7

A. Analysis I GIMU - Precis ion Gyros -

B, Analysis I1 IMU - Precis ion Gyros -

C. Analysis I11 GIMU - Precis ion Gyros -

D. Analysis IV IMU - Precis ion Gyros -

Realignment . . . . e . . 2 7

Realignment . , . . . . 41

No Realignment. . , . . . . 43

No Realignment. , . . .) , 53 E Analysis V GIMU - Crude Gyros -

Realignment . . I . I 55 F. Analysis VI GIMU - Crude Gyros -

G.

No Realignment. . . , . . , 61

Description of Descent and Ascent Trajectory P a r a m e t e r s . . . . , . . a . e . _I . , . * * 67

5

I LIST OF SYMBOLS

IMU

GIMU

BDX, BDY, BDZ

ACBX, ACBY, ACBZ

SFEX, SFEY, SFEZ

MLM

In j

P e r

Hov

Gimballed inertial measurement unit

Gimballes s inertial measurement unit

Range , t rack, altitude uncertainty

Range ra te , t rack rate, altitude ra te uncertainty

Bias drift about x, y, z axes

A.ccelerometer bias along the x, y,

z axes

Accelerometer scale factor uncertainty along the x, y , z axes

Misalignment

Inject ion

P e r ilun e

Hover

7

ANALYSIS O F LEM MISSION INERTIAL UNCERTAINTIES

I1 INTRODUCTION

The major sources contributing to position and velocity

uncertainties during a LEM mission are investigated.

A format is presented (in the appendix) that t races the effects of each uncertainty source from injection of the LEM into its descent orbit through perilune and hover to burn-out.

The format s e rves three purposes:

1. It reveals the important sources of inertial un-

certainties and when they occur, It indicates the effects of "initial condition" o r orbital navigation uncertainties,

It se rves as a common basis for the analysis and comparison of several alternate inertial guidance schemes.

2.

3 .

Three comparisons were made:

1. 2. "Crude" vs "precision'' gyros,

3 .

Gimballed vs gimballess inertial measurement unit,

Realignment of IMU and GIMU between injection and perilune vs no realignment.

Table I summarizes the resul ts obtained when one assumes that each component uncertainty, though unknown, is constant over the entire mission profile.

resul ts if one assumes that each component uncertainty changes in random fashion from one phase to the next within the mission profile.

Table I1 shows the

A detailed analysis of each component contribution

9

f o r both tables is included in Appendices A-F. qualitatively the effects of guidance uncertainties on fuel r e - quirements. tainties f o r a normal ascent f rom the lunar surface.

Table I11 indicates

Table TV summar izes the resultant cut-off uncer-

Figure 1 il lustrates the phases of the LEM mission a s well a s indicating the coordinate systems utilized.

The body of this report w i l l be res t r ic ted to a brief discussion of the selected uncertainty sources followed by an

illustrative example of the analysis, tracing the effects of a

single uncertain.ty source through a l l mission phases.

The analyses involve L E M inertial uncertainties and

initial condition uncertainties only. external sensing during landing is considered. terminal guidance has the principal effect of nulling terminal velocity and altitude e r r o r s ) ,

No scheme employing

(External

F o r Tables I and 11, an abort f rom hover was used instead of a normal launch because the abort case appeared to be most cri t ical with respect to subsequent rendezvous maneuver

fuel requirements,

The position and velocity uncertainties listed in Tables

I and I1 a r e "Root-Sum-Square" values.

range uncertainty is the square root of the sum of the variances':' in range uncertainty due to each uncertainty source.

F o r example, the RSS

If the

::' The variance of a random variable, X, is the average value of the square of the difference between X and i t s average value, 'z- That is :

- 2 Variance (X) = (X - X)

The standard deviation o r ''one s igma variation" of X is the square root of the variance, That is:

'Vvariance (x) = STD. DEV. (x) = O ( X )

10

sources a r e independent (a valid assumption) the RSS range uncertainty is also the square root of the variance of the total range uncertainty. safely be called RMS o r 1 Q uncertainties.

The resul ts in Tables I and I1 may therefore

Certain qualifications regarding the analysis should be

pointed out. F i r s t , regarding accuracy of the GIMUs, two bias drift r a t e s were assumed to correspond to 1 1 crude" and "precision"

gyros. For "precision" gyros, 10 meru drift was used t o see the result that would occur i f gyro performance were not degraded in

the "strap-down'' environment. Fo r ' 'crude'' gyros, 66 . 7 meru (1 .0 degree/hour) drift was used t o gain feel for the t ra jectory e r r o r s that would result f rom gyro performance degradation.

While the best engineering judgment of the Apollo Staff anticipates a ser ious performance degradation in the ear ly application of the

gyro in the "strap-down" environment, there is no sound technical basis for assuming that such degradation can be t reated a s a factor of seven increase in bias drift. This treatment is simply the most

appropriate method in view of the lack of information and t ime needed for a more valid performance comparison.

Secondly, a s wil l be seen, gross t ra jectory e r r o r s associated

with 1 . 0 degree/hour gyro drift can be greatly decreased by realignment fifteen minutes before perilune.

that such a re-alignment , while possible, would ra ther ser iously

interfere with an otherwise order ly and comfortable sequence of

astronaut activities in preparation for the s ta r t of the powered descent. vehicle and about five minutes of t ime .

It should be understood

The re-alignment would require re-orientation of the

11

c

I11 DISCUSSION

c \

..

This study concerns the uncertainties in position and

velocity existing at various phases of the LEM mission as a

result of orbital navigation schemes and LEM inertial instru-

mentation

analyzed (Appendices A-F) will clarify the following discussion.

Orbital Navigation Uncertainties

Reference to a summary sheet of one of the schemes

This category consists of those position and velocity un-

certainties that exist p r ior to LEM injection. the sum of all CM system uncertainties up to this point in the mission.

orbital navigation scheme - Model I - Std (Reference 1).

appearance on the summary sheet is desirable in order that LEM inertial uncertainties be kept in perspective. orbital navigation uncertainties would tend to overwhelm the LEM inertial uncertainties thus diminishing the importance of the la t ter .

They represent

The particular numbers used correspond to an M. I. T. Their

La rge r

LEM - Inertial Uncertainties

The f i r s t uncertainty source l isted under this category,

alignment, means the misalignment of the accelerometer

package which resul ts f rom s t a r tracking uncertainties, angle

read-out uncertainties, etc. Gyro bias dr i f t , accelerometer

bias, and acceierometer scale factor uncertainty constitute the most important inertial uncertainties for the LEM mission .-

though many more exist . (Reference 2 )

Illustrative Example

The example chosen to illustrate the use of appendices utilizes a GIMU with "precision" gyros and a realignment

1 3 k.

between injection and perilune. constant drift of 10 meru (0. 15 degrees/hour) of the y gyro will be t raced to burn-out,

In particular, the effect of the

(Appendix A, analysis I, BDY, page 34 )

The left hand column of this analysis sheet divides the mission into separate phases of instrument utilization, case four phases are delineated. separately, o r independently, s o that we can calculate the final uncertainties when the component uncertainty is assumed to vary from one phase to thc next.

In this

We consider each phase

Within each phase individual uncertainty sources are

listed. (It should be remembered that these a r e , in turn, a result of the single uncertainty source represented by the

particular analysis sheet, BDY in this ca se ) . The following

example may clarify the shorthand notation utilized throughout

the analyses: y Per mlm reads , "the misalignment about the y axis at perilune. 'I T o the right of each l isted source is seen its effects a t perilune, hover, and burn-out. Each of these phases

is described in more detail below.

1. Drift Between Alignment and Injection

Fifteen minutes of drift occuring between initial alignment and injection causes a misalignment about the y axis a t injection of 0.0375' (See F ig 1). Application of 373 feet/second

(essentially radial injection velocity) resul ts in a range ra te uncertainty of 0 24 feet/second at injection because of this thrust vector misalignment.

The perilune effects of this injection velocity uncertainty were obtained through free fall e r r o r propagation equations. (Reference 3 )

The perilune position and velocity uncertainties just

obtained a r e propagated to hover and burn-out by means of a

14

GIMU guidance e r r o r sub-routine'! into which is fed knowledge I I

of the descent and ascent trajectory parameters . this routine (developed by F. Grant - M, I. T. Instrumentation Laboratory) a r e used to determine all effects occurring during, o r being propagated through, any powered phase. (Description of the descent and ascent t ra jector ies used in the e r r o r sub-

routine are included as Appendix G).

The resu l t s of

2. Drift Between Realignment and Perilune

The misalignment at injection has been wiped out by the realignment performed 15 minutes before perilune.

Fifteen minutes of drift occurring between realignment

and perilune causes a misalignment about the y axis at perilune

of @. 0375'.

of this misalignment on position and velocity a t hover and

propagates these uncertainties at hover to burn-out.

The GIMU e r r o r sub-routine determines the effects

In addition, the misalignment at perilune t ransforms to

a like misalignment at hover, the effects of which are propagated to burn-out. (In this case the body and target axes coincide. A more complicated transformation is required if they don't. An x o r z misalignment at perilune resul ts in both an x and a

z misalignment at hover.

3 . Drift During Descent

During the s ix minutes of powered descent the continuous

gyro drift ra te causes position and velocity uncertainties at hover which are, in turn, propagated to burn-out.

In additinn, a misaligfiment at hover, due to the integrated

effect of gyro drift during descent, must a l so be propagated to

burn-out.

drift effects is necessary for the x and z gyros). (Again, a more complicated computation of integrated

4. Drift During Ascent

Finally, the continuous bias drift acting during the ascent

15

w i l l result in uncertainties at burn-out. Again, these a r e

obtained from the e r r o r sub-routine.

There a r e two different ways of handling the columns of uncertainty figures corresponding to perilune, hover, and burn-

out appearing on each analysis sheet. Remember that the ent i re sheet concerns a single instrument uncertainty. argued that the value of the instrument uncertainty is not the same during all phases of instrument utilization, i. e . , the drift during the injection is not the same as the drift during powered ascent, etc. Within each phase, however, it has been assumed that each component uncertainty can be assumed constant.

a s sumes that the instrument uncertainty shifts randomly from one phase to the next, it i s necessary to RSS the position and velocity uncertainties found for each phase.

It could be

If one

An alternate approach would be to consider that the un-

certainty, though unknown, is constant throughout the mission, in which case we arithmetically add the position and velocity uncertainties found f o r each phase,

Both procedures a r e followed on the analysis sheets, ' the la t ter technique is represented on Table I, the fo rmer on Table 11, The actual uncertainties wi l l , most likely, l ie somewhere between these two extremes.

1 6

IV CONCLUSION

The following remarks pr imari ly concern information appearing in summary form on Table I and 11,

Comparisons of analyses I and I1 o r 111 and IV indicate

the effects of a gimballed vs a gimballess inertial measurement

unit. Both systems yield essentially the same resul ts at perilune and hover while the gimballess system gives bet ter

resul ts at burn-out. This is a result of the fact that the body-

mounted gyros and accelerometers are flipped (as the vehicle is reoriented) a t hover so that the sense of their uncertainties

during ascent tends to cancel the uncertainties built up during

descent. This cancellation is much less pronounced i f the uncertainties are assumed to be variable (Table 11).

The effects of crude (1. Oo/hr o r 6 6 . 7 meru) v s precision 0 (0 . 15 / h r o r 10 meru ) gyros a r e found by comparing analysis

I and V o r I11 and VI. than a factor of s ix , all other effects contributing to the total uncertainty figures remain the same. Therefore, the effects of

gyro degradation a r e somewhat subdued. Nonetheless , reference to Table I indicates how significant such degradation is to hover and burn-out conditions, especially in t e r m s of C E P and burn- out velocity uncertainties.

Though the gyro bias drifts differ by more

The effects of realignment vs no realignment between injection and perilune can be seen by comparing analyses I and

111, o r I1 and IV, o r V and VI, In the f i r s t two comparisons,

where precision gyros a r e used, it is seen that the effects

pr imari ly involve la rger hover uncertainties. are employed and the system is not realigned p r io r to perilune,

If crude gyros

1 7

a poor scheme (V) becomes even worse (VI) in position and

velocity uncertainties at both hover and burn-out.

The principal differences between Tables I and I1 concern altitude and altitude ra te uncertainties. cancelled to a large extent because of the sequence of axes rotations i f one can assume constant uncertainties (Table I). The t e r m s a r e significant because they effect landing al t imeter

acquisition altitude and abort t ra jectory lofting. It is therefore important, to find a real is t ic method of analysis with respect to these te rms . inertial guidance uncertainties involve increased fuel consumption.

Table I11 attempts to point out the principal accuracy/fuel relationship without attempting to assign numerical values. The resul ts shown on Table IV suggest that a minimum time between alignment and launch is most cr i t ical , especially in a sys tem

utilizing crude gyros.

These a r e nicely

It is also important to point out that increased

Further discussion of the many ramifications of these resul ts wi l l not be attempted here.

18

V REFERENCES

* ..

1. Monthly Technical P r o g r e s s Report; P ro jec t Apollo Guidance and Navigation Program, M. I. T. Instrumentation Laboratory Report , E - 1306, Per iod

from January 11, 1963 to February 11, 1963.

2. IMU Error Data For Apollo Tra jec tor ies , F rede r i c D. Grant, M. I. T. Instrumentation Laboratory Report , E - 1 2 1 2 , September, 1962.

3. Summary of Error Propagation in an Inertial System,

Janusz Sciegienny, M. I. T. Instrumentation Laboratory Report ,E - 1388, August, 1963

19

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TABLE 111

Effects of Guidance Uncertainties

on Fuel Requirements

Guidance E r r o r ~~~

1. -Perilune Altitude

2 . Altitude late in powered descent

3, Range and t rack late in powered

descent

4, Velocity at cut-

off (Burn-out)

Effect on Fuel

Causes upward bias on nominal perilune altitude, thereby increasing landing fuel,

Defines time and altitude when al t imeter

data is required for safe guidance. Increased altitude e r r o r causes increased altimeter range requirement and ea r l i e r

acquisition which may in turn requi re earlier vehicle pitch-up with resultant landing fuel penalty.

Defines amount of terminal maneuvering

required to land on pre-determined target .

Defines amount of midcourse maneuvering required to place LEM on collision course with CSM.

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6. INJECTION MANEUVER (373 FEET/SECOND ESSENTIALLY

C. REALIGNMENT BETWEEN INJECTION AND PERILUNE

0. PERILUNE ( 5 0 K FEET)

E.

F. BURN-OUT (50K FEET)

ALIGNMENT PRIOR TO INJECTION (80 N.M. CIRCULAR ORBIT)

RADIALLY INWARD)

~~~~~ ~ ~~

HOVER (LESS THAN 1000 FEET) ~~

~~

Figure 1

25

VI APPENDICES

A. Analysis I GIMU - Precis ion Gyros - Realignment

The following represents a detailed outline of a n uncertainty analysis of a LEM abort f rom hover. utilized has the following character is t ics :

The system

1. 2. Precis ion gyros, 3.

Gimballess inertial measurement unit (GIMU),

Realignment between injection and perilune.

The f i r s t two pages summarize the subsequent analysis. The f i r s t summary represents the case where it has been

assumed that the instrument uncertainties a r e constant throughout the LEM mission. The second summary represents a case where instrument uncertainties a r e assumed to vary randomly throughout the LEM mission.

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0

0

m 3 N W

3 0

0 0

i 4

c

.

- c

C C

C

C

C

c C

C

- C

P p.

C

C

C

I: r- c

3

-

3

3

3

3

3

3

- -

! I

n- -7-

0

to

0

" I

0 ,

o <

In o < @a

o c

-4+

0

m 0

d

3

3

n L U

3

3

>

3

3

n 3

.1

3

- p: -

c

C

C

C

C

C

C

0

0

0

0

-

4 r +2

Q 1

B

.- .r( C

N

v) t-

0

0

m

d h

0 0 0 v) 0 0 - 4

m N N 0 0 0

I- m m

d d d

4 ?~

0

N

0 0.

3 3 *

0

0 U

c

3

9

u I

- ? I

3

n ?

a U I

3

c Tc

I r

-

- I -

h m

i-

%

- 3 3

d

D

N 0

0

Lo m

0

ID

- m 0

0

0

r(

0

9

10 N

0

4 -

I

- r- r(

0 I

0

c- Lo

0 0

r- 3

C

Q:

7 - 3

3

0

0

0

0

- 0

0

C

0

C

C

-

r

- * N 0

0

t- 0

0 I

ID -r

0

(1 m

- N 3

3

0

(0 Lo

d

0 m

0

P

- c- 0

0

0

-r 0

0

- n -0

;

3

P

?

3

3

D -I

- 3

3

4

3

n

?

0 M

0

(0 m

- r- 0

0

0

-r 0

9

m m

C

lo

m m m m

0 0

I

c

B. Analysis I1 IMU - Precis ion Gyros - Realignment

The system analyzed i s identical to that utilized in Anal- ys i s I except that a gimballed inertial measurement unit (IMU) replaces the GIMU. The IMU analysis did not lend itself to the

detailed breakdown of Analysis I. Therefore, only a single summary is included, representing the case where instrument uncertainties are assumed to be constant throughout the L E M mission. Comparison of this data with that of Analysis I, Summary

A, indicates the effects of a gimballed vs a gimballess system.

41

T

d

= ? 0

3 0

m r(

d 0

W o m m

o r

C

0 :

o c < O F

.' ,

1

C. Analysis I11 GIMU - Precision Gyros - No Realignment

The system is identical to that utilized in Analysis I except that there is no realignment between injection and perilune. In addition, analyses f o r the following uncertainty sources are

identical to Analysis I. They wil l not be repeated.

ACBX ACBY ACBZ

SFEX SFEY SFEZ

43

r 0

0

r { In

r(

o m N I

LI

! 0

P-

o:

(0

0 8 0 " .

> o o

-Y N

3 0 . 0 a

cc 0 0 -

m rl m o c

r 0 0 :

N

I

.

3

n * 0

c- m. 3

0

0

m

m m m

0

0

cc m

0 3

0

0

t- N t- 3

0

- 0

0

0

0

0 m N

a

- 0

m (D

0

0

0

3

t- t.

0

0

m 9 3

0

0

3 - s

- C

C

C

C

C

- L

- 0

m 4 N

0

0

m m e 3

0

0

3

4

0

C

LI:

(1: -?

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

- C

C

C

C

c

<

3

3

01

0

0

0

0

0

0

0

0

0

- 0

0

0

C

C

C

0 0

7 ' -

0 0 m.7

(3

3 N m t - - 0 0

t - N o m i n =

-- o r m ,

N C

o c

t - u M Lr

c c

c1

(3 c :

Oi CSI - $:

i-

I

51 o c s 1

Oi I

C>' - - c o c

d s :

m i in

& ! i

Y 0

m N a2

r? 0 1-

9

rn rn

3

n 4

4

3

3

N ,-I

N

0

3.5

E 8 E E & i >

x x W N W N N N 0 0

0 0

o c

. .

a

D D

3

2

3

.I

P I

3

- 3

n 2 4

3

0

3 ?..

3

0

-

0

C

C

C

C

C

- -

j i

-

- C

C

a C C

P c

C

T c(

- C

C

C

'i

C

P C

C

Y E - -

- E - €

c- ln

d

0

0 m 0 I

d r)

U d

3

D * In I -- D 3

v I

3

4 n 5

.- n 4

0

m m m I

-- ,-I 10

d

0

m

d * I

(0

rn m

0

,-I

.r(

C

3

C

- - " C

C

C

C

< C c

C

0 0 m u m a N O o c

+I d d c

c

t

r

S !

9, Om ", N t - r

4 0 c d m r . . o o c Y c3

P

i . - 0

1- W

0 I

0

0

4 N N

0

+I-

O

c r-

0

0 > 3

3

3

I-

0

N W

r(

I

0

0

LD

L- m m

0

-4c

0

, I > m

c; . <

0

5

3 3 %

3

3

- 3

3

3

3

3

3

- !x --

c o o

s I- m u c o r n . . c 4 -

c o o

l c o c

I m m

u m m

I

t - m a m m

_ - c

7

I : o <

C

C

C

0

- 0

0

0

I

a c 3 e

C

J .. C r

C

j j E 2 E

2 E E

.I e

4

N

w

rn cd > h 0

4

0.L: c N X N 0 0

1 0 * 0, N - r - r w - 0 0

0 0 0

0, r 0 m

0

Analysis I V

The system analyzed is identical to that utilized in Anal- ysis I1 except that there i s no realignment between injection and perilune.

m a r y A, again indicates the effect of a gimballed vs a gimballess system.

IMU - Precision Gyros - No Realignment - ---- . D.

Comparison of this data with that of Analysis 111, Sum-

53

R W

N d:

0

m ? m

0 c- o!

0

r r 0 - R 0 C

C

0

*

r

d c

$ 3 . I

3

m 0

0

W m

0

m m

-- m 3

0 I

0

m

2

m 9 9

ln 09 r-

-8

l- c'!

ln 0 0 -F

m 0 t- *

m 0 N N

3

@? N 3

O i

@I 0 m

I

- 3 m d

0

cj

0 I

3

0 n m

C

CI: * 1 ..-

C P

O / O

E. Analysis V GIMU - Crude Gyros - Realignment

The system analyzed is identical to that utilized in Anal-

ys i s I except that crude gyros replace the precision gyros.

addition, analyses fo r the following uncertainty sources are identical to Analysis I.

In

They will not be repeated.

Align X Align Y Align Z ACBX

ACBY ACBZ

SFEX SFEY

SFEZ

55

0 0

0 0

0 0

0 0

0 0

o c

o c

o c

o c

_c

I

I 4 c

o c

i o c

G C

o c

J

.

- 0 m 3

W m

0

co W

d

m m m

t- m m

c- m * -- * m

3

m m

0

0 m d

,- 3 u

(0 t- Lo

m r- e 3

m

a

3

0 3

a 4

0 t-

m

3 0

l-

t- N

m N 4

m m m m

3 * 1 0 * _- m (D

W N

m m

v) N

m m m

* m * W

N

s L? v

L1

N m

-- m c -r

0

rn W

N

UY m

- Lo r- e

t- N

3

VI

P- o q o o - m n m " O S ' : d 0 In

m 0 ~ 0 0

- O K 0 0

3

* 6 ;

Lo

* o m 0 0

m o o l o c

N

M * c I :

N O :

0 0 : :

W

0 : o c 0

0

t- O N O C

- I N r - o r - c - * m

W

m 0 - 0 c

3

o a o c d

o o o c

m 0 - o c

6

u m

o m o c

m o o m c

3

N o e o c ,-

J * - N t-

o)

e 0

t-

t- (D

W N 3

0 Lo m m

m W

t- * -- m W

(0 N

* Lo

In N

m 0

m

m m v W

m W

-r *

In

N m 3

-- M u 4

m LO

d

?I 0

m c L3

m

t- * 03

m m In

3

m o m o c m o m -

d & d

C

N

o ~ o o o c

W t - m N . O N m O C

N d d

m m N , o g : o c

0

-r o m o o o c

m a - N O % - C ? O C w m -

m c u t - rn lr:

O O C d d o

o o o o o c

m m v 0 y o -

. o c d c o

{ o $ g o c

N

N o o o o o c

* o o % ~ o c e -

r - 0

@. (0

4 I

0

0

a a a I

C

-

J 3

I

>

>

51 I

3

-4

3

3 U

3

3

3

L'

C

- C

C

C

C

C

C

-

-

3

3

3

r n

I

C - 3

9 -I

n I

3

3

. 0 n

L

C

- C

C

C

C

C

C

-

I

-

3 3 ' " g d s : E E

E E 4

;5" x x c

0 0 0 0 0 - Y

N - m m

d d d

b

.

Ll 0 c 0 0 -r

9 " c

* Q m

7

C 0 9

l-

O C

C o c

r I

c(

0 ::

o c

C

0::

-- r

P

o a

o c

C o a

I

U

0:: r

o c

r 0 :

--

& E

ci d

7 m 2 1

"

0 1

t- N. :

0 1 W ,

t- m l

o <

0 L n <

$ ? ; I

- 4 k

t-

W '4

0

m 9 3 I

0 r-

-r m

0

0 N

W N I -- 0

5

0

0 '4 3 I

0 W -Y m

0

In

0 W

t- N

0

-F t-

m

0 W m m

0

m m 0

--

3 : k 2 E E

a c x s 0 0 0 0

z s N . N 0 0

I 0

W N.

0

m In

In I

o In m m

0

* * I "

- 0 : N I

0

t-

N 9:

0 N

m m I

0

-F

t- I m

- 0

0

0

0

0

0

- -

Y M

5

2 P

m U .-I c

5 .3

-

- (0

N c9

0

0 '4 3 I

0 (0 In r( I

0

m " " +I--

m

u; "

0

0

0 'f:

m m 4

,-I I

0

0

I

m 3

-- 0

0

0

0

0

o o c o c

l r t - O * n O O C

0 3

0 0 o c

0 O G c

c I- E - 0 :: c .-

o o o c

c o o

m lP

0 0 0

0 0 0

0 0 0

a O O Z

3

0 0 0

0

0

0

0

m N

t- 3

C

a t . *z 2

3 n 3

3

3

0 0 1"

c

0

0

0 0

m N

0

0

0

t- m m

0

-

0

0

0

0,

0

0 -

c r

: u c

a E i L a

-

0

0

m 0 W

-3

0

m 4

cn

0

0

m m 3

3

0

__

-- A

3 0

3 0

C c c o c -

0 0

-- *E- .:

0

0

0

0 -

0

0

c

0

C

C

-

- *i -

0 1 i

0

0

0

0

C

C

-

- 2: -

0

0

0

0

0

0 -

C

C

C

C

C

C -

r

L > w o a < . N X

o o c 0 0 '

Lo In , N 3 I

o m '

d o c

Analysis VI

The system analyzed is identical to that utilized in Anal- In

GIMU - Crude Gyros - No Realignment .-.-.----- F.

ys i s I11 except that crude gyros replace the precision gyros . addition, analyses f o r the following uncertainty sources a re identical to Analysis 111. They will not be repeated.

Align X Align Y Align Z ACBX ACBY ACBZ SFEX SFEY S F E Z

6 1

- 3

m In

0

0

0

c 3

0 3

C

- C

a L(

c

C

C

C P U

C

C

C

C

<

- W

3 7 m P-

o N o

t- N

m o m

9

m o * W

c

m 2 0 N

0

m a ?

-_ 0

* 0 4

0 0

0 W

O 3

0

O % m

0 0

m o * N

4 -- -

X

Q U ~m a 4

q 0 0 d

3

-

3

c + U

3

- - U P U

C

C

C

C

C

C

C C

C

3

3

J

3

3

3

3

-

3

3

.-

e

C

C

-

I

3

3

3

-

3

C

3

C

C

C

-

C

C

C

C

<

C

-

N W Lr, VI

e 3

u i *I

3

3

3 W n n

3

-

- - C I

<

t- N

0

0

0

t- d'

0

-4

0

0

C

C

C

C

-

C

C

C

C

C

I In w V

3 0 UJ

* I-

a

z a ir w V z 3

E ! * a, 5 2

C G E E L >

E E 4

x x

0 0 O N I

l o r n r - m

0 0 I

. . , 0 0 ci -

- C

C

C

C a

C 0: m I

0

0 In

* N

- P-

0 I

9

0

0

0 *.

m m N I

3 E

0 0 0 m

2

- C

r d:

0

0

9 d I

0 W m N

0

- m 9 0 4

0

P-

N I N.

0 W m t-

0

0 In N

T -4+

t-

(0 '9

0

m 01 4

0 t- m

0

0 N [D

U I __ 3 d:

3

3 9 * I

3 D

# 1

3

- C

C

C

C

C

C

-

I

1

1

c

C < C

C c

C

C

a

I

,

, I

c

r

C C

2

I

>

>

;

: ! j

I r P

C

C

P C C

a T

P

I r

C

C a r

-

I

E 2 h 00 .+ rn Q

t! Y

[ - e

3 0

--yr

3 0

- =. 0

I

3 0

3 0

c

R o

3 0

4 c

0

m ro d

0

0

* m (0 3

0

0

0

0

0

m N t- rl

0

-- 1 -_ 1

C

($ c

3 I

C

3

L- e n

C

- C

0. U

C

C

C

d 0.

U r

C

- I -

3

3

3

3

3

3

- 3

3

3

3

3

3

- 2 -

C

C

C

C

C

C

- C

C

C

C

C

C

- ,P -

3 1

c E t 0 C

. .- c 0:

h f U

+

E -2 ._ .A

N

0 0 0 L o

2

Description of Descent & Ascent Trajectory P a r a m e t e r s

The descent w a s initiated at a perilune altitude of 50, 000

-I--

G.

feet with the thrust vector oriented to 4O below the local horizontal.

maintained fo r 344 seconds at which point the hover condition w a s defined.

and the Isp at 305 seconds. 0 . 4.

A constant pitch rate of 0.1138 degrees/second was

The thrust level w a s maintained at 10, 000 pounds

The initial t h rus t /mass ra t io w a s

The ascent w a s assumed to initiate a t the hover point

(except f o r the normal ascent case, Table IV, when it initiated

from the lunar surface. ) The initial thrust vector angle w a s 158. 91' CW from the inertial horizontal (approx. 32O CCW f r o m

the local horizontal). A constant pitch rate of 0.1241 degrees / -

second was maintained f o r 343 seconds to cut-off. The thrust w a s maintained a t 4000 pounds and the Isp was again assumed

to be 305 seconds. The initial t h rus t /mass w a s again 0 . 4.

E-1473

DISTRIBUTIGN LIST

Internal

R. Alonso

J. Arnow (Lincoln)

R. Battin W. Bean

E. Berk

P. Bowditch

A. Boyce

R . Boyd P. Bryant

R . Byers G. Cher ry

E. Copps

s. COPPS (MITIACSP) W. Crocker G, Cushman J. Dahlen

E. Duggan J. Dunbar

K. Dunipace (MITIAMR)

R. Euvrard P. Fel leman S. Fe l ix (MITIS &, ID)

J. Flanders

J, Fleming

L. Gediman

F; Grant P. Philliou

Eldon Hall

I> Halzel

D. Hanley W. Heintz

E. Hickey

D. Hoag A. Hopkins

F, Houston M. Johnston

B. Katz A, Koso

M. K r a m e r

W. Kupfer

A. Laats D. Ladd A. LaPointe

J. Lawrence (MIT/GAEC) T. Lawton D. Lickly

R. Magee Go Mayo

J. McNeil R , McKern

R. Mudgett James Miller

John Miller

J. Suomala

J. Nevins G. Nielson

J. Nugent E. Glsson

C. P a r k e r

W. Pa t te rson

J. Po t t e r

K. Samuelian P. Sarmanian

R. Scholten J. Sciegienny N, Sears D. Shansky

T. Shuck W. Stameris E. Smith W. Tanner R. The r r i en W. Toth

M. Trageser R. Weatherbee R. White

L. Wilk

R . Woodbury W. Wrigley D. Yankovich

J, Shillingford

Apollo Library ( 2 )

MIT/ IL Library (6 )

69

Exte rnal

(ref. APCAN; 2 July 1963)

P. Ebersole (NASA/MSC)

W. Rhine (NASA/ RASPO)

S. Gregorek (NAA S &. ID/MIT) T. Hueurmann (GAEC/MIT) AC Sparkp lug Kollsman

Raythe on WESCO Capt: W. Delaney (Afsc/ MIT)

NAA RASPO: National Aeronautics and Space Administration Resident Apollo Spacecraft Pro jec t Officer North American, Inc. Space and Information Systems Division 12214 Lakewood Boulevard Dow ne y , C a1 i f o r nia

CAPE:

HDQ:

A.ME S:

LEWIS:

FRC:

JPL:

LRC :

National Aeronautics and Space A.dministration Kennedy Space Center Cape Kennedy, Flor ida Attn: M r , B. P. Brown NASA He adqua rte r s 1520 H Street Washington, D. C , Attn: Mr . G. M. Low, MD(P) National Aeronautics and Space Administration Ames Research Center Moffett Field, California Attn: Mr . Matthews National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio

National Aeronautics and Space Administration Flight Research Center Edwards AFB, California

National Aeronautics and Space Administration J e t Propuls ion Laboratory Pasadena, California Attn: M r . H, R . Lawrence

National Aeronautics and Space Administration Langley Research Center Langley AFB, Virginia A-ttn: M r . A. T. Mattson

( 3 )

70

GSFC:

MSFC :

GAEC:

NAR.:

National Aeronautics and Space Administration (2 ) Goddard Space Flight Center Greenbelt, Maryland

George C. Marshall Space Flight Center Huntsville, Alabama Attn: Dr . Kuettner

Rethpage, Long Island New York Attn: Mr . A. Whitaker

National Aeronautics and Space Administration (2 )

Grumman Aircraf t Engineering Corporation (1)

North American Aviation, Inc. Space and Information Systems Division 12214 Lakewood Boulevard Dow ne y , C a1 if ornia Attn: Mr. R. Be r ry

GAEC RASPO: National Aeronautics and Space Administration (1) Resident Apollo Spacecraft P ro jec t Officer Grumman Aircraf t Engineering Corporation Bethpage, Long Island, New York Attn: Mr. Jack Small

Pos t Office Drawer D White Sands M i s s i l e Range White Sands, New Mexico

Manned Spacecraft Center Apollo Document Control Group (SDG) Houston 1, Texas

WSMR: National Aeronautics and Space Administration (2 )

MSC: National Aeronautics and Space Administration (45 1

71

GUDDANCE AND NAVIGATION - ibiblio Analysis...errors that would result from gyro performance...

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Transcript of GUDDANCE AND NAVIGATION - ibiblio Analysis...errors that would result from gyro performance...