APPENDIX A
APPENDIX A METEOROLOGICAL DESCRIPTIONS C o n v e n t i o n a ls u r f a c ec h a r t s for 29 A p r i l 1969 show t h a t a f r o n t a l passage o c c u r r e d o v e r W a l l o p s i n t h e early morning h o u r sp r i o rt o the 1200 GMT (0800EDST) map time. However, the s u r f a c e - r e c o r d e d data at Wallopsonlyshowed weak i n d i c a - t i o n so fs u c h a f r o n t a lp a s s a g e . A t 1100 GMT, t h e s u r f a c e wind d i r e c t i o n t u r n e d s h a r p l y from s o u t h e r l y t o n o r t h e a s t e r l y , t h e nn o r t h e r l y . However, a l l through t h i s p e r i o d t h e s u r f a c e wind speed neverexceeded 3 f t / s e c . The two thermograph traces bothrecordedtemperature maxima d u r i n g the n i g h t a t 0600 GMT, followed by a subsequentdrop of some 6 O F i n f o u r By t h i s time t h e s u r f a c er e l a t i v eh u m i d i t y was r e p o r t e d hours.
t o b e 100%. A l l through t h i s p e r i o d , the v a r i a t i o n si ns u r f a c e p r e s s u r en e v e re x c e e d e d 0.02 i n c h e s .
By 1 2 0 0 GMT, s u r f a c e h e a t i n g e f f e c t s were beginning to be reflected i n t h e data. The t e m p e r a t u r e s t e a d i l y r o s e t o a maximum a t approximately 1500 GMT. The s u r f a c ew i n d s became more t u r b u l e n t w i t h g u s t sr e a c h i n g 16 f t / s e c . These changes were accompanied by a drying-outof t h e s u r f a c e layer. By 1700 GMT, t h e wind,which had beenblowingfromeast-northeast, became d e c i d e d l y easterly, s u g g e s t i n g t h e o n s e to f t h e sea breeze. Subsequently, t h e s u r f a c e t e m p e r a t u r e d e c r e a s e d steadily. These v a r i a t i o n si ns u r f a c e parameters for the time p e r i o d i n q u e s t i o n are summarized i n Table I1 o f the r e p o r t .
The s u r f a c et e m p e r a t u r ea n d humidity recorded a t the two sites d i d n o t agree a t a l l times. The largest d i s c r e p a n c i e s o c c u r r e d d u r i n g t h e a f t e r n o o n p e r i o d s of maximum s u r f a c e h e a t i n g . The high t e m p e r a t u r eo f T O 0 F reached a t the n o i s e measurement s t a t i o n was n o tr e a c h e d a t the endof the runway.
A t t h i s p o i n t , a high ofonly 62O F was measured. S i m i l a r l y , I I I I I 1.1 1 . 1 1 1 1 . 1 . - 11,. , .,. .,..,.."_ ..... ....-.-.- "."_..._._ -.. - " .
I I I I 1 I I I 1 1111 111 1 1 1 . 1 1 1 . 1 I I t h e range of r e l a t i v e h u m i d i t y r e c o r d e d a t t h e end of the runway,subsequentto 1500 GMT was less t h a n that recorded a t the n o i s em e a s u r e m e n ts t a t i o nf o r the same p e r i o d .S i n c e p r i o r t o t h i s time, b o t hs e n s o r s were reported approximately t h e same v a l u e s , it a p p e a r s t h a t t h e d i f f e r e n c e ss u b s e q u e n t t o 1500.GMT are notdue t o i n s t r u m e n t e r r o r s b u t reflect l o c a ld i f f e r e n c e si na t m o s p h e r i cc o n d i t i o n s .
The upper a i r data, up t o 3000 f t , are summarized i n the t i m e - s e c t i o n so ft e m p e r a t u r ea n da b s o l u t eh u m i d i t y shown i n Figs. 5 and 6 i n t h e r e p o r t ; time p r o f i l e s o f wind are shown i n Fig. A - 1 . These a n a l y s e s were e x t e n d e dt o t h e s u r f a c e by u s i n g t h e mean v a l u e s of t h e temperatureandhumidity recorded by t h e two hygrothermographsdiscussedpreviously.
Because of t h e i n a d e q u a t e time c o n t i n u i t y i n t h e upper a i r data f o r the morningperiod, the time s e c t i o n sh a v eb e e n drawn only f o r the p e r i o ds u b s e q u e n tt o 1400 GMT. For comparison, t h e i n t e r p o l a t e d p r o f i l e s a t 1030 TMT are shown i n Fig. 7 o f t h e r e p o r t . The most s i g n i f i c a n tf e a t u r e si n these a n a l y s e s are: ( a ) The upward p e n e t r a t i o no f the s u r f a c e h e a t i n ge f f e c tb e t w e e n 1400 GMT and 1800 GMT; ( b ) the r a p i d changes t o n e a r i s o t h e r m a l s t r u c t u r e i n t h e lower layer between 1800 GMT a n d 1900 GMT; ( c ) t h e s u b s e q u e n tp e n e t r a t i o n Of a " c o l dt o n g u e "i n t o the lower l a y e r s ;a n d ( d ) the formation of a moist layer between 1000 f t and 1500 f t s u b s e q u e n tt o 2000 GMT.
These v a r i a t i o n s i n a t m o s p h e r i c s t r u c t u r e may have i m p o r t a n te f f e c t so n the p r o p a g a t i o n .F i g u r e A - 2 f o r example, shows t h e time s e c t i o n p r o f i l e o f the speed ofsoundcomputed from t h e t e m p e r a t u r ep r o f i l e s shown i nF i g . 5. The e f f e c t s O f windhavenotbeenincluded. The v e r t i c a l v a r i a t i o n s i n the speed o f soundshowncannot be a d e q u a t e l y specified from t h e s u r f a c e data alone.
A-2
Too 4 2500
& 2000 LL Y + c cn .- a r
I 1500
I I I I I 1 L J 14 15 EDST 10 i ! 12 13 16 17 ( 8 14 (5 16 17 18 19 G M T 20 21 22 Wind Speed and Direction 29 April 1969 F I G U R E A - 1 . V A R I A T I O N I N W I N D S P E E D A N D D I R E C T I O N D U R I N G FLYOVER MEASUREMENTS ? 3000
"
h i 2000 !OOO L L v e c .- 0 ) I !
1500 1500 50C EOST io i I 12 1 3 I1 4 15 4 6 17 18 GMT i 4 15 16 17 18 19 20 21 22 Speedof Sound (Minus 1100)Ft/Sec 29 A p r i l 1969 F I G U R E A - 2 . V A R I A T I O N I N T H E S P E E D OF S O U N D D U R I N G FLYOVER MEASU'REMENTS
APPENDIX B
APPENDIX B DESCRIPTION OF COMPUTATIONS T h i s appendix summarizes t h e v a r i o u sc a l c u l a t i o n s u t i l i z e d i n the data a n a l y s i s . A s s e e ni nF i g u r e B-1, the a c t u a l p a t h of a n a i r c r a f t i n flight varies about a straight l i n ep a t h . The a c t u a l path of t h e f l y o v e r si n t h i s study, as d e p i c t e do n the a p p r o p r i a t e radar t r a c e s , was approximated by s t r a i g h t l i n e s e g m e n t s ; t h e C a r t e s i a nc o o r d i n a t e s o f these segments, relative t o the radar z e r o p o i n t , were o b t a i n e d as a f u n c t i o n of time from t h e radar tracesandaccompanying time marks. For e a c hf l i g h t , t h i s i n f o r m a t i o n , together w i t h t h e c o o r d i n a t e so f t h e groundmeasurementpositions, was used as i n p u tt o a computer program. T h i s program c a l c u l a t e d , b y l i n e a r i n t e r p o l a t i o n of t h e i n p u t data, t h e p o s i t i o n of t h e a i r c r a f t a t o n es e c o n di n t e r v a l sf o ro n e m i n u t e , s t a r t i n g a t t h e time f o r which t h e c o o r d i n a t e s of the a i r c r a f t were first known.
If the time periodcovered b y the i n p u t data was less t h a n 60 seconds, t h e program e x t r a p o l a t e d a i r c r a f t p o s i t i o n s f o r the times f o l l o w i n g t h e known time p e r i o d b y assuming t h a t t h e a i r c r a f t was f l y i n g d i r e c t l y o v e r t h e f l i g h t t r a c k w i t h the same speed as t h a t i n t h e l a t e s t time i n t e r v a l f o r which i t s a c t u a l speed was known. The assumed a l t i t u d e was obtained. b y t a k i n g a time-weighted averageof the known a l t i t u d e s .
Foreach time increment, t h e a n g l e of r a d i a t i o n , OR9 from the a i r c r a f t t o e a c h measurement p o s i t i o n was determined a c c o r d i n g t o the f o l l o w i n ge q u a t i o n (see F i g u r e E-1): 2 2 2
dl + d2 - d3
0 = 180° - a r cc o s i n e (B-1)
B-1 I I I 1111 where 0 = Angle o f r a d i a t i o n
-
Propagation distance
dl -
-
Distanceof t h e a i r c r a f t a l o n g the s t r a i g h t l i n e
d2 -
segment d e s c r i b i n g its f l i g h t path a t t h e time underconsideration
-
Distancefrommeasurementpositionto the beginning
d3 -
of t h i s l i n e segment
-
Distancefrommeasurementposition t o ground point
d4 -
underneath the a i r c r a f t The r a d i a t i o nt i m e s (to) correspondingtoangles of r a d i a t i o n of 3 0 ' t o 150° at 5 O increments were determined f o r e a c h measurement p o s i t i o n by i n t e r p o l a t i c n o f t h i s angle- time r e l a t i o n s h i p . Then, f o r each of these r a d i a t i o na n g l e s , t h e propagationdistance was c a l c u l a t e d from t h e coordinates of the a i r c r a f t and t h e measurenentposition. A l s o computed were t h e a n g l e o f e l e v a t i o n o f t h e a i r c r a f t and t h e propagation time : h
X = a r c t a n g e n t -
(B-2) a4
- dl
- t o + c (B-3)
tP where X = Angle o f e l e v a t i o n h = H e i g h t o f a i r c r a f t c = Averagevalue o f speed o f sound = Time a t which t h e n o i s e radiated from the a i r c r a f t tP at anangle i s r e c e i v e d on the ground The n e x t c a l c u l a t i o n step consistedofcomparing t h e p r o p a g a t i o nd i s t a n c e st o the d i f f e r e n t measurement p o s i t i o n s f o r t h e same angle o f r a d i a t i o n . For each p a i r o fp o s i t i o n s the d i f f e r e n c ei np r o p a g a t i o nd i s t a n c e s was obtained, as w e l l as t h e amount of i n v e r s e - s q u a r e a t t e n u a t i o n based on t h e r a t i o of thepropagationdistances.
B -2 Forexample, i f dlA and dlB r e p r e s e n t t h e p r o p a g a t i o n t o p o s i t i o n s A and B, r e s p e c t i v e l y ,a n d i f dlA<dlB, d i s t a n c e s t h e n d~~ and where dm is the i n c r e m e n t a lp r o p a g a t i o nd i s t a n c ea n d IAm is the i n v e r s e - s q u a r e a t t e n u a t i o n b e t w e e n the t w o p o s i t i o n s .
I n c r e m e n t a lp r o p a g a t i o nd i s t a n c e sa n di n v e r s e - s q u a r ea t t e n u a - t i o n s were c a l c u l a t e d f o r e a c h p o s i t i o n p a i r at eachangle of r a d i a t i o n , e x c e p t f o r the s i t u a t i o n i n which t h e a n g l e of e l e v a t i o n o f t h e aircraft from some p a r t i c u l a r p o s i t i o n was less t h a n o r e q u a l t o 2 0 ° .
The i n p u t data to a secondcomputerprogram were t h e o n e - t h i r d o c t a v e b a n d n o i s e s p e c t r a a t h a l f - s e c o n d i n t e r v a l s r e c e i v e d a t eachmeasurementposition,and t h e p r o p a g a t i o n times f o re a c hr a d i a t i o na n g l e ,c a l c u l a t e d e a r l i e r . Using these times t h e n o i s el e v e l sr e c e i v e d a t e a c hp o s i t i o n f o r the v a r i o u sr a d i a t i o na n g l e s were determined by i n t e r p o l a t i o n of the h a l f - s e c o n dn o i s e data f o r each frequencyband.
I n a d d i t i o n , t h e half-second time h i s t o r i e s ofeach frequencyreceived a t e a c h p o s i t i o n were p l o t t e d b y t h e computer. From t h e s e plots the n o i s ef l o o r was read b y eye.
The noise l e v e l s as a f u n c t i o n o f r a d i a t i o n a n g l e were n e x t c o r r e c t e d f o r t h e i n f l u e n c e of t h e backgroundnoise b y l o g a r i t h m i c a l l y s u b t r a c t i n g t h e n o i s e f l o o r f r o m t h e a p p r o p r i a t e level. A l l n o i s el e v e l sw i t h i n 3 decibels o f t h e n o i s e floor were e l i m i n a t e d f r o m the a n a l y s i s .
The a d j u s t e d l e v e l s f o r each r a d i a t i o n a n g l e were t h e n t a k e n two a t a time and matched w i t h t h e a p p r o p r i a t e i n c r e m e n t a l p r o p a g a t i o n d i s t a n c e a n d i n v e r s e - s q u a r e a t t e n u a t i o n v a l u e s B-3 computed previously. The e x c e s sa t t e n u a t i o n , m, was t h e n c a l c u l a t e d by t a k i n g t h e d i f f e r e n c e i I z a d j u s t e d l e v e l s a n d removing the i n v e r s e - s q u a r ea t t e n u a t i o n .T h u s , i f LA and LB are t h e c o r r e c t e d s o u n d p r e s s u r e l e v e l s i n a frequencyband r e c e i v e d a t p o s i t i o n s A and B ( p r o p a g a t e d over d i s t a n c e s DIA and DIB) r e s p e c t i v e l y ,t h e n
mAB = LA - LB - : I A m (B-6)
For e a c hr a d i a t i o na n g l e (30° t o 150, at 5 O i n c r e m e n t s ) , v a l u e so f m v s d were o b t a i n e d i n t h i s manner f o r a l l t h e c o r r e c t e d data, i n eachfrequencyband.
L i n e a rr e g r e s s i o nl i n e s were f i t t e d t o the values o f e x c e s sa t t e n u a t i o nv si n c r e m e n t a lp r o p a g a t i o nd i s t a n c e .
The r e g r e s s i o nl i n e s are o f the form m = a, + ald (B-7) The values of a, and dl were o b t a i n e d i n three d i f f e r e n t ways: b yS t a n d a r d‘ . e a s t - s q u a r e sr e g r e s s i o na n a l y s i s , b y a weighted r e g r e s s i o na n a l y s i s ,a n d by a f o r c e d - i n t e r c e p t wei,ghted r e g r e s s i o n a n a l y s i s .
The s t a n d a r d , o r u n w e i g h t e d ,r e g r e s s i o nl i n e s were c a l c u l a t e d f r o m :
ld21m - ldm
a , =
Ncd2 - ( I d ) *
N l d m - Id m
-
al -
Ncd2 - (
where N i s the number of data p o i n t s i n t h e sample.
The weighted r e g r e s s i o n u t i l i z e s a w e i g h t i n g f a c t o r l i n e a r i l y p r o p o r t i o n a l t o t h e p r o p a g a t i o nd i s t a n c ef o re a c h data p o i n t . For t h i s t y p eo fl i n e , t h e followingformulas were used:
a, = cd31dm - Cd2Cd2m
( B - 1 0 )
1d3Cd - ( Id2)
B -4 (B-11) F i n a l l y , i n a d d i t i o n t o a l i n e a r w e i g h t i n g f a c t o r , the forced-weightedregressionline i s d e s i g n e d t o pass through t h e zero p o i n t o f the data, i.e. zero a t t e n u a t i o n f o r a propagation distance of zero. It was computed using (B-12) a. = 0 (B-13) B-5 Actual Path Flown By Aircraft (Approximated by StraightLine Segments)
\
\
AircraftFlightTrack on Giound
\
Noise Measurment Position N F I G U R E B - 1 . S K E T C H I L L U S T R A T I N G P R O P A G A T I O N D I S T A N C E A N D A N G L E S D U R I N G NOISE M E A S U R E M E N T S O F A N A I R C R A F T F L Y O V E R