JOURNAL OF RESEARCH of the National Burea u of Standa rds- D. Radio Propa ga tion Vol. 67D, No. 6, November- December 1963

Chart for Determining the Effects of Ionospheric Tilts Using an Idealized Model l

T. A. Croft and R. B. Fenwick

Contribution from Radioscience Laboratory, Stanford Unive rsity, Stanford, Calif .

(Rece ived June 15, 1963)

In st ud yin g t he t il ted ion osphere, i t is often useful to consider t he action of a n eq ui valen t re fl ecting mirror as a n approx imate substit u te for t he mor e complex ref ract in g layer of l' il'ctrons . Although t he an alogy is crude, it p ermi ts relatively eas.v co mpu tation of resuHs whi ch pr ovide in sight in to t he action of t he real ionosphere.

Us ing t he mirror a nalogy, t he effect of a t il ted ionosp here on a rad io wave has bee n calculat ed for a wide range of ti lt a ngles a nd directions w it hou t approx im a tions. T hl' resul ts a re prese nted on eight charts, each of whic h is calculated for t.wo p ar t icu lar valu l's of the p arameters which m ust be fi xed prior to calculation (mirror h eigh t a nd the d istan ce from tran smitter to t he poin t on the ear th ben eath lhe mirror) . Examples o f chart usc an d impli cations for long- ra nge JI F transmission are a lso disc ussed.

1. Introduction

Effective ionospheric tills can be i mpor tanL i ll d etermining r ay path geom etry in I-IF propagation , par ticularly in si tua tions wll ere takeoff angles IU'e small. A char t has b een derived wher eb ,- th e position of aJl rays originating fro m the grauncl may be determined in space fLfter having been reHected from. a tilled pl ane mirror. The charts relate th e following four par am eters to one another :

1. The tilt angle of the mirror. 2. The orien tation of th e mirror til t. azimu th wi th

r espect to the incident my. 3. The point of intersection of the reflected nt ,·

with the ear th (i f the ray r eturns Lo earth ). . 4. The heigh t above til e ear th , and the later al

displacement of the re rl.ected ray perigee (if th e ray does no t return to ear th) . Charts have been calculated for mirror heights which are represen tative of F 2-layer vir tual re­flection heigh ts, and for transmit ter- to-mirror dis­tances which correspond to t akeoff angles of only a few degrees.

These calculations were originally carried out to demonstra te the ease wi th which ionospheric tilts can create (or des troy) a "round-th e-world" prop­agation mode in which rays travel between succes­sive ionospheric refl ections without returning to earth [Fenwick, 1963]. It is believed that the charts should b e of use to th e scien tific community because they show the effects of ionospheric tilts which are neither purely longit udinal nor purely transverse.

2 . Geometry

It is possible to gain insigh t in to the role of effective ionospheric tilts in determining ray-path geometry by use of the simple geometric model

1 The research reported here was carried ou t under t he Omce of Naval Resea rch con tract Nonr 225(64) and AR P A Order 196-63.

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shown in fi gure 1. A ray from the transmitter is presumed to be re:flec ted from a mirror at heigh t H with a til t angle cj> and tilt a~imu th 8, as sh own: If the resultan t ray refl ected from this mirror intersects the ear th's surface, t he poin t of inter­section has coordin aLes L (the ground distance from the original great circle) and D (the ground el i tance from the poin t on the ear th 's surface under the mirror reflection point) . If the re flected r ay misses the earth 's sm-face, as shown in fi gure 2 a miss distance Ai (i .e., perigee alti tud e) and p~th deviation L are defm ed.

Given the distance from the tr ansmi tter to t he poin t on the ear th's surface und er the minor reflec­t ion poin t Dr, and given H , i t is Lh en possible to calculate D, L , and lv[ as functions of cj> and 8.

The results of eigh t snch calculations are shown on figures 3 through 10 wi th selected valnes of Dr and H as given in table 1.

Mirror-tran srniUer distan ce, Dr M irror heigh t , II

1000 km ] 250 kill 1500 km 1750 km -------1-------------

km 250 ___ • _____ • ___ • ___ • __ ___ • __ _ • _____ ._. __ . Fil! . '> F ig. ~

300 ______ _______ ._.___ Fig . 3 Fig . 4 Fig . G F ig. 9

350 _______________ • __ ____ _______________ __ F ig. i F ig. 10

3. Examples of Chart Use

Assuming that t he maximum effec tive ionospheric tilt which one may expect to encounter normally is on the order of 2 deg, it is in teres ting to determine the effect of such a tilt on r ays incident from several differ ent aspect angles. Consider figUTe 6, where H = 300 km and the path length for a non tilted mirror r eflection surface is 3000 km (i.e., 2 Dr).

TIL TANGLE

MIRROR SIMULATING A TIL TED IONOSPHERE

TRANSMITTED RAY RA Y REFLECTED TO EARTH'S SURFACE

EXTENSION OF GREAT CIRCLE

TRANSMITTER 0T ' 0 AND L ARE GREAT. CIRCLE DlSToUICES

FIGU RE 1. GeometTY lised to deteTmine ej)'ects oj ionospheric tilts on my paths that TetuTn to eaTth.

MIRROR VECTOR IN DIRECTION 0, ¢

TRANSMITTEO RAY REFLECTED RAY WHICH M.lSSES THE EARTH

FIGURE 2. Geometry used for my paths that miss the earth.

Assume ¢ = 2 deg; then, 1. For 8= 0°, a purely longitudinal "forward"

tilt, the resultant ray path misses the earth (M) by 109 km and is undeviated laterally (L= O);

2. For 8= 90°, a purely transverse tilt, D = 1517 km and L = 33.5 km. Hence the point of intersection of the ray with the earth is 33.5 km off the great-circle path defined by

the transmitted ray. 3. For 8= 180°, a longitudinal "backward" tilt ,

D = 922 km and L = O. The 2° tilt reduced path length by about 570 km.

Case I illustrates a situation in which an iono­sphere-ionosphere reflection mode may be launched. It is possible, for instance, that such a mode would not return to the earth's surface until meeting a comparable tilt with 8= 180°.

736

700

1000

1200

E .><

o 1300

1400

1:100

1600

1700

1100

1900

HORIZON

'0

20

'0

.0

~ 50

.>0: .0

70

:::!: " '0

'00

'10

120

"0

.. 0

TAKEOFF ANGLE = II. 8

' OT = 1000 km

'0 °

FIG U RE 3. Com puted effects of ionospheric tiUs /1"om the idealized model f 01' H = 300 km, DT = 1000 km.

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H z 300 km

"

o

E ~

~

70.

I ..

90'

1000

1100

1200

1300

1400

1500

1600

1700

1100

1900

20

JO ., 60

70

10

" 10' "' m

Il. , ..

TAKEOFF ANGLE' 7 .5 0

DT ·1250 km H ·300 km

FIGURE 4. Computed effects of ionospheric tilts from the ideal­i zed model for H = 300 km, D T = 1250 km.

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I

1

7 ••

, ..

1000

1100

E 11 •• .>C

o

1300

\ 400

1>0.

1600

1700

HORII OH

, . ••

E ~ 6.

~

•• , .. 12.

TAKEOFF ANGLE 2.50

DT -1500 km H -250km

FIG U RE 5. Computed eff ects of ionospheric tilts from the ideaL­ized modelfm' H =250 km, D T = 1500 km.

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100,...--___ _

900

1000

1100

o

1500

1600

1700

liDO

1900 'HO'-:IIOH

IJO

TAKEOFF ANGLE 4 .3· DT -1500 km H-300km

FIGURE 6. Computed effects of ionospheric tilts from the ideal­ized model for H =300 km, D T = 1500 km.

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L(km)

900

1000

1100

1200

o 1500

1600

1800

1900 10

1000

100

120

FIG URE 7. Computed effects of ionospheric tilts from the ideal­ized model for H =350 krn, D T = 1500 km.

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TAKEOFF ANGLE 6.0 0

DT = 1500 km

H = 350 km

700

800

1000

. 1 100

1200

E 1300 .><:

o

1400

1500

1600

1700

HOR,IZOH

TAKEOFF ANGLE = 0.10

DT 1750 km

H s 250 km

F I GURE 8. Computed effects of ionospheric tilts from the ideal­ized model for H = 250 km, D T =1750 km.

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8 '

E -""

o

HORIZON

E -""

~

800

'00

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

10

20

30

'0

50

.0

70

80

'0

100

TAKEOFF ANGLE 1.6 0

DT z 1750 km

H z 300 km

FIGURE 9. Computed effects of ionospheric ti lts from the ideal­ized moddfor H =300 km, D T = 1 750.

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900 C--_...L

1000

1100

1200

1300

o

1700

1800

190 0

200 0

HORIZO N

E .lI<

120

TAKEOFF ANGLE = 3 .10

DT 1750 km

H 350 km

FIGU HE 10. Computed effects of ionospheric tilts from the ideal· ized model for H =350 km, D T = 1 750.

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Notice in particular that the 2° tilt will cause a ray to miss the earth for all tilt azimuths between 0° and 82.5°. Since the charts show only half of a figure which would have mirror symmetry about the verti­cal, it follows that all tilt azimuths between +82.5° and -82.5° can create an ionosphere-ionosphere reflection mode. This represents 46 percent of the entire 360° range of azimuths.

Case II illustrates a situation in which a ray is deviated laterally, causing off-great-circle propaga­tion to take place.

It can also be seen, for example, that 13 percent of the azimuth range of a 2° tilt will cause rays to return to earth with a lateral deviation of at least 20 kID. Because of the chart symmetry, another 13 percent will cause 20 km or more deviation but in the opposite diTection .

Case III illustrates a situation in which greatly unequal hop lengths occur in a one-hop geometry. Such a situation is likely to occur, for instance, when rays enter the daylight hemisphere from the night hemisphere transverse to the twilight line.

Here it is seen that a 2° tilt reduces D to 1000 km or less for azimuths between plus and minus 140°, or 22 percent of the azimuth rano·e. For a 3° tilt, 32 percent of the azimuth range will cause this degree of path length reduction.

Thus one could derive from the charts conclusions of the following natme: For I-l=300 km, D T = 1500 km, <p (tilt) =2 °, and random tilt azimuth

1. There is a 0.46 probability that the reflected ray will mi s the earth

2. There is a 0.26 probability that L win exceed 20 km

3. There is a 0.22 probability that the ray. will ret llTn to earth within 1000 km of the muror (as measLLred along a great circle).

4 . Conclusion

A chart has been derived which permits estimation of the effects on the paths of HF radio waves when ionospheric tilts are encountered. The authors are not aware of any other comprehensive description of the action of tilts in other that the simplified cases of purely longitudinal or purely lateral tilt azimuth. It is assumed that the reflection takes place at a tilted plane mirror, bu t otherwise no approximations are involved. Details of the der­ivation, plus the computer program used to produce the charts , have been given by Fenwick [1963]. Tnterested workers co uld easily modify this program if they desire to study some other parameter, such as the angle of inciden ce or the down coming ray.

5. Reference

Fenwick, R . B. (Apr. 1963), Round-the-world high-frequency propagation, TR 71 , Raciioseience Laboratory, Stanford Uni versity, Co ntract Nonr 225(6'1) .

(Paper 67D6-302)

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