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Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Appendix I / Utilities / Earth, Atmosphere and Gravity<br />

_ _<br />

22.6 Earth, Atmosphere and Gravity<br />

22.6.1 Atmospheric Parameters<br />

ATMOSPHERE provides atmospheric data at point (p), directly above point<br />

(d) on the Earth’s surface, as a function of geodetic height [-0.9,32] km.<br />

The speed of sound (VA), static air pressure (PS), static air temperature (TS),<br />

and air density (σA) defined in §19.1-5 are returned.<br />

ATMOSPHERE<br />

ZG ( , V , P , T , ρ , LUNOUT , ISTOP )<br />

Pd, p A S S A<br />

22.6-1<br />

Equation 22.6-1<br />

If the geodetic height is outside the given range a warning is written to the<br />

formatted output file via channel LUNOUT, and the ISTOP flag set to 1.<br />

22.6.2 Earth Curvature Parameters<br />

EARTH_RADII takes the WGS 84 geodetic latitude of point (d) on the<br />

Earth’s surface (λd), and its equatorial and polar radii, returning the<br />

geocentric radius (Pr,d), E/W and N/S curvatures (Rpd , Rmd) from §18.3-5.<br />

EARTH_RADI I<br />

22.6.3 Gravitational Acceleration<br />

( λ , P , R , R )<br />

d<br />

r,<br />

d<br />

p,<br />

d<br />

md<br />

Equation 22.6-2<br />

GRAVITY takes the geodetic height of point (p), its geodetic latitude, and<br />

the radius of the Earth at point (d) directly beneath, returning the<br />

gravitational acceleration from §20.<br />

ZG<br />

ZG ( P , λ , P , k )<br />

gp : = GRAVITY d,<br />

p d r,<br />

d<br />

Equation 22.6-3<br />

When (k = 0) an accurate gravity function is used, otherwise the simplified<br />

model is used.<br />

22.6.4 Conversion from ECEF to WGS84 Co-ordinates<br />

ECEF_TO_WGS84 takes the ECEF position of point (p) which lies on the<br />

geodetic vertical intersecting the Earth’s geoid at point (d), and returns its<br />

WGS84 Geodetic co-ordinates using Olsen’s [O.4] algorithm.<br />

ECEF_TO_WG S84<br />

E<br />

ZG<br />

G E<br />

( P , µ , λ , P , LUNOUT ) ≡ ϕ ( P )<br />

p<br />

d<br />

d<br />

d,<br />

p<br />

E<br />

Equation 22.6-4<br />

Starting with the Earth’s principal radii and eccentricity defined in §18.1,<br />

p

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