Formulae Only- NAV, Avionics

8/11/2019 Formulae Only- NAV, Avionics

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THE VILLAGE IDIOTS GUIDE TO AVIATION NAV FORMULAE!! 1/4 DUHHHH!! Hari Nair

Length of arc of circle = /360 x 2 R

Length of parallel = /360 x 2 RxCos Lat (R=3441 nm).

1 in 60 rule height or dist off /dist along x60 = deg (small angle approximation).Therefore, 60/60x60 = 1.

Eq dia = 12,749 km, Polar dia =12,706 km, difference -43 km or 1/300 approx.

Length of equator =60x360=21,600 nm. 1nm =length of 1 arc of meridian.1nm = 1852 m.1km =1/10,000 of av dist along earths surface from equator to either pole.1 nm ICAO 1852m. 1 nm, 45lat -1853m. 1 nm 90lat=1843m, 1nm, 0lat=1862m1km =3280 ft, 1nm=6076.08 ft (approx also used 1nm=6080 ft).1sm =5280 ft,1 in =2.54 cm, 1m = 3.281 ft, 1nm= 72,913 in. 54 nm = 100 km.

Dist (spacing) of II of lat along a meridian = 60x ch Lat or ch Lat/360 x2 R (R=3441).Dist (departure) of long along a II of Lat = 60x ch Long x cos Lat or (min) = ch Long x cos Lat

Convergency =ch Long x sin lat x 60. Also (in min), =Departure (kts/60) x tan Lat (for Gyro drift)Conversion angle = Convergency.Convergence is angular diff between True North and Grid North.

Scale = Chart Length/ Earth Dist (CL/ED), Scale Factor =CL/RED, always in % age.

Mercator Scale variation = Sec (lat), or to the scale RF multiply denominator by Cos .Multiply denominator of scale by - Cos 2 nd Lat/Cos 1 st Lat

Time in arc 1Long =4 min time, 1hr =15 deg of Long, 1 min time =15 Long, 1 sec time=15 Long.For westwards flights - If LMT Dep and Arr are same and on a parallel, G/S kts=15x60xCos Lat, acspeed = cos lat!! For eastward flights-x2.(on the basis of - 15 Long=1 hr time)

If wind velocity =W, x wind compo is W sin and hd; wind compo is W cos .To find drift angle, first find x wind compo as above,Then vector ac speed and x wind compo, drift angle thus is tan -1 (x wind compo/ ac speed).When the ac is steered into the drift angle, a head wind compo now is resulted, called effectivewind component. Simple compo found is True wind compo.

Imp- if using a scientific calculator for pulling out drift angle and G/S

Max Dr angle =W/V / TAS x 60. Actual Dr angle =max Dr angle x sin of wind-to-track angle.Simple calculated G/S over-optimistic by : (1-cos Actual Dr angle) x (G/S simple calculated)

Gyros both topple at equator, both no drift at equator. Topple = 15.04 x Cos Lat. at pole horizontal axis only drifts (DI), vertical no drift. Drift = (-) 15.04x Sin Lat. Apparent drift moving gyro max on 090T co N Hemi.Total drift = apparent drift + convergency (find d long from G/S and then find convergency)Total drift is increasingly negative (minus) on easterly hdg.

LOS range (nm)=1.05 h (in ft) VHF range(nm)=1.25 (h1+h 2 )(ft). Also LOS(nm) = 12 (FL)Range of surface wave(nm)=3x pwr (Watts).

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C=f c=3x10 8 m/s .,PRP =1/PRF, PW-min range, PRP-max range (divide dist / 2)Depth of modulation =amplitude of signalamplitude of carrierx100 (%age).Doppler freq Fr = F+(2V/ ) x Cos or Fr= F+ 2VF/c x cos x cos ,for Janus Beam Dopplers, Fr= F+4VF/c x cos x cos

True Alt=Pa +(3.5x TxPa1000), T=OAT-ISA temp.True Alt=Pa +(3.5x TxPa1000), T=OAT-ISA temp.Density alt= Pa + 119ft T.Density alt= Pa + 119ft T.

TAS=RAS+ (1.75%RAS x alt (thousands of ft)). TAS=RAS+RAS60x Alt (Thousands of ft).TAS=RAS+ (1.75%RAS x alt (thousands of ft)). TAS=RAS+RAS60x Alt (Thousands of ft).Calibration of ASI is: P = 1/2 x p x V 2 ( 1+ 4xV 2/c2 )Calibration of ASI is: P = 1/2 x p x V 2 ( 1+ 4xV 2/c2 )

Mach no=V T/C, where C=C=38.98 TK. or 644+1.2T CMach no=VTotal Air TempC = T AMBC + T RAT C , where RAT=(V T (kts)/100) 2 .Total Air TempC = T

T/C, where C=C=38.98 TK. or 644+1.2T C

C=(F-32)x5/9, F=(Cx9/5)+32C=(F-32)x5/9, F=(Cx9/5)+32 AMBC + T RAT C , where RAT=(V T (kts)/100) 2 .

ROD (fpm) = GP angle x GS (kts) x 100/60 Glide path angle = ht/dist x 60 (1 in 60).ROD (fpm) = GP angle x GS (kts) x 100/60 Glide path angle = ht/dist x 60 (1 in 60).

FREQ OF OP RADIO AND NAV AIDS ICAOFREQ OF OP RADIO AND NAV AIDS ICAOHF 2-22 Mhz.

NDB -200-1750 KhzVHF 117.975-137 Mhz (137=data ch).

VOR 108-117.975 Mhz- 108 -112 Mhz (shared with ILS freq band, even first first decimal V-R even)- 112-117.975 Mhz. TVORs are on the first band.

ILS Localiser 108-112 Mhz (odd first freq)Glide Slope 329-335 Mhz

Rad alt 4.2 - 4.4 GhzDoppler 8.8-13.6 GhzWx radar 3.2 cm, 9.375 Ghz

Compass Max Dev = Tan B/C (Check phase by circle dia). Zero Dev = Tan C/B.Deviation on a hdg= A + B Sin + C Cos Dev on a hdg due to B = B x sin hdg

X- reply +63 Mhz , VOR whole decimalY- reply - 63 Mhz, VOR half decimal

DME - 960-1215 Mhz

SSR Codes 0000- SSR U/S2000-Entry non SSR area7000-conspicuity code7007 aerial obs7500- hijack7600-R/T U/S7700-a/c in distress3100-mil a/c emergency

SSR -ground-1030,air 1090 Mhz

CP (dist) = DH/(O+H)PNR (time) = EH/(O+H).PNR(dist) = EOH /(O+H), E= endurance in h.Wind effect on NIL wind CP =Dist x wind compo/TAS = dist the CP shiftsupwind

Substract or add from 360 or 180Dev on a hdg due to C = C x cos hdg

+B & +C =

Usable up to 70N/S

- +

- ++ +

- -

o +

- o

Accel errors ANDS North Hemi Accel North, Decel South. Max on East-West, nil on North-South. No error on mag equator (aclinic line).



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Turning errors due to dip (Z compo), SONULiquid swirl error- adds turn error towards north turns in NH. Also, during turns on mag equator,swirl is sole cause of turning error.

NDB or VOR Double the angle & Time & Dist Flown = Time & Dist from NDB or VOR.- Time in Secs/Change in Deg = Time (min) to VOR or NDB.IMP- If turn is less than 90, then multiply value x Sin turn angle.

Pressure 1 hpa=100 pa, 1 mb = 1 hpa, 1013 mb= 101300pa. 1 mb = 100 pa, 1pa=0.01 mb, 1 pa=1 N/m 2,, 1 bar = 1000 hpa. 1 in Hg = 1013 / 29.92x 30 = 1016 ft

Wx Radar . Beam width 3, therefore, use width 1.5 with 1in60 to calculate relative height ofbase or top of cloud, with respect to aircraft.



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Properties Map Projections

Mercator Std Transverse Oblique LambertsPolyconic

Rhumb Line Straight line Curve concaveto nearest pole Curve concave tonearest pole Curve concave tonearest poleGC Curve concave to

equator (convex tonearest pole)

Curve concaveto DM, AMPractically stline near DGC,DM-AM

Curve concave toDGC

Curve concave to IIof origin, practicalpurposes a st line

GC St lines Equator, GCs 90to eq meridians

DM, AM, GCs90 to DM, AM

DGC, GCs 90 toDGC

All meridians semi-GCsperfect st lines.GC on II of origin stline

Useful area Equatorial -600 nmof equator

600 nm of DM 600 nm of DGC Mid latitudes

Scale correct At equator DM DGC Std IIsScalevariation

As Sec of latitude Sec GC distfrom DM

Sec GC dist fromDGC

Correct at std IIs,contracts within andexpands outside.Lesser thanMercator-over 24 lat, scale contractsonly about 1%.

Convergency 0, correct only atequator.

Correct only atDM

Correct only atDGC

Constant for thechart, correct only atII of origin. Alsoconstant of cone=Sine of II of origin


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