Formula for Maths.docx

7/27/2019 Formula for Maths.docx

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FORMULA FOR NAV MATHS

With Flight Computer : Other than W/V maths, you can solve all others with the “Circular Slide Rule(CSR)”. There are 3 scales in CSR – Inner (IS), middle (MS) & outer (OS).

1. Time:

a. Hr at IS & min at MS.

b. To convert min to sec, set RA (Rate Arrow) against min on OS and read the sec on OSopposite to „Seconds‟ arrow (near 35 at MS).

2. Time, Speed & Distance Problems:

a. Speed & distance at OS & time at IS.

b. To find time, set RA against speed at OS and read time at IS against distance at OS.

c. To find speed, set hr at IS / min at MS against distance at OS and read speed at OS againsRA.

3. Fuel Consumption Problems:

a. Fuel consumption & quantity at OS & time at IS.

b. To find time, set RA against consumption at OS and read time at IS against qty at OS.

c. To find consumption, set hr at IS / min at MS against qty at OS & read consumption at OSagainst RA.

4. Conversions:

a. To convert NM to SM, set „NAUT‟ arrow (near 70 at OS) against NM at MS and read SM atOS against „STAT‟ arrow (near 70 at OS) and vice versa. For KM, read against „KM‟ arrow (near 12at OS).

b. To convert US Gallons to Imperial Gallons, set „U.S. GAL‟ arrow at MS (near 13) agains„IMP. GAL‟ arrow at OS (near 11) and read Imperial Gallons at OS against US Gallons at MS andvice versa.

c. Qty vs Wt. To convert US Gallons to Pounds for aviation fuel, set „U.S. GAL‟ arrow at MS(near 13) against „FUEL LBS‟ arrow at OS (near 80) and read pounds at OS against US Gallons aMS and vice versa. For aviation oil, read against „OIL LBS‟ arrow (near 10 at OS). Similar can beapplied for Imperial Gallons.

d. To convert litters to US Gallons, pounds to Kg or feet to meters, align the appropriate arrowson MS & OS and the read the answer from OS & MS.

5. TAS & Density Altitude: (calculated from AIRSPEED CORRECTION window at right side)

a. TAS at OS & CAS at MS.

b. To find TAS, set pressure altitude against OAT in Celsius & read TAS at OS against CAS aMS and vice versa. Read the Density Altitude over the arrow in the DENSITY ALTITUDE window.



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c. To convert Mach Number to TAS, rotate the inner dial till „MACH NO INDEX‟ arrow is visiblein the window, set True/OAT against this arrow & read TAS at OS against Mach No at MS and viceversa.

6. True Altitude: (calculated from ALTITUDE CORRECTION window, left side)

a. Set pressure altitude against OAT in Celsius.

b. Subtract Station Altitude from Indicated/Calibrated Altitude to get Calibrated Altitude AGL.

c. Read correction to Station Altitude at OS against Calibrated Altitude AGL at MS.

d. Add the correction to Station Altitude to get True Altitude.

Note: If the Station Altitude is unknown, read Calibrated Altitude at MS and True Altitude on OS.

7. Converting Feet per Mile to Feet per Minute:

a. Feet per Min at OS & Feet per Mile at MS.

b. Set RA against given Ground Speed & get Feet per Min at OS against Feet per Mile at MS.

c. To convert Mach Number to TAS, rotate the inner dial till „MACH NO INDEX‟ arrow is visiblein the window, set True/OAT against this arrow & read TAS at OS against Mach No at MS and viceversa.

8. Off-Course Problems:

a. Off-Course at OS & Distance at MS.

b. Set Off-Course at OS against Distance-travelled at MS & get Degrees to parallel the track.

c. Set Off-Course at OS against Distance-to-go at MS & get additional Degrees to intercept thetrack.

d. Add both degrees for total correction..

9. Crosswind table: (ACROSSWIND CORRECTION /WIND COMPONENT GRID) Chart/Table isgiven at the bottom of the rectangular Sliding Scale).

a. Calculate the angle between aircraft Course & reported Wind Direction.

b. Find the Head/Tail & Cross Wind component from CROSSWIND CORRECTION /WINDCOMPONENT GRID) Chart/Table at the Sliding Scale. Apply approximation/average method when

wind speed is in between two shown speeds in the table.

c. Remember, wind direction is reported in True heading.

10. Ground Speed & True Heading relating Wind Correction Problems: (calculated from the WindSide of the Slide). To get Ground Speed and True Heading relating Wind Correction, you must know fourthings: (1) True Course, (2) TAS, (3) True Wind Direction & (4) Wind Velocity.

a. Set Wind Direction at IS against „True Index‟ arrow at OS.



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b. Mark Wind Velocity upward from centre point (Grommet) on the Azimuth Disc (middletransparent circular portion).

c. Set True Course at IS against „True Index‟ arrow at OS.

d. Slide Wind Velocity mark to match TAS at the Speed Arcs.

e. Read Ground Speed from Speed Arc passing under Grommet.

f. Get Wind Correction Angle from between Centre Line & Wind Velocity mark.

g. Apply Wind Correction Angle to obtain True Heading.

11. Wind Direction & Velocity Problems: For this, you must know four things: (1) True Course(2) Ground Speed, (3) True Heading & (4) TAS.

a. Set True Course at IS against „True Index‟ arrow at OS.

b. Move the slide until Grommet falls over given Ground Speed at the Speed Arc.

c. Calculate Wind Correction Angle from the difference of given True Heading & True

Course. Determine whether Wind Correction Angle is left or right. If True Heading is higher thanTrue Course, then Wind Correction Angle is right and vice versa.

d. With Grommet over given Ground Speed, find the point where Wind Correction Angle(left/right) intersects TAS Speed Arc. Mark the point with pencil.

e. Rotate the Azimuth Disc until the pencil mark is on the centre line between Grommet & TrueIndex.

f. Read Wind Velocity by counting the lines between the Grommet & the pencil mark.

g. Read Wind Direction under True Index.

For General Nav Maths: You need to know the following:

1. Variation (between TN & MN) & Deviation (between MN & CN)

Variation East Magnetic least, Variation west Magnetic bestVariation East Compass least, Variation west Compass best

2. Calculation of change of Long (Ch Long), Lat (Ch Lat) and corresponding position & distance (alongSame Meridian, Lat or different and in same hemisphere or different)

a. Departure/Distance = DLong X cos Lat or cos MLatDLong=Ch Long X 60

* Use this formula to find Ch Long at a given or calculated MLat



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4. For Mercator Chart:

Convergence = Ch Long X sin Lat or sin MLat , Conversion Angle (CA) = ½ Convergence

A straight line track on a Mercator chart is a rhumb line. The Rhumb line between two points will always benearer to the Equator than the corresponding Great Circle. Conversely, the Great Circle between two pointswill always lie nearer the Pole than the Rhumb line. Remember, radio waves travel along great circles.

For plotting: GC bearing must be converted in RL bearing before plotting. Except ADF bearings, convert al

other bearings to True bearing (ie. QTE) (this is GC bearing) and then apply CA to get RL. With ADF, findout True bearing first (this is GC bearing), and then apply CA to get RL.

For VOR problems, use VOR variation. For NDB problems, use aircraft variation.

For VOR reading, get QDM, then from QDM to QDR (QDM+180 or the VOR tail reading / radial), then applyvariation at VOR to get QTE.

For ADF with RBI, 1st get the ac true heading by applying ac variation, if any and then add RBI reading withit to get GC bearing. For ADF with RMI, apply ac variation, if any, to RMI reading to get GC bearing.

Bearing from 000 to 180 Bearing from 180 to 360

North Pole RL = GC + CA RL = GC - CASouth Pole RL = GC – CA RL = GC + CA

Scale at latitude = Scale at Equator x Secant Latitude

Scale A secant AScale B = secant B

5. For Lambert’s Conformal Chart:

Convergence = Ch Long X Constant of Cone (Cof C); Sin Lat= Cof CSize Segment = Sin Lat X 360;

Except for meridians which appear as straight lines, rhumb lines are curves concave to the pole of the projection(eg. parallels of latitude).

Except for the meridians which appear as straight lines, great circles appear as curves concave to the parallel of origin.

Convergence is annotated Easterly when True north lies to the East of Grid north and Westerly when Truenorth lies to the West of Grid north.

Changes towards East Changes towards West

North Pole Convergence West Convergence East

South Pole Convergence East Convergence West

Bearing from 000 to 180 Bearing from 180 to 360

North Pole Convergence West Convergence East

South Pole Convergence East Convergence West

Convergence East True least, Convergence west True best



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6. Scale Representation:

a. Representative Fraction (RF) = Chart Length (CL) / Earth Distance (ED).b. cos Lat A x Scale Denominator Lat B = cos Lat B x Scale Denominator Lat A (Mercator)

7. Aircraft Magnetism Questions:

Deviation = Difference between MH & CH. If MH is to the left, then Deviation is Minus.

Coefficient A = Sum of all Deviation / No of DeviationCoefficient B = Deviation East – Deviation WestCoefficient C = Deviation North – Deviation South

Again, Coefficient B = Deviation / Sin Heading; Coefficient C = Deviation / Cos Heading

8. True Bearing (TB) = Relative Bearing (RL) + True Heading

9. PET/ CP: X=DH/(O+H) where X= Dist to return, D=Total distance, H=GS home, O=GS outbound

PSR or PNR: T=EH/(O+H) where T= Time to PSR, E=Safe Endurance, H= GS home, O=GS outbound

10. Fuel Calculation:

Volume WeightI litre - 0.22 Imp Gals - 0.264 US Gals lIb = 0.454 Kg (454 gms)1 Imp Gal - 4.55 litres - 1.20 US Gals 1 Kg = 2.2lbs1 US Gal- 3.79htres - 0.83 Imp Gals

Volume X Specific Gravity = Weight, therefore:

To convert kgs to litres, divide Kgs by SG and to convert lbs to IMP GALLS, divide Ibs by SG x 10To convert liters to kgs, multiply liters by SG and to convert IMP GALLS to lbs, Multiply IMP GALLS by SG x 10

SFC = Fuel Flow (Kgs/hr) / Groundspeed (nm/hr) SGR= Groundspeed (nm/hr) / Fuel Flow (Kgs/hr)Max Range = Fuel Available x SGR Max Range = Fuel Available / SFC

11. ROD: Rate of Descent (ROD) = Angle x 100 x Ground speed/60

For Radio Nav Maths:

1. R = 1.25 X ( HT + HR), where R= Range, HT=Height of Tx, HR= Height of Rx

2. C = fƴ, where C= Velocity of RF=300X10, f= Frequency in Hertz, ƴ= Wave length

3.

QTE=True track from the Station QDR=Magnetic bearing from the StationQUJ=True track to the Station QDM= Magnetic bearing to the Station

4. 1 in 60 Rule: (Drift or Distance off track / Distance travelled or to travel) X 60 = Drift Angle

5. For VOR, Cone of Confusion = Altitude in NM X Tan 50



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6. PRI=1/PRF where PRI=Pulse Recurrence Interval (in sec, PRF=Pulse Recurrence Frequency (inpps).

For maths convert PRI in microsecond (means in 10), RF = 300 X 10

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