avform

This spreadsheet implements many of the formulae in my Aviation Formulary. (http://williams.best.vwh.net/avform.htm) No significant effort has been expended on protecting against invalid inputs. 1.00 Released under the GNU GPL 12/30/00 EAW. No warranties apply! 1.01 Added sunrise/sunset and wind direction in "three GS" calculation. 1/16/01 1.02 Added DME-DME worksheet. 1.03 Added rhumb direct calculations. 1.03.1 Corrected bug in calculation of longitude of apex- which occured if the initial heading was southerly. 1.03.2 Corrected bug in the calculation of the wind direction in the "wind given three groundspeeds". 1.04 Add rhumb inverse calculations. 1.04.1 Corrected typo in cell J27/Intersection - computing distance 4->6 (Thank you Real Jantzen) 1.05 Corrected bug in std atmosphere sound speed using Fahrenheit. 1.06/7 Added spheroid direct and inverse. Convert lat/lon to UTM and MGRS coords. 1.08 Fixed bug in I/O routines when degrees=0 for latitude or longitude. 1.09 Added spheroid/sphere rhumb direct and inverse to the spheroid page. 1.10 Fixed DME-DME sheet - broken by 1.08 fix. 1.11 Copied formulae on spheroid table fixed. Added options for DD.DDD and DD:MM:SS.SS output. 1.12 Corrected bug in ellipsoidal rhumb lines along parallels. (Thank you Christian Dost) 1.13 Refixed the 1.10 fix. 1.14 Extra distance and bearing rows were incorrectly copied on spheroid sheet. Negative distances for due west rhumblines fixed. 1.15 Sign E/W error in the display of longitudes in column N of the spheroid sheet. 1.16 Fixed bug in rhumb ellipsoid direct calcs for 270 azimuths. (Thank you Will Miles) 1.17 Tweaked accuracy of ellipsoid inverse and direct

Usage Notes: Mandatory inputs are green, optional inputs are yellow, outputs are red. Intermediate results are hidden in uncolored columns,and can be restored with Format|Columns|Unhide. The calculational work is done in Visual Basic modules which you can access with Alt-F11.Units for input/output distances are set on each Great Circles sheet.Lat/lons can be entered in a variety of formats. You must start or end with [NSEW]. Then DD.DD DD:MM.MM DD:MM:SS.SS formats are supported.The separator can be a colon and or any number of spaces. See the first page for examples. The sheets are protected to prevent accidental damage- unprotect with Tools|Protection|Unprotect Sheet

Great Circles Given the location of two points [lat1,lon1] and [lat2,lon2] compute the distance and bearings between them. Show the locations of the apex and nadir of the great circle. Optionally: Compute the locations along the course at intermediate values of latitude, with along track distance (from 1) and the local true course. Compute the locations along the course where it crosses specified parallels, with along track distance (from 1) and the local true course. Compute the locations along the course at specified distances, with the local true course. Additional rows can be added by copying.

Great Circles 2 Given the location [lat1,lon1] and initial bearing, show the locations of the apex and nadir of the great circle thus defined. Optionally: Compute the locations along the course at specified distances, with the local true course. Compute the locations along the course at intermediate values of latitude, with along track distance (from 1) and the local true course. Compute the locations along the course where it crosses specified parallels, with along track distance (from 1) and the local true course. Given a point, find the closest point to it on the great circle, with the along and cross-track distance. Additional rows can be added by copying. Intersection Find the points of intersection (5 & 6) of two great circles. Each circle is defined either by two points on it, or by a point and initial bearing. In the latter case the point cannot be a pole. Choose the input type by entering 1 or 2 in the appropriate box. The method used (http://www.best.com/~williams/intersect.htm) associates each great circle with a unit vector perpendicular to it. The intersections lie in the direction of the cross-product. Garbage will be produced if the two great circles are the same.

DME-DME Given two points at (lat1,lon1) and (lat2,lon2), find the points 3a and 3b at distances d13 and d23 from points 1 and 2- if they exist.

Lat-Lon to UTM & MGRS Convert lat/lon points to UTM and MGRS grid references.

Spheroid table Lookup table of a and f used by spheroid

Spheroid Computes the location of points of known distance and azimuth from an initial lat/lon along the spheroid geodesic ("great circle"). Compares the results to the standard great circle model on a sphere. xtd-err and atd-err are the distances across and along the great circle that the spheroid end-point lies. Computes the distance and bearing between two locations using both spheroid and spherical earth models. Makes corresponding calculations using rhumb lines instead of geodesics. Rhumb Given initial point (lat1,lon1) and a bearing, find the lat/lons of points on the rhumb line at given distances. These distances cannot exceedthe distance to the corresponding pole, where the rhumb line ends. Given two points (lat1,lon1) and (lat2,lon2) find the rhumb line distance and bearing between them.

Wind Unknown Wind Find wind speed and direction, given true airspeed (TAS), ground speed, course and heading. Courses and headings are in degrees. Speeds are in any (but the same) units. Unknown heading and ground speed. Solve for heading and ground speed, given TAS, course and wind- the standard pre-flight planning problem. TAS and wind speed from three ground speeds. This is a way to get your TAS when the wind is unknown but you can determine your groundspeed (eg by GPS). Fly three headings 120 degrees apart- eg 10,130 and 250 degrees. Note the three groundspeeds. From these one can obtain the TAS and windspeed (but without knowing which is which! Hopefully the TAS is the larger of the two!) With exact data, the results are exact, independent of the wind. The method works best in light winds (say less than 20% of the TAS). As the windspeed increases, the method becomes increasingly sensitive to errors in the input. These are minimized if one of the three directions is chosen to be approximately downwind.

StdAtm Find temperature, pressure, density and sound speed as a function of altitude for the 1976 US Standard Atmosphere. Implemented for the first two layers (up to 20km ~ 65617 feet). There are two tables, on the left for heights in feet, on the right for heights in meters. Different units can be chosen by setting the switches at the top of the corresponding columns. Heights can be changed in the first two rows.

Altitude Pressure Altitude - what an altimeter indicates when set to 29.92" Indicated Altitude- what an altimeter indicates when set to the local altimeter setting, equals true altitude at field elevation. Field Elevation- the height above MSL of the altimeter setting reporting point. True Altitude- height above MSL. Density Altitude- height in the ISA (International standard atmosphere- see above) with the same air density. Provides means of computing these quantities.

Sun Calculate the time of local sunset given latitude, longitude and date. Depending on how far the sun is required to dip below the horizon, we have "official sunset", and the end of civil, nautical and astronomical twilight. Enter the time difference to UTC (eg PST = -8 ) to get local time.

Distance and bearing between points lat/lon format 1deg:min:sec nm

latitude1 N33:57.00 distance #VALUE! #VALUE!longitude1 W118 24 00.00 deglatitude2 40 38N bearing 1->2 #VALUE!longitude2 73:47:00W bearing2->1 #VALUE!

UNITS maximum latitude #VALUE!nm=1 km=2 sm=3 at longitude #VALUE!

1 minimum latitude #VALUE! at longitude

along GC

Latitudes of point on GC bearingintermediate longitude W111 intermediate latitude #VALUE! #VALUE!intermediate longitude W110.00 intermediate latitude #VALUE! #VALUE!intermediate longitude 100W intermediate latitude #VALUE! #VALUE!intermediate longitude E00 01 00 intermediate latitude #VALUE! #VALUE!intermediate longitude W120 intermediate latitude #VALUE! #VALUE!

Crossing parallelsintermediate latitude N36:23.65967428 intermediate longitude 1 #VALUE! #VALUE!

intermediate longitude 2 #VALUE! #VALUE!

intermediate latitude N34:00:00 intermediate longitude 1 #VALUE! #VALUE!intermediate longitude 2 #VALUE! #VALUE!

intermediate latitude S34 intermediate longitude 1 #VALUE! #VALUE!intermediate longitude 2 #VALUE! #VALUE!

Points given distance from 1 towards 2nm

distance 100 point latitude #VALUE! #VALUE!point longitude #VALUE!

distance -100 point latitude #VALUE! #VALUE!point longitude #VALUE!

0=DD.DDDD, 1=DD:MM.MMMM,2=DD:MM:SS.SSsm

#VALUE!

along GC

nm#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!

#VALUE!#VALUE!

Lat/lon given radial and distancemaximum latitude #VALUE!

latitude1 N42:36 at longitude #VALUE!longitude1 W0:01:00 minimum latitude #VALUE!bearing from 1 135.0000 at longitude #VALUE!

UNITS nm=1 km=2 sm=3 lat/lon format (0/1/2) 0=dd.dd 1=dd:mm.mm 2=dd:mm:ss.ss1 1

Points given distance from point 1 along-GCnm bearing

distance 1.5 lat #VALUE! #VALUE!lon #VALUE!

distance 1000 lat #VALUE! #VALUE!lon #VALUE!

distance 2000 lat #VALUE! #VALUE!lon #VALUE!

distance -100 lat #VALUE! #VALUE!lon #VALUE!

Latitude of point on GCintermediate longitude W111:00:00.00 intermediate latitude #VALUE! #VALUE!intermediate longitude W110:00:00.00 intermediate latitude #VALUE! #VALUE!intermediate longitude W100 intermediate latitude #VALUE! #VALUE!intermediate longitude E80 intermediate latitude #VALUE! #VALUE!intermediate longitude W120.0 intermediate latitude #VALUE! #VALUE!

Crossing parallelsintermediate latitude N36:23.6597428 intermediate longitude 1 #VALUE! #VALUE!

intermediate longitude 2 #VALUE! #VALUE!intermediate latitude 34N intermediate longitude 1 #VALUE! #VALUE!

intermediate longitude 2 #VALUE! #VALUE!intermediate latitude 34S intermediate longitude 1 #VALUE! #VALUE!

intermediate longitude 2 #VALUE! #VALUE!

Along- and cross- track distance distancealong

latitude N44:30 closest latitude #VALUE! #VALUE!longitude W110:30 closest longitude #VALUE!latitude N43:15.35 closest latitude #VALUE! #VALUE!longitude W115:13.1568863 closest longitude #VALUE!latitude N34:39 closest latitude #VALUE! #VALUE!longitude W116:33.0 closest longitude #VALUE!

0=dd.dd 1=dd:mm.mm 2=dd:mm:ss.ss

along-GCnm

#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!

#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!#VALUE!

distancecross

#VALUE!

Great circle #11

lat/lon format 0=dd.dd 1=dd:mm.mm 2=dd:mm:ss.sslatitude1 N0:00:00 2longitude1 W0:00:00latitude2 N2:00:00longitude2 E10:00:00bearing 90.00

Great Circle #22

latitude3 N0:00:00longitude3 E10:00:00latitude4 N40longitude4 W110bearing 360.00

Intersectionsnm km sm nm km

latitude5 #VALUE! dist 1-5 #VALUE! #VALUE! #VALUE! dist 1-6 #VALUE! #VALUE!longitude5 #VALUE! dist 2-5 #VALUE! #VALUE! #VALUE! dist 2-6 #VALUE! #VALUE!latitude6 #VALUE! dist 3-5 #VALUE! #VALUE! #VALUE! dist 3-6 #VALUE! #VALUE!longitude6 #VALUE! dist 4-5 #VALUE! #VALUE! #VALUE! dist 4-6 #VALUE! #VALUE!

crs 1-5 #VALUE! crs 1-6 #VALUE!crs 2-5 #VALUE! crs 2-6 #VALUE!crs 3-5 #VALUE! crs 3-6 #VALUE!crs 4-5 #VALUE! crs 4-6 #VALUE!crs 5-1 #VALUE! crs 6-1 #VALUE!crs 5-2 #VALUE! crs 6-2 #VALUE!crs 5-3 #VALUE! crs 6-3 #VALUE!crs 5-4 #VALUE! crs 6-4 #VALUE!crs1-3 #VALUE!

=1 defined by two points, =2 defined by one point and (true) bearing

sm#VALUE!#VALUE!#VALUE!#VALUE!

nm=1 km=2 sm=3 DME- DME WorksheetUNITS 1 1 lat/lon format 0=dd.dd 1=dd:mm.mm 2=dd:mm:ss.ss

dist (nm)latitude1 N43:36.00 dist 1->3 120.0000longitude1 W117:51.96latitude2 N43:28.00 dist 2->3 135.4500longitude2 W114:12.00

brg 1->2 #VALUE! dist 1->2 #VALUE!brg 2->1 #VALUE!

latitude3a #VALUE!longitude3a #VALUE!latitude3b #VALUE!longitude3b #VALUE!

brg 1->3a #VALUE!brg 2->3a #VALUE!brg 1->3b #VALUE!brg 2->3b #VALUE!

Latitude/longitude conversion to UTM and MGRS coordinates.Help!!

Latitude Longitude Latitude Longitude Latitude

Deg Min Sec Deg Min Sec DegMin Deg Min Deg

N 34: 15: 18.00 W 88: 36: 0.00 N 34: ### W 88: ### ###N 34: ### W 88: ### ###

<------------------------------------------- Copy Rows 7, 8 or 9 below as desired --------------------------------------------------------------------------------------------------------------------------------------------------->

N 72: ### E 9: ### ###

Latitude/longitude conversion to UTM and MGRS coordinates.

Ellipsoid a 1/fWGS84 6378.137 298.257223563Longitude

Deg MGRS UTM Check MGRS to UTM

-88.600000 #VALUE! #VALUE! #VALUE!-88.600000 #VALUE! #VALUE! #VALUE!-88.600000 #VALUE! #VALUE! #VALUE!

<------------------------------------------- Copy Rows 7, 8 or 9 below as desired --------------------------------------------------------------------------------------------------------------------------------------------------->

9.600000 #VALUE! #VALUE! #VALUE!

Coding MGRS digitsStandard 1 5

Ellipsoid a (km) 1/f

CustomWGS84 6378.137 298.257223563NAD27 6378.2064 294.9786982138NAD83 6378.137 298.257222101WGS66 6378.145 298.25GRS67 6378.16 298.2472IAU68 6378.16 298.2472WGS72 6378.135 298.26Clarke66 6378.2064 294.9786982138GRS80 6378.137 298.257222101Krasovsky 6378.2064 298.3Bessel 6377.39716 299.1528128

WGS84 6378.137 298.2572236NAD27 6378.206 294.9786982

Lat/lon given radial and distance/Distance and bearing between lat/lons- ellipsoid and sphereUNITS nm=1 km=2 sm=nm 1ELLIPSOID WGS84=1, NAD2

#REF! 1SPHERE 1nm/1'=1 FAI=21nm/1' 1lat/lon format 0=dd.dd 1=dd:mm.mm 2=dd:mm:ss.ss

Points given distance and bearing from point 1

latitude1 N42:36.00longitude1 W117:51.96bearing from 1 51.0000

Great Circle Ellipsoid Great Circle Spherenm deg:min fwd azimuth deg:min

distance 100 lat #VALUE! #VALUE! lat #VALUE!lon #VALUE! lon #VALUE!

distance -100 lat #VALUE! #VALUE! lat #VALUE!lon #VALUE! lon #VALUE!

Distance and Bearing between pointsGreat Circle Ellipsoid Great Circle Spheredistance bearing (deg) distance

latitude1 N45:0:0 nm #VALUE! #VALUE! #VALUE!longitude1 W0:0:0 Rhumb Ellipsoid Rhumb Spherelatitude2 N45:0.0001 distance bearing (deg) distancelongitude2 E100 #VALUE! #VALUE! #VALUE!

Great Circle Ellipsoid Great Circle Spheredistance bearing (deg) distance

latitude1 N45:0 nm #VALUE! #VALUE! #VALUE!longitude1 W0:0 Rhumb Ellipsoid Rhumb Spherelatitude2 N45:1 distance bearing (deg) distancelongitude2 E100 #VALUE! #VALUE! #VALUE!

latitude1 N42:36.00 nm #VALUE! #VALUE! #VALUE!longitude1 W117:51.96 Rhumb Ellipsoid Rhumb Sphere

latitude2 N42:36.00 distance bearing (deg) distancelongitude2 W118:04.5799 #VALUE! #VALUE! #VALUE!

latitude1 N42:36.00 nm #VALUE! #VALUE! #VALUE!longitude1 W117:51.96 Rhumb Ellipsoid Rhumb Spherelatitude2 N43:38.9320 distance bearing (deg) distancelongitude2 W116:05.4787 #VALUE! #VALUE! #VALUE!

Lat/lon given radial and distance/Distance and bearing between lat/lons-

Cross and along trackdifference between

Great Circle Sphere GC ellipsoid and sphere Rhumb Ellipsoid Rhumb Spherefwd azimuth nm

#VALUE! xtd-err #VALUE! lat #VALUE! #VALUE!atd-err #VALUE! lon #VALUE! #VALUE!

Great Circle Spherebearing (deg)

#VALUE!Rhumb Sphere

bearing (deg)#VALUE!

#VALUE!Rhumb Sphere

Lat/lon given radial and distance- rhumb lineDist to

latitude1 N 25:47.5900 N. pole #VALUE! nmlongitude1 W80:17.4300 S. pole #VALUE! nmbearing from 1 45.0000

UNITS nm=1 km=2 sm=1

FORMAT lat/lon format 0=dd.dd 1=dd:mm.mm 2=dd:mm:ss.ss1

Points given distance from point 1 nm

distance 100 lat #VALUE! #VALUE!lon #VALUE! #VALUE!

distance 5448.13 lat #VALUE! #VALUE!lon #VALUE! #VALUE!

Distance and bearing between points- rhumb linenm

latitude1 N 33:57 Dist #VALUE! #VALUE!longitude1 W118:24 Bearing #VALUE! #VALUE!latitude2 N 40:38longitude2 W 73:47

UNITSnm=1 km=2 sm=

Wind Triangles

Unknown wind

Course 300 deg Wind Dir #VALUE!Heading 305 deg Wind Speed #VALUE!TAS 130Ground Speed 125

Unknown Heading and Ground Speed

Course 300 deg Heading #VALUE!TAS 130 Ground Speed #VALUE!Wind Dir 8.3 degWind Speed 15

Headwind and Crosswind Components

Wind Dir 60 deg Headwind #VALUE!Wind Speed 20 Crosswind #VALUE!Rwy Dir 30 deg

TAS and Windspeed from three (GPS) ground speeds

GS1 130 TAS #VALUE!GS2 140 Wind Speed #VALUE!GS3 140

HDG1 40 Wind Dir(from) #VALUE!HDG2 160HDG3 280

The results assume that the TAS is in fact greater than the wind speed. If the opposite is the case, swap TAS and Wind Speed. This method becomes more sensitive to measurement errors in the groundspeeds as the wind speed increases. The wind direction is not required to be known. However, if it (approximately) known, choosing one of the three headings to be downwind minimizes the effects of measurement errors.

Units of speeds (knots, mph etc) do not matter as long as they are consistent.

The three headings must differ from each other by 120 degrees (eg 40, 160 and 280)

The results assume that the TAS is in fact greater than the wind speed. If the opposite is the case, swap TAS and Wind Speed. This method becomes more sensitive to measurement errors in the groundspeeds as the wind speed increases. The wind direction is not required to be known. However, if it (approximately) known, choosing one of the three headings to be downwind minimizes the effects of measurement errors.

Units of speeds (knots, mph etc) do not matter as long as they are consistent.

1976 Standard Atmosphere up to 20km (65617 ft)

0 0 4 1 2 1ft C lbs/ft2 slugs/ft3 knots meterHeight Temp Pressure Density Sound Speed Height

1575.42 #VALUE! #VALUE! #VALUE! #VALUE! 1506411111 #VALUE! #VALUE! #VALUE! #VALUE! 333

-500 #VALUE! #VALUE! #VALUE! #VALUE! -4000 #VALUE! #VALUE! #VALUE! #VALUE! -200

500 #VALUE! #VALUE! #VALUE! #VALUE! 01000 #VALUE! #VALUE! #VALUE! #VALUE! 2001500 #VALUE! #VALUE! #VALUE! #VALUE! 4002000 #VALUE! #VALUE! #VALUE! #VALUE! 6002500 #VALUE! #VALUE! #VALUE! #VALUE! 8003000 #VALUE! #VALUE! #VALUE! #VALUE! 10003500 #VALUE! #VALUE! #VALUE! #VALUE! 12004000 #VALUE! #VALUE! #VALUE! #VALUE! 14004500 #VALUE! #VALUE! #VALUE! #VALUE! 16005000 #VALUE! #VALUE! #VALUE! #VALUE! 18005500 #VALUE! #VALUE! #VALUE! #VALUE! 20006000 #VALUE! #VALUE! #VALUE! #VALUE! 22006500 #VALUE! #VALUE! #VALUE! #VALUE! 24007000 #VALUE! #VALUE! #VALUE! #VALUE! 26007500 #VALUE! #VALUE! #VALUE! #VALUE! 28008000 #VALUE! #VALUE! #VALUE! #VALUE! 30008500 #VALUE! #VALUE! #VALUE! #VALUE! 32009000 #VALUE! #VALUE! #VALUE! #VALUE! 34009500 #VALUE! #VALUE! #VALUE! #VALUE! 3600

10000 #VALUE! #VALUE! #VALUE! #VALUE! 380010500 #VALUE! #VALUE! #VALUE! #VALUE! 400011000 #VALUE! #VALUE! #VALUE! #VALUE! 420011500 #VALUE! #VALUE! #VALUE! #VALUE! 440012000 #VALUE! #VALUE! #VALUE! #VALUE! 460012500 #VALUE! #VALUE! #VALUE! #VALUE! 480013000 #VALUE! #VALUE! #VALUE! #VALUE! 500013500 #VALUE! #VALUE! #VALUE! #VALUE! 520014000 #VALUE! #VALUE! #VALUE! #VALUE! 540014500 #VALUE! #VALUE! #VALUE! #VALUE! 560015000 #VALUE! #VALUE! #VALUE! #VALUE! 580015500 #VALUE! #VALUE! #VALUE! #VALUE! 600016000 #VALUE! #VALUE! #VALUE! #VALUE! 620016500 #VALUE! #VALUE! #VALUE! #VALUE! 640017000 #VALUE! #VALUE! #VALUE! #VALUE! 660017500 #VALUE! #VALUE! #VALUE! #VALUE! 680018000 #VALUE! #VALUE! #VALUE! #VALUE! 700018500 #VALUE! #VALUE! #VALUE! #VALUE! 720019000 #VALUE! #VALUE! #VALUE! #VALUE! 740019500 #VALUE! #VALUE! #VALUE! #VALUE! 760020000 #VALUE! #VALUE! #VALUE! #VALUE! 7800

0 C1 F

1 psi2 in Hg3 Hpa, mB4 lbs/ft2

1 slugs/ft32 kg/m3

1 ft/sec2 knots3 m/sec

1 slugs/ft3

2 kg/m3

3 rho0UNITS UNITS

20500 #VALUE! #VALUE! #VALUE! #VALUE! 800021000 #VALUE! #VALUE! #VALUE! #VALUE! 820021500 #VALUE! #VALUE! #VALUE! #VALUE! 840022000 #VALUE! #VALUE! #VALUE! #VALUE! 860022500 #VALUE! #VALUE! #VALUE! #VALUE! 880023000 #VALUE! #VALUE! #VALUE! #VALUE! 900023500 #VALUE! #VALUE! #VALUE! #VALUE! 920024000 #VALUE! #VALUE! #VALUE! #VALUE! 940024500 #VALUE! #VALUE! #VALUE! #VALUE! 960025000 #VALUE! #VALUE! #VALUE! #VALUE! 980025500 #VALUE! #VALUE! #VALUE! #VALUE! 1000026000 #VALUE! #VALUE! #VALUE! #VALUE! 1020026500 #VALUE! #VALUE! #VALUE! #VALUE! 1040027000 #VALUE! #VALUE! #VALUE! #VALUE! 1060027500 #VALUE! #VALUE! #VALUE! #VALUE! 1080028000 #VALUE! #VALUE! #VALUE! #VALUE! 1100028500 #VALUE! #VALUE! #VALUE! #VALUE! 1120029000 #VALUE! #VALUE! #VALUE! #VALUE! 1140029500 #VALUE! #VALUE! #VALUE! #VALUE! 1160030000 #VALUE! #VALUE! #VALUE! #VALUE! 1180030500 #VALUE! #VALUE! #VALUE! #VALUE! 1200031000 #VALUE! #VALUE! #VALUE! #VALUE! 1220031500 #VALUE! #VALUE! #VALUE! #VALUE! 1240032000 #VALUE! #VALUE! #VALUE! #VALUE! 1260032500 #VALUE! #VALUE! #VALUE! #VALUE! 1280033000 #VALUE! #VALUE! #VALUE! #VALUE! 1300033500 #VALUE! #VALUE! #VALUE! #VALUE! 1320034000 #VALUE! #VALUE! #VALUE! #VALUE! 1340034500 #VALUE! #VALUE! #VALUE! #VALUE! 1360035000 #VALUE! #VALUE! #VALUE! #VALUE! 1380035500 #VALUE! #VALUE! #VALUE! #VALUE! 1400036000 #VALUE! #VALUE! #VALUE! #VALUE! 1420036500 #VALUE! #VALUE! #VALUE! #VALUE! 1440037000 #VALUE! #VALUE! #VALUE! #VALUE! 1460037500 #VALUE! #VALUE! #VALUE! #VALUE! 1480038000 #VALUE! #VALUE! #VALUE! #VALUE! 1500038500 #VALUE! #VALUE! #VALUE! #VALUE! 1520039000 #VALUE! #VALUE! #VALUE! #VALUE! 1540039500 #VALUE! #VALUE! #VALUE! #VALUE! 1560040000 #VALUE! #VALUE! #VALUE! #VALUE! 1580040500 #VALUE! #VALUE! #VALUE! #VALUE! 1600041000 #VALUE! #VALUE! #VALUE! #VALUE! 1620041500 #VALUE! #VALUE! #VALUE! #VALUE! 1640042000 #VALUE! #VALUE! #VALUE! #VALUE! 1660042500 #VALUE! #VALUE! #VALUE! #VALUE! 1680043000 #VALUE! #VALUE! #VALUE! #VALUE! 1700043500 #VALUE! #VALUE! #VALUE! #VALUE! 1720044000 #VALUE! #VALUE! #VALUE! #VALUE! 1740044500 #VALUE! #VALUE! #VALUE! #VALUE! 1760045000 #VALUE! #VALUE! #VALUE! #VALUE! 1780045500 #VALUE! #VALUE! #VALUE! #VALUE! 1800046000 #VALUE! #VALUE! #VALUE! #VALUE! 1820046500 #VALUE! #VALUE! #VALUE! #VALUE! 1840047000 #VALUE! #VALUE! #VALUE! #VALUE! 18600

47500 #VALUE! #VALUE! #VALUE! #VALUE! 1880048000 #VALUE! #VALUE! #VALUE! #VALUE! 1900048500 #VALUE! #VALUE! #VALUE! #VALUE! 1920049000 #VALUE! #VALUE! #VALUE! #VALUE! 1940049500 #VALUE! #VALUE! #VALUE! #VALUE! 1960050000 #VALUE! #VALUE! #VALUE! #VALUE! 1980050500 #VALUE! #VALUE! #VALUE! #VALUE! 2000051000 #VALUE! #VALUE! #VALUE! #VALUE!51500 #VALUE! #VALUE! #VALUE! #VALUE!52000 #VALUE! #VALUE! #VALUE! #VALUE!52500 #VALUE! #VALUE! #VALUE! #VALUE!53000 #VALUE! #VALUE! #VALUE! #VALUE!53500 #VALUE! #VALUE! #VALUE! #VALUE!54000 #VALUE! #VALUE! #VALUE! #VALUE!54500 #VALUE! #VALUE! #VALUE! #VALUE!55000 #VALUE! #VALUE! #VALUE! #VALUE!55500 #VALUE! #VALUE! #VALUE! #VALUE!56000 #VALUE! #VALUE! #VALUE! #VALUE!56500 #VALUE! #VALUE! #VALUE! #VALUE!57000 #VALUE! #VALUE! #VALUE! #VALUE!57500 #VALUE! #VALUE! #VALUE! #VALUE!58000 #VALUE! #VALUE! #VALUE! #VALUE!58500 #VALUE! #VALUE! #VALUE! #VALUE!59000 #VALUE! #VALUE! #VALUE! #VALUE!59500 #VALUE! #VALUE! #VALUE! #VALUE!60000 #VALUE! #VALUE! #VALUE! #VALUE!60500 #VALUE! #VALUE! #VALUE! #VALUE!61000 #VALUE! #VALUE! #VALUE! #VALUE!61500 #VALUE! #VALUE! #VALUE! #VALUE!62000 #VALUE! #VALUE! #VALUE! #VALUE!62500 #VALUE! #VALUE! #VALUE! #VALUE!63000 #VALUE! #VALUE! #VALUE! #VALUE!63500 #VALUE! #VALUE! #VALUE! #VALUE!64000 #VALUE! #VALUE! #VALUE! #VALUE!64500 #VALUE! #VALUE! #VALUE! #VALUE!65000 #VALUE! #VALUE! #VALUE! #VALUE!65500 #VALUE! #VALUE! #VALUE! #VALUE!

0 3 2 3 C hPa mB kg/m3 m/secTemp Pressure Density Sound Speed#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!

0 C1 F

1 slugs/ft3

2 kg/m3

3 rho0

1 psi2 in Hg3 Hpa, mB4 lbs/ft2

1 ft/sec2 knots3 m/sec

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Alt Setting Unit 1(1=in Hg 2=hPa)

Pressure altitude from Indicated Altitude etc.

Indicated altitude 1000 feet Pressure Alt 1000Altimeter Setting 30.15 in Hg Altimeter Setting 30.15 in HgPressure Alt ### feet Indicated altitude ###

Density altitude from pressure altitude and temperature

Pressure altitude 8000 feetTemperature (C) 18 CDensity altitude ### feet

Density altitude from indicated altitude, altimeter setting and temperature

Indicated altitude 7906 feetAltimeter Setting 29.82 in HgTemperature (C) 18 CDensity altitude ### feet

True Altitude

Indicated Altitude 8000 feet Indicated Altitude 8000 feet Indicated Altitude 8000 feetField elevation 5000 feet Field elevation 5000 feet Field elevation 5000 feetOAT 5 C OAT 5 C OAT 9 CISA deviation 4 C True Altitude ### feet Temp at field 15 CTrue Altitude ### feet True Altitude ### feet

It is not easy to get an accurate true altitude (actual altitude above MSL) from an altimeter. You needto know not only the pressure at some point of known elevation below you (satisfied by having the local altimeter setting), but also the vertical profile of the air temperature between that point and your aircraft. Setting the altimeter to the local altimeter setting compensates for non-standard surface pressures.The altimeter then reads "indicated" altitude, which would be true altitude only if the temperature profile was that of the "standard" atmosphere. Deviations of the actual air temperature from standard causes the pressure to change with altitude at non-standard rates. In the end, what matters is the verticallyaveraged deviation from standard temperature, "isadev". This could be obtained from a radiosonde balloon sounding, if one were available- one would then use the first of the three calculation methodsto obtain true altitude. In the second column, the only available temperature is the OAT at altitude, and the assumption is made that below you, the lapse rate is standard (ie 2C/1000' as in the standard atmosphere). In the third column, one also has the temperature at the field (the altimeter setting location) available,and the lapse rate between the field and the altitude is assumed constant. In the fourth column, the temp at the field is available, but not the temperature at altitude (useful for precomputation). Below the inverse of the computation in (4) is made, finding indicated altitude, given true altitude. To the extent these latter assumptions are correct, the result will accurate...

True Altitude 8000 feetField elevation 5000 feetTemp at field 15 CIndicated Altitude ### feet

Indicated Altitude 8000 feetField elevation 5000 feetTemp at field 15 CTrue Altitude #VALUE! feet

Sunrise and sunset

deg minLatitude N40: 54.0000 Date 06/25/90Longitude W74: 18.0000 Timezone -4

sunrise sunsetUTC local UTC local

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