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ISA Standard Atmosphere - Graph paper

Because graph paper with relative density of the "Standard Atmosphere" in abscissa is painful to find in stationeries, I made a small program that generates such sheets based on the standard equations and which can printed out with Adobe Acrobat Reader.


The repartition of the divisions on the abscissa is proportional to the variation of the density ratio versus the altitude. Sigma is defined by the standard equations below for each of the six atmospheric layers:

Density ratio: Sigma =  RhoAlt / RhoSL (SigmaSL = 1)

SI Metric units Imperial units
Layer 1
Sea Level to 11'000 [m]

Sigma = (1 - Alt/44329) 4.255876

Sea Level to 36'089 [ft]

Sigma = (1 - Alt/145442)4.255876

Layer 2
11'000 [m] to 20'000 [m]

Sigma = 0.297076 * e( (10999 - Alt)/6341.4 )

36'089 [ft] to 65'618 [ft]

Sigma = 0.297076 * e((36089-Alt)/20806)

Layer 3
20'000 [m] to 32'000 [m]

Sigma = (0.978261 + Alt/201010)-35.16319

65'618 [ft] to 104'987 [ft]

Sigma = (0.978261 + Alt/659515)-35.16319

Layer 4
32'000 [m] to 47'000 [m]

Sigma = (0.857003 + Alt/57944)-13.20114

104'987 [ft] to 154'199 [ft]

Sigma = (0.857003 + Alt/190115)-13.20114

Layer 5
47'000 [m] to 51'000 [m]

Sigma = 0.00116533 * e( (46998-Alt)/7922 )

154'199 [ft] to 167'323 [ft]

Sigma = 0.00116533 * e((154200-Alt)/25992)

Layer 6
51'000 [m] to 71'000 [m]

Sigma = (0.79899 - Alt/184800)11.20114

167'323 [ft] to 232'940 [ft]

Sigma =(0.79899 - Alt/606330)11.20114

Link to an useful Standard Atmosphere Calculator

You will find in the following Adobe Acrobat PDF files, several sets of sheets to meet various requirements such as paper format and orientation, or the units which are used. Each set contains 6 sheets with altitude ranging from Sea Level to layer 1, to Sea Level to layer 6. The ordinates are in millimeters or tens of inches. By using good quality paper with a good resolution printer, the printouts will be of quite good quality. In fact, the final quality only depends on the paper and the printer which are used.

(Right click to save the files onto your hard disk. About 80KBytes each)

A4 paper, Landscape, SI metric units : atmos_A4L_SI.pdf
A4 paper, Portrait, SI metric units : atmos_A4P_SI.pdf
A4 paper, Landscape, Imperial units : atmos_A4L_Imp.pdf
A4 paper, Portrait, Imperial units : atmos_A4P_Imp.pdf
US Letter paper, Landscape, SI metric units : atmos_LetterL_SI.pdf
US Letter paper, Portrait, SI metric units : atmos_LetterP_SI.pdf
US Letter paper, Landscape, Imperial units : atmos_LetterL_Imp.pdf
US Letter paper, Portrait, Imperial units : atmos_LetterP_Imp.pdf

IMPORTANT: A4 sheets are to be printed solely on A4 paper, and US Letters ones are to be printed on US Letter paper! To obtain an accurate output with correct proportions, be sure to uncheck the "shrink to fit" and the "auto-center" options, as well as any other size adjustment that Adobe Acrobat Reader could do. You might need to check how your printer handles the margins and set it to allow the whole content to be printed. Take care of any option that could change the proportions or re-center the document.

Get Acrobat Reader

Eric Voisard

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