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Algorithms


Witch
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Now I know everyone here has seen the density and pressure altitude charts-O-many, but has anybody ever seen the algorithm, or mathmatical formula, used to make these charts?

 

Reason you ask? I'm programming a Visual Basic application-or trying to-to do all the math for the Robbies. I've done it before with the Body Surface area of a human. Finding that algorithm was a pain to say the least. I finally found it in a text in the math library at the U of O.

 

Anyway, anyone know where I might find these elusive mathmatical formulations?

 

And don't tell me I spelled mathmatical wrong either. I'm a lover, not a dishwarsher.

 

Later.

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Warsh this...

 

 

altitude - (local altimeter - 29.92)1000feet = Pressure altitude

 

Wait, wait. There's more...

 

current temp - (15º - 2º(Altitude/1000)) = degrees difference

 

(degrees difference * 120feet) + Pressure altitude = Density Altitude

 

 

 

 

 

 

 

Or you can look at a chart...

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Is the temperature in celsius or farenheit?

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The following contains some formulae concerning altimetry and the standard atmosphere (1976 International Standard Atmosphere).

 

At sea-level on a standard day:

 

the temperature, T_0 = 59°F = 15°C = 288.15°K (°C=Celsius °K=Kelvin,

T°K=T°C+273.15)

the pressure, P_0 = 29.92126 "Hg = 1013.250 mB = 2116.2166 lbs/ft^2

= 760.0 mmHg = 101325.0 Pa = 14.69595 psi = 1.0 atm

the air density, rho_0 = 1.2250 kg/m^3 = 0.002376892 slugs/ft^3

The standard lapse rate is T_r= 0.0065°C/m = .0019812°C/ft below the tropopause h_Tr= 11.0km= 36089.24ft

 

Above the tropopause, standard temperature is T_Tr= -56.5°C= 216.65°K (up to an altitude of 20km) Standard temperature at altitude h is thus given by:

 

T_s= T_0- T_r*h (h < h_Tr)

= T_Tr (h > h_Tr)

= 15-.0019812*h(ft) °C (h < 36089.24ft)

 

--------------------------------------------------------------------------------

 

Variation of pressure with altitude:

 

p= P_0*(1-6.8755856*10^-6 h)^5.2558797 h<36,089.24ft

p_Tr= 0.2233609*P_0

p=p_Tr*exp(-4.806346*10^-5(h-36089.24)) h>36,089.24ft

 

--------------------------------------------------------------------------------

 

Variation of density with altitude:

 

rho=rho_0*(1.- 6.8755856*10^-6 h)^4.2558797 h<36,089.24ft

rho_Tr=0.2970756*rho_0

rho=rho_Tr*exp(-4.806346*10^-5(h-36089.24)) h>36,089.24ft

 

--------------------------------------------------------------------------------

 

Relationship of pressure and indicated altitude:

 

alt_set in inches, heights in feet

P_alt_corr= 145442.2*(1- (alt_set/29.92126)^0.190261) or

P_alt_corr= (29.92-alt_set)*1000 (simple approximation)

P_alt= Ind_Alt + P_alt_corr

 

--------------------------------------------------------------------------------

 

Relationship of pressure and density altitude:

 

D_Alt=P_alt+(T_s/T_r)*(1.-(T_s/T)^0.2349690)

(Standard temp T_s and actual temp T in Kelvin)

An approximate, but fairly accurate formula is:

 

D_Alt=P_Alt+118.6*(T-T_s)

where T and T_s may (both) be either Celsius or Kelvin

 

--------------------------------------------------------------------------------

 

Density altitude example:

 

Let pressure altitude (P_alt) be 8000 ft, temperature 18°C.

 

Standard temp (T_s) is given by

 

T_s=15-.0019812*8000=-0.85°C = (273.15-0.85)°K=272.30°K

Actual temperature (T) is

 

18°C=(273.15+18)°K=291.15°K

 

Density altitude (D_Alt) = 8000 +(272.30/.0019812)*(1-(272.30/291.15)^0.2349690)

= 8000 + 2145 = 10145ft

or approximately:

 

Density Altitude=8000 +118.6*(18+0.85)=10236ft

 

 

OK, I would love to be able to claim that I had worked all those formulae out, but alas even I couldn't do that! So even though I don't think you can copyright a mathematical formula I'll give credit where credit is due.

 

These are published on a website linked below:

Aviation Formulary by Ed Williams

 

I love those formulae, especially the spherical geometry ones. I made myself a flight planner, which would work out the distances between two lat longs, the wind drifts, PNR, sunset / sunrise etc..etc.. Most of the formulae I got from that site.

 

As for aircraft specific ones, they are much more difficult. I don't even know if they manufacturers have any formulae per se, as I think their numbers are from trial and error. If anyone knows where I can find algorithms for S76 performance data I'd be chuffed!

 

Have fun.

 

Joker

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Joker, I saw that and my brain spilled out my ears. Now I wished I had paid more attention in math and science class.

 

Ok, I think I can work that into some sort of code. That BSA nomogram wasn't that hard, maybe this one won't be either. We'll see.

 

Anyhow, thanks fer the info.

 

Later

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