Witch Posted July 4, 2006 Report Share Posted July 4, 2006 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. Quote Link to comment Share on other sites More sharing options...
niftyben Posted July 4, 2006 Report Share Posted July 4, 2006 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... Quote Link to comment Share on other sites More sharing options...
Witch Posted July 4, 2006 Author Report Share Posted July 4, 2006 Is the temperature in celsius or farenheit? Quote Link to comment Share on other sites More sharing options...
joker Posted July 4, 2006 Report Share Posted July 4, 2006 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°KActual 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 Quote Link to comment Share on other sites More sharing options...
500E Posted July 4, 2006 Report Share Posted July 4, 2006 Joker Heavy number thing, will use graphs\charts my brain would explode Quote Link to comment Share on other sites More sharing options...
Gomer Pylot Posted July 4, 2006 Report Share Posted July 4, 2006 Ed Williams' site is one of the web's great resources, and should be bookmarked by every pilot. Quote Link to comment Share on other sites More sharing options...
Witch Posted July 5, 2006 Author Report Share Posted July 5, 2006 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 Quote Link to comment Share on other sites More sharing options...
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