# Fuel efficiency for endurance and range in jet aircraft...

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I've been trying to piece together a flight performance advisory display for a project, and I'm having some difficulty..I've been trying to KISS it by using Carson's factor of 1.316 to derrive what I need based on D/Lmax, but the numbers are not looking good, probably because this was never intended to be used for high performance jets.I've got:Best endurance mach = D/Lmax / 1.316 (and then converted to mach)Best Range mach = D/Lmax (and then converted to mach)What I really NEED is: 1) best endurance and range speeds at the current altitude and weight.2) best projected endurance and range speeds at the best projected operating altitude based on the current weight.I've been all over the net trying to find formulas I can actually understand, but I keep running into equations I simply can't read well enough to code out. Does anyone know a site with useful formulas written as basic, easy to understand expressions?Thanks,--Jon

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Hello Jon,Um ... formulas you actually understand. Perhaps you can give me a list of those :-).At max endurance (and range for piston prop a/c) Profile drag equals vortex induced drag.CD = CDp + CDi so at max endurance CDp = CDiCDp is a .air file parameter and CDi = 1/(pi*AR*e) also parameters.For max range with a pure jet and NO mach drag effects the speed is sqrt(sqrt((2)) = 1.316 higher.Actually your formulas were wrong. Max endurance is where L/D is max and max jet range is where MN * L/D is max.You could get a book which explains this and then you could figure out the code.Have you seen:http://www.lerc.nasa.gov/WWW/K-12/airplane/short.html athttp://perso.wanadoo.fr/hsors/FS_Soft/aerolinks.htmlwhere there is other info?

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>I've been trying to piece together a flight performance>advisory display for a project, and I'm having some>difficulty..>>I've been trying to KISS it by using Carson's factor of 1.316>to derrive what I need based on D/Lmax, but the numbers are>not looking good, probably because this was never intended to>be used for high performance jets. In fact, I display Rs and Es (Specific Range and Specific Endurance) in my XML Jet Test display. I also display current Range and Endurance, both to empty, and with some reserve. Best Endurance for a jet is at or near max of L/D. Best Range (mileage) is theoretically occurs when Cdi = Cdp/3. Which results in a ratio of 2^1/3 = 1.26 between Speed, Min Drag and Speed, Best Range. I used 'speed' above. CAS is implied, though EAS might be more appropriate. Regardless, my Jet Transports give best range around IAS = 1.22 IAS min/drag. I figure it's due to compressability effects becoming significant at even the low FL's and Mach numbers the above applies to.>What I really NEED is: >1) best endurance and range speeds at the current altitude and>weight. Best Range is especially difficult to work out. Boeing explains how in their "Jet Transport Performance Methods" manual. One still needs curves for the actual AC. Though, they also give a pair of constants for their B707, 727, 747, etc. which can be used in simple formulas to determine range based on TO weight. They appear to apply only to LRC Mach and one still has to fly the AC on the optimum flight profile.>Thanks,>--Jon Even the formulas developed for prop AC over 70 years ago assume constant engine and prop efficiency. So, are only approximations of actual performance. Ron

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Thanks very much for the replies guys. Very useful and much needed info there. The NASA link was outstanding too, I found everything I could possibly need right there, explained in terms which even and idiot like me can understand.This one is loaded with equations I can use. http://www.grc.nasa.gov/WWW/K-12/airplane/sumran.htmlSince I'm also doing a flight model, I have all the coefficients I need to do the calculations.--Jon

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Oh one more question if you don't mind:In order to determine the Cl portion of the Cl/Cd (L/D), I need to poll the simulation dynamically for AoA, correct? Since the Cl will change based on AoA. But the only formula that seems to apply in this case is something called the "Thin Airfoil Theory", which is expressed as Cl = 2 * pi * AoA(radians). But this does not account for wingtip Di. Is there a way to increase the acuracy of Cl using some .air value for wingtip Di?Thanks again--Jon

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Hello Jon,make this (e) less than unity:7=12,int32,*Induced Drag Constant * 655367h=Cdi at Cl=1: 1/e*Pi*Aspect_Ratio|e=Efficiency factor:0.5 - 0.9 (Oswald*Planform)|AR=b^2/S (geometrical)|1101:50 must be set correctlyAlso see the Decode Forum linked from Herve's site when it comes back.http://www.avhistory.org/scripts/MegaBBS/f...w.asp?forumid=5Ian

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