Hi Dan.
To save Eniclyth any more work, I’ll try. But I hate trying to explain things I don’t really know a lot about though!!
“I guessed that at about FL350 the A340 would have 7% compressibity i.e. cd tot = cdo + cdi +cdcc = 1.07(cdo + cdi).”
The coefficient of drag for the aircraft (CD) is the sum of the parasitic drag coefficient (CDO), induced drag coefficient (CDI) plus the compressibility drag coefficient correction (CDCC). I’ve used capitals to designate that we’re referring to a complete aircraft, not to just an airfoil section.
“cdtot is the sum of all the wetted areas plus a fiddle factor for protuberances times a finishing coefficient, usually 0.0036. This area is then divided by the wing area to give cdo. I usually add the trim drag coefft into cdo, for example Boeing quote 0.0144 for their 744 cdo but I take 0.015 which is spookily accurate when it come to fuel consumption.”
The above paragraph is unfamiliar to me.
**Eniclyth, can you expand a bit please?***
I’ve always taken the total CD as the sum of the three coefficients of drag, using a representative area as simply the wing area, ie Total Drag D = .5 * rho * V squared * wing area * CD
“cdi the induced drag is the square of the lift coefft divided by pi x aspect ratio x Oswald's "e". For the DC10 "e" was 0.83, the 744 "e" is 0.86 and the 777 "e" is 0.89 about as high as you can go.”
Perhaps I’d add that the aspect ratio and e factor are both in the denominator, ie CDI=(CL squared)/(pi * e * AR)
The math that produced the above was dependant on a perfectly elliptical lift distribution along the span, ie zero at the tips, increasing elliptically to the root. The spitfire is often cited as an example, but I believe it only had an elliptical wing planform, and not an elliptical lift distribution, although the planform would have helped it attain a near elliptical distribution. Some factors that reduce this perfect elliptical distribution are changing airfoil shape across the span (chord and camber), twist, and of course straight leading and trailing edges and tips (simpler to manufacturer). And so…. The Oswald efficiency factor e was included to allow for these real life affects. Typically ranges as per E’s post.
“cdo for a DC9 is 0.02, a 737 0.0176, a 777 0.013. In cruise when lift coeffts go above 0.55 the aircraft tends to have little buffet margin left so the highest first cruise altitude is usually the density altitude where cl = 0.55 for the chosen speed. likewise when weight falls off in cruise you will step up when the new cl is 0.55. eventually you cannot step up any more and cl rolls off. when it gets down to about 0.4 compressibilty has dropped from about 7-7.5% to 5-6%, speed and weight and altitude dependent. 737NGs, 777s, A330/340s can run at L/D of 19-ish when cl is 0.5-0.55; 744s 17.5. “
I think the above is straight forward
“specific fuel consumption is 0.65lb/lb-hr for 737NG at FL350 cl 0.5-0.55, 0.59 for a 744 and 0.57 for a 777. the distance you travel in cruise is (v knots/sfc) x L/D x natural logarithm(start weight/finish weight). So your A340-500 at 480 kts FL350 will travel 20.5 nm per 1000lb from the equation distance = (480/.587)*19.55*0.001283 assuming I am right in guessing compressibility at 7%. I made cl 0.522 and cdtot 0.0267 which is the 19.55 term in above equation. It feels right to me but I can only speak with authority on the 777 and the 744.
NB I forgot to say what weight didn't I ?...780000lb!!! When the weight falls to 480000lb expect 28.2nm/1000”
Above is where the math starts. **I think** Enicalyth has figured Drag from .5 rho S CD Vsquared. In cruise, this equals thrust required. Then knowing lbs of fuel burned per lb of thrust generated, per hour, he figures out fuel consumption. I didn't think one needed Breguet’s range formula for a jet aircraft but E's use on natural logs perhaps indicates so. I’ve yet to find a quiet few hours to do my math to come up with E’s numbers.
If you’ve got a calculator in the cockpit, you’ve really no need for flight manual data.
Make any sense Dan?
Enicalyth, sorry you got no reply on your 737 data request. Of course, I'd of helped, but I figured C172 data wasn't what you needed.
Hawk