B2707SST From United States of America, joined Apr 2003, 1384 posts, RR: 58 Posted (11 years 7 months 1 week 2 days 6 hours ago) and read 12550 times:
A question for all you aerodynamicists out there:
I'm working on a project which entails converting several aircraft performance manuals into Excel. The goal is to allow a user to enter the desired payload and range in a spreadsheet automatically calculates the appropriate takeoff weight, fuel consumption, and flight time. For takeoff, departure, climb, descent, and landing, this isn't a problem, as fuel consumption, time, and distance are presented graphically. I pick several representative points and have Excel give me a quadratic equation for the curve.
For the cruise segment, specific range curves relating specific range (nm/kg) and Mach number for a given cruising altitude are the only data presented. Time and distance can be calculated with the selected cruise Mach number, distance to top of descent, and ISA values for Mach 1. To calculate fuel consumption:
Given the calculated true airspeed (assuming zero wind), rearranging to solve for gal/hr gives a point estimate of fuel flow at a particular weight. However, the aircraft's weight is changing constantly, so I can't just multiply by the hours spent at cruise.
The specific range curves are only given at discrete weights. I'd like to find a continuous function that describes fuel consumption as a function of weight, altitude, and Mach number. Is there a way to do this? Specifically, I'm trying to find a way to interpolate between the various SR curves, but am not having much luck. Any suggestions?
Another manual shows specific range versus aircraft weight at a given Mach number, which is much easier to work with!
PS - This is not for a real airline, so absolute accuracy is not required.
QantasA332 From Australia, joined Dec 2003, 1500 posts, RR: 22
Reply 1, posted (11 years 7 months 1 week 2 days 3 hours ago) and read 12406 times:
In my studies, I haven't come across any functions that directly relate fuel consumption to weight/altitude/Mach number, now that I think about it! Perhaps a fellow 'A.net aerodynamicist' knows of them, if they do indeed exist...
Phollingsworth From United Kingdom, joined Mar 2004, 825 posts, RR: 4
Reply 3, posted (11 years 7 months 1 week 1 day 23 hours ago) and read 12323 times:
You want is an engine map. SFC won't change with weight, but will with Mach and altitude. The problem is the engine will be operated off design. I don't have Mattingly in-front of me. But with SFC you can use the cruise-climb Breguet range equation. For cruise, Thrust=Drag, the equation becomes:
Wfuel/Wstart = 1 - exp[-(SFC * Range)/(V * L/D)]
where L/D is the lift to drag ratio. If you use the SR and the starting weight you can back out the SFC and L/D it the points you are given. This should get you your engine deck. Make sure your units are consistent.
As for getting a simple equation out of this, you will need to perform a multiple linear regression. You may need to use another tool as it seems Excel only does single regression. Multiple is not all the difficult and there are probably a number of references on the web. I could also do the regression for you if you sent me the data table.