PPRuNe Forums - View Single Post - Mathematical functions in performance diagrams
Old 27th May 2021, 09:42
  #19 (permalink)  
Trim Stab
Join Date: Feb 2010
Posts: 1,754
I get the impression you are coming at the problem from a certification point of view, which is not really the objective of the OP or indeed myself.

In my case I fly a collection of DA42MPPs for aerial work. There are three different engine-types in our fleet (CD-135, CD-155, and AE300), and multiple different aircraft appendages (fat square nose for survey camera, a long bellypod for lidar work, a nose with EO/IR camera (which sometimes as to be flown with even draggier cover on ferry flights), sometimes we have a scotty uplink dome on the back, sometimes radar or GSM intercept equipment on the underside, and other combinations. All of these variants have different performance. When we get a new variant, I need to work out quickly a performance model as I need to fly them on a long delivery trip, usually through Africa where there can be long distances between airfields, and one occasion to South America - and there is no usable data in the FOM. To do this I just select the data sets of "nearest" previous configurations that I have flown previously (these have around a thousand real observed data points throughout flight and engine performance envelop) -i and build a new approximate model. In an hour or so of test flying, I can get enough real observed performance to massage the data sets into a more precise model (there are good statistical tools in spreadsheets to do this). I then have an accurate enough model to route-plan so that know what power setting I will have to fly to achieve any given leg in quickest time but arrive with regulatory fuel reserves. As I fly a new variant I keep adding real observed data to the model, and prune out the old data. This eventually leads to a highly accurate model.

Also for survey and ISR flying, FOM performance data is not relevant. Eg for a survey profile, I may need to fly 250nm to the AOI, then descend to survey GPS elevation, fly the AOI at a constant groundspeed, then fly back and arrive with regulatory minimums. This sort of profile is really impossible to plan efficiently without a decent performance model. But with the accuracy of the data I now have, I can make a fuel plan in around five minutes prior to a flight, inputting just winds, QNH, temps and pressures from Windy, and then know in advance exactly what power settings and FLs I need to select on outgoing in incoming legs, exactly what PA I need to descend to for the survey, what power setting I will need to achieve the correct groundspeed, and exactly how long I can spend on the productive survey flying. When I fly the profile, I get back to base within a few minutes of predicted time, and within 2% of my predicted final reserve fuel. It is thus greatly improves the productivity of our aircraft per engine hour.

I can even adapt the methodology quickly to entirely new types - a few years ago we got an AS350 for some survey work with external LIDARs and cameras bolted to the skids - within just a few hours of test-flying to gather observed data I could adapt the model to the helicopter.

I presume you are referring to the cited example. Certainly a simple presentation but not much in it will be linear, I fear. Generally, in my experience, one is at risk going beyond a third order equation ... nor is that necessary. If it appears to be so, one needs to segment the line data.

I don't see why there should be a "risk" - as long as you do not attempt to extrapolate outside of your data set. For my model of power setting as a function of IAS, Density Altitude and mass I use fourth order of all three variables. R comes out at 0.98. I don't see any harm in using higher orders - it just increases accuracy. I am using fifth order for some of the other parts of the model (particularly engine performance at high altitudes) For the OPs example, I would probably use third order for all three variables - but suggested he start with lower orders if he is not familiar with LINEST function.

This comment causes me some concern as it infers the use of needlessly high order equation simulations. One needs to keep in mind that extrapolation of certification data is a no-no and would be difficult to defend in court in the extreme.

I am not using my calculations for certifications and it is purely for my personal use, so no chance of ending up in court! But I build into the model safeguards to make it impossible to accidentally extrapolate outside of the observed data set. As long as you stay within your data set, higher orders greatly increase accuracy. Out of curiosity I have got data right through the flight envelope and the curve near the bottom of the lift/drag curve, or near the stall would be really inaccurate if I did not use high orders.
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