# How to perform a "first principle" performance calculation?

I am a PhD student on flight dynamics and control. This week I was given an assignment to do some research on methods of aircraft performance calculation. After some search on the Internet, I found that traditional methods depended on tabulated data on the airplane flight manual (APM), and about a decade ago, both Boeing and Airbus started to do performance calculation using "first principle" method.

I read on an Advisory Circular document that provides a definiton of this method:

A calculation using basic parameters such as lift, drag, power or thrust, etc. with the equations of motion. (AC No: 25.1581-1, Change 1.)

And an Airbus document gives some explanation on this method:

The next step in the performance calculation process, referred to as OCTOPUS (Operational and Certified Takeoff and landing Universal Software), not only offers the same advantages as TLC but also drastically changes the performance calculation method. It is no longer based on pre-computed data, but uses the “first principle” mode that allows a real on-time computation to benefit from a higher takeoff weight. Instead of smoothed pre-computed performance results, the OCTOPUS performance database contains all the airplane and engine characteristics, enabling performance computation based on physics equations. In addition, OCTOPUS introduces a new and improved takeoff chart format, with its use of multi-configurations and influences. ("Getting to Grips with Aircraft Performance", Airbus)

However, I have not found any paper or report on this topic. Is there anybody out there who could help by offering some details of this method, or, providing some references?

The equations of motion are the easy part. In essence, you look at all forces affecting the aircraft (lift, thrust, drag, weight) and balance them with proper control settings (elevator, throttle) and accelerations (if thrust > drag, the forward acceleration is (thrust - drag)/mass).

This you repeat over and over, one timestep at a time. The next timestep sees the aircraft at a new speed, which you get by multiplying the forward acceleration with time, and altitude if the climb speed is nonzero. The new, changed mass is the old mass minus the fuel consumed during the last timestep. And so on. This involves coordinate translations as some forces are defined in the aerodynamic and others in the airplane coordinate system. NASA Langley has published an open source software which does exactly that (LaRCsim).

For very high precision you can even model the inertias and calculate which aileron deflection is needed to arrive at a desired roll rate in the next timestep, but even without that you will get very precise data if the forces are correct.

The hard part is to arrive at the correct forces. We have had several questions here asking for the aerodynamic data of modern airliners, and every time the answer was: They are kept secret. You need to do your own analysis, and it is the same with engine data. Older methods relied on tabulated data, but in order to calculate conditions outside of the validity of the table they need to calculate the forces analytically. To get an idea what parameters need to be considered, look at this answer about the Boeing SCAP module.

However, even some crude assumptions can get you very close to the real result.

• I find that basic lift/drag data is surprisingly accurate for (flight) performance in Obert’s “Aerodynamic Design of Transport Aircraft”, however I haven’t found similar open data on engine performance, mainly thrust/fuel flow relation. I am not sure how close one can get by simulation of the engine gas dynamics equations using similar open data. For (certified) takeoff and landing performance, additional considerations come into play, too, as that depends also on spoiler, brake and even test pilot characteristics. Dec 30, 2017 at 16:57
• Thank a lot, Peter. I am familiar with the modelling of aircraft dynamics and flight simulation since they are required for the validation of the control system design. As for the modelling and the subsequent performance calculations/simulations, aerodynamic data and the engine model are indeed crucial, though not easy to obtain (if not unattainable). For now, I am trying to figure out how to perform a "first principle" performance calculation, i.e. the procedures and methods, etc. And actual calculation of a specific type of aircraft is out of my current scope. Jan 1, 2018 at 6:01
• Yesterday I searched the web and found that Jeppesen and Boeing both proposed a performance calculation tool (Jeppesen/Boeing), in Jeppesen's brochure, it is explicitly stated that 'first principle' method is employed. I guess it is the same case with the Boeing product, since 'real-time' calculation is included as a feature. Jan 1, 2018 at 6:36
• I also searched Engineer Village and Web of Knowledge (two big journal database), however, I could not find any academic paper or report explaining the specific techniques required for such calculations, which seems weird. I wonder if it is already covered in classical flight mechanics textbooks. Maybe I need to hit the books again... Jan 1, 2018 at 6:36
• @Tomas: Yes, textbooks should cover the topic well. The Internet cam too late, so what you need is still mostly in books. For a database on drag and lift I recommend the books by Sighart Hoerner. However, you should indeed pick a specific type or create a generic one. In the end you need the actual forces, masses, thrust and fuel consumption data. For engine simulation use Gasturb - I always produced an engine deck from it and scaled that up and down when parameters changed in my models. Jan 1, 2018 at 7:55

It's the aerodynamic and inertial data also used in Full Flight Simulators (FFS). Both Airbus and Boeing provide the data package for Level D FFS, where at the beginning of the flight the instructor enters payload, CoG, fuel load etc and the resulting aircraft dynamics are used for simulating flight.

You could have a look in open source PC flight simulator software such as FlightGear, which has aerodynamics and flight dynamics models for both A320 and B737. Simplified and not certified of course so no reference to actual fidelity, but they should get a reasonable result if the simulated dynamics are in the ballpark.

• Thanks for your answer. So I guess you mean the main difference lies in the data utilized to perform the calculation, whereas the basic calculation method is the same, either in the traditional way based on tabulated data, or the 'modern' way using "first principle" method. Is that the case? Jan 1, 2018 at 6:42
• "A calculation using basic parameters such as lift, drag, power or thrust, etc. with the equations of motion". The "equations of motions" bit is clear, the "basic parameters" can cause a bit of confusion in this. The old method reference consisted of tabulated data. The First Principle uses the result of equations of motion as reference. Both the old method and the First Principle method can use the same aerodynamic data as input, probably also in the form of tabulated data, with the First Principle delivering much higher granularity and accuracy. Many more Degrees of Freedom available. Jan 1, 2018 at 6:54
• I understand your point, using equations of motion as an analysis tool provides more fruitful results and capabilities in performance calculation. Have you ever read any paper or report explaining specifics of using the First Principle Method? Jan 1, 2018 at 7:02
• I am familiar with the same methods from working on the source code for aerodynamics, engines and flight dynamics models of Full Flight Simulators. I haven't read a paper explaining specifics of First Principle, however from the definition I understand that it is exactly identical to FFS. Jan 1, 2018 at 7:12
• Your work sounds cool! Thank you for your reference, I'll go to find some papers in the FFS area to read. Jan 1, 2018 at 7:46

The only way to properly do a „first principle“ calculation is by (numerically) evaluating the basic equations of motion found in flight mechanics text books. Unfortunately this requires a lot of information on aircraft characteristics (e.g. drag data or engine parameters) that generally aren’t published for most aircraft due to their business sensitivity. Sidenote: Estimates can get you pretty far!

Manufacturer provided software like OCTOPUS (Airbus) or BPS (Boeing) contains a method of numerically evaluating the (often simplified) equations of motion and the required aircraft databases but aren’t publicly available to the best of my knowledge.

• Yeah, I understand that to achieve a certain degree of accuracy, information as aerodynamic coefficients and engine models are necessary. But for now, I am interested in the specific techniques/procedures required to carry out "First Principle" calculations. Yesterday I searched Engineer Village and Web of Knowledge (two big journal database), however, I could not find any academic paper or report explaining the specific techniques, which seems weird. I wonder if it is already covered in classical flight mechanics textbooks. Jan 1, 2018 at 6:32