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I'm risking a question that might be "opinion based", but I hope it will not be seen as that.

This question is touched upon in the following questions:

What are the differences between PC and professional simulators?

Is this opinion on personal computer flight simulators too strict or is it actually true?

What are the limitations of the aerodynamics modelling used in flight simulators?

However, they fail to answer what I'm asking here, even if some particular things are discussed, such as stating that the coefficients are a mixture of CFD, wind tunnel data and flight test data, or that gust loads can be modeled with Markov matrices. However, no flight model package or system is named that I could see.

For racing simulators, or car simulators, simulators that are accurate are sometimes referred to as Milliken & Pacejka or "Pacejka-like", depending on the particular implementation. This appears to be a reference model that many simulators are compared against. I'm not a tyre simulator expert, so forgive me if I just said something that is stupid.

What about flight simulation? The flight model part of the simulator, is there a "gold standard", that is typically used with most respectable simulators?

Flight simulator games often talk about the "flight model" and describe it as accurate. While I can easily imagine that this flight model is based on some simplification of Navier-stokes,

I have software background myself, and although I didn't write a flight simulator myself yet, I understand the need to simplify, and that no simulation will ever be 100% accurate. All models will inherently have various trade-offs and make some sort of sacrifices. However, that doesn't mean there isn't a relatively accepted way of performing such simulation.

I'm not asking for an opinion based answer, "this model is the best". I'm certainly not asking for a list of "the best" flight simulators. I'm curious what underlying flight model is used -- that said, I wouldn't mind one or two examples of "this famous model described in the following academic paper, is used in flight simulator X and Y".

Basically, I'm simply curious if, in the industry, a typical model or small set (a couple) of models are considered either the actual "gold standard" or more of a de facto standard.

If there is no such thing, that pretty much every flight simulator does it differently, then I'll accept that as an answer. If there is a small set of terms that everyone in the industry is familiar with, I'd love to know then. It would let me easily search up papers that describe these systems.

I'll also accept an answer that lists an overview paper on the challenges of accurate flight simulation on modern computer systems.

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14 CFR Part 60 regulates what constitutes a Flight Simulator Training Device (FSTD) for a particular aircraft model. FSTD is divided into two broad categories: Full Flight Simulators (FFS) and Flight Training Devices (FTD). A big difference between the two categories is FFS requires having motion cues, whereas motion cue is optional on FTD. Furthermore, the required accuracy of simulated flight dynamics (compared to flight test results) is much more stringent for FFS than is for FTD.

Each FFS and FTD is further divided into qualification levels (Level A to D for FFS, Level 4 to 6 for fixed-wing FTD). The higher the level, the more fidelity the simulator has to the actual aircraft. You may only get credit for Part 61 if you get training on the simulators with the appropriate levels for the systems/flight phases you are working with.

The simulator manufacturer must submit a Qualification Test Guide to the FAA to demonstrate that the simulator is good enough on aerodynamic model, flight deck, visual system, motion cue, sound system for the appropriate level.

Anyone can make a flight simulator, to any arbitrary level of fidelity; but making a flight simulator good enough for the FAA is hard and expensive. Read this for a more in-depth but lay-man explanation of the different qualification levels.

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  • $\begingroup$ This is rather the formal side of things. Yes, it must be formally demonstrated that the simulator behaves according to the selected level. But it doesn't answer the core question: how such models are built. $\endgroup$ – Zeus Aug 26 at 7:38
  • $\begingroup$ Also, I disagree that the "single biggest difference" between FFS and FSTD is motion. In practice most FSTDs (at least of higher levels) have motion. Rather, it's a totally different level of certification effort and fidelity. $\endgroup$ – Zeus Aug 26 at 7:47
  • $\begingroup$ @Zeus The OP was asking "what is the gold standard for flight simulator", and not how simulations/models are made. I come from an airframer background so my expertise stops at the physical modeling. However, it's my understanding that Level D simulation models are supplied to high qual level FFS/FSDT, interchangeably. The optionality of motion cue is from cursory examination of Part 60 texts, and seems to be upheld by the secondary source in the post. $\endgroup$ – Jimmy Aug 26 at 14:33
  • $\begingroup$ 'Supplied?' The model is the core of the simulator; all the hardware around it is secondary. It may happen that for companies that produce both FFS and FSTD (which is not very common) part of the model is shared, but often they are very different. In fact, most of FSTDs (except for the highest level perhaps) are built on 'gaming' engines such as X-Plane or P3D: for them, only 'generic' representation of a class of aircraft is required, and this is arguably a much more fundamental difference than motion. $\endgroup$ – Zeus Aug 27 at 0:30
  • $\begingroup$ @Zeus Upon cross-checking the Objective Tests between FFS and FDT of Part 60, I agree with your statement. Amended my answer. $\endgroup$ – Jimmy Aug 27 at 1:05
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As far as I can tell, there are two general approaches:

  • Solid body dynamic simulation with lots of experimental coefficients.

    Most of the aerodynamic effects are simply summed for the whole aircraft, though the more advanced simulators need to calculate the wheel position and wing and fuselage flexing to get proper reactions mainly at landing. But it is still just a few elements, so it is not computationally intensive and can be very accurate if enough data is available.

    The problem is getting that data. Lift curve for angle of attack and velocity, pitch moments for angle of attack and velocity, roll response to side-slip, pitch response to side-slip, lift response to slide-slip, pitch damping, roll damping, yaw damping, also ground effect and so on and on and on.

    This seems to be the usual approach for the big simulators (as far as sources are publicly available; the vendors tend to keep the details confidential), because the manufacturer collects all the data during design anyway—from flight tests, wind tunnel and lately computational fluid dynamics situations.

    It is also easy to show that it matches the behaviour of the real aircraft.

    Disadvantage is that the data is often lower quality or not available at all for attitudes too far from the normal flight envelope, so the simulation is less realistic in upsets. But for flight training that does not actually matter, because the point is to avoid getting in those attitudes at all.

  • Blade element theory simulation.

    In this approach, the geometrical model of the aircraft is broken down to elements and the aerodynamic forces on each are estimated using some basic lift and drag models and then summed for the whole aircraft.

    This is not as accurate as the former if you have all the coefficients available, but allows still quite good simulation of aircraft that you don't have that data for, including aircraft not yet built, so it is sometimes used in design validation to get rough idea whether a proposed design will handle well.

But in general, the flight dynamics model is a tiny part of what a flight simulator must do. The instrument behaviour must be simulated with their lag and errors, effects of various system failures can be quite complex etc. And then there is of course driving all the hardware of more realistic simulators.

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The flight simulation model code for Level D sims is protected copyright from the manufacturer of the simulators.

What about flight simulation? The flight model part of the simulator, is there a "gold standard", that is typically used with most respectable simulators?

The gold standard is: accurate simulation of all of the physics involved in training a pilot on how the aeroplane and all of its systems respond. The complete code that complies with Level D is huge, about a 30 man year effort. A list of source code files would be:

  • Environment: atmosphere and navigational geography.
  • Aerodynamics: implementation of aerodynamic forces and moments in six degrees of freedom.
  • Flight dynamics: response of the aircraft upon forces and moments. Including aeroelasticity effects.
  • Ground reactions.
  • Crash conditions.
  • Aircraft systems interface (AFCS, AGPWS, FMCS etc.)
  • Mass and balance.
  • Aircraft systems. All the ATA chapters (autopilot, flight controls hydraulics etc etc). This is a huge amount of code, which also captures all of the system failure effect handling that pilots are trained in. Hydraulic system pressure loss causes reduction in max. surface deflection, depending on dynamic pressure etc etc.

I understand the need to simplify, and that no simulation will ever be 100% accurate. All models will inherently have various trade-offs and make some sort of sacrifices. However, that doesn't mean there isn't a relatively accepted way of performing such simulation.

The accuracy, trade-offs and sacrifices are determined by: what standard is the software written for. Compliance to the standard must be demonstrated.

If there is no such thing, that pretty much every flight simulator does it differently, then I'll accept that as an answer.

The understanding and capturing of the underlying physics is the only correct way of writing simulation code. Used to be a bit of a black art in the nineties, tools like Simulink make constructing block diagrams and system responses a lot more accessible. But every new simulator company must re-write from the ground up, using physics simulation.

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  • $\begingroup$ The last paragraph is not quite true. Even physics simulation can be done on very different levels; Jan's answer mentions two of the most common approaches. But in the end, any 'cheating' is acceptable if the model behaves like real, and it can be demonstrated. Most rigid interactions are 'cheated' rather than solved physically. The OP mentions Pacejka's approach: this is outright cheating (this is a 'magic formula' that works in practice, instead of solving the tyre physics), and it's very common. As for rewriting, like with most software, there are freeware simulation engines out there. $\endgroup$ – Zeus Aug 26 at 7:19
  • $\begingroup$ With the compliance, it may be confusing to say 'standard'. Rather, validity of the behaviour must be demonstrated (to the extent stipulated by the simulator level). This may not be trivial because validity of the source data must also be demonstrated. But the software writing standards per se for simulators are not specifically regulated, unlike the avionics and other airborne stuff. $\endgroup$ – Zeus Aug 26 at 7:32
  • $\begingroup$ @Zeus "As for rewriting, like with most software, there are freeware simulation engines out there" I know, I've used one for testing the aero and flight dynamics model of a nav trainer helicopter, including systems simulation, that we wrote and is used for training at the moment. Not on a Level D simulator though, that is a different kettle of fish and you don't get away with much cheating at all without introducing bugs somewhere else that will get you into trouble $\endgroup$ – Koyovis Aug 26 at 7:37
  • $\begingroup$ Well, of course, one rarely just uses someone's model, even if it's allowed. But like with any established software (like OS), it's rarely happens that a new project 'must rewrite from the ground up': there is enough stuff to build upon, even if by just using the experience and approaches. $\endgroup$ – Zeus Aug 26 at 7:58
  • $\begingroup$ As for cheating, I can assure there's plenty of it even at Level D. There are things that are simply not realistic (or not worth) to calculate 'physically' in real time, and 'cheating' can give better (more accurate) result than 'honest' simulation. For example, when the model assumes wing flex at certain frequency, this is, by and large, 'cheating': it's not realistic to do FEA of the airframe in real time. Similarly, it may be more reasonable to induce skidding directlty instead of simulating rubber tyre properties. Failures and other random events are also in this category. $\endgroup$ – Zeus Aug 26 at 8:08

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