About the MiG-21bis Flight Model

[Smyth]

I finally got around to trialing the MiG-21 recently and was not surprised to find some issues with the flight performance model; they have been discussed before many times and various data has been shared. With that in mind, it was odd to hear through the Discord grapevine that Magnitude 3 does not believe there is enough evidence to show anything wrong. Maybe that was a miscommunication, or maybe the good data has been lost in years of noise on the topic. Therefore I have made an attempt to summarize the key points in one place.

This will take some time to explain, because the data available in the public domain is confusing and sometimes appears contradictory. It takes careful comparison along with some calculation and context to sort out what is real. For that reason this manifesto report will be split into three parts:

1. What real world data is available in the public domain, and what is useful.
2. What in-game data can be easily measured, and how it compares to those real world sources.
3. My opinions on what it means for the game (I will try to keep this last part short)

Part One – the manuals:

Unlike some other contemporary fighters, there do not seem to be any flight test reports or “practical aerodynamics” textbooks in the public domain for the MiG-21. Fortunately many operational manuals contain some level of useful aerodynamic information. The ones already available on the internet for the -21bis include:

• Soviet technical description manual
• Polish technical description manual
• Pilot’s flight manual in Serbian (for Yugoslavia), English (for Arab states), and Polish

Throughout these manuals there are four key charts repeated which are relevant to a discussion of turn performance.

1. Coefficient of Lift,
2. Available G
3. Sustained G
4. Sustained turn time

Unfortunately the same chart does not always agree between manuals. However by cross-examining the various documents we can rule out some obvious miss-prints, and establish which charts are useful.

To enable this cross examination, it is important to realize that these four charts are really only two sets of data, with each pair of parameters related by well-known equations:

1. Normal acceleration ‘N_y’ = (C_L * A_ref * .5 * ρ * v²)/(m*g)
2. Turn Time = 2π / (sqrt(N_y² – 1)*g/v)

Let's start with C_L, because is the most basic property of the four. Fortunately the different MiG-21 manuals all basically agree on this one.

The relevant graph gives non-dimensional lift coefficient versus angle of attack in arbitrary units. These units are not really degrees, but some function proportional to the true angle of attack. The flight manuals do not specify exactly what that function is.

Tech manual version:

Pilot’s flight manual version:

The hand-drawn lines are slightly different between versions, but they show the same two expected trends:

1. Coefficient of lift is almost constant for constant AoA, until compressible flow effects become significant around M0.7
   • This is expected by definition of CL as a non-dimensional coefficient valid for incompressible flow.
2. Maximum lift increases at low speed with increasing AoA of stall.
   • For fast jets (unlike "normal" aircraft) 'stall' is often a function of loss of stability, sometimes combined with a limit of horizontal tail effectiveness. Loss of stability does not normally correspond to a fixed AoA.

In other words, both of these trends are the expected behavior for a supersonic fighter with a low aspect ratio wing.

To emphasize that this is the expected behavior, here is a similar plot for a similar jet (Mirage F1) with AoA on the vertical axis. Note that just as the MiG-21 manual quotes 33 units as the stall AoA, the Mirage manual quotes 17 units. On both aircraft the true stall AoA is higher than the quoted limit over most of the envelope.

 

Now also the same plot for the MiG-23. With wings swept (45 and 72 positions) the coefficient of lift increases slightly as Mach increases for a fixed AoA. The line of maximum lift is not tied to a fixed angle, and instead increases with decreasing speed. All this is just like the MiG-21.

Charts for other aircraft are obviously not directly relevant to the performance of the MiG-21, but I include them because it is important to have context for what is normal and plausible.

 

Next it’s time to compare graphs of available G, which should all agree with the Cl figures. Unfortunately this is not quite the case.

Pilot’s flight manuals show only 28 units AoA:

Polish tech manual shows two unknown lines. The chart legend mentions 28 units and maximum lift, but they are unhelpfully both dashed lines, while the chart uses one solid and one dashed line. Helpfully enough the dashed lines do match the solid lines for 28 units in the pilot’s manuals seen above, which suggests that “CZmaks” was intended to be the solid line in this drawing.

It would be nice if the Russian language tech manual clarified this for certain, but sadly it does not. The lines are clearly the same as the other versions, but the legend is reversed with 28 units now shown above the ‘maximum’!

Something is wrong, but how to tell for sure which version is correct? The next step is to convert CL to G and see which version the CL plots match. I will use the tech manual chart mostly because it is linear which makes things easier.

• Red line at maximum lift CL = 1.32 – (0.4*M)
• Green line at 28 units is a constant CL = 0.7

Lift calculated from those CL at sea level standard conditions and 23m2 reference area overlays perfectly with the lines in the manuals, only the labels for “28 units” and “maximum” are reversed in the Russian-language print. The green line also matches the one labeled “28 units” in the pilot’s flight manuals.

Considering that the CL plot agrees between all manuals, that it agrees with the plausible expectation set by other jets, and that the pilot’s flight manuals all show lift at 28 units matching the CL plots at 28 units, there is not much ambiguity left. Whoever drew this legend by hand in the 70s flipped the label of the lines by accident, just like the draftsman of the Polish manual accidentally drew different lines on the plot and the legend. Drafting errors are common in old technical documents, and context clues are the key to resolving contradiction.

 

Keeping the possibility of mistakes and contradiction in mind, it’s time to look at sustained turn performance.

All the manuals provide sustained G charts for both standard afterburner and emergency afterburner at 7500kg with 2x R13 series AAM.

Pilot’s flight manuals:

Tech manuals:

This new discrepancy is obvious right away. The tech manual shows around 6.5G peak for standard afterburner, while the flight manual shows 6.5G peak for emergency afterburner. The other lines are all similarly offset.

To get more context we can try to cross-examine against the sustained turn time plots, although they only exist in the tech manuals.

Here are military (dry) thrust and standard afterburner:

And emergency afterburner:

For comparison I digitized the 1km line for standard afterburner, converted from turn time to turn rate, and then turn rate to sustained G force in the flight path axis using the equations mentioned above.

It matches quite well.

For the pilot’s manual charts, there is no turn time to overlay against, but we can compare the shape at least. To enable that I digitized the sustained G chart in the pilot’s flight manual, and converted that into turn time.

There’s no point overlaying this with the tech manual because we already know the best turn time will be different. However it does show the same trend versus speed, shared with all other supersonic jets. The best sustained turn performance occurs at a relatively high Mach number, degrades gradually below that, and then more quickly at low speed.

It’s unfortunate that the sustained turn graphs disagree in absolute value, but to some extent I don’t really care because the purpose of this analysis is only to establish what is plausible, not what the exact values should be. What really matters is the shape of the curve, or in other words which speed the aircraft performs best at.

Edited February 28 by Smyth
format

[Smyth]

Part Two – DCS:

With a basic grasp of the real-world data, it is time to look at the behavior of the MiG-21bis module in DCS World.

Let’s start again with coefficient of lift. This is straightforward enough to measure. Perform a decelerating turn at constant AoA, record the altitude, TAS, and G-force at a few different speeds, then calculate CL at each point.

My result is not as clean as it could be, but it says all that needs to be said. I’m confident this is accurate because it matches what several other forum members have measured in the past.

In very simple terms, the lift at 28 units indicated AoA is swapped with the line of maximum lift, just like the chart in the Russian language tech manual. According to all the evidence from part one, this is not correct. 28 units is not even the maximum lift in-game.

There are two possible explanations:

1. The ratio of indicated AoA units to true AoA degrees on UAA-1 in the DCS MiG-21bis simulation is not constant and increases rapidly at low speed.
2. The parameter of lift vs mach in the DCS MiG-21bis simulation is not correct.

The first possibility can be quickly eliminated because the ratio of AoA units to degrees in-game currently decreases slightly at lower Mach numbers. Here is my measurement at 28 units. Other forum members have measured this in more detail.

At low speeds, this is about 13 degrees of true AoA generating CL of at least 1.15 --- an extremely steep lift curve for a wing with an aspect ratio of about 2.2. How steep is 1.15/13 exactly? There is no wind tunnel data easily available for the MiG-21, but we can sanity check this against abstract literature, or other delta wing designs.

Fortunately NASA makes this easy. They reported on a scale model test in the 1970s comparing the F-5A wing with some other planforms (https://ntrs.nasa.gov/citations/19740018330). More specifically, they tested an un-cambered tailed delta wing with AR=2.1, and a swept wing with AR=2.8. While the report does not say “Fishbed” or “Phantom”, just take a look and judge for yourself what they were thinking of (in 1974 America):

The real MiG will vary slightly from this proxy, but not by much. Here is the CL NASA measured for each wing:

Remember what I said about drafting errors? Fortunately NASA only connected two dots incorrectly, and the legend is correct as confirmed by other pages of the report.

Here is the page for the delta specifically. I have added where the DCS MiG-21 lands.

It is over 60% steeper, even assuming the chart in the MiG-21 manual represents tail installed but without deflection. Notice also that the test CL at 13 degrees is 0.72, just about equal to what the manuals claim for 28 units. Coincidence? Maybe.

This is only one data point, so it’s also good to sanity check with the expectations of abstract literature. Fortunately delta wings are very well studied, and at this point almost a standard teaching aid for wind tunnel tests. Using the Polhamus model for vortex lift (https://ntrs.nasa.gov/citations/19670003842), I get CL(15deg) = 0.76 for AR=2.1. That matches perfectly to the line for δh = “off” in the chart above.

The lift curve of the DCS MiG-21 is simply not plausible. CL/deg of 0.09 belongs to a completely different category of wing.

One might reasonably assume that an implausible lift curve slope will result in other implausible behavior. In other words, it’s now time to look at sustained turn rate. This module is quite famous in the multiplayer PvP community for sustaining its best turn rate at minimum speed, but proponents often point out that the real sustained G charts do not go down below 0.5 Mach. True enough, but really beside the point. We can look at the turn time chart and see the problem without extrapolating anything.

To illustrate, I’m going to borrow data from the extremely useful compilation of automated testing by @totmacher at dcs.silver.ru. I hand-flew some tests before my two week trial ran out to sanity check that the extreme low speed performance is not an artifact of the automated testing. A .trk is included, but the precision of the automated test is simply far better than what hand flying can achieve. If more data is really needed to illustrate the problem, I know some other community members have been collecting extensive hand-flown data recently.

Now here is an overlay of that automated test against the tech manual turn-time chart for standard afterburner at 1000m altitude:

Turn rate at higher speeds matches OK (probably this is where it was validated in development). To see the real problem, just look at the slope of the curve at M0.5:

• The turn rate of the real aircraft is slowing down
• The simulation is not

We also know that the turn rate even gets faster (turn time goes down) below that speed in the simulator, but it’s not necessary to look there when the problem is already evident. Showing data from in-game below the minimum speed of the IRL plots seems to generate a lot of controversy for some reason, so I am avoiding that.

[Smyth]

Part Three – Conclusion:

Here I will editorialize a bit.

Without seeing the lift, drag, and thrust models used inside the flight model, it’s hard to tell if the incorrect CL curve and the incorrect turn-time curve are related. Either way, they both need to be fixed.

In absolute terms the maximum lift is a bit too high, but that is not the problem I’m concerned about. The virtual pilot does not ‘feel’ it. What is immersion-breaking once you notice it is a jet with a small, low-aspect ratio wing generating peak lift at 15 degrees of AoA or less. Those are straight-wing propeller plane angles. Additionally, the way CL increases at low speed reduces the normal variation of AoA with speed. Practically speaking that will degrade the responsiveness of the aircraft when the pilot tries to control airspeed correctly with AoA, especially on landing approach. I think there is a reason so many DCS players struggle to make stabilized landing approaches in the -21.

Likewise the steady turn rate being slightly too high is not the main problem. The main problem is the shape of the curve. On the real MiG-21, slowing down below M0.5 decreases performance. On the simulated MiG-21 right now it does not lose any performance, and experienced players know to hold AoA in the red and slow down to stall speed for maximum turn rate. This becomes almost a complete inversion of reality when thinking of tactics and flying technique.

I don’t want to beat a dead horse much longer, but it’s worth saying again that there is not even one supersonic jet known to behave this way. There are too many diagrams to show here and many of them I am probably not allowed to post. Instead I will just list the fighters that we either see in DCS or know from public data do not turn faster at minimum speed, and leave finding the charts I am looking at as an exercise to the interested reader:

• MiG-19
• MiG-23
• MiG-29
• Su-27
• F-4
• F-5
• F-8
• F-14
• F-15
• F-16
• F-18
• F-20
• F-100
• F-104
• Mirage III
• Mirage F1,
• Mirage 2000
• JF-17
• Draken
• Viggen

That is a long list, but alone does not mean the MiG-21 cannot have a second turn rate peak at its stall speed. What is does mean is that this behavior is only believable if specific data backs that up. The specific data we do have does not.

Lift_uua_28_clean_2.trk Fishbed_sustained_7511_r3s.trk

[MiG21bisFishbedL]

This is a good post and I hope you find pirate gold somewhere soon.

I'm not sure about the discord scuttlebutt, I rarely believe any of that since it rarely turns out to be legit, but I'd feel the more pressing matter is just how small Mag3 is and how they're dedicated to the Corsair.

The frustration there is that they've been at it for years on the Corsair. I feel that's absolutely valid. It'd be kind of fantastic to actually get this fixed sooner rather than later, especially since the MiG's been out for 10 years; this coming Sept is the anniversary.

[rossmum]

Would be nice to see this looked at and it's good to see a fairly detailed and grounded look into it instead of having 1-2 relevant posts lost in a sea of unrelated complaints or complaints around other aspects of the FM (incorrect or not). It's very easy to build bad habits with things as they are and I'd be curious to see what the effect is on some other things where the numbers don't quite line up (takeoff run distances for example).

[BIGNEWY]

I have closed this thread on the third parties request so the thread does not become cluttered with unnecessary information. 

thank you