I have often encountered claims that testing proves performance of modern BVR missiles. Baloney.
Most if not all missile tests nowadays are against QF-4, which has 50% greater turn radius than the F-15 (itself hardly an agile aircraft compared to more modern fighters), and even QF-16 will be weighted down by necessary equipment added. None of them are anywhere as agile as modern fighters, and UAV always has inferior OODA loop compared to a manned fighter, even if operator is sitting right there, whereas drone can’t really compare. In other words, missile Pk based on testing is unrealistically optimistic, even if UAVs/drones used were equipped with modern onboard jammers.
Further, all graphs and videos of tests show target aircraft in a steady state sustained turn. This leaves more than enough time for missile to adapt. For this very reason pilots never use sustained turns to avoid missiles, but rather a combination of maximum acceleration, maximum turn and transient performance (in particular, quick rolls). Which means that probability of kill for radar-guided BVR missiles might be an order of magnitude worse than what is achieved in tests, at the very least.
F-15 has a 9g corner speed of 385 kts for instantaneous turn and a 5 g corner speed of 425 kts for sustained turn at combat weight. Rafale has 11 g corner speed of 330 kts for instantaneous turn with 2 wingtip missiles and 9 g corner speed of 350 kts for sustained turn at combat weight; Typhoon’s sustained turn performance is said to be the same. F-4 has a 7,5 g corner speed of 425 kts for instantaneous turn. This means that….
v^2 / r = a
a / G = g
v = speed of aircraft in turn
r = radius of turn
a = acceleration due to turn
G = acceleration due to gravity (9,81 m/s2)
g = g loading in turn
330 kts = 169,8 m/s
350 kts = 180,1 m/s
385 kts = 198,1 m/s
425 kts = 218,6 m/s
IRIS-T can achieve 60 g at Mach 3, which at 30.000 ft would be 909,3 m/s.
AIM-120 can achieve 40 g at Mach 4, which at 30.000 ft would be 1.212,4 m/s
S-400 can achieve 60 g at Mach 4,5 and sea level (1.531,3 m/s), and 20 g at Mach 4,5 and 30 km (1327,05 m/s?).
Thus turn radius is:
Rafale (instantaneous): 267,16 m
Rafale (sustained): 367,38 m
F-15 (instantaneous): 444,49 m
F-15 (sustained): 958,59 m
F-4 (instantaneous): 649,72 m
IRIS-T (instantaneous): 1.404,73 m
AIM-120 (instantaneous): 3.745,96 m
S-400 (instantaneous): 3.983,8 m / 8.975,85 m
It can be seen that the F-4s sustained turn radius is almost certain to be greater than 1.400 meters. Far greater in fact, due to its draggy airframe and low thrust-to-weight ratio compared to modern fighters (0,86 at combat takeoff weight, worse than Gripen). Now, for fun… F-35 can pull 4,6 g sustained, most likely (an estimate I found) at M 0,85 or above at 20.000 ft, which translates into >269 m/s, for a turn radius of >=1.604 m. In other words, F-35 has sustained turn performance similar to the F-4 (assuming that figures I found for the F-35 are correct, which is a big if except for the g value).
These values don’t really correspond (missile ones are for sea level, while values I used for aircraft are typically at 20-40k feet, which leads to lower turn rate and larger turn radius), but they should give an idea – of both missile performance relative to aircraft, and of aircrafts’ relative performance (and how illogical is it to base missile performance versus Rafale on performance of that same missile versus F-4 drone).
While this is just a speculation, 5 times the g rule probably comes from v^2, since typical WVR missile can achieve Mach 2,5 and typical cruise speed is cca Mach 1, then square difference gives a factor of 5, which corresponds to the rule that missile needs to pull number of gs that is g(m) = [v(m)/v(a)]^2 * g(a). The missile will rarely be fired from an ideal position, and if it flies an intercept path – which indeed does reduce turn capability necessary to hit a target in a sustained turn – and aircraft changes direction of the turn, missile is in far worse position than it would be if it had flown chase path; this means that it has to pull more g than it would normally have to, maybe (depending on relative positions) even more than it would have to match aircraft’s turn capability.
Now, we have turn radius. Turn circumference would be:
Rafale (instantaneous): 1678,78 m
Rafale (sustained): 2.308 m
F-15 (instantaneous): 2.792,8 m
F-15 (sustained): 6.023 m
F-4 (instantaneous): 4.082 m
F-35 (sustained): 10.078 m
IRIS-T (instantaneous): 8.826 m
AIM-120 (instantaneous): 23.537 m
S-400 (instantaneous): 25.031 m / 56.397 m
Combine this with speed and we get turn times:
Rafale (instantaneous): 9,89 s
Rafale (sustained): 12,82 s
F-15 (instantaneous): 14,1 s
F-15 (sustained): 27,55 s
F-4 (instantaneous): 18,67 s
F-35 (sustained): 37,47 s
IRIS-T (instantaneous): 9,71 s
AIM-120 (instantaneous): 19,41 s
S-400 (instantaneous): 16,35 s / 42,5 s
Thus turn rates are:
Rafale (instantaneous): 36,4 deg/s
Rafale (sustained): 28,1 deg/s
Typhoon (sustained): ~28 deg/s
F-15 (instantaneous): 25,5 deg/s
F-15 (sustained): 13,1 deg/s
F-4 (instantaneous): 19,3 deg/s
F-35 (sustained): 9,6 deg/s
IRIS-T (instantaneous): 37,1 deg/s
AIM-120 (instantantaneous): 18,5 deg/s
S-400 (instantaneous): 22 deg/s / 8,5 deg/s
Going by numbers alone, IRIS-T has high probability of kill in ideal conditions, and quite dangerous even if launch conditions are less than ideal – ignoring, of course, any countermeasures, as well as the fact that actual performance of IRIS-T at altitudes where aircraft performance is calculated here will be less than the numbers listed (both IRIS-T’s and AIM-120s turn rates are calculated for sea level, and will be less at medium, and far less at high, altitude). AIM-120 on the other hand has a low chance of hitting a modern fighter if latter is trying to avoid getting shot at all, and can only hit a target that is either not maneuvering or is pulling a steady-state sustained turn (in other words, flying in an easily-predicted circular path). In either case, performance of missile does not negate the need for a maneuverable platform – in IRIS-Ts case, attacking aircraft has to be capable of maneuvering into the perfect six-o-clock position in order to maximize probability of a kill, while AIM-120 is easy enough to evade that it does not negate a need for visual-range dogfight even if IFF requirements are ignored. Achieving a six-o-clock position is important for two reasons. First, it minimizes the amount of turning that missile has to do even though it reduces missile’s range. Second, missile achieving a kill position relative to targeted aircraft does not necessarily result in a kill – if missile’s flight path is perpendicular to that of a target, there is a large possibility of missile exploding on far side of a target and doing no damage; such possibility actually exists for any flight path that is not parallel to the target, albeit it is not as large as for the strictly perpendicular flight path.
(Note here: F-35 values are basically unknown, and I have found different turn values – see below.)
Rafale has also pulled 10,1 g at 448 kts for 24,6 deg/s.
I have also found following turn rate data. Where it conflicts with the above calculations, said calculations should be taken as more reliable:
Rafale A: 32-35 deg/s instantaneous, 24 deg/s sustained
Gripen C: 30 deg/s instantaneous, 20 deg/s sustained
Typhoon: 30-35 deg/s instantaneous, 20-25 deg/s sustained
F-22: 28 deg/s sustained
F-35A: 15 deg/s instantaneous, 12 deg/s sustained
F-15C: 21 deg/s instantaneous, 15-17 deg/s sustained
F-16C: 26 deg/s instantaneous, 18 deg/s sustained
F-18E: 24 deg/s instantaneous, 15-18 deg/s sustained
Su-27: 27 deg/s instanteneous, 21 deg/s sustained
Su-35: 32 deg/s instanteneous, 22,5 deg/s sustained
F-4E: 19,3 deg/s instantaneous, 14,7 deg/s sustained
MiG-23ML: 16,7 deg/s instantaneous, 14,7 deg/s sustained