Its not a matter of prediction, but kinematics. R-27RE has maximal range of 117 km, but againist a fighter that is closing in at same altitude, its effective range is 65.5 km. At a tail chase againist a fighter, its 16,5 km.

i know R-27RE are used at the moment but how about modern future missiles Ex: ramjet R-77 ( may be same performer as Meteor ) and RVV-BD ( probably same as R-37 )

Lets assume for a second both flies at 12000 meters;

12000 meters is only 39.370ft but since they both detect the other from 300-400 km isnt it more logical for them both to climb to higher altitude + accelerate to very high speed before launching missile to give their missiles more energy ? EX : 18000 meters ( 59055ft )

At 5Gs @ 2500 km/h, MiG-31 will have 4 deg/s turn rate, and 10km turn radius. It this bad? Not at all, as missile has to slowly turn with the MiG to plot an intercept course. To put it this way; 15 seconds is what it takes to give 60 degrees angle to target, getting immune to many types of missiles it fires and still maintain radar lock. 45 seconds is what is required for a 180 degree turn and retreat at will. 7,5 seconds is what it takes 30 degrees climb angle to achieve 347m/s climb rate at 2500 km/h, and furter 12,5 seconds (for a total of 20 seconds) to get from 18000 meters to 22340 meters.

here is what i can find
http://img3067.imagevenue.com/img.php?image=38572_MiG31vsF14_122_482lo.jpg

MiG-31 and F-14A are compared at M1.4@5km, M1.4@10km and M2.2@17km. The data given from top:
> thrust/weight ratio
> sustained load factor (g)
> instantaneous load factor (g)
> sustained turn rate (deg/sec)
> instantaneous turn rate (deg/sec)
> sustained turn radius (km)
so basically at 17km ( 55774ft ) the turn radius of mig-31 is about 34 km rather than 10 km (probably mig-31 can only turn 5Gs at slower speed ? )

maintain at least M2.5+ airpspeed to catch its target.

The time it takes for a missile to lose 25% of its velocity after burn out at supersonic speeds.
Never @ > 100,000 m (~300,000 ft) ; in space
~150 seconds @ 24,000 m (~80,000 ft)
~70 seconds @ 18,000 m (~ 60,000 ft)
~25 seconds @ 12,000 m (~ 40,000 ft)
~10 seconds @ 6,000 ft (~20,000 ft)
~5 seconds @ Sea Level
so it seem that if fighter climb higher before launching their missiles then their missiles can remain fast for really long

Add to that, I completely ignored the fact MiG-31 will be firing its own missiles too. So it begins by; Su-35 fires its missile at 110 km, MiG-31 detects this illumination via RWR, fires its R-33S. R-27RE momentarily touches M4.5 then after a few seconds booster deplates and missile glides 60-70% of its flight. R-33S sustains maybe 80-100 km of its flight at M4.5. What happens? R-33S reaches target first, and

sustain for 100 km at mach M4.5 is equal to about 65 seconds , are you sure R-33S rocket burn that long ? wasnt it a solid fuel rocket ? , normally i only heard rocket burn for maximum of 6-7 sec

Given the number of advanced long-wavelength systems appearing and their ability to interface directly with SAM units, the F-35 is a hilarious waste of time. The T-50, not so much, as the US has never really put much effort into VHF-band systems. You need big-ass transmitters for one, making them unsuitable for airborne or naval use.”

-Sean O’Connor (SOC).

I will have to disagree with this
SPY-1 and THAAD radar seem very good to detect low RCS target, while US don’t have many VHF radar, their air defence system are pretty decent ( very powerful radar), another thing is that t-50 likely go in service much latter than f-35, so I won’t say either f-35 or T-50 more useless than the other

True, but that is circumstential. If pilot wants, MiG-31 can always stay slow to M1.2 at 17000 meters, and dive to 13000 meters to gain M2.0+ speed then climb if necessary. From the MiG-31 pow, it should never allow target to shoot back succesfully.

the problem is after reach mach 2.0+ it can’t really turn, so probably take a while to climb to altitude with very shallow angle

There is indeed likely to be a resonant effect and VHF frequencies, but it would be naive to assume that this has been ignored by engineers involved in designing low-observable aircraft and missiles.

There is, to the best of my knowledge, nothing in the public domain on low-observable techniques for use against VHF radar. However, at a recent defence exhibition, I saw a document (not in the public domain) that indicates that such techniques exist and have been fielded.

While some Russian companies do cite a range capability against the F-117 for some of their recent VHF radars, the fact that the US do not make their low-observable aircraft available to these companies for the purpose of radar tracking trials, we must assume that these claimed performance figures are little more than theoretical estimates based on Russian estimates of the F-117’s radar cross section.

one technique that I have heard of is to increase the size of the object ( but that only work for big aircraft)

I don’t know what kind of tech you reffer about but it kind of unlikely that f-22 and f-35 have such technology in them even if they exist because these 2 aircraft was designed a long time ago

A quick look at their images will tell the above statement is not true;

R-33 (490kg)

look so much like PHOENIX though

You can not fool physics. Higher speed means friction and friction means heat. Heat must be discharged somewhere. If you keep the heat inside the whole aircraft will radiate heat or it will overheat with all it’s high tech inside. This is insane for modern aircrafts. This means you have to get rid of the heat and this can be gathered by IR-sensors. Nothing radiating is invisible. Even LPI radar you can spot with modern latest technology and sensitive broad band ESM gear. If your opponent knows you are there, but he doesn’t know where, he can take adequate measures to spot you. For example switch on bistatic/multistatic radars, long wavelength radars and EO sensors. IMHO even today a real stealth aircraft is an absolute silence aircraft with no radiations and no heat footprint.

actually they have managed to make a tank invisible in infrared
http://www.huffingtonpost.co.uk/2014/03/31/pl-01-stealth-tank_n_5061795.html

AESA radar cannot be detected by ESM not only because it is low power beam but also because it transmit in unpredictable pattern thus ESM system cant recognize it from background noise

No. High speed is not useful for stealth aircraft. Speed means warm-up of the surfaces and that means stealth is useless because the aircraft can be spotted by IIR-sensors. The hotter the surfaces (the higher the speed) the longer the range it can be spotted by IIR-sensors.

A stealth fighter is stealth when it doses not emit any radiation. No radar, no ECM, no heat radiation, no communication…

that is wrong
for stealth fighter now , they still have radar but LPI radar , they obviously have heat radiation because they moving through the air
and spotted by IIR sensor doesnt mean much if you cant target it ( limit by the LRF range about 40-60 km ) so fast speed could be useful for stealth fighter if they was trying to run away

I can do even better.

Foxhound was design for the sole purpose of being an constant threat to Bomber, AWACS and Tanker platforms. But not fighters, it is designed to zoom around them alltoghter.
Whereas the Flanker IS designed to engage fighters. Its called Airsuperiority.

mig-31 cannot dogfight obviously but there no reason why it can’t use missiles to attack other fighter from BVR,