Actually you did not. I understand the principles. Now we should prove that ramjet has higher NEZ than rocket in every case. I'm sure Meteor has better NEZ than PL-12 but with PL-15 it is not so easy to determine. The PL-15 will receive a second boost and increase its speed to mach 4 again and can perform this boost as it closes the distance to target to some determined and desired range. It is mathematically impossible for us to determine the exact curves and relationship between NEZ and distance between missile and target.
Only person who agrees with you is an Indian who probably cannot even do basic calculus and to expect him to understand how NEZ is calculated? Come on. We need to know specific impulse, thrust to weight, engine thrust, burn time, potential energy, missile aerodynamics, and with assuming ramjet and rocket cases are both with totally identical settings of launch, optimum travel, and target movement.
I'll say again, it is impossible to determine which has higher NEZ with available information (1) and it is impossible to say ramjet is always got better NEZ than rocket (2). If Ramjet powered air to air missiles is definitely always better NEZ than rocket only, then China would only be using ramjet air to air BVR missile and the USA and Russia also would only use ramjet air to air BVR missile. Our ramjet technologies and available development resources are far greater than France. Yet none of these three countries prefer ramjet for many reasons only partly to do with performance not being much better than single pulse and against dual pulse who knows.
Dual pulse patterns we don't know. Maybe second pulse kicks in after 30 seconds of non accelerated flight. Maybe after 3 mins, maybe the burn time is 2 seconds or maybe 10 seconds. It could all be dynamic and depend on how missile's software calculates best intercept probability and does trajectory update and second burn in non-intuitive ways.
The standard escape maneuver is the same for all against all missiles. It is to turn away from and basically keep making missile turn and lose energy with updated intercept points. Maybe aircraft would reduce altitude and then climb due to climbing being hardest so you want missile to try and climb up to you so you must first reduce altitude so that it has to later climb towards you and this is much more energy costly than lateral movement.
NEZ for ramjet would not change. The only difference between ramjet and dual pulse is that ramjet sustains missile speed at around mach 3. Dual pulse missile will reduce to maybe below mach 2 while the aircraft is performing this. Then the dual pulse second burn will accelerate missile again to around mach 4. That's better speed than the ramjet powered one. Think about it like this. The missile is launched at around initial velocity of mach 1 from the fighter (let's assume) and first burn usually accelerate missiles to around mach 4 at mach 1 launch speed. For second burn, maybe the burn is just as long or longer who knows this is what I'm saying. And this second burn should accelerate to mach 4 again or around that. This is more final energy than the ramjet missile.
The dual pulse method uses 100% of available missile potential energy while the ramjet always uses <100% potential energy unless we are talking about ramjet missile out of fuel. If the ramjet missile is out of fuel, it is heavier and slightly less aerodynamic in comparison.
No matter how you calculate ramjet vs dual pulse, ramjet is less efficient in use of available energy. The question is how much each has in available energy. The answer is unknown since we don't know specific details.
I have done these sorts of calculations but not for NEZ type of scenario. We need data to have simulation.
But I can say the above and the above is correct and indisputed fact. Ramjet is less aerodynamic and would be heavier so when both missile types run out of fuel then the ramjet missile is disdvantaged if it needs to turn... if it needs to travel straight only then it has momentum advantage but this is not the case since the fighter will turn a lot. If neither missiles run out of fuel then the pulsed missile gets to use up 100% of available energy while the ramjet one still has some fuel remaining. Again in this respect it is a disadvantage.
The problem like I said already but will have to say again is that we don't know the specific details on how much potential energy the fuel and rocket or fuel and ramjet gives PL-15 and Meteor.
Now for the last question of NEZ. Proof that Meteor type ramjet style doesn't have significantly better NEZ is that USA, China, and Russia all prefer rocket powered missiles for BVR and even long range BVR missiles. We have all played with ramjet BVR missiles. I mean we all have any types of ramjet weapons. China even has many types of scramjet and sodramjet weapons and aircraft in testing and flying and landing too. I think if ramjet is distinctly superior, we would all be using such things since 1980s.
Maybe ramjet does in certain circumstance engagements offer clearly better NEZ but maybe those circumstances are rare and does not justify increased cost and time to build. Maybe ramjet only offer very slightly better NEZ and definitely doesn't justify increased cost.
To calcualte NEZ, it is again super complicated and even if we make some assumptions for the dual pulse rocket one, it can potentially still have better NEZ since it gets to accelerate to much faster speed than the ramjet missile and all at the end phase of flight where this speed is most important.
So end of flight the missiles will be at mach 3 for ramjet and mach 3.5 or so for dual pulse if both are just run out of fuel as they intercept target or if there is a tiny bit of fuel left.
OR end of flight the missiles will be at mach 2 or lower for ramjet and mach 3 or so for dual pulse if both already exhausted fuel for 20 seconds. The thing is that dual pulse would not allow itself to fire second burn that early and as long as is within its range, will fire second stage so that it has maximum speed upon interception.
When the PLAAF tested PL-12 based ramjet BVR missile, they would have determine it is just not worth extra cost. How much extra improvement over how much cost and then they never publicly pursued this. Ground up ramjet missile probably exists in PLAAF inventory since it's been leaked for nearly 10 years now. It might be a more long ranged missile and purposed for against large and slow aircraft. Smaller inventory for special mission cases.
For typical case, you need a lot of missiles rather than smaller number of slightly better missiles. Better is just better electronics and sensors and better fighter or stealth fighter.
One thing to remember is that a rocket powered small missile will climb much easier and faster than even a empty F-15 on full afterburner. So if the strategy of climbing at end is employed, the missile climbs much better when the rocket is kicking. That's the whole point of dual pulse. The rocket is back at the very end of interception flight.