Of course it is zilch, because you have none by using your argument for a flat ballistic trajectory.
You ran out of credible arguments for the DF-21 a long time ago. So now you are treading into the absurd. There is no such thing as a 'flat ballistic trajectory'. But there is flat
TER, meaning less of an arc, in comparison to others. Even if it is merely one degree off, it can be described as flat
TER.
For example...
RT-2UTTH Topol M - Wikipedia, the free encyclopedia
The first stage has three rocket motors developed by the Soyuz Federal Center for Dual-Use Technologies. This gives the missile a much higher acceleration than other ICBM types. It enables the missile to accelerate to the speed of 7,320 m/s and to travel a flatter trajectory to distances of up to 10,000 km.
Just because some ballistic trajectories may be flatter than others does not mean a gravity turn is not required. If there is a rocket motor powerful enough and with sufficient duration, then we can have a missile that will cruise at 1000 m altitude, for example, then there is no need for a gravity turn. So no, I do not owe you any explanation about any 'flat ballistic trajectory' because there really is no such animal.
I already have given you a definition of an ideal gravity turn from you own wiki source, look it up. Let me make it more simple for you, an ideal gravity turn is a maneuver of a rocket or missile that the only(ideal) force used to change the angular moment of inertia(turn) is the gravity force(gravity).
For the example I give to you in my previous post, for the same target, I can achieve it by an ideal gravity turn ascending phase by using minimum pitch, so the missile exit its boost phase around angle of 55 degree, or it can use a less ideal gravity turn ascending phase by using excessive pitch, so that the missile exit the boost phase around 35 degree. Also I can achieve those angles by mixing different set of duration of boost phase and thrust induced steering.
No...What you gave is a hilarious misunderstanding of the relevant paragraph. From what basis can you claim that 55 deg is 'ideal' and others are 'non ideal'? Show us a source that says so.
But here it is again for all to see...
Gravity turn - Wikipedia, the free encyclopedia
The pitch over maneuver consists of the rocket gimbaling its engine slightly to direct some of its thrust to one side. This force creates a net torque on the ship, turning it so that it no longer points vertically. The pitch over angle varies with the launch vehicle and is included in the rocket's initial guidance system,[1] for some vehicles it is only a few degrees while other vehicles use relatively large angles (a few tens of degrees). After the pitch over is complete the engines are reset to point straight down the axis of the rocket again. This small steering maneuver is the only time during an ideal gravity turn ascent that thrust must be used for purposes of steering. This pitch over maneuver serves two purposes. First, it turns the rocket slightly so that its flight path is no longer vertical, and second, it places the rocket on the correct heading for its ascent to orbit. After the pitch over the rocket's angle of attack is adjusted to zero for the remainder of its climb to orbit. This zeroing of the angle of attack reduces lateral aerodynamic loads and produces negligible lift force during the ascent.
A gravity turn is not the only mean to ascent to orbit. If the American Space Shuttle could take off like an aircraft and is equiped with powerful enough engines, it could achieve orbit gradually through aerodynamic exploitation until the atmosphere is too thin. And if you think that is not possible: SR-71. That aircraft's maximum altitude is still secret but all knows that figure is high enough that a rocket motor would propel the aircraft into orbit. Another mean is to simply power straight up. But the reason why the Space Shuttle, satellite launchers and ICBM uses a gravity turn is to reduce gravity loss...
RSE 24
A helicopter hovering over one spot is a perfect example of a mass being held up by raw horsepower. This is gravity loss. Gravity loss is the thrust of a rocket that is expended to counteract the force of gravity. It is maximum at liftoff, and zero as the payload enters orbit.
At moment of lift-off, immediately there is gravity loss. An inclined trajectory coupled with a high power-to-weight ratio and we have an 'ideal' method to achieve orbit. The duration of our stay in orbit depends on our mission, of course. That mean this phrase '
ideal gravity turn ascent' is translated as: the gravity turn is the ideal method of orbital ascent. Not that there are animals like 'ideal gravity turn' and 'non ideal gravity turn' as you tried to pass off here. So if you are confident that there is such a thing as 'non ideal gravity turn' then show us a source that says so. We are still waiting and am willing to be corrected by a credible external and non-bias source.
I never mentioned about gravity turn before because it is irrelevant to my point of how the boost period (acceleration phase) will affect the overall trajectory since the gravity force relatively remains the same throughout the flight path, which at this point you still have not answered how the duration of the boost phase does not affect the trajectory of the missile yet.
I never said it does not. But I have no problems schooling you...
The longer the
VERTICAL part of the boost phase, the less physical stress the vehicle has to endure because the vehicle would leave the lower/denser atmosphere sooner. The downside to a
PURELY vertical ascent is the aformentioned 'gravity loss', which cost us in terms of large fuel load which naturally contribute to overall vehicle size, also because of 'gravity loss', such a purely vertical climb
DOES NOT contribute to orbital velocity. Improved guidance and control technology allow us to create that 'gravity turn' where lateral stresses on the off-vertical vehicle are minimized. As time and experience goes by, we have a decreasing vertical portion of the boost phase and a sooner entry into the gravity turn, which
IS a part of the boost phase. In multistage vehicles, the shedding of empty fuel tanks, aka continual mass reduction, and a reduction of gravity loss thanks to an inclined vehicle, allow the vehicle to gain orbital velocity more rapidly. So does the duration of the boost phase affect the trajectory of a missile? Yes, what else but because it is a segment of the overall travel? There is a side benefit in that the gravity turn is best indicator of a trajectory profile and the sooner the entry into the maneuver the better the predictive process of that trajectory.
And do not tell me that you never 'mentioned' about the gravity turn. You never 'mentioned' it because you cannot mention it because never knew about it as part of the boost phase in the first place as evident by that 'non ideal' version you are still trying to pass.
Let's see who doesn't understand the concept here.
Trajectory optimization - Wikipedia, the free encyclopedia
See the problem here, if the gravity turn as you emphasized is the only factor in your assumption of predicting the flight path of the missile and since the AoA is 0 for any gravity turn as you assumed, and the only the changes of AoA is before the gravity turn with minimum pitch. Tell me why even bother with the history of AoA command.
First...I never claimed that the gravity turn is the only factor in estimating flight path.
Second...Here are the relevant paragraphs...
Trajectory optimization is the process of designing a trajectory that minimizes or maximizes some measure of performance within prescribed constraint boundaries. While not exactly the same, the goal of solving a trajectory optimization problem is essentially the same as solving an optimal control problem.
The selection of flight profiles that yield the greatest performance plays a substantial role in the preliminary design of flight vehicles, since the use of ad-hoc profile or control policies to evaluate competing configurations may inappropriately penalize the performance of one configuration over another. Thus, to guarantee the selection of the best vehicle design, it is important to optimize the profile and control policy for each configuration early in the design process.
Consider this example. For tactical missiles, the flight profiles are determined by the thrust and load factor (lift) histories. These histories can be controlled by a number of means including such techniques as using an angle of attack command history or an altitude/downrange schedule that the missile must follow. Each combination of missile design factors, desired missile performance, and system constraints results in a new set of optimal control parameters.
This is not about trajectory optimization
BY a missile but about weapons development, specifically missile development in creating more accurate missiles via detailed flight records such as AoA degrees, thrust, duration...etc...etc...Notice the plurals: 'flight profiles', 'flight vehicles' and 'control policies'. This means for any specific flight, the missile is not making several 'trajectory optimization' processes but that the missile's programed flight path(s) are
ALREADY optimized based upon historical data from past missiles. In other words, your wiki source is not about
A particular missile in flight but about
THE missile as a weapons development over time and experience.
Just like the gravity turn gaff, you keep making these interpretation mistakes because you have no relevant experience and are trying to salvage some face for a losing argument.
Also as soon as the missile is not in a vertical flight anymore, it already enters a gravity turn. Your statement of "The moment the vehicle is in a gravity turn, it cannot maneuver for course correction," is dubious.
No...It is not dubious. Any maneuvers outside of what is programmed affect range. Fuel is finite. I was not speaking technically because there are no technical limitations on creating maneuverable ICBMs if we wanted to. I was speaking of 'policy' and it is that we should maneuver no more than what is necessary.
Here is the definition of 'policy'...
Policy - Wikipedia, the free encyclopedia
A policy is typically described as a principle or rule to guide decisions and achieve rational outcome(s). The term is not normally used to denote what is actually done, this is normally referred to as either procedure or protocol. Whereas a policy will contain the 'what' and the 'why', procedures or protocols contain the 'what', the 'how', the 'where', and the 'when'. Policies are generally adopted by the Board of or senior governance body within an organisation where as procedures or protocols would be developed and adopted by senior executive officers.
See that? The 'rational outcome' we desire is to hit a ground point at so-and-so time within a so-and-so diameter circle (CEP). So the 'principle' or 'rule' is that we should not maneuver beyond necessities. That mean once inside a gravity turn, the missile should not, or in accordance to 'policy', it
CANNOT maneuver. Course corrections are usually at terminal. But again, what I said should not be construed to be from a technical perspective.
Really!!?? Why do we need radar for here? I thought you only need to know the state of missile when it enters a gravity turn to know the trajectory of its path up to the "orbit".
And you thought wrong. There are two moving bodies here: the missile and the interceptor. Since we are using fixed coordinate system to create collision intercept, real time updates of
BOTH bodies are necessary.
NWS JetStream - Exactly how does radar work?
By measuring the shift in phase between a transmitted pulse and a received echo, the target's radial velocity (the movement of the target directly toward or away from the radar) can be calculated. A positive phase shift implies motion toward the radar and a negative shift suggests motion away from the radar.
Gaps between echoes compresses as the two bodies nears each other. Conversely they widens if the bodies are moving away from each other. Phase (shift) Derived Range Acceleration (PDRA) estimations are created for trajectory predictions and, believe it or not,
RECONSTRUCTION. Target state contain (x y z) position, velocity and acceleration.
Previously, I showed how fixed coordinate system sees a target state:
X = [x y z Vx Vy Vz]T or [x y z x-dot y-dot z-dot]T
Where X = state vector, T = time, V = velocity and the standard xyz axes.
For target range acceleration estimate, basic target state is seen as:
X = [R(RRC) V(RRC) A(VTC)]
Where R(RRC) = [x y z]T is the target position the east-north-up (ENU) radar reference coordinates.
Coordinate Systems, Basis Sets, Reference Frames, Axes, etc.
Local East-North-Up (ENU) system
In any ENU system, {dX, dY, dZ} is a right-handed orthogonal system.
Where V(RRC) = [x-dot y-dot z-dot]T is the target's velocity inside RRC.
Finally, A(VTC) = [a(v) a(t) a(c)]T is target's acceleration in the right-handed velocity-turn-climb (VTC) coordinates system.
The radar echo phase shift information from all three elements -- R V A -- can be used for both prediction and reconstruction and if the radar is sophisticated enough it can predict as well as reconstruct at the same time regardless of its position in respect to the target.
I still do not want to engage in a mathematical one-upmanship game here but what I do want to show the readers is that your simplistic assertions in the previous pages regarding flight path prediction bears no resemblance to what has been in place for decades. If we go back to this illustration...
...Collision navigation by the missile does not care where the bogey came from. Pure pursuit navigation (PPuN) require a true tail chase situation and air-air interceptions seldom allow us that luxury. That leave us the much more complex proportional navigation (PN) based hybrid intercept laws that require the missile to constantly (re)calculate the closing distance between bogey and itself. Even if the missile is behind the target, the laws are still PN based. In the PN based scheme, the missile does not care where the bogey came from or its thrust. The missile cares only for the closing velocity between the bogey and itself at any point in space/time. No different for ICBM collision intercept. The incorporation of phase shift data rendered origination data quite -- pointless.
So yes...Really.
Of course it does answer why an ICBM should or shouldn't in this case be built more structurally robust, because it doesn't need to.
If the ICBM does not need to be more structurally robust than a satellite launcher, then why did you criticized me for legitimately comparing the two? Remember this...
You are comparing the rigidness of a commercial rocket to a missile here????
In the equation, it tells you that for the same material used to construct satellite launcher or missile and assuming both casting has the same material property and has the same endurance for stress, the one with smaller diameter will experience less stress per unit area for the same pressure applied to it. Thus, the one with smaller diameter can endure higher g forces during a maneuver than the one with larger diameter. Of course for missiles and rocket the calculation of each of the stress point during maneuvers is more complicated, but the principle is still the same. Let me give you a demonstration here using the DF-31(ro=1125mm, ri = 975mm) and CZ-2 (ro = 1675mm, ri=1525mm) here since their lifting capacity is more or less the same, if let's say the same pressure 100 MPa is applied to both. The stress at the out surface is
For DF-31, the Hoop stress σc = 704 Mpa, the Axial stress σa = 402 Mpa
For CZ-2, the hoop stress σc = 1069 Mpa, the Axial stress σa = 585 Mpa
What it means here is for DF-31 to experience the same structure stress as CZ-2, more pressure is needed. In here, let's say CZ-2's critical pressure load is 100 Mpa, then DF-31's critical pressure load would be 145 Mpa. So if the maximum g force CZ-2 can sustain is 10, then DF-31's maximum g force is 14.5 g. Thus gives DF-31 more maneuverability. Therefore your statement of "it should not maneuver if it is to retain structural integrity." is false even if it is true for commercial rockets.
You argued that a missile is more physically robust than a 'commercial rocket'...
Commercial rockets are not designed to endure high stress manuvers that modern missiles have to withstand.
...But you show no source to support your claim, and that a missile should be so because it
IS more maneuverable, but again you show no source to support your claim. The math you presented is irrelevant and it serves nothing more than to distract from the fact that you consistently failed to support your claims with nonbias sources.
So according to you...
Q - Why should a satellite launcher be less physically robust than a missile?
A - Because the missile is more maneuverable.
Q - Why should the missile be more maneuverable?
A - Because the missile is not a satellite launcher.
What the hell kind of argument is that? In road racing, your opponents are threats so it behooves you to have a highly responsive and maneuverable car. In air combat, someone is trying to kill you so it behooves you to have a highly maneuverable aircraft. How is a satellite launcher a threat to a missile?
Here is the real logical thought process...
An ICBM is usually launched from home territory, so what is the need to make the thing maneuverable? None other than one slight pitch over. So why should it be any more physically robust than a satellite launcher? Not at all. So what if the fuel used allows for a smaller diameter tank? If anything, I would keep the same dimensions but pack it with more fuel for higher speed and for greater range. So if I build a vehicle that has just enough structural strength to carry a payload to a location, then what I said is very correct -- that 'it should not maneuver if it is to retain structural integrity'.
This is why you guys and your desperation to exaggerate anything Chinese are soooo entertaining.