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Thread: missile flight theory

  1. #1
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    missile flight theory

    I would like to discuss the theory of aerial target engagement by a missile. But I would like the discussion to be very theoretical, with as little references to actual missiles as possible. Basically, I'd like to discuss the physics and fundamental doctrine of usage of missiles.

    So let us say we have a platform that is flying at 10.000 meters at a speed of 200 m/s. It fires a generic medium range air to air missile. The missile's initial velocity is therefore around 200 m/s. But the booster module of the rocket engine fires up and within 5 seconds it accelerates the missile to around 1000 m/s. Booster module is done and now the rocket engine is on sustainment module - which lasts for another 10 seconds, keeping the speed more or less constant.

    Let us first assume the flightpath is fully horizontal, at 10.000 meters. 15 seconds have passed, the rocket motor is gone, and missile is doing 1000 m/s. It has traveled approximately 13-14 kilometers (I assume).
    Now what? There is a target, which was at the time of firing 50 kilometers away from the firing platform. It was doing 200 m/s, and still is, going straight toward the missile. The distance from the target to the missile is now 33-34 km.

    Without going into whether the missile will hit or not, which doesn't interest me in this paragraph - what happens with the missile? Assuming, for example, aim7-level area and drag coefficient, how quickly will missile's speed decrease? what will its velocity be after another 15 seconds, if the missile tries to maintain altitude? Alternatively, what will missile's velocity be after 15 seconds from burnout, if the missile allows for 500 meters lower altitude at the point of interception? (lets say the target is 500 meters lower)

    Important question also is> which equation tells us about missile deceleration?

    I have lots more questions but this is enough for starters. I do hope we can have an informed theoretical discussion here.

  2. #2
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    There has been a lot of arguments over the performance of A2A missiles here --
    some of which are well backed by facts, some are so far out there it is like claiming that
    they fly on hyperdrive.

    I want to take this opportunity to introduce everyone to a very simple formula that
    can be used for estimating the performance of a missile. It goes like this:-

    Change in Velocity (Delta V) = 10 x Specific Impulse x LN (initial weight / final weight) m/s

    This assumes that all the fuel is used to get the missile as fast as possible and
    none is used to provide just enough thrust to sustain a given velocity.
    In otherwords, it assumes an all-boost motor not a boost sustain motor.

    For example, let'a take a look at the AIM-120A AMRAAM which we have some decent info on...

    Launch weight = 335 lbs (Published stats)
    Motor weight = 156 lbs (WPU-6/B HTPB rocket motor weight as per Raytheon)
    Approximate specific impulse = 245 seconds (typical of HTPB solid motors)
    Approximate fuel fraction of motor = 85% (typical of robust aluminum cased aerospace rocket motors)

    OK... if 85% of the motor's mass is the fuel, we have about 132 lbs of fuel in the AMRAAM-A
    -- roughly a 39.4% fuel fraction (sounds about right). So let's run the numbers...

    Delta V = 10 x 245 x LN(335/(335-132)) = 1227 m/s

    The formula predicts that the AMRAAM will go about 1227 m/s (~Mach 3.7) faster than it started.
    If it is launched at say Mach 1.5 it'll be going Mach 5.2.
    In reality the AMRAAM doesn't go that fast.
    The reason is that not all the fuel is used to get it as fast as possible.
    The AMRAAM's motor is a boost-sustain design.
    It is probably grained to take the weapon to abut Mach 2.5~2.8 faster than it started at
    (Mach 4+ in a typical Mach 1.5 release).
    The rest of the fuel is shaped to burn much more slowly to keep it's velocity at
    or near the achieved maximum out to a longer range before the motor burns out.


    Well, for any given fuel fraction and specific impulse,
    a designer can decide how fast he wants to go and how long he wants to stay at
    or near the peak velocity achieved. For instance, if a missile carries 40% of its launch weight
    as fuel and uses the typical a modern HTPB propellant motor, it can:-

    (1) Spend 25% to get an approximate Mach 2.1 delta V and 15% on sustaining that speed for a relatively long while.
    (2) Spend 30% to get an approximate Mach 2.7 delta V and 10% on sustaining that speed for a shorter while.
    (3) Spend 40% to get an approximate Mach 3.8 delta V have no sustain burn time at all.

    BTW, in reference to the above comment on deceleration... it doesn't really work that way.
    If a missle starts at Mach 4 at burn out and decelerates 25% to Mach 3 after 10~15 seconds,
    it WILL NOT decelerate to Mach 2 (another 33% from Mach 3) after 20~30 seconds.
    This is impossible because aerodynamic drag (Fd = Cd x A x 0.5 x P x V^2) is a function of
    the square of velocity.
    As velocity decreases, drag force decreases exponentially in relation to it.
    Hence, if the drag for at Mach 4 causes a 25% loss in velocity in 10~15 seconds,
    there is no way a much lower drag force at Mach 3 will cause a 33% loss in velocity after
    another 10~15 seconds.
    What happens is that deceleration is non-linear;
    you start off steep and the slope flattens out over time as velocity and hence drag drops.
    It'll take a missile a heck of a lot longer to decelerate from Mach 4 to Mach 2 compared to
    say Mach 2 to Mach 1 for instance.



    Actually it also depends a heck of a lot on altitude (air density)...
    Let's plug some numbers shall we?

    Question: How much thrust is needed to sustain Mach 3.0 in an AAM like the AMRAAM?

    Drag force (Newtons) = 0.5 x P x V^2 x Cd x A

    P = Density of Air (kg/m^3) ; ~1.29 kg/m^3 @ sea level; ~0.232 kg/m^3 @ 12,000 m
    V = Velocity (m/s) ; Mach 1 = 340 m/s @ sea level; ~295 m/s @ 12,000 m
    Cd = Co-efficient of Drag ; ~ 0.6 to 0.95 for rockets depending mostly on finnage,
    nose and tail profile
    A = Sectional Area (m^2) ; ~ 0.025 m^2 for a 7" diameter missile.

    For an AMRAAM like AAM going at high altitudes (40,000 ft)...

    Drag Force @ Mach 3 = 0.5 x 0.232 x (295x3)^2 x 0.70 x 0.025 = 1590 Newtons = 357 lbs
    Drag Force @ Mach 2 = 0.5 x 0.232 x (295x2)^2 x 0.70 x 0.025 = 707 Newtons = 159 lbs
    Drag Force @ Mach 1 = 0.5 x 0.232 x 295^2 x 0.70 x 0.025 = 177 Newtons = 39.8 lbs

    The same missile going Mach 3 at Sea Level...

    Drag Force @ Mach 3 = 0.5 x 1.29 x (340x3)^2 x 0.70 x 0.025 = 11,744 Newtons = 2640 lbs
    Drag Force @ Mach 2 = 0.5 x 1.29 x (340x2)^2 x 0.70 x 0.025 = 5,219 Newtons = 1173 lbs
    Drag Force @ Mach 1 = 0.5 x 1.29 x 340^2 x 0.70 x 0.025 = 1,305 Newtons = 293 lbs

    Assuming that there is no sustainer,
    the deceleration experienced at Mach 3 by the 203 lbs (empty) missile is

    Deceleration @ Mach 3 = -F / mass = -1590 / (203 x 0.454) = -17.3 m/s^2 = - Mach 0.059/sec @ 40,000 ft
    Deceleration @ Mach 2 = -F / mass = -707 / (203 x 0.454) = -7.67 m/s^2 = - Mach 0.026/sec @ 40,000 ft
    Deceleration @ Mach 1 = -F / mass = -177 / (203 x 0.454) = -1.92 m/s^2 = - Mach 0.0065/sec @ 40,000 ft

    Deceleration @ Mach 3 = -F / mass = -11744 / (203 x 0.454) = -127 m/s^2 = - Mach 0.39/sec @ sea level
    Deceleration @ Mach 2 = -F / mass = -5219 / (203 x 0.454) = -56.6 m/s^2 = - Mach 0.17/sec @ sea level
    Deceleration @ Mach 1 = -F / mass = -1305 / (203 x 0.454) = -14.2 m/s^2 = - Mach 0.042/sec @ sea level

    OK... enough of the math and the formulas... what does all these mean?
    Well, it means that while coasting at Mach 3 an AAM is going to lose about less than 2% of
    its velocity a second at high altitudes while it stands to lose about 13% of its velocity at
    sea level! Huge difference isn't it?
    Remember though that the rate of deceleration actually DECREASES as the
    missile's velocity decreases.
    It is easy to see that one can claim that a missile can burn out burn out its booster
    and sustainer and be effective out to over 100 km at high altitudes or be useful only
    against helos after 10km on the deck!

    Also, we can make a pretty educated guess as to how much thrust the sustainer has to make.
    An AMRAAM class missile with a 400 lbs sustain thrust will be able to stay
    above Mach 3 at high altitudes and stay about Mach 1.2 at sea level.
    An AMRAAM class missile carrying about 10% of its launch weight as sustainer
    grained propellant will be able to keep this level of thrust lit for 20.5 seconds
    in addition to whatever the boost time was using the 30% of its fuel to get a
    roughly Mach 2.7 Delta V after launch.
    A missile like this when fired at Mach 1.5 will reach Mach 4+ and keep
    above Mach 3 for the duration of the sustainer at high altitudes.
    It will also reach about Mach 2.5 and keep above about Mach 1.2 at sea level.
    A motor grained for this thrust profile can have a 10 second boost at ~ 2460 lbs thrust and
    a 20 second sustain burn at 400 lbs thrust -- this is a 5:1 boost sustain ratio.
    This is also about right for thrust profiles of star grain vs
    core burn solid propellant burn rate profiles.




    Another rough rule of thumb:-

    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

    Remember, fractions over time are not additive.
    In otherwords, if a missile loses about 25% of its velocity in 10 seconds,
    in the 10 subsequent seconds (t =20s) the missile loses approximately another 25% of
    the remaining 75% not a 100%. Total velocity loss is ~43.75% not 50%.

    This is highly collated to the fall in air density.
    Drag = 0.5 x P x V^2 x Cd x A.
    Holding everything else constant Drag falls proportionally to density.
    Drag also falls exponentially with Velocity which accounts for the loss in velocity
    in the given time slices being about 25% instead of closer to 40%.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    Booster module is done and now the rocket engine is on sustainment module - which lasts for another 10 seconds, keeping the speed more or less constant.
    Newer designs tend to go for an all-boost engine because dual mode engines work great on paper but they tend to leave a lot of unburnt propellant in actual products.

    Let us first assume the flightpath is fully horizontal, at 10.000 meters.
    No BVR missile does this, they start a climb to:
    1) reduce drag (thanks to the lower air density)
    2) be able to trade altitude for speed in the second part of its trajectory

    Even the latest Sidewinder variant will include the option for lofted trajectory to increase range (with the addition of a GPS-based INS).

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    Quote Originally Posted by Blue Apple View Post
    Newer designs tend to go for an all-boost engine because dual mode engines work great on paper but they tend to leave a lot of unburnt propellant in actual products.
    Is this the case for all missile types, of would it differ on range? This obviously makes a lot of sense for SRAAM, and possibly MRAAM, but BVR's?

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    Another problem is that a missile lose agility even faster than it loses speed.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    What also contributes to velocity loss after burn-out is decreased sectional density compared to the unfired missile (worsening ballistic coefficient), and - depending on missile design - a certain amount of trim drag (as the rocket fuel burns off the CoG moves forward, and a missile is designed to fly stable when dropped).
    "Distiller ... arrogant, ruthless, and by all reports (including his own) utterly charming"

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    Here's some numbers from the only honest missile manufacturer out there

    The DRDO said Astra will be able to be launched from different altitudes but those alterations would affect the range.
    It will cover nearly 70 miles when launched from an altitude of just more than 9 miles
    but only 27 miles when fired from an altitude of 5 miles.

    At sea level the range is expected to be 13 miles.
    Active homing range will be nearly 16 miles.

    A longer range version, the Astra Mark 2, will have a 93-mile head on range with a tail chase range of 21 miles.
    http://www.upiasia.com/Business_News...9881279199751/
    70 miles =60nm=110km
    9 miles=14 km
    5 miles =8km
    27 miles=23nm=43km
    13 miles=11 nm=20km
    16 miles=14nm=26km
    93 miles=81nm=150km
    21 miles=18nm=34km

    As we can see, an impressive 93 miles=81nm=150km range on a head on shrinks to a mere quarter on a tail chase, (21 miles=18nm=34km)
    which would be the first thing the shot at fighter would do, equipped with MLD/MAWS, and reasonable high alt agility.
    If he then proceed to take a dive, we can shave off half of that quarter,
    for an effective range of that 150 km missile in practical term is
    ~10 miles=9nm=17km, = well within visual range.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    Thanks a lot for your answers. Obligatory, your post was very thorough, it was just the kind of post I was hoping to get for this topic. I would really like to encourage everyone to use real equations as much as possible and try not to simplify everything with rule of thumbs. I gobbled up all the figures and now i have a clearer image of what exactly is going on.

    Declassified documents tell us that aim7f has 5 seconds of boost phase and 10 seconds of sustainment phase. Does anyone have data backed by proof for other missiles of same or newer vintage? Do we have any idea about duration of boost and/or sustain phases in newer missiles, in the amraam A class?

    Regarding the top speed of a missile - i have to ask if the air itself prevents the missile to reach its top speed, that it would otherwise reach in vacuum? Just like a falling object through air stops accelerating at a certain point, reaching its terminal velocity, shouldnt a missile also stop accelerating due to too much drag? I ask that because the deltav= 10 * spec.impulse*ln(m1-m2) equation is great but nowhere does it mention air density and drag. Which equation would help us get info adjusted for terminal velocity, on top of the mentioned data?

    The rule of thumb for the rate a missile decelerates is great, but is there an equation that gives a bit more precise data? (i would imagine it would use derivations ?)

    Also, to make things a bit more realistic - all this until now didnt include gravity. I know what roughly happens when we have gravity, but the important question is just how much of it happens? Just to keep flying straight, finless missile will have to compensate for the gravity force vector and trim a little bit, inducing drag. Now, i suppose actual missiles create most of their lift on their own, canceling out the gravity force - but by how much?

    And, naturally, most medium and long range missiles now use lofted trajectories. But do we have any data anywhere indicating more precisely what kind of trajectories are used? I once read about aim-54 going to 30 km altitude as a part of its quasiballistic trajectory. Is that also used for various amraams and the like today for max range? At which horizontal point of trajectory is apogee reached? At what altitude is that?

    And the ASTRA manufacturer data is great! I would imagine similar set of figures can be used for various other missiles of the same class.

    What about the change of CoG that the Distiller mentioned? How much, in percentage, would that influence speed and/or range in short and how much in long ranged shots? Is there an equation for that? I would much rather calculate everything for myself, so i can learn, then just have the answer offered to me.

    There are more interesting topics left, of course, but i would rather go step by step and concentrate on these for now, then go on to agility/manouverability.

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    Thumbs up

    Quote Originally Posted by obligatory View Post
    Here's some numbers from the only honest missile manufacturer out there

    The DRDO said Astra will be able to be launched from different altitudes but those alterations would affect the range.
    It will cover nearly 70 miles when launched from an altitude of just more than 9 miles
    but only 27 miles when fired from an altitude of 5 miles.

    At sea level the range is expected to be 13 miles.
    Active homing range will be nearly 16 miles.

    A longer range version, the Astra Mark 2, will have a 93-mile head on range with a tail chase range of 21 miles.
    http://www.upiasia.com/Business_News...9881279199751/
    70 miles =60nm=110km
    9 miles=14 km
    5 miles =8km
    27 miles=23nm=43km
    13 miles=11 nm=20km
    16 miles=14nm=26km
    93 miles=81nm=150km
    21 miles=18nm=34km

    As we can see, an impressive 93 miles=81nm=150km range on a head on shrinks to a mere quarter on a tail chase, (21 miles=18nm=34km)
    which would be the first thing the shot at fighter would do, equipped with MLD/MAWS, and reasonable high alt agility.
    If he then proceed to take a dive, we can shave off half of that quarter,
    for an effective range of that 150 km missile in practical term is
    ~10 miles=9nm=17km, = well within visual range.
    Great stuff there obligatory.
    I allways knew that a missile range was very depended on the launch altitude, but i have never seen it so spesific as here.
    Keep up the good work!
    Thanks

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    Max speed is absolutely dependent on altitude/density
    Fd=1/2pv^2CdA
    http://en.wikipedia.org/wiki/Drag_equation
    Drag force in Newton = 0.5 x P x V^2 x Cd x A

    P = Density of Air (kg/m^3) ; ~1.29 kg/m^3 @ sea level; ~0.232 kg/m^3 @ 12,000 m
    V = Velocity (m/s) ; Mach 1 = 340 m/s @ sea level; ~295 m/s @ 12,000 m
    Cd = Co-efficient of Drag ; ~ 0.6 to 0.95 for rockets depending mostly on finnage,
    nose and tail profile
    A = Sectional Area (m^2) ; ~ 0.025 m^2 for a 7" diameter missile.

    For an AMRAAM like AAM going at high altitudes (40,000 ft)...

    Drag Force @ Mach 3 = 0.5 x 0.232 x (295x3)^2 x 0.70 x 0.025 = 1590 Newtons = 357 lbs

    The same missile going Mach 3 at Sea Level...

    Drag Force @ Mach 3 = 0.5 x 1.29 x (340x3)^2 x 0.70 x 0.025 = 11,744 Newtons = 2640 lbs

    How much thrust does the sustain mode produce ?
    less than what it takes to equal that of drag at sea level.
    It would be interesting to know what thrust Meteor has, (T=D) altho
    it has to be taken into account that missile is faster and thus has more drag to overcome

    Since a BVR missile has comparatively small control surfaces,
    it is harmless by the time it decelerated down to M2, so assume M3,
    gravity force is insignificant compared to drag at M3.

    No clue about trajectory, except that a fast target has moved far away by the time missile arrive, so not sure how useful vs fighter.

    To add sectional density & shift in Cg into equation is begging for problem,
    and would require not only data but also test flights and plot in what the function doesnt explain.
    Cg is moving forward so at least it doesnt start to flip, but does get nose heavy and so impact agility negatively, OTOH it is also lighter.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    But how long do rocket engines last nowadays? I would imagine they moved away from the Sparrow's 15 second. Are we closer to 20 or 30 seconds nowadays for an amraam type missile? Aim54 was once quated to have a engine lasting for 27 seconds. But that is another kind of missile with different mission profile.

    Obligatory, are you saying that most mid range BVR missiles will not really use lofted trajectories that much? I probably misunderstood something there. I would imagine midcourse corrections would solve most of the problems that long flight times would produce.

    If the missile is going downwards in the latter half or last third of its trajectory, how much would that slow down the deceleration? If it impacts the deceleration, then the equations we saw before arent enough to get the final speed. Basically, what would be the final realistic speed, before impact, for an amraam type missile at say 70 km away, what would it be at 100 km away, and what would it be for a RVV-BD type of weapon at 200 km away?

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    To my knowledge the only real advancement in rocketing is from taking the major part of the fuel in flight (Ramjet), any other increase in flight comes not from better fuel, but lofted trajectory, higher alt. at launch and better initial speed.
    Phoenix is a giant of a missile so it has large fuel tank, but then the size & weight comes with momentum/agility penalty.

    Drag still account for the vast majority of deceleration.
    A fighter can be expected to change direction as the MAWS go off,
    mid course correction to adjust for that just makes things worse if the fighter makes more than one turn, since the missile will have to aim so far in advance.
    ( It could easily have to change/overcompensate direction 150* each time a fighter maneuver, consuming energy status at a screaming rate)

    IMO it is senseless to use solid rockets against maneuverable fast targets if the rocket has to fly 70 km
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    Obligatory , you 're the man

    Cheers .
    I say what I mean and I do what I say .

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    Quote Originally Posted by totoro View Post
    But how long do rocket engines last nowadays? I would imagine they moved away from the Sparrow's 15 second. Are we closer to 20 or 30 seconds nowadays for an amraam type missile? Aim54 was once quated to have a engine lasting for 27 seconds. But that is another kind of missile with different mission profile.

    ...
    http://www.youtube.com/watch?v=mXTDrLs2n_E

    That version of AIM-120 burns out after 8 seconds.
    "Distiller ... arrogant, ruthless, and by all reports (including his own) utterly charming"

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    Yes, 8 sec worth of burn is also my info on latest AMRAAM
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    So it is true that newer bvr missiles use just a single profile rocket engine? What sort of improvement could we be looking at, in amraams 8 second burn, compared to sparrows 5 second boost phase burn, thrust wise?

    Is it safe to assume that the likes of mica, r77, pl-12 and the rest also use single profile rocket motors? Do WVR missiles today use dual or single profile rocket engines?

    I still can't really get my head around the final speed figure. I'd really need an equation for that, not just a thumb rule. How do i calculate a missile's speed at any given point past the moment the rocket engine dies, along its flight profile? Lets say its a profile where the missile is fired at 12 km altitude and reaches an apogee of 20 km, then starts shallowly diving towards the target. would that flight path even be realistic?

    I really want to be sure about the approach speed portion of the whole issue, before we can go onto the another intersting topic - agility/manouverability.

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    Also, one can find video clips of VL mica launches - but sadly it is not clear if the engine shuts off or the missile is just too far away for a rocket plume to be visible. though, in two separate clips that 'Im not sure moment' is around 5 seconds after the launch...

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    There is an important exception to the single burn rocket rule: Meteor. It can boost, cruise, then throttle up for the terminal phase.
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    The basic formula is
    v=vi +-at

    v = speed
    vi = initial speed, mach 4 after 8 sec
    a = deceleration*
    t = time

    * a function could explain this if you are upp to snuff on integral calculus,
    otherwise
    F=1/2 x P x V^2 x Cd x A

    F= force
    P = Density of Air (kg/m^3) ; ~1.29 kg/m^3 @ sea level; ~0.232 kg/m^3 @ 12,000 m
    V = Velocity (m/s) ; Mach 1 = 340 m/s @ sea level; ~295 m/s @ 12,000 m
    Cd = Co-efficient of Drag ; ~ 0.6 to 0.95 for rockets depending mostly on finnage,
    nose and tail profile
    A = Sectional Area (m^2) ; ~ 0.025 m^2 for a 7" diameter missile.

    or easier yet,
    a = -17 m/s^2 @ 12.000 m,
    i would just assume -12 m/s^2 on average at high alt, and several times more at low alt. before the missile can be considered utterly worthless due to decreased speed & therefore insufficient pressure on control surfaces

    so then
    v= 1360 +-12*t (high alt)

    it took 8 sec to make it 1360 m/s and got 5.5 km head start, but will get another x head start depending on launch speed
    (speed of the launching a/c, perhaps up to 10 km total in best case)
    Last edited by obligatory; 19th December 2011 at 02:04.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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    thank you, obligatory.

    So now we come to the agility and/or manouverability.

    Say we have a missile with a rocket motor that has just burned out - and it is doing lets say 1200 m/s at that moment, at 12 km. Its target is at 10 km altitude, some 60 km away, but approaching the general direction of the missile at 200 m/s.

    For scientific purposes we'll assume no decoys, jamming, no failure of any systems on both the target and the missile. Everything works as it should. let us also assume missile has really long ranged radar of its own so it doesnt need course corrections. it is fully fire and forget.

    1. What happens if the target suddenly starts turning 20 degrees left? Will the incoming missile assume the target will continue going that way and redirect itself sufficinetly so it meets that path when it crosses 60 km?

    Or will the missile lead the target a bit, but not too much, as it is quite possible and probable the target will manouver some more in god knows which direction?

    How will those manouvers of the missile influence its speed, on top of the speed loss we would see from drag?

    2. Let us assume the target just went on that course up until the point where missile was 20 km away from it. then the target started a very hard manouver to get the missile to bleed more energy. Would the missile at such distances try to fully lead the target? What if, at 10 km away, the target tried to change direction? Or even go up, vertical? Would that help?

    Let us assume the target is, realistically, with some load, doing 7 G manouvers. Let as assume the missile can do 50 g manouvers.

    How much speed would the missile lose in all those manouvers?

    Another important question is - how quickly would the missile adapt to the new situation? I don't want answers like "sufficiently fast so we don't need to calculate it", i'd really rather prefer concrete numbers. Are we talking about one second? a tenth of second? A thousandth of a second? a missile does need to process the signal, interpret it, calculate the course adjustment, actuate its fins and stabilize itself on a new course. and perhaps do that several times a second or more.

    Those would be scenarios where missile was fired quite far away, with much of its speed already bled.

    What would happen if the same missile was fired from a shorther distance, so once its rocket motor burned out, the missile would be just 20 km away from the target, also head on?

    Again lets assume the target magically knows the precise moment it would be best to manouver. and does 7 g manouvers, versus missile's 50 g manouvers. Is it a simple matter of missile staying within targets maonuver envelope? or is there more to it? would barrell rolls, for any reason, help the target?

    I know the g force increases exponentially with speed - but would that mean the missile is too fast too manouver the way it should? or if the missile is sufficently slow to follow the manouvers - would that make it so devoid of energy the target could escape?

    Would the missile lead the target and start its manouvers from afar, not having to match the G load limits (in percentages of max) of the target? Or would that be too dangerous and the missile would have to follow the tail of the plane more closely at least until its really close? What about the tiny amounts of time needed for course correction by the missile? is that even a factor? Missile does, in the end, react to the target, and not even a magical supercomputer with magical superactuators can react 100% the way it should in zero time.

    I would once again like to reiterate that i know this is not a realistic setup, but im not looking for that now - i need a simplified setup with controlled variables to understand some basic concepts first.

  21. #21
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    To my knowledge AMRAAM is max 35g, Mica 50g,
    but that is right at max speed so only valid 8 sec after launch,
    and i'm guessing at max alt. 6000 m, and even that is an overstatement, since while low density is great for low drag/ good range, the same lack of density provide insufficient resistance on control surfaces, (and bwr has comparably tiny surfaces) it would help to check out wing loading, in fact we need wing area.
    When the missile turn, sectional area is no longer 0.025 m^2 as in head on,
    but much much more, first you have the entire length and then you need to add the wing area to get drag force, how much depend on angle of attack.
    A beginning would be to calculate area at 30* and see how drag rise.

    I don't know reaction time, but the consensus is that if the missile didn't get a perfect start, (as in head on, no maneuvering) it can't make up for it later when fuel empty.

    To my knowledge AAM's are aiming ahead of the target Pro-Nav, so the further away the easier to mess it up by forcing it to switch flight path towards center of earth or the stars, this should be best done during boost.

    I think it help to contemplate the extremes, vacuum, the missile fly forever, but can't change direction a single degree, and water, where it won't make more than a few meters, but will turn very fast, and then anything in between on a falling scale.
    And also calculate a couple of examples, or more if you have patience
    Last edited by obligatory; 19th December 2011 at 09:32.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

  22. #22
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    shouldnt g force limit be the same, regardless of speed? only difference being, at higher speeds the turn radius will be much greater. also, at too low of a speed, the drag during the turn might kill the missile, since it doesnt have sustained thrust through the turn, like the target plane does.

    also, are you suggesting g force is also limited by altitutude and air density? i dont understand that either. again, i understand thinner air will make for less of a turn, as there is less force acting on the control surfaces, but that shouldnt have any connection with max g force. or should it?

    real questions are: how much does manouvering at high altitudes lower missile's manouverability?

    if a projectile is doing, say, 200 m/s during a 7 g manouver - it will have a turn radious of some 540 m. if a projectile is doing 1200 m/s during a 7 g manouver - it will have a turn radius of some 13.500 meters. If the projectile wants to go 1200 m/s but keep the 540 m turn radius, it would have to withstand some 260 Gs. obviously no missile does that, but im just saying...

  23. #23
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    No, just make the air thin enough, or non-existent as in space, and the missile can't pull a single g. (no force is acting on the object, and so it can't change anything)
    Or at the other hand, when the missile is at stall speed M0.7 or so, or why not at speed = 0.
    Look at the extremes and then make a falling scale.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

  24. #24
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    i see. that does make sense. but just by looking at the extremes, how can i make a (even a semi correct) function which would give me the sense of how much G (in percentage of maximum G force) can a missile pull at which altitudes?

    Does the air density closely correlate that? So, say, if the manufacturer says a missile can do 50 G - and then again we assume that's the highest possible g force, does that mean it can do those 50gs ONLY at low altitudes, where air is densest?

    But there's another predicament. At low altitude drag is bigger, so missile is slower. so less mass of air goes over the control fins per given period of time and less force is used on those control surfaces. So by going higher, the missile is faster and thus more air is used to make up a force. I need to know how those two curves (functions) interact. How much does flying faster compensates the loss of lift/loss of manouverability due to the higher altitude?

    I'd really need a graph of missiles envelope, but i cant find those. Can i just assume its similar to a fighters flight envelope graph? Or would that be completely incorrect?

  25. #25
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    You can calculate drag force at various speed & alt., and indeed already got enough numbers to make a plot. (see post with drag force at various speed & alt)
    It is clear that even at a full mach lower, there is still 4 times more force/resistance at low alt. vs high alt., which is the exact same resistance as you need to turn.
    It would not surprise me one bit if the agility is given at best condition low alt.,
    while in the same breath range is given at best condition high alt.
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

  26. #26
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    What happens if the target suddenly starts turning 20 degrees left? Will the incoming missile assume the target will continue going that way and redirect itself sufficinetly so it meets that path when it crosses 60 km?
    I'd suggest you google "missile" and "proportional navigation".

    Another important question is - how quickly would the missile adapt to the new situation? I don't want answers like "sufficiently fast so we don't need to calculate it", i'd really rather prefer concrete numbers. Are we talking about one second? a tenth of second? A thousandth of a second? a missile does need to process the signal, interpret it, calculate the course adjustment, actuate its fins and stabilize itself on a new course. and perhaps do that several times a second or more.
    The missile doesn't "adapt to a situation", it doesn't run some kind of decision software. Once the target is acquired by the seeker, the missile trajectory is directly commanded by the seeker return through a closed-loop system.

    Adjustment would be continuous for an analog loop and likely 100Hz or more for a digital one.

    Would the missile lead the target and start its manouvers from afar, not having to match the G load limits (in percentages of max) of the target?
    Pro-Nav* doesn't care about the acceleration of the target, only its velocity vector. High-g manoeuvres far from the missile would only result in the target slowing down, making the missile's task easier. IF one has to avoid a missile, it's better to go down, change course and try to jam the datalink. It's only if all that fails that you'd try a hard-g turn at the last moment.

    *advanced proportional naviagation uses an estimate of the target acceleration but it can only be used with a radar seeker and should only be used at close range as it's easier to fool and can lead to missile overcorrections (=lost energy).

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    "Distiller ... arrogant, ruthless, and by all reports (including his own) utterly charming"

  28. #28
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    Firefox freezes when i try open it, can someone upload it ?
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

  29. #29
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    Question

    Quote Originally Posted by obligatory View Post
    Firefox freezes when i try open it, can someone upload it ?
    I use Chrome 16, and no problems opening. Firefox 8 doesn't seem to have a problem either. Just right-click on the link and choose "Save Link As" followed by "Save File" and run it from the hard if the browser is giving trouble....

    But Chrome 16 & Firefox 8 works fine for me....

    PS: Jackson.pdf - 2.97 MB
    Last edited by QuantumFX; 20th December 2011 at 05:03. Reason: added a link

  30. #30
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    Here is info on R-77 & other missiles, that echoes what is known on how drag force influence missiles
    http://forum.keypublishing.com/showt...highlight=mald

    http://www.x-plane.org/home/urf/avia...siles/aam.html
    the missile will require about five times the G capability of the target to complete a successful intercept.
    -Robert L Shaw

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