missile flight theory

I came across this
http://www.x-plane.org/home/urf/aviation/text/missiles/aam.html

Nice link, but it gave me a headache. Could have been better in a tabular or graphical form.

I came across this
http://www.x-plane.org/home/urf/aviation/text/missiles/aam.html

Yes, i would go for 2* also, or even less actually. or more specifically it should start out very low to nonexistent,
but increase as speed decrease.
The altitude OTOH i think is less than 14km on an average,
you also have to include ascend & descend.
Vs hard targets that can be expected to fly high, (F-22/EF) i expect none will try a shot BVR, they will close in
to increase Pk & decrease reaction time.
Vs easy targets, (Jaguar) the target fly at so low alt so a large part of flight will have to be low alt. i.e flight is more resembling a circle

5 degrees would roughly mean twice the drag than it would have without worrying about maintaining altitude. Though this is quite imprecise. Maybe it is 2 degrees? But let us assume it is 5 degrees, would twice the drag mean roughly half the range? so 75 kms travelled, without ballistic trajectory, without manouvering, and end speed would be mach 2.25? And that is even for 18 kms of flight altitude, which i do agree is quite a bit, close to the operating limit of most missiles. So in more realistic profiles we could be looking at like 60 or so km? Now that looks quite low, though.

So either the angle is quite a bit less than 5*, or the added drag, say twice as much, does not equal half the range, but impacts range significantly less. I would expect the former is more likely and that angle of attack is closer to 2 degrees.

Hmm, you need to assume an AoA that the missile keep to counter gravity,
and then add the drag that induce, like we did with the 30* example for maneuvering, but obviously less angle for level flight. <5* IMO

18 km alt is a bit on the high side even with ballistic trajectory,
most fighters rarely operate over 12 km i think.

I recently remembered this thread when i was calculating ranges for various missiles which, upon rereading what was said here, left me a bit puzzled.

It was said that, as a rule of thumb, missiles loses 25% of speed every:

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, assuming our missile is going, say, mach 4 at 18 km altitude, it would, after 70 seconds of deceleration, cross another 81 km and at that point still be going strong at mach 3. It would go on, for another 70 seconds, crossing aditional 61 km, stilll going mach 2.25. So at that point, calculating in at least initial 5-6 km crossed during the engine burn phase, we are looking at total horizontal distance travelled of nearly 150 km.

Of course, during that time, the missile should lose quite a bit of altitude. I used a very rough approximation of terminal velocity thanks to this calculator http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/fallq.html

and this curve for air density with altitude http://www.aerospaceweb.org/question/atmosphere/q0046b.shtml

and it should work out that missile would lose at least 10 perhaps 15 km of altitude during those 148 seconds. Sadly, i cant figure out a more precise range of numbers as it is hard to approximate drag coefficient for side projection of a missile…

Naturally, a real missile would not lose altitude that fast but would trade increased drag/decreased range for altitude. So the question is: by how much? How much would range suffer if missile tried to lose no more than 50m of altitude per second?
How much would range suffer if missile tried to maintain altitude? at what speed and distance travelled would the missile start losing altitude?

(all this ignores the likely possibility of depressed ballistic trajectories, of course, but it is complicated enough without those…)

To calculate time for the turn you will have to look at how much the missile have to turn to head at interception point at that moment, so that depend on range to target, (it has to aim very ahead, almost flying parallel, if it is still a long way to target)
it depend on target speed, (likewise if target is fast)
and it depend on how much the target changed direction.
Energy is always going to be an issue, even if the target is not moving at all,
you will still need at least enough speed to remain in controlled flight,
and stall speed for an AMRAAM is likely low transonic.

The last ditch effort is more likely a maneuver to get out of the missiles view,
in both cases i guess flying an S is the preferred option,
it’d be great if a pilot would want to comment on this.

Speed should be less of an issue at low alt. with regards to maneuverability since there is still so much pressure on control surfaces. (and everything else)
In general i would assume wing loading is a critical issue at high alt. regardless of what’s flying fighter/missile, but at low alt thrust is more important. Or in other words, maneuverability is the issue at high alt., and require low wing loading,
and/or very high speed for control surfaces to have a measurable effect, while thrust (or lack of) is the pressing issue at low alt., and a missile has none usually.
Actually i think low wing loading is not necessarily a good thing at low alt.,
because the wings will function as a giant air brake in a maneuver, it could well be that you could plot in curves where a favorable wing loading is optimal at a specific alt. So who knows, perhaps those fighters with high wing loading will out-turn skinnier fighters in sustained turn at low alt., at least if thrust is equal, (i don’t know really) but i’m convinced thrust is everything at low alt.

12 times more drag sounds about right, i projected similar figures. but do we have any way of knowing for how long so much drag is applicable? are we walking a turn that will last half a second? or two seconds? the difference in accumulated extra drag through time is considerable.

also, what about smaller corrections during cruise phase? the added drag from those, which is surely smaller, perhaps just two or three times bigger than nominal drag, cant last for long. i would imagine the missile would change its direction by a few degrees in perhaps a tenth of a second. is that about right?

another important question is – what happens when loss of energy isnt an issue? what happens when missile is engaging a target perhaps 20 or so km away? rocket motor just burned out and theres like 5 km to go to the target. missile has plenty of speed and energy left. is all that excess speed bad for the missile in such a situation? or does it make no difference for the manouverability?

Assuming the missile fly at 30* AoA during a turn at M3 & 40.000 ft, that is
Drag force (Newtons) = 0.5 x P x V^2 x Cd x A
0.5×0.232x783225x0.7xsin30(0.18×3.7)=20987 N, 4718 lbs
compare to 357 lbs in straight flight, some 12 times increase in drag, almost twice as much as the drag at low lv,
in other words it is flying straight into the wall during maneuvering, and this doesnt even take into account drag from fins that occur in a maneuver.
But i would assume sin20, just that i havn’t got a pocket calculator.
OTOH the added area from fins in AoA probably justify sin30 value

Thank you, obligatory. I do believe theres enough data in this thread now so one can interpolate range figures for a variety of missiles and flight profiles. One thing missing, though, is manouverability data. Just how much (quantifiable!) drag would a turn of a missile produce? Lets say its target is 100 km away and keeps turning 5 degrees left, then right every 5 seconds. How much drag would the course corrections on the missile produce? and how much would the range suffer?

I found a piece of data from x-31 flight testing, where it said its FBW FCS made 40 adjustments per second, as it was an unstable platform. I would guess that gives us a decent ballpark figure for how quickly a missile can react to a new condition.

Also, what about terminal manouvering? lets say theres just 10 km to the target, and the plane goes vertical, full AB. Maybe its doing 200 m/s, on a good day. Missile is one km above the plane, but is now obviously turning upwards so it intercepts the plane where it will be 10 seconds from that point. Its motor is burned out, it crossed some 50 or so km, perhaps it is doing some 1000 m/s. (do correct me if im wrong). How much drag is such a relatively hard manouver gonna produce for the missile and how much speed is it going to lose in the process? Everything is going on at around 10 km altitude….

Here is info on R-77 & other missiles, that echoes what is known on how drag force influence missiles
http://forum.keypublishing.com/showthread.php?t=18280&highlight=mald

http://www.x-plane.org/home/urf/aviation/text/missiles/aam.html

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

Firefox freezes when i try open it, can someone upload it ?

Interesting?

http://www.jhuapl.edu/techdigest/TD/td2901/Jackson.pdf

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).

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. 😮

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?

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.

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…

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