AIM 120's

[GGTharos]

I'll see if I can find some data to find out what's going on with these missiles ... but I think SK would be way ahead of the game than me here.

[SwingKid]

I don't think radius can be discounted so lightly SK, you still have to compress and shove the air aside, and that takes energy, and that energy bleeding is drag. Frontal area increases by the square of radius, so a doubling of radius (say from 150 mm to 300 mm) means four times as many atmospheric gas molecules to be both shock compressed and shoved aside, to make way for the missile's path; in other words, every missile has to evacuate the gas in front of it, equal to its radial area, in order to even project forward through a gas.

 

Well, I'm not an aerodynamicist, but even the little research I did for miniZAP became quite involved and featured a lot of unintuitive surprises that are difficult to explain in a forum like this.

 

Some things I learned:

 

Form drag doesn't depend nearly so much on the streamlining of the nose of a body, as it does on the tail. Even though pressure may build up around the nose, that high-pressure air is still laminar, whereas the low-pressure air at the tail is turbulent and therefore much more "draggy". This is why so many aerodynamic designs, from airfoils to automobiles like the VW Beetle, feature a characteristic "teardrop" shape with streamlining at the tail, and often even a rounded nose. Of course a rocket nozzle in the tail is hard to streamline, but you can still see some missiles and artillery shells designed with "boat-tails" to minimize form drag.

 

Even while not discounting form drag though, we should recognize that it does depend only on cross-section, whereas viscous drag depends only on length, and internal volume is a function of both. Since viscous drag increases with length and form drag increases with cross-section, we should be able to agree there there exists some length-to-diameter ratio that provides an optimum balance of both for a given internal volume. I mean obviously an extremely thin, extremely long missile with practically no cross-section is going to have negligible form drag, but still have viscous "skin" drag due to its extreme length. In this case, making the missile even longer and thinner than it already is won't help - you need to make it shorter and fatter to reduce the viscous drag, because there isnt any form drag to reduce. The only thing we can really argue about is what that "magic" dimensional ratio is, where one type of drag starts to dominate over the other.

 

According to my best sources, the "magic" length-to-diameter ratio is 11:1, which is coincidentally near the dimensions of both the AIM-54 and AA-9, which are coincidentally both supposed to be designed for minimum drag and maximum range, even at the expense of maneuverability.

 

miniZAP does not discount form drag in its calculations. But the fact that AIM-120 and other missiles have length significantly greater than 11 diameters suggests that for these other missiles, the viscous ("skin" or "friction") drag dominates the form drag, and our intuitions about form drag alone are inadequate to describe the real aerodynamics at work.

 

From what I have read/learned, such skin frictional drag is the minor component of total drag, at supersonic velocities; due to the buffering effect of the forward and outward directed compressive shock-cone boundary, which generally accelerates the gasses around the missiles path; and thus thins them out, particularly near to the skin, compared to the sub-sonic situation

 

The fact that wave drag, which is a third kind of drag, dominates over viscous drag at supersonic speeds, is not in any way evidence that form drag dominates over viscous drag. Wave drag is not strictly dependent on cross-sectional area - the shock wave forms around the pointy tip of the object no matter its size. Now, you can argue "why does miniZAP bother with form and viscous drag, then, if wave drag is dominant?" Well, it turns out you need the former two in order to calculate the latter anyway, since wave drag is just expressed as a coefficient.

 

(consider it, if supersonic skin drag were the major drag component, instead of the minor, then the F-22 might struggle to even achieve supersonic cruise, for its skin area is massive compared to the size of the aircraft–much larger in skin area than any previous fighter; yet it supercruises like blazes, because skin-drag is very low, when compared to the supersonic sectional-area drag component--it’s the shock-buffering, behind the compressive and dispersive (gas) cone, which makes skin-friction the minor drag component at above acoustic shock velocity in a gas).

 

First, the F-22 is not shaped like a missile and makes a poor comparison. It has a much smaller "length-to-diameter" ratio than 11:1 so we could argue the form drag should be dominant for the F-22 anyway and it doesn't contradict our missile discussion. (I'm not sure how this helps it attain supercruise though, since drag is ultimately drag, it doesn't matter which kind dominates over the other, so long as the total doesn't exceed the thrust.)

 

More surprisingly though, viscous drag for pipes and cylinders does not depend on total surface area, but rather only on the length. The width dimension cancels out somehow in the math (honestly, I don't even understand why, it just does).

 

At subsonic, the gasses immediately around the missile skin are highly compressed, and therefore denser and present much greater kinetic skin frictional resistance, but at supersonic velocity, the reverse occurs, the gas become much more rarefied behind the shock cone, and so the skin-friction drag component plummets accordingly.

 

I asked a professor about this who said no, skin-friction viscous drag continues to take place behind the shock wave as before and continues to increase with speed... It just "increases at a decreasing rate," I think. Then he started talking about the temperature of the air behind the shock wave and I started getting lost.

 

In which case, the bigger missile not only has the much larger radial area, it likewise (generally) creates the larger shock cone area of gas acceleration,

 

"larger shock cone area" is something I can't agree with. Every shock wave should theoretically spill out to infinity, AFAIK. This is why sonic booms can be heard from so far away, regardless the size of the object making them.

 

I'm not sure why you think this the less important drag factor? Can you maybe clarify some SK, thanks.

 

To repeat, I think what you have tried to describe is not form drag at all but rather wave drag, which does not really depend on cross-sectional area. So we are probably simply talking past each other - you saying "it's not the viscous drag" and me saying "it's not the cross-sectional area" and in a sense, both being right, since it's really the wave drag.

 

I have to say what really surprises me though is that you seemed to expect the R-27ER to have longer range than the AIM-54C. If nothing else the fact that the AIM-54C is documentedly so long-range should be a confirming hint that being "fat" does not necessarily mean draggy...

 

Hope this helps,

 

-SK

[GGTharos]

SK, your proggy does have a few problems ... I've got the sparrow looping on a 3000m to 3000m shot at launch speed of 1100km/h and target speed 900km/h.

 

I hope you work out some of those bugs man! ;D

[SwingKid]

The wave drag is on turns divided in (wave) drag due to volume and (wave) drag due to lift. It can be proved that the wave drag is proportional to the volume and inversely proportional to the fourth power of the body length. ..."

 

Interesting.. This part I didn't know. miniZAP uses the wave drag coefficient as a sort of "calibration factor" - i.e. I know the range performance for R-27R, so I tweak the wave drag until I get that result in miniZAP. Then I use that same wave drag expression to calculate the range of missiles I didn't know.

 

-SK

[SwingKid]

SK, your proggy does have a few problems ... I've got the sparrow looping on a 3000m to 3000m shot at launch speed of 1100km/h and target speed 900km/h.

 

I hope you work out some of those bugs man! ;D

 

I think you discovered an undocumented feature that I use for program calibration. The "Loft Glide Logic" is really a tri-state - on, off, plus a third "grayed" state that tells the missile to make a high-G turn after motor burn out. I needed to study these turns to calculate maneuvering drag, and then left the feature there in case anyone ever challenged that part of my work.

 

If you ever see something weird, you can save the input parameters to a text file with one of the buttons. Then the same effect can be reproduced later without wondering, "now what did I do that one time?"

 

-SK

 

P.S. And yes, onething we learn from miniZAP is that forget about boost:sustain ratios... loft is such a huge performance-enhancer that I am really interested in studying everything I can about it. Thanks for the videos!

[GGTharos]

RGR SK. Seriously, could we request for some features?

 

Also I'd like to know what 'security maneuver', 'lifting body' and 'rounded nose' does if possible.

 

Basically what I'd ask for is if we could do something like give it a range of inputs to run through and have a range of outputs produces in a file if possible.

 

EG: I put it 'use aspect 180through 0 by one degree, save pairs of RMAX vs. aspect, repeat for altitudes 1000-25000' every 1000' "

 

(Yes, I know the format will sure look different ;) )

 

Basically with those little additions you could start drawing RMAX zones for various launch profiles which would be neat. I could do it by hand but who wants to do 189=0 points by hand? (and then do it again for diff loft angles etc)

[F l a n k e r]

Oh, I can’t resist! I must meddle in this so technical conversation! Your posts are very precise and I can only add that the shock waves are simply the transformation (dissipation) of the mechanical energy into the thermal one (pardon me, I don’t know if the English terms are correct!). The mechanical energy is supplied by the engine, so is limited, and so the section of the shock wave, that in air tend to transform itself, away from the body who generates that, in an isentropic wave (an acoustic wave: the boom). For the axisymmetric bodies the things are in some way different: we have the conic shock wave.

The flat shock wave compress the air in 10E-06 cm, the conical ones continue to compress the air even back. This is traduced (by physics lows) in minor energy loss. Hope my poooor English is understandable… and helpful!

[SwingKid]

RGR SK. Seriously, could we request for some features?

 

It doesn't hurt to ask... :) I do think I took miniZAP about as far as it can go though (see below), and have a different programming project these days.

 

Also I'd like to know what 'security maneuver', 'lifting body' and 'rounded nose' does if possible.

 

Security maneuver:

Immediately after launch, the R-27R (AA-10) turns downwards and away for a moment, to help prevent rocket motor exhaust from being ingested by the launching fighter's engine intake. Only after this first fraction of a second does it actually start guiding on the target. Since I happened to have good data about this maneuver for the AA-10, I decided to include it in the model to see how much practical effect it would have on maximum range (apparently, very little). Judging from the way the AIM-120 exhaust in the Archer video seems to be steering downwards immediately before it starts climbing, maybe the AIM-120 uses such a maneuver also.

 

Lifting body:

The conical nose radomes of the AIM-7 and other missiles of that generation are designed simply to minimize drag when moving forward. The more tapered nose of missiles like AIM-120 and R-77, however, are designed to do more. When the missile has positive angle of attack, more air hits the lower surface of this radome than the upper, generating lift. It's something like the way a speedboat noses into the air while moving forward, but a better comparison is with "dynamically unstable fly-by-wire" aircraft, in which a slight turn has a tendency to generate even more turn unless there is a very good computer control system to counterbalance. The unstable "lifting body" missile design allows the missile to be steered by smaller, tail-mounted control surfaces that use less power and let the missile stay controllable for a longer flight time with the same battery (in turn, allowing long-flying lofted shots). In miniZAP, this parameter gives an experimental "boost" to the amount of lift generated for a given angle of attack, allowing the missile to generate less induced drag to sustain level flight at a given speed.

 

Rounded nose:

Radar seekers have pointy noses and IRH seekers have rounded noses. The effect of the rounded nose comes into play when the missile is supersonic - the wave drag is increased by a certain amount (I can't remember exactly, found it on the web somewhere around 5-20%). Some people intuitively seem to think the rounded nose should be responsible for IRH missiles having shorter range than radar missiles, but in fact the cumulative effect is apparently quite small.

 

Basically with those little additions you could start drawing RMAX zones for various launch profiles which would be neat. I could do it by hand but who wants to do 189=0 points by hand? (and then do it again for diff loft angles etc)

 

Well, I can save you some time here... miniZAP results will give you an (incorrect) perfect circle, centered on the average of head-on and pursuit aspect range. The missiles in miniZAP aren't really homing on the target, doing any PN "sidewinding" or anything like that as they accelerate and decelerate - miniZAP treats them almost as artillery shells to figure out purely "aerodynamic" range. No matter what you enter as the target aspect, the missile itself will really fly the same distance (see "Flight Range" in the Trajectory Calculation column) - the target motion is simply added or subtracted to get a theoretical "Rmax".

 

A real missile chart would look more egg-shaped than circular, because of all the draggy PN course corrections being done against laterally moving targets as the missile accelerates and decelerates, for example:

 

 

As such, I don't think it would be especially useful to add such a feature as you've described to miniZAP just yet - you would end up with mostly incorrect charts. Someone with access to real data once took a look at miniZAP and said that with the correct (i.e. unknown to me) loft angles and other parameters entered, the missile flight for the first 30 seconds corresponded well with reality, but after that the miniZAP model apparently doesn't slow them down enough. If I could get more data this is the first thing I'd try to improve, but at this point I ran out of non-secret sources and had to stop. Simply increasing the drag coefficient arbitrarily was a no-go because for everything that I did have data for, the model was (after much work) finally calibrated correctly - IMHO better to have part of it working exactly, than all of it working vaguely. I suspect that real-world missiles just wiggle their fins more in flight or something than they do in miniZAP, and that accounts for the extra drag.

 

Thanks for interest!

 

-SK

[GGTharos]

SK, have you read the missile anvigation PDF's I sent you?

 

From them it would be easy to connclude (IMHO) that the fins indeed do 'wiggle'.

 

TO start with, an exmaple: Usuallyw hen you see a sidewinder launch is 'wobbles' when you look at it tail-on.

 

This is posisbly (but not necessaily) due to wither BANG-BANG style navigation or because of the seeker settling time, which is very similar to gunsight settling time with old WWII sights when radar wasn't available.

Another possibility is precicely what you mentioned about unstable airframes before: perhaps the guidance system has to work all the time to maintain the proper trajectory with a 'lifting body' instead of just a straight ballistic shot.

 

 

Do you, by any chance, know the reason for No_Escape zones being modelled as an aircraft doing a single 6-G break-turn away followed (possibly) by a high-g turn into the missile?

 

Is it due to constraints on the pilot's ability to haul g (I refer to LOMAC's 'yoda maneuver' against the 120 and the 77 for example), the airframe's ability to haul g, or a combo, or perhaps due to a BVR F-Pole joust?

[SwingKid]

SK, have you read the missile anvigation PDF's I sent you?

 

Only the first two so far, they're pretty long. IIRC the first one deals a lot with SAMs, command and beam-rider guidance, the second with PN...

 

From them it would be easy to connclude (IMHO) that the fins indeed do 'wiggle'.

 

TO start with, an exmaple: Usuallyw hen you see a sidewinder launch is 'wobbles' when you look at it tail-on.

 

This is IMHO a little different.. a Sidewinder doesn't generally fly for more than 30 seconds and its wiggle is a direct result of PN guidance.

 

A missile that flies for more than 30 seconds in miniZAP is likely to be using some kind of loft. Ideally (i.e. except for the odd radio-command course correction), the loft flight should be purely ballistic, with the control fins locked in the straight position for minimum drag, until the missile gets close to the target and actually starts making PN homing course corrections. Of course, those corrections should only be happening for the last 10 seconds or so. Which, if I am to trust my critic, leaves a window of about a minute of ballistic flight (between the first 30 seconds of "accurate modelling" and the last 10 seconds of PN), where miniZAP missiles are apparently less draggy than the real thing. So I postulate that the fins on the real missile may be doing something other than staying locked straight during this time, but I don't have any real proof. My argument is based simply on a very high confidence in my own work on miniZAP - when I check the drag coefficients with simulated unpowered, wingless artillery shells, it gives results very similar to published values.

 

Another possibility is precicely what you mentioned about unstable airframes before: perhaps the guidance system has to work all the time to maintain the proper trajectory with a 'lifting body' instead of just a straight ballistic shot.

 

Yes, this is more along the lines of what I was thinking. It would sort of imply the missile was trying to "fly", instead of being purely ballistic, but this might be a practical necessity in real life if the airframe is strongly unstable. The critic did not specify if it was one of the "lifting body" missiles he had tested.

 

Do you, by any chance, know the reason for No_Escape zones being modelled as an aircraft doing a single 6-G break-turn away followed (possibly) by a high-g turn into the missile?

 

Is it due to constraints on the pilot's ability to haul g (I refer to LOMAC's 'yoda maneuver' against the 120 and the 77 for example), the airframe's ability to haul g, or a combo, or perhaps due to a BVR F-Pole joust?

 

I'm not sure I understand the question... You mean, "why 6 G and not 9 G?" - Sorry, I don't know. Or, "why with a turn back into the missile?" - I didn't hear that one before. I believe that nowadays the Rmax2 has been renamed Rtr - "turn and run". i.e. just a high-G turn away from the missile and 1 G acceleration away to some max speed.

 

-SK

[GGTharos]

Ah..my question related to a technique used in LOMAC ...

 

Basically you can be shot at from 10nm head on and do a hard weave left-to-right a few times and defeat an AIM-120 or R-77 (totally drain them of speed) ... in all the cases I heard of, never is such a possibility modelled against an incoming target when generating the range diagrams - merely a 'break turn away from missile at x amount of G's'.

[SwingKid]

Ah..my question related to a technique used in LOMAC ...

 

Basically you can be shot at from 10nm head on and do a hard weave left-to-right a few times and defeat an AIM-120 or R-77 (totally drain them of speed) ... in all the cases I heard of, never is such a possibility modelled against an incoming target when generating the range diagrams - merely a 'break turn away from missile at x amount of G's'.

 

Oh, that I CAN answer - it isn't done, because it's too hard. :)

 

If you notice how long it takes miniZAP on your PC to calculate how far a missile will fly, without taking any guidance methods into account... miniZAP is named after ZAP, or Zone Acquisition Process, the software that calculates missile engagement zones for real fighter HUDs, taking instantaneous altitude, speed, aspect etc. into account. There are all kinds of look-up tables and approximations being used for faster performance. Complex anti-missile maneuvers by the target take too long to compute in real-time, at the procesor speeds that are found in fighter cockpits.

 

-SK

[GGTharos]

Right - however there's no problem running a missile simulation against such a target for a couple days on a Cray to generate diagrams ... but eh :)

 

Ok SK, thanks. :)