[HN Gopher] Math breakdown: Anime homing missiles
       ___________________________________________________________________
        
       Math breakdown: Anime homing missiles
        
       Author : ibobev
       Score  : 653 points
       Date   : 2023-02-02 18:14 UTC (1 days ago)
        
 (HTM) web link (blog.littlepolygon.com)
 (TXT) w3m dump (blog.littlepolygon.com)
        
       | Voltage wrote:
       | Great article! I didn't know about Rotation Minimizing Frames or
       | the double reflection method.
       | 
       | I've run up against the issue of unexpected twisting of splines
       | at work more than once.
        
         | TheRealPomax wrote:
         | They're also known as Frenet frames, or Bishop frames, if
         | you're going to dig into them in the future.
        
           | Voltage wrote:
           | Thanks for the tip.
           | 
           | I thought I recognized your handle! You wrote the "A Primer
           | on Bezier Curves" article. Thanks for providing that amazing
           | resource, it's been invaluable during my learning process.
        
             | TheRealPomax wrote:
             | I did indeed, always nice to hear folks enjoyed it!
        
           | Jasper_ wrote:
           | Frenet frames are simply any orthonormal frame. A rotation-
           | minimizing frame is a frame that has minimal twist from some
           | previous frame.
        
             | TheRealPomax wrote:
             | What they are, and what people call things, are two
             | different things though. Ran into lots of folks calling
             | them Frenet frames while looking this up myself several
             | years ago.
        
       | kilgnad wrote:
       | I've been a fan of macross for a long time but the mecha games
       | always suck. The main problem is that the movement isn't as fluid
       | as the anime.
       | 
       | I've only seen one good game capture the essence of the animes
       | while being a fair and good game. It's an old game called virtual
       | on. It's a fast paced mecha game with rocket boosted dashing
       | along lines of commitment. That line of commitment means that
       | when you dash with your mecha it forces the mecha into a single
       | permanent dash in a single direction for about 3 seconds. This
       | restriction actually makes you feel like you're pulling off
       | incredible dodges of anime homing missiles. The graphics are old
       | but it's the only game I've ever seen pull off the same feeling
       | as an anime.
       | 
       | See video:
       | 
       | https://youtu.be/SoUGqhPQFI0?t=279
       | 
       | It's old, but for it's time it was incredible. Also the controls
       | involve dual joysticks at the arcade to really get the feeling
       | that you're controlling a vehicle.
        
       | PaulHoule wrote:
       | There is a whole area called 'pursuit theory' about how to guide
       | a missile to a target that produces very interesting curves.
        
         | mLuby wrote:
         | It's going to be even more wild in space when missiles can
         | glide.
         | 
         | Children of a Dead Earth allowed some simulations around this
         | concept.
        
           | ranger207 wrote:
           | Missiles already glide. Most air-to-air missiles fire for
           | only a little bit right after they're fired, then spend the
           | rest of the flight coasting. Long range missiles propel
           | themselves on a lofted trajectory to preserve energy, falling
           | on their targets from above. In general, missiles can burn
           | energy very quickly by making high-G turns, but can't recover
           | energy, while aircraft are the opposite, being unable to
           | maneuver as quickly as missiles but being able to constantly
           | add energy. Some missile evasion tactics exploit this
           | asymmetry. But of course, for every countertactic there is a
           | counter-countertactic. The new innovation in missiles is dual
           | pulse missiles, which have two rocket motors so that after
           | firing, coasting, and approaching the target, the second
           | pulse can fire and give the missile more energy to defeat
           | countermaneuvering. The MBDA Meteor is an example of a
           | missile with a dual pulse motor, except that instead of
           | having two motors, it just has one which can be turned on and
           | off.
        
       | iamwil wrote:
       | My first job out of college was working for a lab that did stuff
       | for Air Defense. We did stuff like missiles that shot down other
       | missiles for the Navy. Anyway, in my naivety, I asked the more
       | senior engineers why we don't shoot missile plumes. Lots of cheap
       | missiles in the hopes that one hits. (I didn't mention the idea
       | was from watching anime.)
       | 
       | They told me that the backfire from the exhaust of one missile
       | might ignite the one behind it if we did stuff like that. That
       | said, I've seen videos of ships firing missiles in relatively
       | quick succession. Just not like the Itano Circus, however.
        
         | [deleted]
        
         | im3w1l wrote:
         | After seeing videos of n-copters dropping grenades on soldiers
         | in the Ukraine-Russia war, I do think there is evidence of a
         | move to small and cheap technology.
        
         | supercheetah wrote:
         | It's not a bad idea. It's just a practical reality of their
         | interaction with each other that causes a problem that's hard
         | to workaround.
        
           | JohnBooty wrote:
           | The challenge with "lots of smaller missiles" is really
           | range, I think. You want to hit the target from as far away
           | as possible. That takes fuel, which puts limits on how small
           | you can go.
           | 
           | The longest-range version of the AIM-120 has a range of
           | 160km, and missiles under development promise even longer
           | ranges than _that,_ so that kind of tells you what they
           | prioritize.
           | 
           | One tangential thing to understand is that air to air
           | missiles are proximity fuzed. They don't need to precisely
           | impact their target, they just need to get close.
        
             | Aeolun wrote:
             | I think this is mostly because longer range sounds like a
             | great thing when you don't have hundreds of missiles to
             | defend against.
             | 
             | It'd be nice if there was a similar defense against
             | saturation bombing.
        
               | JohnBooty wrote:
               | I think this is mostly because longer range
               | sounds like a great thing when you don't have
               | hundreds of missiles to defend against.
               | 
               | You're optimizing for the wrong thing. Today's missiles
               | are extremely lethal and good at finding their targets.
               | The challenge is getting close enough to launch them
               | without getting killed by other aircraft or ground-to-air
               | defenses. Ground to air defenses are getting cheaper and
               | more lethal all the time.
               | 
               | If you take human pilots out of the equation, obviously
               | this changes things (your aircraft can be cheaper and you
               | worry less about losing one) but not entirely. You still
               | have to figure out how to deliver the missiles without
               | getting shot down and while remote piloting is cool, it's
               | still subject to jamming and such.
               | 
               | Minus the cool swirly anime effects, pilots certainly
               | _do_ have the option of firing multiple missiles at a
               | given target. Fire one missile from beyond visual range,
               | wait, and then fire another one. This is very common in
               | DCS, which is obviously _not_ reality but is a pretty
               | decent simulation according to a lot of actual pilots.
               | Not sure what actual fighter pilot doctrine is there and
               | if that 's a real world practice as well.
        
         | JohnBooty wrote:
         | For many air-to-air and ground-to-air missiles, we cheat and
         | improve the hit probability another way: proximity fuses.
         | 
         | Example - https://en.wikipedia.org/wiki/AIM-9_Sidewinder
         | 
         | They detonate _near_ the target rather than impacting it
         | directly. This greatly improves the chance of success. Jets are
         | fragile, so this is almost always sufficient to take them out
         | of commission.
        
         | User23 wrote:
         | The MX sort of did that on the reentry side.
        
         | auxfil wrote:
         | Thank you for calling it by it's proper name and not "Anime
         | Homing Missiles"
        
         | brmgb wrote:
         | > That said, I've seen videos of ships firing missiles in
         | relatively quick succession. Just not like the Itano Circus,
         | however.
         | 
         | Saturation attack is indeed a tactic used. The idea is to time
         | your attack for missiles to arrive on your target at the same
         | time independantly of when they are launched and of their
         | trajectories.
         | 
         | Also, a missile hit for anti-missile defense probably doesn't
         | look like what you expect. There is no need to reach the
         | incoming missile spot on. The goal is to explode in its
         | vicinity preferably slightly in front of it. Incoming missiles
         | are fast enough that impacting either debris or the explosion
         | shockwave will disable them if they are close in a radius which
         | is not that small.
        
         | bhhaskin wrote:
         | It makes far more sense to do something like that in space
         | instead of in the atmosphere. You could spread the missiles out
         | a little before ignition. But you would also need some kind of
         | swarm logic and tracking to make sure they don't bump into each
         | other.
        
           | XorNot wrote:
           | Ostensibly the Generation 2 Ground Launched Small Diameter
           | Bomb munitions will do something like this - i.e. they're
           | capable of independently acquiring targets, and then de-
           | conflict the target acquisitions to ensure they don't all
           | track on the same one.
           | 
           | Basically the idea being that you fire a whole lot of them at
           | the enemy trench somewhere over there, and on terminal
           | approach they independently assign themselves to specific
           | interesting looking targets.
        
             | somat wrote:
             | Sort of like the CBU-97, it's mission profile is
             | ridiculously insane. First 10 sub munitions are ejected
             | out. A parachute slows the downward movement of the sub
             | munition carrier. A rocket then spins it up to a high speed
             | where it starts flinging shaped charge skeet at vehicles in
             | range. these skeet then detonate once they detect they are
             | above the vehicle.
             | 
             | My reaction was the same as when I first learned about how
             | jpl was going to get the curiosity rover down to the
             | surface of mars with a rocket crane. "There is no way
             | something that complicated would actually work."
             | 
             | https://en.wikipedia.org/wiki/CBU-97_Sensor_Fuzed_Weapon
        
             | Aeolun wrote:
             | Must've been a fun job training them what a valid target is
             | :/
        
               | red-iron-pine wrote:
               | Probably pretty easy. Anything that's not flat terrain,
               | kinda irregular in shape, and a fixed distance from
               | another target, e.g. 3 meters or something, to ensure a
               | reasonable spread.
        
         | cjbgkagh wrote:
         | The UK Starstreak anti-aircraft missile has 3 submunition darts
         | to improve hit probability. There is nothing wrong with the
         | idea per se, you can design around backfire. The Metal Storm
         | gun has multiple munitions stacked in the same tube.
         | 
         | I figure the problem is more that it's hard to scale down
         | missiles to the point the plume would make economic sense.
        
           | bob1029 wrote:
           | One well-guided missile can be infinitely more effective than
           | 1000 poorly-guided missiles.
           | 
           | Unless you are seeking a penetration aid against defenses, I
           | don't see much point. There are far cheaper ways to deliver
           | mass on target if you simply want to spam the enemy.
        
             | rcme wrote:
             | Depends on what you're defending against. Drones are
             | effective because they're cheap so they can be sent in
             | large numbers to overwhelm air defense even if each
             | individual drone is an easy target.
        
               | nradov wrote:
               | The type of cheap drones that can be sent in large
               | numbers lack the range to attack ships unless they're
               | really close.
        
               | littlestymaar wrote:
               | "Cheap drone" doesn't need to be off the shelf quadcopter
               | drone, fixed-wings custom drones like the Iranian Shahed
               | 126 are still dirt cheap compared to typical anti-ship
               | missiles.
        
               | nradov wrote:
               | Those lack the sensors needed to detect and track a
               | moving ship. Good sensors are expensive, and consume a
               | lot of power.
        
               | littlestymaar wrote:
               | But you don't need one sensor per drone, but one per
               | swarm with the same target (and any kind of data link
               | between members of the swarm). And by the time the swarm
               | is within reach of the protection weapons of the target,
               | it's probably close enough for the fairly basic sensors
               | onboard of every drone to be able to work on its own if
               | the target drone is destroyed (for instance: GNSS up to
               | the last know position of the ship, and then just
               | computer vision at close-range).
        
               | rcme wrote:
               | A ship isn't exactly a small target. You could probably
               | track it just fine with a satellite and update the target
               | GPS coordinate of the drones manually. An aircraft
               | carrier only moves at 55 km/h maximum.
        
               | iamwil wrote:
               | Apparently, the oceans do a lot of radar scattering that
               | makes it harder to spot ships from the guidance systems
               | of missiles. Not sure what the state of the art is
               | nowadays though.
        
               | nradov wrote:
               | Nope. Ships are very small targets in very large oceans.
               | Have you ever even been on a boat out of sight from land?
               | 
               | Reconnaissance satellites will be the first casualties in
               | any future high-end conflict. Modern militaries have to
               | plan around the expectation that their space-based
               | platforms will be unavailable or severely degraded.
               | 
               | Radar ocean reconnaissance satellites can detect ships
               | under any weather conditions but they are are large,
               | heavy, expensive, and can provide only intermittent
               | coverage. Smaller satellites with optical or IR sensors
               | can potentially provide more coverage but are less
               | effective at night or with clouds.
        
               | rcme wrote:
               | Apparently China is already tracking U.S. aircraft
               | carriers via satellite: https://www.scmp.com/news/china/s
               | cience/article/3177079/chin...
               | 
               | And sure, you need to wait for a clear day, but that
               | doesn't seem like too big an obstacle. Also, while space-
               | based platforms will be targets, it's unclear how
               | effective counter measures are. Identifying targets is
               | challenging and deploying replacements is worth the cost
               | if you can eliminate a large portion of an adversary's
               | naval power.
        
               | nradov wrote:
               | This is nothing new. The USSR was tracking US aircraft
               | carriers via satellite since the 1960's. China is only
               | now catching up.
               | 
               | Carriers are certainly vulnerable to an extent, but
               | detecting one with a satellite is only one step in the
               | kill chain. Carrier strike groups already carry some
               | limited anti-satellite weapons that can hit targets in
               | LEO. There is an active arms race underway by the
               | superpowers to boost those capabilities, and also (as you
               | stated) to develop a prompt launch capability to replace
               | satellite attrition losses within hours rather than
               | scheduling launches years in advance.
        
               | littlestymaar wrote:
               | That's basically how most Anti-ship missile work: you
               | give them GPS coordinate for the rough location and then
               | the missile uses an active radar homing system for
               | terminal guidance. (You want the missile to keep quiet as
               | long as possible anyway, to avoid being detected and
               | reducing the time the crew has to react to the threat).
        
               | actionfromafar wrote:
               | So far. There are many ways to make longrange, fuel
               | efficient flying things.
        
               | nradov wrote:
               | What are those ways? Do they also allow for large sensors
               | and warheads?
        
               | actionfromafar wrote:
               | Just being the overconfident random internet person with
               | ideas:
               | 
               | launch 100 vehicles, slow flying, potentially with
               | gliding capabilities, converging from all directions onto
               | a target at the same time, ditching main wings and piston
               | engine at the last minute, firing a rocket to gain speed,
               | and overwhelm air defence by sheer numbers. Combine low-
               | flying attack profiles with "dive-bomb from above". Large
               | sensors can be mitigated with mesh-networking between
               | vehicles and sensor fusion, maybe different kinds of
               | sensors on different vehicles. Slow-flying means they can
               | carry heavier warheads thanks to more lift and less drag.
               | 
               | If slowly circling at high altitude, you also tie up
               | resources keeping track of them.
               | 
               | Quantity is its own quality, and all that...
               | 
               | this is all without even bringing "AI" into the mix, but
               | if you could, you can give them "goals" instead of
               | targets.
        
               | nradov wrote:
               | It is possible in principle to build a loitering cruise
               | missile with those features. It will not be small or
               | cheap, at least not if you want something with the range
               | and endurance to seek out and attack a ship on the open
               | ocean in any weather conditions. Add up the cost and
               | weight for all of those components you listed.
               | 
               | As a point of comparison, the latest Block IV Tomahawk
               | missiles already do most of what you described. They cost
               | about $2M each and weigh about 1.5 tons. Only the largest
               | warships can potentially carry 100 such missiles.
               | 
               | Russia has used small, cheap cruise missiles like the
               | Iranian Shahed-136 drones with some limited success
               | against Ukraine. In a naval conflict such drones could
               | have some value as harassment weapons against surface
               | vessels operating in the littorals. But those drones are
               | useless against moving ships over the horizon.
        
               | actionfromafar wrote:
               | Those Shahed drones are too small. I'm just thinking from
               | first principles, if an ultralight plane has a range of
               | 500km and has a 100kg pilot in it which could be subbed
               | for a warhead, you could do an awful lot of damage with
               | hundreds of such things in the air.
        
               | nradov wrote:
               | Your numbers are way off. Ultralight airplanes don't have
               | ranges anywhere near 500km, nor do they have the payload
               | capacity to carry the necessary sensors and associated
               | electrical generator. Ultralights are also barely faster
               | than surface warships, and are too flimsy to operate in
               | severe weather. Seriously, you guys need to quit watching
               | silly scifi cartoons and do some actual math.
        
               | Retric wrote:
               | Submunitions think ICBM or cluster bombs. There's a
               | tradeoff, because smarts means less room for the deadly
               | bits.
               | 
               | Some kind of smart bomblets could be very effective vs
               | traditional military bases which use sandbag walls to
               | limit how effective traditional munitions are. Smarter
               | drones could be more useful when trying to clear a
               | forest.
               | 
               | Anti ship missiles on the other hand need large warheads
               | to be effective. But launching multiple is preferred due
               | to CIWS/point defense weapon systems.
        
               | nradov wrote:
               | Smart submunitions launched from drones have been a thing
               | for decades.
               | 
               | https://news.northropgrumman.com/news/releases/bat-
               | submuniti...
        
               | Retric wrote:
               | Yea, though BAT is designed for armored vehicles not
               | personal.
               | 
               | Military UAV's are also huge. I assume when people are
               | thinking drones they are downscaling to the 1-10kg range
               | not full sized aircraft with a 50 foot wingspan.
        
               | justsomehnguy wrote:
               | Just take a bigger drone truck to get them there.
               | 
               |  _happy Protoss Carrier noises_
        
               | Aeolun wrote:
               | I'm absolutely in favor of a massive airship spewing
               | hundreds of drones :)
        
             | chongli wrote:
             | The question I have is: can you scale down the well-guided
             | missile? I thought guidance is mostly an issue of fast
             | chips and well designed software. But perhaps you need big
             | missiles if you want them to fly fast and have a lot of
             | range.
             | 
             | Talking about anti-air of course. Lots of small missiles
             | aren't going to be effective against hardened ground
             | targets.
        
               | JohnBooty wrote:
               | But perhaps you need big missiles if you want them to
               | fly fast and have a lot of range.
               | 
               | I'm just a layperson but this has always been my
               | understanding. Modern air combat is all about firing from
               | beyond visual range, so I think they optimize pretty
               | strongly for that.
               | 
               | See my other answer, though - air to air missiles ARE
               | generally (always) proximity fuzed. They don't need to
               | precisely impact the target, they just need to get close.
        
               | XorNot wrote:
               | More then that, air-to-air missiles generally are
               | designed to blow a load of metal shrapnel through
               | whatever they "hit": so there's a problem where if you're
               | fleeing from a missile and it explodes behind you, even
               | though it "missed" the payload can still hit the plane it
               | was chasing if the plane doesn't change trajectory.
        
               | nradov wrote:
               | Sensors matter a lot for guidance. In order to build an
               | effective radar guided missile it needs a fairly large
               | array. So in practice the minimum missile diameter ends
               | up being something around 7 inches. Long range surface to
               | air missiles have to be much wider than that.
               | 
               | Data links also make a big difference. So the missile
               | needs another fairly large antenna to receive guidance
               | cues from other platforms.
        
             | lobocinza wrote:
             | > One well-guided missile can be infinitely more effective
             | than 1000 poorly-guided missiles.
             | 
             | Only true if it can target a high value unit or
             | concentration of units which value exceed the missile cost.
             | 
             | Anti-air is a different scenario than artillery. Startreak
             | targets are fast evading and employ countermeasures that
             | attempt to trick the missiles target acquisition. I'm out
             | of my depth but I believe the justification for the 3
             | missiles was improving the odds of hitting the target as
             | that add redundancy and kind of triple the resolution of
             | the targeting systems where a single missile with better
             | electronics might be less effective and more costly.
        
         | winter_blue wrote:
         | Doesn't a howitzer shoot multiple middles at once? (Or are they
         | shot in quick succession?)
        
           | ygra wrote:
           | Quick succession. Due to the projectiles taking a while to
           | arrive on target (especially for high-arcing trajectories)
           | this gives you the effect of multiple projectiles arriving
           | simultaneously on target: https://en.wikipedia.org/wiki/Artil
           | lery#Multiple_round_simul...
           | 
           | It also places some demands on fire control and loading to
           | achieve the high fire rate; I'm not sure manually-loaded
           | howitzers are capable of that in general (e.g. the German PzH
           | 2000 automates everything from loading shells and propellant
           | to firing).
        
       | cainxinth wrote:
       | Reminds me of playing Panzer Dragoon Orta on the original Xbox.
        
       | Pxtl wrote:
       | This video should probably have an epilepsy warning based on
       | those strobe-light explosions. I adore the strobe-lights and they
       | make me nostalgic as hell for early-'90s 3D games like SNES
       | Starfox and Lightspeed/Hyperspeed, but the technique was retired
       | for good reasons.
       | 
       | As for the effect itself, I wonder if it would make sense to try
       | this with a boid algorithm so they move as a "flock". Most
       | attempts at anime=missiles I've seen either just look too chaotic
       | or the missiles while initially launched at wide angles gradually
       | consolidate into a tightly-packed blob.
        
       | Justsignedup wrote:
       | Dear Mechwarrior developers: Pay this man all the moneys and put
       | it into the game!
        
         | speed_spread wrote:
         | Agreed, Itano Circus SRM-6 should be standard.
         | 
         | So I'm a mechslut. Today I bought Mechwarrior 5, installed it
         | played for an hour and uninstalled it out of boredom and
         | disgust. When inspired, Mech games can be SO COOL but I think
         | it's just too easy to go with the cheap arcade mode and plain
         | physics.
        
           | SinParadise wrote:
           | Mechwarrior 5 is kind of meh without mods. I played with the
           | following:
           | 
           | VonBiome for more battlefields, YetAnotherMechLab,
           | YetAnotherMechlabMechs, YetAnotherWeapon and
           | YetAnotherWeaponClan for mechlab and additional weapons.
           | XenoAI MissionYAML and CoyotesMission to improve mission
           | variety and difficulty.
        
           | Justsignedup wrote:
           | The problem with MW games is the following:
           | 
           | 1) They were not built for simulation. The TT rules are good
           | for just that.
           | 
           | 2) The companies coding then haven't been great at it.
           | 
           | 3) Pirhana games has terrible leadership and coding skills.
           | 
           | Honestly MW5 had a ton of potential, but eclipsed by terrible
           | coding. Like the spawn effects are bad, and they had to do
           | spawns because they couldn't figure out how to disable
           | scripts for inactive units, or how to make things efficient,
           | or whatever. Basically yeah.
           | 
           | Also I'm thinking LRM-20s with that effect. Cheff's kiss.
        
       | rustypotato wrote:
       | What kind of glitches would you experience in this context
       | without rotation minimizing frames? If the missiles are a non-
       | symmetrical shape, I would guess that you could see some
       | "snapping" in its rotation, but if the missile is something like
       | a centered sphere, my intuition is that the snapping wouldn't be
       | perceptible.
        
       | BoppreH wrote:
       | I love these gamedev articles on specific solutions for making
       | gameplay feel good. It has a freedom and artistic drive that I
       | miss in other technical writing.
       | 
       | And if the article left you with an itch for a space mecha game
       | with missile barrages, here's a suggestion: Strike Suit Zero[1],
       | or its arcade version, Strike Suit Infinity[2].
       | 
       | It's cheap, short, with memorable gameplay and a lovely
       | soundtrack[3].
       | 
       | [1] https://store.steampowered.com/app/209540/Strike_Suit_Zero/
       | 
       | [2]
       | https://store.steampowered.com/app/234160/Strike_Suit_Infini...
       | 
       | [3] https://www.youtube.com/watch?v=2eDWgwucK5w
        
         | omnibrain wrote:
         | Great to see that here. I used to play EVE in the same corp
         | with some of the devs.
        
           | kazmerb wrote:
           | o7m8
        
       | [deleted]
        
       | allenu wrote:
       | Really cool! I always wanted to see a shooter that made use of
       | the Itano Circus style. I always imagined it would be fun and
       | stylish to fly around dodging missiles like that. Is there a
       | shooter out there that does that?
        
         | stevenwoo wrote:
         | Nier Automata has schmup sections but they are scattered around
         | mainly 2D/3D fighting action game with a very long version at
         | the end of the game. The player shoots more missiles like that
         | versus the computer using them, it's more effective for the
         | player to bat the missiles away with the mech sword versus
         | avoiding the enemy missiles.
        
         | prova_modena wrote:
         | Older games, but "Omega Boost" and "Zone of the Enders" 1 and 2
         | are great examples of trying to realize this style.
        
       | vlovich123 wrote:
       | I'm curious what plotting tool the author used to create those
       | slick illustrations.
        
       | crispisulcans wrote:
       | Cool design! I would love for some folks who are into this stuff
       | to try their hands at this missile defence programming game
       | https://openprocessing.org/sketch/745415 (click the </> button at
       | the top)
        
       | mcnichol wrote:
       | Can I just say, only being a portion of the way through the
       | article, you are a natural teacher/communicator.
       | 
       | You have a very kind, knowledgeable, and effective way of
       | explaining.
       | 
       | I'd like to point out how much I appreciate how you introduce
       | technical specifics and elaborate concisely enough that those who
       | know and those who don't can share an article without feeling
       | talked past or down to.
       | 
       | One persons opinion. With your communication style a high bar
       | I've been pursuing for some time, I just want to share a sincere
       | appreciation for it!
        
         | [deleted]
        
       | Arrath wrote:
       | The end result does look very cool
        
       | bee_rider wrote:
       | It definitely looks neat.
       | 
       | I don't really see the point of doing this for one target per
       | missile (other than aesthetics which is a perfectly valid
       | reason!)
       | 
       | But, if multiple were heading at a single target, I guess they'd
       | be harder to dodge? Multiple trajectories and all that.
        
         | tstrimple wrote:
         | Not just dodge, but it would be harder to counter them all with
         | flak or Close In Weapon Systems (CIWS) as well.
         | 
         | https://en.wikipedia.org/wiki/Phalanx_CIWS
        
         | Armisael16 wrote:
         | The real-life reason for this wild spiraling behavior would be
         | that the launch tube isn't pointed directly at the target and
         | the missile overcorrects. That's actually how the sidewinder
         | missile got its name.
         | 
         | This kind of mid-flight course change is a characteristic of
         | real missiles in other cases , though:
         | 
         | * almost anytime a submarine or ship launches, the missile goes
         | straight up for a little bit to clear the ship before sharply
         | turning
         | 
         | * if you shoot a guided missile straight up unguided to clear
         | terrain (eg a hill) before turning on guidance you'll see this
         | 
         | * cruise missiles in the gulf wars famously did this by
         | following the street grid - even turning at street light
         | 
         | * if you launch a torpedo in a random direction then activate
         | guidance later it can disguise where you are, since the torpedo
         | is coming from a different direction
        
           | icegreentea2 wrote:
           | Ohohoh. The craziest reason for the missile to go a little
           | conky has got to be the energy management steering maneuver
           | in THAAD (dunno if other missiles do it as well) - https://en
           | .wikipedia.org/wiki/Terminal_High_Altitude_Area_De...
        
             | z303 wrote:
             | Another was Sprint. Turning towards the target before it
             | gets too fast. Limiting the stress on the airframe and
             | energy required.
             | 
             | https://en.wikipedia.org/wiki/Sprint_(missile)
             | https://youtu.be/YZZV464z9g8
        
           | bee_rider wrote:
           | Good points! I was 100% thinking of this from the point of
           | view of a video game, without stating it, haha.
        
           | magila wrote:
           | I always assumed the Sidewinder missile was named based on
           | the snake's ability to sense prey by thermal radiation.
        
             | Armisael16 wrote:
             | It was a bit of both, really (and the snaking path was only
             | present in early versions of the missile).
             | 
             | Sorry to mislead!
        
           | MonkeyMalarky wrote:
           | Apparently HIMARS rockets do it too to avoid counter-battery
           | fire. In videos from Ukraine you can see them launch at one
           | angle then change direction after clearing a good distance
           | from the launcher.
        
           | paganel wrote:
           | The Russian Onyx missiles also have an interesting-looking
           | initial phase of the launch [1]
           | 
           | [1] https://youtu.be/2-22myhg_nE?t=9
        
           | sdmike1 wrote:
           | > cruise missiles in the gulf wars famously did this by
           | following the street grid - even turning at street light
           | 
           | That's fascinating! Do you have more info on this?
        
         | scotty79 wrote:
         | I think they behave a bit too wild in the first stage of
         | flight.
         | 
         | I think I'd create separate launch animation that smoothly
         | morphs into this flight animation.
        
         | blincoln wrote:
         | I always assumed having missiles behave like this would have
         | some neat advantages (harder to shoot down, harder to predict
         | the intended target, harder to automatically trace back to the
         | launcher, etc.) and that the only reason real missiles didn't
         | typically do it was the complexity of making sure they didn't
         | hit each other or something else sitting outside of the
         | shortest path.
         | 
         | It seems like it could be done, e.g. pre-program all of the
         | missiles with randomized paths that didn't intersect, and sweep
         | the entire potential flight path area with radar or similar and
         | exclude volumes with obstructions. That really is an awful lot
         | of complexity that could make things go wrong, though.
        
       | somat wrote:
       | Probably why I am not a game dev but when the author mentioned
       | and discarded the iterative solution in favor of the closed form
       | solution. I immediately thought how cool it would would be to
       | have some sort of deep involved simulation that would in the end
       | create the same effect.
       | 
       | One reason a missile might spiral like that is in order to have a
       | simplified seeker head and control assembly, you only seed to
       | seek and control on one axis and you spin the whole missile to
       | scan over two dimensions. the missile will always overshoot a
       | little but correct once it rotates around the other way. while
       | this makes for a far simpler seeker and control setup it wastes a
       | lot of energy so you need a bigger engine for the equivalent
       | range if you had a two dimensional seeker/control missile.
       | 
       | Another reason is to make the anti-missile solution much harder.
       | It still wastes a lot of energy.
        
         | mLuby wrote:
         | Deep involved simulation you say?
         | 
         | Check out Nebulous: Fleet Command https://youtu.be/Oe-71-3khyA
         | specifically 1min in they show off the missile seeker
         | customization and sprint phase programming. The game is like if
         | you combined The Expanse with Homeworld.
         | 
         | In general I've found the devlogs interesting--same YouTube
         | channel I linked above.
        
           | AlexAndScripts wrote:
           | I highly recommend Nebulous, I did some modding for it a
           | while back and the dev is really friendly and helpful. I was
           | never actually that good at it, but it's really fun and has
           | an extremely high skill ceiling.
           | 
           | It runs on Linux with the exception of the main menu video.
        
           | somat wrote:
           | In the same vein is the game "From the Depths". It is just
           | this side of unplayable due to it's systems and simulations.
           | several times now I have started a campaign, enthusiastically
           | go through the tutorials and immediately go combat
           | ineffective when I forget how to assemble a functioning
           | internal combustion engine power train.
           | 
           | https://www.youtube.com/watch?v=QhTNESwAzs4
           | 
           | Note that that trailer absolutely fails to convey the
           | mysteries found in trying to design a functioning missile
           | system.
        
           | SinParadise wrote:
           | honestly everything Microprose and Hooded Horse is instabuy
           | for me. well, almost instabuy.
        
       | MrLeap wrote:
       | I like using PID controllers for this kind of thing. They make it
       | easy to get "authentic" looking behavior. By tuning the params
       | you can adjust to behave anywhere from smooth like silk to wild
       | overcorrections.
       | 
       | They look really lively, I'll post a video on twitter or
       | something.
       | 
       | https://en.wikipedia.org/wiki/PID_controller
        
         | TheRealPomax wrote:
         | Yeah but now you made tuning the PID parameters your day job =(
        
           | HelloNurse wrote:
           | If you like machine learning, you can simulate the game in
           | suitable test scenarios and evolve high-performance missile
           | controllers. Like in real life at the firing range, without
           | engineers.
           | 
           | Of course, bad controllers that can be exploited by the
           | player to make missiles miss are usually fun, as are slight
           | variations of PID parameters in the same missile salvo, to
           | disperse them organically.
        
           | MrLeap wrote:
           | If tuning to taste gets old, just use an infinite series of
           | PID controllers to tune your PID parameters.
        
             | TheRealPomax wrote:
             | And that's how an XKCD comic gets born.
        
         | fho wrote:
         | I just read
         | [this](http://brettbeauregard.com/blog/2011/04/improving-the-
         | beginn...) yesterday. It details the effort that went into
         | making the Arduino PID library more robust compared to the
         | "beginners PID".
        
           | themeiguoren wrote:
           | As a controls engineer, this is still the best one-stop shop
           | I've found for making PIDs a lot more usable & robust.
           | There's a few things I'd add but this covers the major bases.
        
             | fho wrote:
             | So ... what would you add? :-)
        
         | mwkaufma wrote:
         | I wrote about those ages ago, when I was working on the game
         | ABZU
         | 
         | https://www.tumblr.com/giantsquidology-blog/144615245984/flu...
        
           | camtarn wrote:
           | Heh, great article! One of those engineering efforts where
           | you're trying to get to the point where the user doesn't
           | notice any of the fancy math, just that the controls always
           | seem to Do the Right Thing.
        
       | rilindo wrote:
       | The term for this is Itano Circus, made famous in Macross
       | 
       | https://www.youtube.com/watch?v=pgwORRFIiuE
        
         | grimgrin wrote:
         | And here's 20 minutes of Itano Circus
         | 
         | https://www.youtube.com/watch?v=BzXfVgYCxWI
        
           | YeGoblynQueenne wrote:
           | Cheers. Now I have to think of a way to model that kind of
           | thing shooting out of a Stormsurge:
           | 
           | https://warhammer40k.fandom.com/wiki/KV128_Stormsurge?file=K.
           | ..
        
           | jvanderbot wrote:
           | To be fair, some of the "circus" aspect could be explained by
           | noise in the tracker, rather than noise in the launch
           | direction or trajectory tracking (as TFA proposes). Mostly I
           | say this because the directions tend to diverge more as they
           | get closer to a highly dynamic target.
        
         | kitsunesoba wrote:
         | A well-animated Circus is always a treat.
        
         | Kukumber wrote:
         | that's not the "term", that's "as seen in X anime"
         | 
         | bastardizing technical "terms" irritates me
        
           | howenterprisey wrote:
           | https://en.wikipedia.org/wiki/Itano_Circus
        
           | numpad0 wrote:
           | Itano circus is not an in-universe term, it's named after an
           | artist Ichiro Itano who is associated with it.
        
             | Kukumber wrote:
             | You don't say: a painting using cubism style is a "Picasso"
             | 
             | The author that popularized it doesn't get attribution de-
             | facto for every paintings that uses cubism
             | 
             | Slightly rotating your missile propulsion system with an
             | auto-targeting system doesn't make it "Itano"
             | 
             | You don't say "Mr Smith's way of braking" because you saw
             | him drift
             | 
             | There is something about the weeb culture that's very
             | corrosive about culture in general
             | 
             | That's very concerning for this generation of technicians
             | 
             | https://llvm.moe/
        
               | JohnBooty wrote:
               | There is something about the weeb culture          that's
               | very corrosive about culture in general
               | That's very concerning for this generation of
               | technicians
               | 
               | I'd love to hear more of these thoughts.
        
               | numpad0 wrote:
               | TIL it's called eponym[1]. Diesel engines, pasteurized
               | milk, Petri dish, even _mentors_ , ... I can tell you
               | it's much less common in ideographic languages, as the
               | definition can be encoded into spelling by choice of
               | ideographs, if that is what you would appreciate :)
               | 
               | 1: https://en.wikipedia.org/wiki/Eponym
        
               | s-lambert wrote:
               | Just because you see something in "weeb culture" doesn't
               | mean it's unique to "weeb culture". Naming things after
               | people happens everywhere, even in programming, booleans,
               | bezier curves, Turing machines, etc.
        
               | somethingreen wrote:
               | These terms come from Sakuga scene where artist
               | attribution and appreciation are a big part of it. See
               | also "Yutapon Cubes", for example.
               | 
               | Also we absolutely do identify art styles after their
               | creators if the style is distinct enough, but doesn't
               | necessarily establish a new branch, e.g. Escher, Warhol,
               | Wes Anderson.
        
         | nvader wrote:
         | I've also heard it called Roboteching, from the samish
         | reference:
         | 
         | Warning info hazard tvtropes :p
         | 
         | https://tvtropes.org/pmwiki/pmwiki.php/Main/Roboteching
        
           | creamyhorror wrote:
           | It seems like "roboteching" refers more to the sudden
           | synchronised turning of the missiles towards the target, and
           | "Itano Circus" / "Macross Missile Massacre" is the general
           | term for near-simultaneous missile spam. Definitely very
           | aesthetically pleasing. https://tvtropes.org/pmwiki/pmwiki.ph
           | p/Main/MacrossMissileMa...
        
             | uranusjr wrote:
             | Itano Circus is about the entire choreography of the entire
             | fighting sequence, more than the missiles but combined with
             | unrealistically agile robot actions and dynamic camera
             | placing/movement.
        
         | SigmundA wrote:
         | I have to believe Itano Circus was inspired by Saturn rocket
         | fireworks, at least that what I though as a kid.
         | 
         | https://www.youtube.com/watch?v=IS_7nY19kXw
        
         | jvanderbot wrote:
         | I think I should be watching more Macross
        
         | 082349872349872 wrote:
         | These are sometimes worth frame advancing for easter eggs. DYRL
         | in particular had a sequence where mid-circus (IIRC) a Kirin
         | beer can goes one way, and a Budweiser can goes in the opposite
         | direction.
         | 
         | [Edit: https://www.youtube.com/watch?v=wckZcVFLU24
         | 4:54 anime girl as missile nose art       5:40 not kirin, but
         | "hataiko" (hataiko?)       5:41 defo budweiser (also from the
         | Valkyrie?)
         | 
         | I was wrong, but not badly mistaken. There may be more; I'm
         | stopping here.]
        
       | anyfoo wrote:
       | > Many people are intimidated by math, but keep in mind that you
       | don't need to understand everything to use it.
       | 
       | This is key. And then if you're like me, you might after all
       | become interested in actually understanding, and something new
       | opens up.
        
       | tlhunter wrote:
       | I always wanted a modern Omega Boost
        
       | psychphysic wrote:
       | Better off using the integration method and if they miss they
       | miss.
       | 
       | Or maybe you're not. But impossible to doge homing missiles
       | doesn't feel very game like or realistic and works only against
       | static targets.
        
       | causality0 wrote:
       | Very interesting read. Regarding the example animation, is that
       | lifted directly from chapter 1 mission 4 of Robotech Battlecry or
       | is an astonishingly good recreation?
        
       | munificent wrote:
       | What a fun article! If it were, I would probably have tried two
       | simpler tweaks:
       | 
       | 1. Instead of bothering to compute tangent frame sweeping along
       | the path, just use a fixed frame that's tangent to a line drawn
       | from the start to the end point. (And then pick a random fixed
       | rotation angle.)
       | 
       | 2. Just use value noise instead of simplex noise. Or, hell, just
       | stack a couple of sine waves with randomly chosen phase and
       | frequency.
        
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