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Comment by sandworm101 | Hacker News Reader

A missile will generally not care about distance. What matters is direction/angle. Distance is irrelevant. Just keep pointing at the target and eventually you will get there, assuming you are faster. So the direction to the strongest reflection, or greatest doppler shift, or combination of both, will suffice to get the missile to the target even without range data.

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That was true for earlier radar guided missiles. The latest ones are smart enough to account for distance and calculate an energy optimized intercept course rather than just pointing straight at the target.

Missile systems. Such complex approaches are calculated and controlled by the launching platform. A radar-guided missile will normally not "see" the target on its own until long after launch, until near endgame. Whether the actually missile has the brains to make such calculations is different than whether the entire system has the ability.

The missile knows where it is by knowing where it isn’t.

Say derivative without saying derivative

By subtracting where it is from where it isn't, or where it isn't from where it is (whichever is greater), it obtains a difference, or deviation.

For the confused (or to get more confused!):

https://youtu.be/bZe5J8SVCYQ

after a minute, I was expecting a reference to the Turbo Encabulator.

It's been a long time since homing missiles aimed directly at the target. The AIM-9 Sidewinder entered service in 1956, and it aimed at where the target will be, not where it is.

Some early IR missiles do aim slightly ahead of the target's bearing, but they don't really 'know' where they or the target are located in time and space. It is one thing to tell a missile to aim 10% to the left of a target bearing (which isn't simple in 3d space) another for that missile to understand its relative position. The early sidewinder used a single IR sensor behind a spinning reticule made of slots. This wasn't a camera with multiple pixels. It was one big pixel. The "brain" would alter the missiles course according to the position of that spinning reticule and the blinking signal from the lone sensor. There was no concept of range. At best, the brain could keep the target at a specific angle. This was achieved through literally re-drawing the reticule to include a solid band at the appropriate angle. So long as the target was behind this dark band the sensor would not blink and the missile would fly strait. Should the target move, the blinking would start and the missile would turn to put it back in the blank/dead zone.

https://images.app.goo.gl/N3mTpDUeeJW6W7wu9

You don't need to have an understanding of 3d space, positioning, range to target, trajectories etc to create an intercept course.

The underlying principle of proportional navigation, which is what the first few generations of IR missiles use to navigate, is constant bearing decreasing range. If a missile maintains absolute bearing to a target, it will collide with that target. The first generation AIM-9, which was the first useful IR missile, didn't aim "slightly ahead" of its target, it pointed itself at the exact point where it would collide with its target, assuming the target was moving at constant speed in a straight line.

The spinning sensor that you mention was on a gimbal, it wasn't pointing along the boresight. The spinning caused it to act as a gyroscope, so it would maintain its orientation in absolute space. The gimbal would track the sensor so that it was pointing at the target, and the same inputs were fed into both the gimbal and the missile's control surfaces. Therefore, if the bearing was changing, that would cause the missile to maneuver in such a way that the bearing would stop changing. If the bearing wasn't changing, the missile would not maneuver. This is all you need to do to point the missile at the exact point where it will intercept a non-maneuvering target.

As a first order approximation, the assumption of a constant speed straight line target is a useful one, given the technological limitations of the time.

https://en.wikipedia.org/wiki/Proportional_navigation

https://en.wikipedia.org/wiki/Constant_bearing,_decreasing_r...

https://qph.fs.quoracdn.net/main-qimg-a0e376f321a658b5d99e25...

> Just keep pointing at the target and eventually you will get there

Surely they can't use this poor of an optimization strategy? If the target is moving perpendicular to you, you want to point slightly ahead of the target so you intercept them as quickly as possible.

‘Pointing at’ in this case means maintaining a constant bearing to target, with decreasing range. If anything it’s easier for a moving guidance system to achieve that than to point at the target.

Link for clarification:

https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing...

Except that, in the case of a missile, you cannot assume decreasing range. We assume that the missile knows to aim ahead of the target, but determining which way is ahead and which behind is tricky. If it is chasing a hotspot, a single point, getting that wrong means worsening your approach. A strait/boresight approach might not be ideal but it avoids the question over which offset is ahead and which behind the target.

Continuously pointing directly at the target tends to result in the missile being unable to generate the needed turn rate at the conclusion of the intercept. If the missile has a large warhead, that might not matter so much, but air-to-air missiles tend to be small.

Yes. So one strategy is to aim at a point midway between the target's current position and its projected position. This puts the missile on the target's tail, which is a good attack position when the target evades.

If you're a missile seeker, all you have as input is a two-dimensional forward view of where in your forward cone the target is - either deflection and azimuth, or x and y offset - it's like a dot on a scope. Let's assume cartesian x and y input for simplicity.

So as you track, you can measure where it is, and how fast it's apparently moving in those two degrees of freedom - so you know x, y, dx and dy (and I guess you know higher degree deltas too).

To hit it (assuming it's in front of you) all you need to do is make control inputs to bring dx and dy to zero - you don't care what x and y are. If dx and dy are zero, if you're faster than the thing you're tracking, you're going to hit it - that's constant bearing, decreasing range.

Making control inputs to bring x and y to zero as well as dx and dy is a harder problem! You need to control four degrees of freedom to do that.

And making control inputs just to try to bring x and y to zero without controlling dx and dy is a good way to miss the target completely - obviously if you get x and y to 0 but dx and dy are nonzero, the target is going to move away from zero, requiring more control input, which might increase dx or dy, causing you to need even stronger control input...

So the upshot is: you don't have to back out the target's absolute trajectory, figure out its true velocity and your own relative velocity, determine range to target and offset where you're pointing to compensate for time of flight - just get it to stay on the same bearing from your perspective, and you're done.

Most missiles don't see in two dimensions. They are not cameras. They "see" using complex arrays of mirrors prisms and reticules feeding light to a single detector. Only the latest missiles have seekers that work with 2d images.

Constant bearing is possible, but if you are tracking behind, above, or below the target then you don't get any advantage, taking a longer route than direct/pure chase. The missile needs a mechanism to estimate the target motion rather than only it's relative bearing. That isn't simple. Many manpads instruct the user to aim ahead so that the missile locks into a lead path, but accidentally aim up/down/behind and they will lock into a lagging approach.

If I understand your objection correctly, you're saying that there are two directions that maintain constant bearing between the missile and the target, one bearing that brings the missile closer to the target, and one bearing that sends the missile farther away. This is true, but in reality it doesn't ... make any sense. If the pilot points the missile in remotely the same part of the sky, the closing bearing is the only bearing in the front quadrant of the missile.

Historically, I don't think any missile designed to target aircraft has ever been fielded which use the strategy you suggest. (lots of air to ground missiles do) It works fine if the target is flying straight and level, and you fire from directly behind them. But if the target has even a shallow turn towards you, the rate at which the missile will need to increase its rate of turn will increase exponentially as it closes with the target. If the target is aware it's being shot at and from what angle, all it takes to avoid the missile is to keep it at your 3/9 o'clock positions (steadily turning towards it) and it will miss every time.

The first generation of radar guided air to air missiles in the 1940s use beam riding. The missile would attempt to keep itself between the target and the shooter.

The first generation of (infrared) AIM-9 Sidewinder missiles in the 1950s used a mechanical system to perform proportional navigation; it spun the sensor at a fairly high rate of speed, causing it to act as a gyroscope. The sensor was pointed towards the target on an internal gimbal. But since the sensor was a gyroscope, if corrections had to be made, this meant the target was not at a continuous bearing. So the same corrections were sent to both the gimbal and the missile's control surfaces.

These days, everything just has a microcontroller in it, so there's no need to design such electro-mechanical Rube Goldberg contraptions to get proportional navigation to work.

It can be easier in terms of getting to a far away target, of maximizing range, but pointing strait has an advantage. As the target moves forwards the missile will be dragged behind, which reduces the relative angle at intercept, reducing the targets ability to make a last second maneuver. An direct approach IR missile can literally fly up the tailpipe of a fast target.

Yes, even old ordnance like the Sidewinder, which entered service in the mid-1950s, would aim ahead of the target.

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