5 ms·

Link for clarification: https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing_range https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing...

by giva 5y ago

sandworm101 5y ago
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.
- thrill 5y ago
  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.
  - Animats 5y ago
    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.
- jameshart 5y ago
  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.
  - sandworm101 5y ago
    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.
- nwallin 5y ago
  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.

Link for clarification: https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing_range https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing...

by giva 5y ago

Link for clarification: https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing_range https://en.wikipedia.org/wiki/Constant_bearing%2C_decreasing...

sandworm101 5y ago

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.

thrill 5y ago
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.
- Animats 5y ago
  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.
jameshart 5y ago
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.
- sandworm101 5y ago
  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.
nwallin 5y ago
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.