Proportional navigation

[dietlbomb]

I used to work for a company that manufactures missiles. Unlike rockets, missiles have the ability to change their trajectory to hit their target. The simplest algorithm used in missile guidance systems is called proportional navigation. Using proportional navigation, the guidance system steers the missile to drive the angular rate of the line-of-sight vector (the vector from the missile to the target) to zero. If the missile has enough agility to follow this rule, and if the missile is faster than the target, proportional navigation guarantees that the missile will hit the target.

In real life, we use proportional navigation (or something like it) intuitively. A great example is baseball players running to the exact spot they need to be to catch a fly ball. They run at a speed where the angle they are looking toward the ball is constant, and by doing so they easily catch the ball in stride.

In the discussion of the Black Riders' trajectory while pursuing Frodo to the Ford of Bruinen, I couldn't help but think of the concept of proportional navigation. I would think that the riders would behave similarly to trained athletes, and take the optimal path to intersect their target. Even though their horses were slower than Frodo's, they would intuitively follow this sort of path.

Read more about proportional navigation on Wikipedia: https://en.wikipedia.org/wiki/Proportional_navigation

Sorry this wasn't a question, but just an observation.

 

[Kate Neville]

I used to work for a company that manufactures missiles. Unlike rockets, missiles have the ability to change their trajectory to hit their target. The simplest algorithm used in missile guidance systems is called proportional navigation. Using proportional navigation, the guidance system steers the missile to drive the angular rate of the line-of-sight vector (the vector from the missile to the target) to zero. If the missile has enough agility to follow this rule, and if the missile is faster than the target, proportional navigation guarantees that the missile will hit the target.

In real life, we use proportional navigation (or something like it) intuitively. A great example is baseball players running to the exact spot they need to be to catch a fly ball. They run at a speed where the angle they are looking toward the ball is constant, and by doing so they easily catch the ball in stride.

In the discussion of the Black Riders' trajectory while pursuing Frodo to the Ford of Bruinen, I couldn't help but think of the concept of proportional navigation. I would think that the riders would behave similarly to trained athletes, and take the optimal path to intersect their target. Even though their horses were slower than Frodo's, they would intuitively follow this sort of path.

Read more about proportional navigation on Wikipedia: https://en.wikipedia.org/wiki/Proportional_navigation

Sorry this wasn't a question, but just an observation.

Oh, but valuable information for the Mythmoot re-enactment

 

[Luke of X (Fmr. Twitter)]

Two things I have thought about recently re-listening to some of these sections.

Proportional navigation jives with what I thought I might have said at the time. Two riders make a straight line for the Ford, in an attempt to cut Frodo off and get there first. They are not intercepting, they are moving to block.

The two that ride straight for Frodo are attempting to intercept, but the presence of Asfaloth was not known nor anticipated. They cannot catch the elf-horse, but as was mentioned, the plan was formed and they stuck to it.

If Frodo and Asfaloth are making a straight line to the Ford, and the two Riders moving to block are making a straight line, these other two Riders are actually making an arc, or curved line, as they are constantly readjusting their trajectory to try and stay on a course that will intercept. This is a common occurrence in ships or airplanes when the interceptor misjudges the speed of the target and ends up missing, usually falling behind.

The other thing is the speed of Asfaloth. Nobody mentioned it then or since, but I can't believe it wasn't brought up that the Kentucky Derby, a 1 1/4 mile race (or 10 furlongs if you're Tolkien) is the approximate distance we're told from the edge of the tunnel to the Ford. Secretariat ran that distance in 1:59.4 in 1973. There had been horses who ran that in 2:01 in the 30s and 40s. In Tolkien's own England the Epsom Derby (at 1 1/2 miles, or 14 furlongs) had a record time of 2:26.6 in 1945, and an average winner of 2 min 35 seconds.

Asfaloth is cookin' at a sub 2 minute pace once the command to noro lim is given.