This blog entry is a continuation of part 1 on the PAC- 3 missiles. In the first blog, the information of a Hwasong-12 missile launch was calculated from a real life launch. That information was used to create the trajectory of a hypothetical missile launch that would collide with the defensive Patriot missile. In this part 2, the trajectory of the Patriot missile will be calculated, therefore determining the point at which the two missiles will collide together in the air. In this hypothetical launch, the Patriot missile is being launched from Daegu, South Korea and the Hwasong-12 is being launched from Sudan, North Korea.
The PAC-3 missile system contains its own radar, transmitter and computer, allowing it to guide itself. Right before it is launched, the radar finds the target and aims for a direct hit. At this speed there is absolutely no room for error. If the missile miscalculates by even 1/100th of a second, it will be off by more than 30.5 meters.
This is a German version of the PAC-3 missile launcher.
The total distance between the two cities is 453 km. The PAC-3 has a range against a ballistic missile of 20 km. `It has a speed of Mach 4.1. The radar detects an incoming missile at 100 kilometers. Within 3 seconds of launch, the missile is traveling at Mach 4.1 (1.39 km/s) It is going to be assumed that the Hwasong-12 missile is pointing directly at the space where the Patriot missile is being launched from.
There is a response time from when the radar detects to when it fires, but for this experiment, we are going to say that it is the same as when the radar detects it.
This video gives a short explanation on how the Patriot system detects incoming missiles and intercepts them as well as some of the inner workings of the missile.
Using the projectile motion equations, the rough flight pattern of the Patriot missile can be found. The two equations are: y= -4.9t^2+1390*cos(37)t and x=1390*sin(37)t. These equations are used to determine the height at a specific time. Hypothetically, the point of collision can be determined by projectile motion. But in real life, the missile has its own tracking system that it uses to finialize the trajectory of the missile. So that means that the projectile motion can only do so much because it does not go in a straight flight pattern. The physics behind a true missile launch is extremely complex but the rudimentary trajectory calculations of a missile launch are able to be calculated in the equations above.
The PAC-3 missile system contains its own radar, transmitter and computer, allowing it to guide itself. Right before it is launched, the radar finds the target and aims for a direct hit. At this speed there is absolutely no room for error. If the missile miscalculates by even 1/100th of a second, it will be off by more than 30.5 meters.
This is a German version of the PAC-3 missile launcher.
The total distance between the two cities is 453 km. The PAC-3 has a range against a ballistic missile of 20 km. `It has a speed of Mach 4.1. The radar detects an incoming missile at 100 kilometers. Within 3 seconds of launch, the missile is traveling at Mach 4.1 (1.39 km/s) It is going to be assumed that the Hwasong-12 missile is pointing directly at the space where the Patriot missile is being launched from.
There is a response time from when the radar detects to when it fires, but for this experiment, we are going to say that it is the same as when the radar detects it.
Using the projectile motion equations, the rough flight pattern of the Patriot missile can be found. The two equations are: y= -4.9t^2+1390*cos(37)t and x=1390*sin(37)t. These equations are used to determine the height at a specific time. Hypothetically, the point of collision can be determined by projectile motion. But in real life, the missile has its own tracking system that it uses to finialize the trajectory of the missile. So that means that the projectile motion can only do so much because it does not go in a straight flight pattern. The physics behind a true missile launch is extremely complex but the rudimentary trajectory calculations of a missile launch are able to be calculated in the equations above.
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