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MIM-104 Patriot (PAC-3) Part 1

MIM-104 Patriot (PAC-3 Missile)

The Patriot missile is designed to identify and then track and hit an oncoming missile. The missiles vary in size but some may be as small as 10 feet long. The target may also be These missiles can be traveling at two to four times the speed of sound. This particular missile depends on radar. The radar (THAAD) can track the missile as far as 50 km away. The missile is comprised of five main components as seen in the picture below. The PAC-3 weighs about 700kg, and is 5,800mm in length. It has a diameter of 410mm. The wingspan is 920 mm. Its flight altitude is 24,200 m until it collides with its target. It has a range of up to 20 km against ballistic missiles. Also it has a launch platform which is a trailer which can move as well as have the missiles spin around itself to get the best angle to the target. 


Currently, Raytheon as well as many other subcontractors are working on Patriot missiles for South Korea, United Arab Emeritus, Turkey, and Japan. Focusing on South Korea, they are in the process of refurbishing eighteen out of there fifty launchers with PAC-3 missiles. They currently have eight technical sights most of which are also army bases. There are six launchers per base. Most of these bases are inland but there are two to three bases on the east and west coasts. Most of the bases are in the northern part of South Korea (as the primary threat to South Korea is from the North). If a missile was located in the city of Daegu, it is unable to reach a missile fired from North Korea, but it does protect the southern half of South Korea. There is an army base in Seoul as well as one further north which holds many of the 50 Patriot missile systems. They are close enough to shoot down a missile that is fired from North Korea. The South Korea Patriot missile is the first line of defense if a missile was to be shot at the United States from North Korea.



The exact figures for any of the Patriot missiles are strictly confidential. There is no way of determining exactly what the measurements are. On the other hand, there are rough estimates from previous tests that the data can be assumed from. The angle that the missile launcher on the trailer is set at is an exact angle that is unknown but is between 35 and 40 degrees. The initial velocity is zero but the final velocity is estimated. The acceleration varies depending on how much fuel is in the motor, which causes a difference in how much fuel it burns. Basically, the amount of fuel equates to thrust which then determines how far how fast the missile can travel. The missiles can reach up to a traveling height of 24,200 meters. The acceleration can be estimated at Mach 4.1. The acceleration depends on how much fuel is inside the missile as well as how fast that it burns up but it can be generalized as Mach 4.1. The radar can track missiles in two different ways. It can use a heat sensor to track the incoming missile or it can depend on satellites to guide it towards the missile. 

Projectile motion can be used to calculate the collision point between the missiles. It is assumed that the missile is aiming on a direct route for the point of release of the other missile. It is also assumed that the missile is firing from the ground because the exact height of the trailer is unknown. A Hwasong North Korean Missile is launched at an angle of about 80 degrees. 

Hwasong-12: This is an official test fire by North Korea that was partly recorded. It is going to be used to determine the collision distance between a similar missile and the Patriot defensive missile. (May 15th test run)

Vx = ΔX/ΔT
3700km/1020s = Vx
Vx = 3.62 km/s --> 3627.45 m/s

ΔY = Vi*t + 1/2*a*t²
0 = Vi *(1020 s) - 4.007 * (1020)²
0 = 1020 * Vi - 4.17 x 10⁶
4.17 x 10⁶ = 1020 * Vi
Viy = 4087.14 m/s

3627² + 4087² = 5464²
5464 = average velocity

acceleration = thrust - weight
a = 50 tons - 28 tons -( -9.8)
a = 45,359.2 kg - 248,932 N
a = 8.014 m/s²

Tan-1 (4087.14/3627.5) = 48.41
Ө = 48.41°


Δpos
Vi
V average
A
T
X
3,700,000m
3627.5 m/s
5464.75 m/s
0 m/s²
1020 s
Y
0m
4087.14 m/s

-8.014 m/s²
1020 s

Hwasong -12 (test fire projected results)

Distance from Sudan, North Korea to Daegu, South Korea = 453 km

1020s*453km = 3700km* t
t = 124.881s

acceleration = thrust - weight
a = 50 tons - 28 tons -( -9.8)
a = 45,359.2 kg - 248,932 N
a = 8.014 m/s²

ΔY = Vi*t + 1/2*a*t²
0 = Vi *(124.881 s) - 4.007 * (124.881s)²
0 = 1020 * Vi - 4.17 x 10⁶
4.17 x 10⁶ = 124.881 * Vi
Viy = 500.4 m/s

Vx = ΔX/ΔT
453km/124.881s = Vx
Vx = 3.62 km/s --> 3627.45 m/s


3627² + 500.39² = 5464²
3661.8 = average velocity

Tan-1 (500.39/3627.5) = 56.83
Ө = 56.83°

Δpos
Vi
V average
A
T
X
453,000m
3627.5 m/s
3661.81 m/s
0
124.881 s
Y
0m
500.40 m/s

8.014 m/s²
124.881 s


Part two will discuss the PAC-3 Patriot missile information as well as the point at which they collide.

Citations:

  • Brain, Marshall. “How Patriot Missiles Work.” HowStuffWorks Science, HowStuffWorks, 28 Mar. 2003, science.howstuffworks.com/patriot-missile.htm.
  • Reilly, Richard. “Interview on Information about Patriot Missiles.” 12 Oct. 2017.
    • (Mr. Reilly is currently working with the Patriot launchers in South Korea)

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