40 Questions
What is the equation for finding Qbo for maximum range conditions?
Qbo = 2sin(θ/2) / (1 + sin(θ/2))
What is the expression for the time of free-flight?
t_ff = 2√(a / μ) ⋅ (π - E1 + e sin E1)
What is the effect of launching errors on the free-flight range?
Launching errors affect both down-range and cross-range errors.
What is the expression for the cosine of the eccentric anomaly (E1)?
cos(E1) = e + cos(θ/2)
What is the type of error that causes a missile to hit to the right or left of the target?
Cross-range error
What is the source of down-range errors in a missile's trajectory?
All of the above
What is the name of the angle that maximizes the range of a projectile?
θ
What is the effect of incorrect launch azimuth on the missile's trajectory?
It causes cross-range errors.
What is the approximate semi-major axis of a ballistic missile?
6372 km
What is the primary force that determines the missile's path during re-entry?
Atmospheric drag
What is the shape of a missile's trajectory during free-flight?
Elliptical
What is the purpose of the guidance and navigation system during powered flight?
To adjust the missile's trajectory
What is the physical process that occurs during re-entry?
Energy dissipation by friction
What is the non-dimensional parameter Q defined as?
v^2 / (v_cs * μ)
What is the altitude at which re-entry typically begins?
100 km
What is the objective of the free-flight range equation?
To find the free-flight range of a missile
What is the range of an Intercontinental Ballistic Missile (ICBM)?
over 5500 kilometers
Which of the following classes of ballistic missiles has a range of between 1000 to 3000 kilometers?
Medium Range Ballistic Missile (MRBM)
What is the range of a Theatre Ballistic Missile (TBM)?
between 300 to 3500 kilometers
Which of the following is also called a semi-ballistic missile?
Quasi Ballistic Missile
What is the range of a Battlefield Range Ballistic Missile (BRBM)?
less than 200 kilometers
Which of the following classes of ballistic missiles has a range of over 1000 kilometers?
Strategic
What is the range of a Submarine launched Ballistic Missile (SLBM)?
over 5500 kilometers
What is the range of an Intermediate Range Ballistic Missile (IRBM)?
between 3000 to 5500 kilometers
What is the expression for d in terms of rbo and φ?
d = rbo sin(φbo)
What is the equation that combines equations (11) and (12)?
sin(2φbo + φbo) = sin(φ)
What is the condition for maximum range trajectory?
sin(2φbo + φbo) = 1
What is the value of φbo for maximum range conditions?
φbo = (180 - φ) / 4
What is the name of the equation derived from combining equations (11) and (12)?
Flight path angle equation
What is the relationship between rbo and rbo'?
rbo + rbo' = 2a
What is the expression for d in terms of rbo and φ, in a different form?
d = rbo' sin(180 - 2φbo)
What is the condition for a single solution to the flight path angle equation?
sin(2φbo + φbo) = 1
What is the direction of the rotation of the Earth?
From west to east
What is the characteristic of the free-flight portion of a ballistic missile trajectory?
It is inertial in character
Why do we need to compensate for the motion of the launch site and the target?
Because of the Earth's rotation
What is the expression for the speed of any launch point on the surface of the Earth?
Vo = 1524 cos L0 (ft/sec)
What are the components of the true velocity v?
vN, vE, vZ
How can the true velocity, flight-path angle, and azimuth be found?
From the components of the true velocity
What is the angle formed at O in the figure?
The difference in longitude between the launch point and the aiming point
What is the term for the difference in longitude between the launch point and the target?
DN
Study Notes
Maximum Range Trajectory
- The maximum range angle attainable with a given Qbo can be found from equation (15)
- Qbo can be solved for maximum range conditions:
Qbo = (2sin(/2)) / (1 + sin(/2)) - The maximum range condition occurs when the flight-path angle equation yields a single solution
Time of Free-flight
- The value of eccentric anomaly can be computed by taking
1 = 180 - /2 - The time of free-flight can be obtained from
t_ff = 2(a^(3/2) * (π - E1 + e sin E1)) / μ
Effect of Launching Errors on Free-flight Range
- Variations in speed, position, and launch direction will produce errors at the impact point
- Errors can be categorized into down-range errors (errors in the intended plane) and cross-range errors (out-of-plane errors)
- Cross-range errors can be caused by lateral displacement of the burnout point or incorrect launch azimuth
Ballistic Missile Components
- Examples of ballistic missiles include Iraq's Scud Missile and the United States' Minuteman III
- Ballistic missiles can be categorized into different classes based on their range, including intercontinental ballistic missiles, intermediate-range ballistic missiles, medium-range ballistic missiles, and short-range ballistic missiles
Categorization of Ballistic Missiles
- Ballistic missiles can be categorized based on their range, with different categories including tactical ballistic missiles, theatre ballistic missiles, intermediate-range ballistic missiles, and intercontinental ballistic missiles
- Submarine-launched ballistic missiles and quasi-ballistic missiles are also types of ballistic missiles
Ballistic Missile Trajectory
- The trajectory of a ballistic missile can be divided into three stages: powered flight, free-flight, and re-entry
- During free-flight, the trajectory is part of a conic orbit, typically an ellipse
- The re-entry phase involves the dissipation of energy by friction with the atmosphere
This quiz covers the calculation of maximum range trajectory, including the equations and formulas used to determine the maximum range angle and Qbo.
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