Maximum Range Trajectory
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Questions and Answers

What is the equation for finding Qbo for maximum range conditions?

  • Qbo = sin(θ/2) / (1 + sin(θ/2))
  • Qbo = 2sin(θ/2) / (1 + sin(θ/2)) (correct)
  • Qbo = sin^2(θ/2) / (1 + sin(θ/2))
  • Qbo = 2sin(θ/2) / (1 - sin(θ/2))

    • What is the expression for the time of free-flight?

  • t_ff = 2√(a / μ) ⋅ (E1 + e sin E1)
  • t_ff = √(a / μ) ⋅ (π - E1 + e sin E1)
  • t_ff = 2√(a / μ) ⋅ (π - E1 + e sin E1) (correct)
  • t_ff = √(a / μ) ⋅ (E1 + e sin E1)

    • What is the effect of launching errors on the free-flight range?

  • Launching errors have no effect on the free-flight range.
  • Launching errors only affect down-range errors.
  • Launching errors affect both down-range and cross-range errors. (correct)
  • Launching errors only affect cross-range errors.

    • What is the expression for the cosine of the eccentric anomaly (E1)?

    <p>cos(E1) = e + cos(θ/2)</p> Signup and view all the answers

    What is the type of error that causes a missile to hit to the right or left of the target?

    <p>Cross-range error</p> Signup and view all the answers

    What is the source of down-range errors in a missile's trajectory?

    <p>All of the above</p> Signup and view all the answers

    What is the name of the angle that maximizes the range of a projectile?

    <p>θ</p> Signup and view all the answers

    What is the effect of incorrect launch azimuth on the missile's trajectory?

    <p>It causes cross-range errors.</p> Signup and view all the answers

    What is the approximate semi-major axis of a ballistic missile?

    <p>6372 km</p> Signup and view all the answers

    What is the primary force that determines the missile's path during re-entry?

    <p>Atmospheric drag</p> Signup and view all the answers

    What is the shape of a missile's trajectory during free-flight?

    <p>Elliptical</p> Signup and view all the answers

    What is the purpose of the guidance and navigation system during powered flight?

    <p>To adjust the missile's trajectory</p> Signup and view all the answers

    What is the physical process that occurs during re-entry?

    <p>Energy dissipation by friction</p> Signup and view all the answers

    What is the non-dimensional parameter Q defined as?

    <p>v^2 / (v_cs * μ)</p> Signup and view all the answers

    What is the altitude at which re-entry typically begins?

    <p>100 km</p> Signup and view all the answers

    What is the objective of the free-flight range equation?

    <p>To find the free-flight range of a missile</p> Signup and view all the answers

    What is the range of an Intercontinental Ballistic Missile (ICBM)?

    <p>over 5500 kilometers</p> Signup and view all the answers

    Which of the following classes of ballistic missiles has a range of between 1000 to 3000 kilometers?

    <p>Medium Range Ballistic Missile (MRBM)</p> Signup and view all the answers

    What is the range of a Theatre Ballistic Missile (TBM)?

    <p>between 300 to 3500 kilometers</p> Signup and view all the answers

    Which of the following is also called a semi-ballistic missile?

    <p>Quasi Ballistic Missile</p> Signup and view all the answers

    What is the range of a Battlefield Range Ballistic Missile (BRBM)?

    <p>less than 200 kilometers</p> Signup and view all the answers

    Which of the following classes of ballistic missiles has a range of over 1000 kilometers?

    <p>Strategic</p> Signup and view all the answers

    What is the range of a Submarine launched Ballistic Missile (SLBM)?

    <p>over 5500 kilometers</p> Signup and view all the answers

    What is the range of an Intermediate Range Ballistic Missile (IRBM)?

    <p>between 3000 to 5500 kilometers</p> Signup and view all the answers

    What is the expression for d in terms of rbo and φ?

    <p>d = rbo sin(φbo)</p> Signup and view all the answers

    What is the equation that combines equations (11) and (12)?

    <p>sin(2φbo + φbo) = sin(φ)</p> Signup and view all the answers

    What is the condition for maximum range trajectory?

    <p>sin(2φbo + φbo) = 1</p> Signup and view all the answers

    What is the value of φbo for maximum range conditions?

    <p>φbo = (180 - φ) / 4</p> Signup and view all the answers

    What is the name of the equation derived from combining equations (11) and (12)?

    <p>Flight path angle equation</p> Signup and view all the answers

    What is the relationship between rbo and rbo'?

    <p>rbo + rbo' = 2a</p> Signup and view all the answers

    What is the expression for d in terms of rbo and φ, in a different form?

    <p>d = rbo' sin(180 - 2φbo)</p> Signup and view all the answers

    What is the condition for a single solution to the flight path angle equation?

    <p>sin(2φbo + φbo) = 1</p> Signup and view all the answers

    What is the direction of the rotation of the Earth?

    <p>From west to east</p> Signup and view all the answers

    What is the characteristic of the free-flight portion of a ballistic missile trajectory?

    <p>It is inertial in character</p> Signup and view all the answers

    Why do we need to compensate for the motion of the launch site and the target?

    <p>Because of the Earth's rotation</p> Signup and view all the answers

    What is the expression for the speed of any launch point on the surface of the Earth?

    <p>Vo = 1524 cos L0 (ft/sec)</p> Signup and view all the answers

    What are the components of the true velocity v?

    <p>vN, vE, vZ</p> Signup and view all the answers

    How can the true velocity, flight-path angle, and azimuth be found?

    <p>From the components of the true velocity</p> Signup and view all the answers

    What is the angle formed at O in the figure?

    <p>The difference in longitude between the launch point and the aiming point</p> Signup and view all the answers

    What is the term for the difference in longitude between the launch point and the target?

    <p>DN</p> Signup and view all the answers

    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

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    Description

    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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