Kinematics Analysis of Millenium Falcon Turbolaser Impact

in "The Empire Strikes Back"

Written: 1998.08.01

This document represents an attempt to quantify the energy involved in the sudden angular acceleration of the Millenium Falcon after being hit by a turbolaser or laser blast in "The Empire Strikes Back". The basic assumption is that turbolasers use mass-less particles. If the particles in a TL bolt do not carry mass, then their momentum can be calculated using the equations for the momentum of light, and their power levels can be estimated from the kinetic effect upon the Millenium Falcon.

Controlling Equations:

  1. The momentum of a laser bolt of any given energy level is p = U/c

  2. The moment of inertia for a cylinder rotating about its central diameter is:
    Moment of Inertia formula

  3. The torque necessary to induce a given angular acceleration is T = Ia

  4. The torque resultant from an externally applied force is T = Fx

  5. The force corresponding to a momentum increase during a known timeframe is F=p/t

Units:

Derivation of Formula:

As per Newton's third law of motion, for every action there is an equal and opposite reaction. Therefore, the reaction torque corresponding to the Falcon's angular acceleration must be equal to the torque applied by the turbolaser:

T1 = T2
\ Ia = Fx
F = p/t
\ p = Ia t/x

However, a = w /t and the two time terms refer to the same time element (the angular acceleration must occur in the exact same timeframe as the duration of the turbolaser impact). Therefore, the a t term simplifies to w, and the above equation simplifies to:

p = Iw/x
\ p = U/c
\ U = cIw/x

Estimates for variables

There are no canon figures for the length, width, thickness, and mass of the Millenium Falcon. However, Robert Brown has done extensive work analyzing this famous star freighter in his Falcon web-site at www.synicon.com.au/sw/mf/falcon.htm. I used his figures for the saucer diameter and height of the Falcon:

Calculations

Step 1: Calculate moment of inertia:
Moment of Inertia formulaSubstituted values
\ I = 7.44E7 kg·m²

Step 2: Calculate turbolaser energy:
U = cIw/x
\ U = 3E8 · 7.44E7 · 2.29 / 7m
\ U = 7.29E15 J = 7290 TJ

Step 3: Compensate for the angle of approach:
Incoming TL bolt
We can estimate from the above snapshot that the turbolaser approached at an angle of roughly 30 degrees. This means that the energy estimate must be divided by sin(30°) to account for geometric factors. Therefore, the energy of the TL bolt would be 14580 TJ.

Conclusion

If turbolasers use mass-less particles such as photons (eg. if their operating principle is similar to lasers), and my estimate for the Millenium Falcon's mass is correct, then turbolasers carry approximately 14580 TJ of energy. The turbolaser appears to strike during a single 1/30-second NTSC frame in this sequence, but to be conservative we should assume that the bolt duration is roughly 1/15 seconds. Therefore, the corresponding turbolaser power level is 218700 TW.

As an aside, the rotational kinetic energy of an object is 0.5Iw² at non-relativistic rotational speeds. Therefore, 3.902E8 joules of rotational kinetic energy were added to the Millenium Falcon. However, the physics of collisions involve conservation of linear or angular momentum rather than conservation of kinetic energy, which only happens in elastic collisions.



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