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Speed of Falling Saruman: Lord of the Rings

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Abstract

The purpose of this analysis is to determine the speed of Saruman after falling from the top of the tower Orthanc.

Introduction

This scene is from Chapter 4, "The Voice of Saruman," in the extended edition DVD of The Return of the King (2003). In this scene, Saruman the white wizard is trapped in his tower and is talking to Theoden the King of Rohan (as well as other members of the Fellowship of the Ring). He is then stabbed several times by Wormtongue, his former ally. After the stabbing, Wormtongue is shot with an arrow by Legolas, the elf in the Fellowship. Wormtongue falls backwards but Saruman topples off the edge of Orthanc onto a spiked wheel.

Saruman falling

We are going to determine two values of the speed of Saruman using the formulas

v2 = vo2 + 2as

and

v = vo + at

Where

Procedure

Saruman on top of his tower

Gandalf next to Wheel

Trial Person 1
Time (s)
Person 2
Time (s)
1 7.46 7.34
2 7.05 7.03
3 7.34 7.16
4 6.89 6.85
5 6.84 6.99
6 7.21 6.84
7 7.18 7.16
8 7.08 6.91
9 7.21 7.23
10 6.99 7.10

Analysis

The first method for finding the speed of Saruman as he hits the wheel is to use the equation

v = vo + at

where vo is 0 m/s and a = g = 9.8 m/s2.

The average of the trials is 7.09 seconds. Substituting the known values into the equation,

v = 0 m/s + (9.8 m/s2*7.09 s) = 69.5 m/s (155.5 mph).

The second method for finding the speed of Saruman is

v2=vo2+2as

where vo is 0 m/s, a = g = 9.8 m/s2, and s = 132.19 m. Substituting the known values into the equation, v2 = 2*9.8 m/s2*132.19 m = 2590.92 m2/s2. Thus v = 50.9 m/s (113.9 mph).

Conclusion

Based on this analysis and by using our first method, Saruman's velocity is 69.5 m/s (155.5 mph) as he hits the spike. However, his true velocity is somewhat less than this because air resistance decreases his acceleration. By using our second method, Saruman's velocity is 50.9 m/s (113.9 mph). Of the two methods, the second is the better approximation because it uses the height that he falls even though the acceleration is still slightly less than g.

Sources of Error

One source of error for this analysis is that we neglected air resistance. Air resistance would decrease Saruman's acceleration which would lead to a smaller final velocity.

Another source of error is that while Saruman is falling, he is also rotating. Since he is rotating, the acceleration is not constant due to change in drag because of change in his projected area.

Gina Castellano, Jenna Conversano -- 2005

Physics on Film
  1. Commercials
    1. Speed of a car: Honda Civic Si commercial
  2. Feature Films
    1. Power of a mutant: Storm from X-Men
    2. Speed and mass of a dodge ball: Dodgeball: A True Underdog Story
    3. Speed of a rogue bludger: Harry Potter
    4. Speed of falling Saruman: Lord of the Rings