Nuts & Volts - September 2005

Near Space

G is 6. 67 X 10-11 M is 5. 98 X 10²⁴

Doubling your distance from the center of Earth (not the altitude above sea level) decreases the force of gravity, the acceleration it creates, and your weight by a factor of four, that is, 1/2²= 1/4. With Equation 1, I calculate that one of my near spacecraft at an altitude of 100,000 feet experiences a 1% reduction in Earth’s gravity.

The acceleration due to centrifugal force depends on your velocity squared and the inverse of your distance from the center of rotation, or,

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A_C= V²/ (R_e+ h) Equation 2

When standing on a tower fixed to Earth’s surface, your orbital period around Earth remains fixed at 23 hours and 56 seconds (rounded to 24 hours or 86,400 seconds). You can calculate your velocity by multiplying the height of the tower above the center of Earth (R_e+ h) by two times pi and dividing by the length of a day in seconds ( 86,400 seconds).

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V = (2 X pi X (R_e+ h) ) / 86,400 Equation 3

Substituting the equation for velocity (Equation 3) into the equation for acceleration (Equation 2) creates a single equation for calculating the centripetal acceleration,

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A_C= ( 4 X pi²X (R_e+ h) ) / 86,400²Equation 4

To determine the effect of climbing a tall tower, we combine the effects of gravity and centrifugal force. By combining the accelerations due to gravity (towards the center of Earth) and centrifugal force (away from the center of Earth), I was able to generate the following chart (shown in Figure 1) of total (or net) acceleration as a function of height above the center of Earth.

Tsiolkovsky’s SE was a tower tall

SEPTEMBER 2005

enough to reach a stationary orbit for the planet it stood on. Cargo rode up the tower until it was in geostationary orbit and able to be released without crashing back to Earth.

Now, Tsiolkovsky didn’t think it was possible to build a SE. For one reason, building a tower taller increases its weight. In order to remain standing, as the tower’s weight increases, its strength must also increase. Without changing the nature of the tower, its strength is increased by widening it.

Since the weight of the tower increases as you approach the surface of Earth, the tower must get wider as you approach its base. However, widening a tower’s base adds weight to the tower which, in turn, requires the tower’s base to be even wider. At some point, we reach the maximum height permitted by the tower’s construction and materials.

Yuri Artsutanov, a Leningrad engineer, performed the first serious engineering study of the SE in his paper, “Into Space with the Help of an Electric Locomotive.” His study was published in 1960 in the pages of the Soviet newspaper Pravda. No one took notice of his results, perhaps as a result of publishing his study in a habitually dishonest newspaper.

Artsutanov’s initial SE was one millimeter wide and capable of carrying 900 tons of cargo into geostationary orbit (I believe this is 900 tons per day). The beauty of Artsutanov’s SE is that it can bootstrap itself. Only a thin ribbon needs to be flown into space. The tower’s climbers then make trips up and down the SE, adding additional ribbons each trip. Once the SE was a thousand-fold stronger, it could lift 12,000 tons of goods per day to geostationary orbit, or the equivalent of one fully loaded Space Shuttle launch every four minutes.

A 1960s Convair feasibility study on the use of tall towers for astronomy, high altitude research, rocket launching, and communications determined that the tallest possible

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