Should The Space Elevator Ever Be A Reality?
Will the Space Elevator ever be a reality? Tim Engstrom
The Cost of Space
The cost of shipping payloads into space is currently thousands of dollars per kilogram[1]. Rockets are used for this job, subjecting the cargo to severe changeable g-forces, generating extreme pollution. The cost of launching a satellite by rocket is typically between $50 million and $400 million dollars[2]. Geosynchronous orbits at 35,786 km are significantly more expensive to achieve than Low Earth orbits at less than 2,000 km. A space Elevator could reduce the average lift costs to Geosynchronous orbit from about $25000 per kilogram to less than $220 per kilogram[3][4]. However the initial costs to establish the elevator would be very high at around $20 billion …show more content…
Newton’s laws of motion govern the motion of an object in an inertial reference frame which is one which is not accelerating. As a rotating reference frame is constantly accelerating, a centrifugal force must be introduced in order for Newton’s Laws of Motion to apply. Centrifugal force is a useful concept in analysing behaviour in rotating systems and is the apparent force acting outwards to counteract the centripetal force. This apparent force results from an objects tendency to continue in a straight path due to its inertia.
A simple model of the Space Elevator considers it to be a uniform free standing tower. This tower is not a compression structure however, but instead one in which its weight is counterbalanced by the outward centrifugal force on it, so that it exerts no force on the ground beneath. This tower is in tension along its entire length, with the tension varying along its length so that each small section of the tower is in equilibrium under the action of the varying gravitational, centrifugal and tension forces acting on it. The diagram below shows a small section of length dr of this …show more content…
Similarly there is a tension acting downwards TD and the weight of this portion of cable, W. These forces must be in equilibrium for any portion of the cable because relative to the surface of the Earth there is no vertical motion. The difference between TU and TD at any point can be expressed as dT, as the segment is of length dr.
If we consider an element such as this at Geosynchronous height, then the Weight and the Centrifugal force are equal and opposite such that W= FC , and so it follows that the tension upwards must equal the tension downwards (TU = TD) in order for the element to be in equilibrium. This indicates that the gradient of the tension at this point is 0 as dT is 0. Below this point, W > FC , so TU > TD , so the gradient is positive. Above geosynchronous height, FC > W , so TD > TU , so the gradient is negative.
Therefore, the tension is a maximum at geosynchronous height and decreases to zero at each end. Thus, the system is a free standing
The Cost of Space
The cost of shipping payloads into space is currently thousands of dollars per kilogram[1]. Rockets are used for this job, subjecting the cargo to severe changeable g-forces, generating extreme pollution. The cost of launching a satellite by rocket is typically between $50 million and $400 million dollars[2]. Geosynchronous orbits at 35,786 km are significantly more expensive to achieve than Low Earth orbits at less than 2,000 km. A space Elevator could reduce the average lift costs to Geosynchronous orbit from about $25000 per kilogram to less than $220 per kilogram[3][4]. However the initial costs to establish the elevator would be very high at around $20 billion …show more content…
Newton’s laws of motion govern the motion of an object in an inertial reference frame which is one which is not accelerating. As a rotating reference frame is constantly accelerating, a centrifugal force must be introduced in order for Newton’s Laws of Motion to apply. Centrifugal force is a useful concept in analysing behaviour in rotating systems and is the apparent force acting outwards to counteract the centripetal force. This apparent force results from an objects tendency to continue in a straight path due to its inertia.
A simple model of the Space Elevator considers it to be a uniform free standing tower. This tower is not a compression structure however, but instead one in which its weight is counterbalanced by the outward centrifugal force on it, so that it exerts no force on the ground beneath. This tower is in tension along its entire length, with the tension varying along its length so that each small section of the tower is in equilibrium under the action of the varying gravitational, centrifugal and tension forces acting on it. The diagram below shows a small section of length dr of this …show more content…
Similarly there is a tension acting downwards TD and the weight of this portion of cable, W. These forces must be in equilibrium for any portion of the cable because relative to the surface of the Earth there is no vertical motion. The difference between TU and TD at any point can be expressed as dT, as the segment is of length dr.
If we consider an element such as this at Geosynchronous height, then the Weight and the Centrifugal force are equal and opposite such that W= FC , and so it follows that the tension upwards must equal the tension downwards (TU = TD) in order for the element to be in equilibrium. This indicates that the gradient of the tension at this point is 0 as dT is 0. Below this point, W > FC , so TU > TD , so the gradient is positive. Above geosynchronous height, FC > W , so TD > TU , so the gradient is negative.
Therefore, the tension is a maximum at geosynchronous height and decreases to zero at each end. Thus, the system is a free standing