Studies on Ground Based Accelerators

Introduction

"Ground-based accelerator" is another way of saying gun. Gun launch to space has been considered many times in the past.

For the present studies, the focus will be accelerators that provide a major component of the energy needed to reach an orbit in space. There are many other sled concepts in which an accelerator provide an initial boost to a conventional rocket. These concepts are intended to replace some of the impulse provided by a first stage, or allow for horizontal takeoff. Sleds provide only a small percentage of the total delta V need for orbit.

Some links on guns and other accelerators

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Studies

Combined aerodynamic trajectory and orbital mechanics solutions

First published; 9/4/2011. Last update: 9/4/2011

In the previous studies ("Orbital Mechanics and Delta V Requirements for Gun Launched Projectiles" and "Aerodynamic Losses for Gun Launched Projectiles") we separated the lossless orbital mechanics calculations from the aerodynamic trajectory calculations for the initial portion of the projectile path. In trying to use the results, I found that integrating the two sets of results into a single design and mission was difficult. Therefore, the two solutions have been functionally combined Mathematica so that initial gun conditions and rocket impulse requirements can be calculated for a specified orbit height, including an estimate of the aerodynamic losses. As before, projectile lift is used as an alternative to building the gun at an angle.

The Detailed Calculation Notebook ("combined_gun-to-orbit_model.nb") loads four additional packages. These packages are the functions developed in earlier studies, saved in package format. The packages are contained in "spaceLaunch.zip" available by selecting the "Dependencies" link below. The zip file should be expanded into a folder called spaceLaunch placed in the Mathematica search path. In typical installations, the full folder path would be "C:\Documents and Settings\user\Application Data\Mathematica\Applications\spaceLaunch"

Computable Document Format HTML Pages PDF Version Detailed Calculation Notebook Dependencies

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Orbital Mechanics and Delta V Requirements for Gun Launched Projectiles

First published; 7/16/2011. Last update: 7/19/2011

An earth-based gun can be used to send a projectile into space, but the trajectory will eventually bring the projectile back to the surface. Any practical orbit requires an additional change in velocity, presumably using traditional on-board rocket propulsion, in order to achieve a useful orbit. For the purposes of the study, it is assumed that the desired final orbit should be circular at a specified altitude. In this study, we address the preferred strategy for reaching a specified orbit in terms of the total rocket-burns change in velocity and the gun launch parameters. The design goal is to maximize the payload fraction of the projectile, which equates to minimizing the change in velocity that must be imparted by the on-board rocket.

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Aerodynamic Losses for Gun Launched Projectiles

First published; 7/16/2011. Last update: 7/19/2011

A major consideration for an earth-based accelerator is atmospheric drag. Drag loses mean that the gun exit velocity must be higher so that there is sufficient remaining energy to reach the desired orbit. This study addresses the loss of velocity due to drag. Aerodynamic heating must also be considered, and this topic should be addressed in a later study. Of interest is the use of an accelerator to reach velocities such that only a minimum rocket burn will be required to circularize the orbit. For this purpose, a velocity at the outer edge of the atmosphere of 8-10 km sec is needed.

There are a couple of strategies available to reduce drag loss. The first is to reduce the impact of drag on the projectile by increasing the ballistic coefficient. A second strategy is to build the gun such that the exit is at high altitude, and therefore above most of the atmosphere. To this end, we can consider the highlands of the near-equatorial region, mountains, and towers. Launch angle is yet another strategy. A high angle for the initial trajectory limits the distance traversed within the atmosphere. Finally, I'd like to examine an additional strategy that I have not seen published before; using a projectile with aerodynamic lift to change the trajectory path. The benefit is similar to using a steep launch angle, but the use of lift my allow for a horizontal or near horizontal gun, which should reduce the construction cost.

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Sites

First published; 7/16/2011. Last update: 7/19/2011

This is a not very rigorous look at possible site locations for a 10km long accelerator near the equator. I wanted to see how difficult it would be use high-altitude locations. The research tool was simply Goggle earth, and the discover that Goggle earth will allow you to plot elevation profiles along a specified straight line. The rough conclusion is that it would be difficult to find a mountain that did not require a lot of deep tunneling. High plains are more promising. Shallow ocean sites are also interesting if a sea-level launch can be tolerated.

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Curved Tracks

First published; 7/16/2011. Last update: 7/19/2011

I've seen proposals that an accelerator track (or gun tube) could curved near the end to change the projectile exit angle. That sounds suspiciously blithe considering the accelerations involved. The following files are from a very raw Mathematica notebook that looks at the track profile required to get a desired angle change, given a constant lateral acceleration. If 200g lateral accelerations can be tolerated, the track geometry is reasonable for a 10 deg angle change. Allowing for a curved track would make more mountain-top sites practical.

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