Emergency Acceleration Profile

In Robot Dawn, the advent of Cold Fusion and the EmDrive make it possible to discuss trajectories over long distances within the Solar System in terms of continuous acceleration instead of orbital mechanics. The limiting factor with vehicle acceleration is what is tolerable to the spacecraft and its passengers. Human beings are limited in their capacity to tolerate high g-forces for long periods of time and are thus the determining factor.

When getting from one place to another within the Solar System in an emergency situation, the recommended acceleration profile in its simplest form is to have high acceleration at the beginning of the trajectory for as long as the passengers can withstand it followed by a reduced acceleration for the long duration of the trajectory for passenger comfort until the midpoint is reached. Halfway there, this reduced acceleration is reversed to decelerate the vehicle for arrival at the destination. This is then followed by a high deceleration comparable in both magnitude and duration to that at the beginning of the trajectory when having reached the destination. The result is the acceleration profile shown below.

Note that all accelerations experienced during the trajectory sum to zero, which would indicate that the velocity at beginning and end are the same, also zero. Granted that when going say from Earth to Jupiter the velocity of the spacecraft is that of Earth in orbit about the Sun and when arriving at Jupiter, the spacecraft would have to have the same velocity as Jupiter in its orbit about the Sun, but these velocities are small when compare to those achieved by the spacecraft during the trajectory and have been ignored along with other subtleties for ease in understanding the mechanics of getting from place to place within the Solar System.

The reason for this acceleration profile is that building up high velocity as soon as possible will get you to your destination more quickly than using just a sustained lower acceleration that humans can tolerate continuously. Humans can generally handle 4-gs for three hours (NASA-STD-3001 Rev. A, page 47) in an emergency situation but are only comfortable at 1-g for significant durations. Of course, this is just a conceptual profile, and an optimal one for any particular trajectory would would be more nuanced. Certainly no one would subject a human crew to an instantaneous 4-gs at the beginning of a voyage. There would be a slow buildup followed by a continuous high acceleration, followed by a slow reduction to 1-g for the sustained portion of flight. Even the 1-g portion might be elevated since humans can tolerate somewhat more than 1-g for days at a time.

The time savings for going from Earth to Mars (a distance of 236 million miles in the fall of 2070) is 16 hours or about 15% of the total time.

During the second half of Robot Dawn, Mazzy Nova and crew use this type of trajectory when making an emergency return to Earth from the O’Neill colony at SE-L4 to try to save Cambria from terrorists. Earlier in the story, Misaki also has occasion to travel at high speed from Earth to Europa, the smallest of Jupiter’s four Galilean moons, to assassinate a man and his human source robot.

The positions of the planets relative each other, the Sun and the Lagrange points in the fall of 2070 are important to the story as it develops. I used my planetarium software, Starry Night, to discover this Solar System information. I have shown the approximate positions of the planets along with some calculated geometry on a map of the Zodiac in the figure below. Since all the planets’ orbits lie approximately within the ecliptic plane, it is a two-dimensional geometry problem.

Although I’ve not mentioned it in the story, the inquisitive reader may wish to keep this Solar System geometry in mind when reading about the excursions between planetary systems. As a reference, I have also provided below a simplified plot of the time it takes going from point-to-point within the Solar System for three different continuous acceleration levels, 1/2-, 1- and 2-gs.

This plot takes into consideration a constant acceleration at the stated magnitude for the first half of the trajectory and a constant deceleration at the same magnitude for the second half of the trajectory. After all, you do have to come to a stop when you get to your destination if you don’t want to go whizzing past.

The distance from Earth to Moon is about 240 thousand miles. The distance from the Earth to the Sun, one astronomical unit (AU) is about 93 million miles (150 million kilometers). The distance from one planet to another is dependent on the positions of both planets in their orbits about the Sun but are assumed to be relatively unchanged for the short period of time of the story in the fall of 2070. The shorter the distance, the higher percentage time savings due to the time of high acceleration being the same in all cases since it is limited only to the length of time humans can withstand it.

As an aside, I should explain a bit of terminology associated with humans experiencing g-forces as they appear at times during Robot Dawn‘s Narration. It is an explanation of the direction of acceleration relative to the human body, and it has to do with what the acceleration does to the eyeballs inside the head. Thus, the terms “eyeballs in,” “eyeballs out,” “eyeballs up,” and “eyeballs down,” came into use mid-20th century in the vernacular of the test pilot. All this is explained here. A search of the text for “eyeballs” yields over 40 hits.