SWM wrote:Vince, you neglect the point that 20 light-minutes in normal space equates to about 20 light-seconds in the alpha band of hyperspace. So, if an enemy ship is sitting in the alpha band at the hyper-limit, and a freighter enters hyper at the hyper-limit on the opposite side of the star, the freighter will pop up a mere 40 light-seconds away from the enemy ship. Easily inside detection range and missile range. A ship in the alpha band can cover the entire hyper-limit of the star.
You need to reread the quote:
Boldface, italics and underlined text is my emphasis.More Than Honor, The Universe of Honor Harrington, (1) Background (General) wrote:Navigation, communication, and observation all are rendered difficult by the nature of hyper-space. Formed by gravitational distortion, hyper-space itself acts as a focusing glass, producing a cascade effect of ever more tightly warped space. The laws of relativistic physics apply at any given point in that space, but as a hypothetical observer looks "outward" in hyper-space, his instruments show a rapidly increasing distortion. At ranges above about 20 LM (359,751,000 km.) that distortion becomes so pronounced that accurate observations are impossible. One says "about 20 LM" because, depending on local conditions, that range may vary up or down by as much as 12%—that is, from 17.6 LM (316,580,880 km.) to 22.4 LM (or 402,921,120 km.). A hypership thus travels at the center of a bubble of observation from 633,161,760 to 805,842,240 km. in diameter. Even within that sphere, observations and measurements can be highly suspect; in effect, the "bubble" may be thought of as the region in which an observer can tell something is out there and very roughly where. Exact, precise observations and measurements are all but impossible above ranges of 5,000,000 to 6,000,000 km., which would make navigational fixes impossible even if there were anything to take fixes on.
The maximum physical range of a single drive missile, accelerating at 42,500 gravities for 180 seconds, is only 6,750,00 km (per The Short Victorious War, Honor Harrington's Navy, Naval Weaponry). 6,750,000 km is ~ 22.5 light seconds. So a merchantman that translated into hyper and is 40 light seconds away in hyper from a raider lying doggo in the alpha band is completely out of the maximum physical weapons range (both energy and single drive missile range) of the raider.
"Exact, precise observations and measurements are all but impossible above ranges of 5,000,000 to 6,000,000 km" in hyperspace (per More Than Honor, The Universe of Honor Harrington, (1) Background (General)). "Exact, precise observations and measurements" are exactly what is needed to direct weaponry (either energy weapons or impeller drive missiles) at a target, if you expect to hit it. 5,000,000 to 6,000,000 km is ~ 16.7 to ~ 20 light seconds. So a merchantman that translated into hyper and is 40 light seconds away in hyper from a raider lying doggo in the alpha band is completely out of the maximum effective targeting weapons range (both energy and single drive missile range) of the raider.
Using a K9 star (dimmest star that could have a habitable planet?) for the smallest hyper limit of 13.64 light minutes or 818.4 light seconds in normal space. Assume the starting point for the merchantman is 5 light minutes in normal space from the star (assumption: a planet at this distance from a K9 star would be in the Goldilocks zone). Assume that the merchantman (the size of an SD) accelerates at a constant effective 124 gravities (with an effective 35% inertial compensator safety margin on a civilian inertial compensator, maximum acceleration 190 gravities) directly towards a point on the hyper limit directly opposite a least-time course, dodging the star enroute.
(For the sake of simplicity, I'm going to assume that merchantman can and will accelerate faster to stay a safe distance from the star and then correct course, but the effective constant acceleration will be as if the ship accelerated at a constant 124 gravities on a line extending from a planet 5 light minutes from the star, through the star, and terminating at the hyper limit on the far side of the star from the planet. I'm also assuming that the ship will correct for the velocity of planet's orbit around the star.)
Additional assumption: An SD sized merchantman's civilian grade hyper generator takes 30 minutes (my SWAG) to fully power up to translate to the next higher band, after initially expending power in translating into the alpha band from normal space. See References and data sources at the end of this post.
The merchantman effectively travels 18.64 light minutes (normal space) from the planet, effectively accelerating at 124 gravities. It arrives at the hyper limit with a normal space velocity of ~ 28,546 kps ( ~ 9.5% of lightspeed, well below the .3 c limit), having effectively accelerated for ~ 23,491 seconds or ~ 6.5 hours. The merchantman immediately translates into hyper and immediately decelerates as a result, bleeding off 92% of its velocity in translation, and carrying ~ 2,284 kps of velocity across the hyper wall into the alpha band.
An SLN raider (Rampart-class DD, maximum acceleration ~ 519 gravities, 80% acceleration ~ 415 gravities, with figures computed from Shadow of Freedom, where Vice Admiral Oxana Dubroskaya told Governer Dueñas at Saltash: “Sir, our Rampart-class destroyers are only half that big, and their maximum acceleration rate, with zero safety margin on the compensator, is only five-point-zero-nine KPS squared.” Italics are the author's.) lying doggo in the alpha band band of hyperspace, at rest (zero velocity) relative to the hyper limit, detects the merchantman translation at 25.6 light seconds, too distant to target to immediately target (both physically out of SDM range and out of effective target range) and instantly accelerates in the alpha band of hyper space directly towards the merchantman at a constant 415 gravities for 30 minutes. The raider will achieve a velocity of 7,321 kps and will have traveled a distance in hyper of 6,588,540 km or ~ 22 light seconds.
The merchantman continues accelerating at 124 gravities in hyper space (assuming no gravity wave nearby) for a further 30 minutes while it recharges its hyper generator before translating into the next higher hyper band. The merchantman achieves a velocity of ~ 4,471 kps, and travels a further 6,079,500 km or ~ 20.3 light seconds in hyper.
After the 30 minute stern chase, the SLN Rampart-class DD raider is now 23.9 light seconds distant from the merchantman. The merchantman is physically out of SDM range ( ~ 22.5 light seconds), as well as the maximum effective targeting range in hyper ( ~ 20 light seconds maximum) from the raider. The merchantman immediately translates into the beta band and escapes from the pursuing raider.
Repeating the above scenario with no safety margin on either the raider (519 gravities acceleration) or the merchantman (190 gravities acceleration) but all other factors kept the same:
The merchantman effectively travels 18.64 light minutes (normal space) from the planet, effectively accelerating at 190 gravities. It arrives at the hyper limit with a normal space velocity of ~ 35,335 kps ( ~ 11.8% of light-speed, well below the .3 c limit), having effectively accelerated for ~ 18,977 seconds or ~ 5.3 hours. The merchantman immediately translates into hyper and immediately decelerates as a result, bleeding off 92% of its velocity in translation, and carrying ~ 2,827 kps of velocity across the hyper wall into the alpha band.
An SLN raider at rest (zero velocity) relative to the hyper limit, lying doggo in the alpha band of hyperspace, detects the merchantman translation at 25.6 light seconds, too distant to target to immediately target (both physically out of SDM range and out of effective target range) and instantly accelerates in the alpha band of hyper space directly towards the merchantman at a constant 519 gravities for 30 minutes. The raider will achieve a velocity of 9,155 kps and will have traveled a distance in hyper of 8,239,500 km or ~ 27.5 light seconds.
The merchantman continues accelerating at 190 gravities in hyper space (assuming no gravity wave nearby) for a further 30 minutes while it recharges its hyper generator before translating into the next higher hyper band. The merchantman achieves a velocity of ~ 6,179 kps, and travels a further 8,105,400 km or ~ 27 light seconds in hyper.
After the 30 minute stern chase, the SLN Rampart-class DD raider is now 25.1 light seconds distant from the merchantman. The merchantman is physically out of SDM range ( ~ 22.5 light seconds), as well as the maximum effective targeting range in hyper ( ~ 20 light seconds maximum) from the raider. The merchantman immediately translates into the beta band and escapes from the pursuing raider.
Note that all of the above assumes the merchantman translates out at a point directly opposite the least-time course translation point. It doesn't have to translate out directly on the point, it can translate out anywhere the open end of a narrow cone intersects the hyper limit (with the cone's point the planet the merchantman starts from, and the center-line of the cone passing through the cone's point, the star, and the star's hyper limit), with the maximum width of the cone determined by how close the merchantman is willing to come into missile range of the raider.
It only gets worse for the raider as the star's spectral class goes up towards F0 (hottest star class that could have a habitable planet?). The distance to the hyper limit from the star increases, the distance a habitable planet would be from the star increases. Both of which increase the merchantman's head start. And widens out the angle of the cone. The same applies if the cycle time of a civilian hyper generator for an SD size merchantman is less than my guess of 30 minutes.
Calculation of initial distance in hyper of merchantman by raider:
Distance in normal space = 2 * hyper limit = 27.28 LM = 1,636.8 LS
Distance in alpha band of hyperspace = 1,636.8 LS / 64 = 25.6 LS (rounded to one decimal place)
References and data sources:
One light second in the alpha band = 64 light seconds in normal space:
At All Costs, Chapter 57 (computed from Apollo's transmission speed along the alpha wall with ships and ACM in normal space)
General information on hyperspace, military and civilian compensator safety margins:
More Than Honor, The Universe of Honor Harrington, (1) Background (General)
Maximum range of a single drive missile (SDM):
The Short Victorious War, Honor Harrington's Navy, Naval Weaponry
Infodumps:
Acceleration by ship mass
Hyper Limits by stellar spectral class
Hyper generator modes of operation
Uniform acceleration formulas from Wikipedia:
Acceleration
Other information from Wikipedia
Speed of light (in meters per second)
Gravity of Earth (rounded to one decimal place)
My scientific wild ass guess (SWAG) of 30 minutes for an SD size merchantman civilian hyper generator to cycle up to translation to the beta band from the alpha band, after undergoing initial translation from normal space to the alpha band--based on the above Pearl and how long it would take for a Scientist's military grade hyper generator to cycle to translate from normal space to the alpha band, after translating from the alpha band to normal space (16 minutes--12 minutes to standby readiness and 4 more minutes to cycle up to an actual translation:
A Rising Thunder, Chapter 20
Calculations were rounded off to two decimal places (light minutes), one decimal place (one Earth gravity of acceleration--mps, light seconds, hours) or no decimal places (gravities--acceleration, light seconds, km, kps).