The Mercury Planetary Book of Jovian Chronicles has some details about running freighters between the planets. On page 0072 and following it states the following information:
The formula is based on the number of Equivalent Burn Points a captain or pilot wishes to spend to make the trip. Half the EBPs are spent accelerating the vessel at the start of the journey, while the other half are spent decelerating the ship at its destination. The ship is assumed to be coasting (not firing its engines) during the middle. Average planetary distances can be found on page 168 of the Jovian Chronicles Rulebook. Acceleration time is calculated through the second formula. Deceleration time is equal to acceleration time. Procedure requires freighters to accelerate at Combat Speed or less during normal operations.
Travel Time in hours = (Distance in kilometers / (EBPs spent x 15))/3.6
Acceleration or Deceleration Time in hours = EBPs Spent / Combat Speed in MPs x 30
It seems here two different concepts of space flight are mixed in a way that would not work in reality. The Jovian ships are basically capable of flying under constant thrust as fuel mass and volume is relatively low compared to modern rockets. One would expect that ships use that advantage and go wherever they want to in a straight line (actually every straight line between two planets would be an elliptical curve in the end due to their constant movement). Constant thrust would assure maximum delta V and minimum flight time. Ships could start their flight at any time, without the need to wait until starting point and end point are as close to each other as possible. Many would wait for that time window, nonetheless. Fuel may be cheap but it’s not for free and time can be spent more efficiently waiting for a flight window on a station than by sitting on a ship burning away while taking the longest possible route.
The mentioning of coasting in between start and stopping phase sounds like a different approach, though. Ships that have to take energy efficient flight routes have to choose transfer orbits, that allow them to coast without main thrust for the longest part along a calculated orbit that takes them from the orbit of the start point to the orbit of the end point. This is called a Hohmann Transfer and it requires the ship to wait for a fitting time window to start. Hohmann Transfers take up a lot of time, the ship will not accelerate or decelerate while coasting and thrusting for a short start phase will not allow it to gain a high delta V for the coasting part. The ship has to fire auxiliary engines while coasting to counter the gravity pull of the sun as well as that of the start point planet and the end point planet, too.
The flight times for constant thrust and coasting flights will differ greatly. Constant thrust allows a ship to reach many targets within a couple of days, when coasting we talk about months to reach even the closest targets.
So you would either have slow thrust engines and very limited amounts of fuel, enforcing you to use Hohmann Transfers and long coasting trips OR you have powerful thrusting engines and almost unlimited fuel, allowing you to constantly thrust towards any target any time and reach it much faster.
Let’s take a freight ship making a trip from Earth to Mars, for example. The mean distance between Earth and Mars is 272.6 million kilometers. This is our distance at the starting point. A radio signal will travel that distance in 15 minutes, before the planets have moved very far. By the time your ship reaches Mars, Earth will have gone almost 3/4th around the Sun already, while Mars has not yet moved behind the sun from your startpoint’s view.
Let’s say our freight ship tries to make the run as fast as possible, and will burn as many fuel points as necessary to get there soon. The Caravan-class Medium Freighter has 1.000 Equivalent Burn Points it can spend for the trip. One half for accelerating, one half for decelerating, while coasting in between.
The Mercury book gives us this formula for this case:
Travel Time in hours = (Distance in kilometers / (EBPs spent x 15))/3.6
T = (272,600,000/15.000)/3.6
T = 5,048 hours or 210 days or almost 7 months
That’s only slightly faster than what NASA calculates for a trip to Mars with modern technology (about 8.5 months). And it requires the ship to coast the major part of the journey along a Transfer Orbit.
The main rulebook gives this general formula to calculate time until midpoint in seconds:
T(s) = 1d6 * SQRT (half distance in meters / acceleration in m/s)
T = 1d6 * SQRT (136,300,000,000/1.96133)
T = 1d6 * 263,616.5
giving us results from 263,616.5 to 1,581,699 seconds or 3 to 18 days until midpoint (6 to 37 days for the total distance). This is a totally different result and does neither fit to Transfer Orbit times nor constant thrust results (see below).
The other approach would be to allow the ship to constantly thrust at it’s maximum acceleration rate of 0.2 g when fully loaded up until midpoint, turn around and continue its flight path constantly thrusting to decelerate. In that case the flight path or transfer orbit will be much shorter and flatter.
T = 2 * SQRT (Distance in m / Acceleration in m/s)
T = 2* (SQRT (272,600,000,000 / (0.2*9.80665)))
T = 2* (SQRT (272,600,000,000 / 1.96133))
T = 2* 372,810 = 745,620 seconds or 207 hours or 8.63 days
(reaching a maximum velocity at midpoint of 730 m/s)
The freighter could get to Mars even faster (6 days and 2 hours) without the Turnover manouver but then it would fly by Mars at a velocity of 1033 km/s. This could work for military ships in intercept missions, for example.
It is unclear, whether ships in Jovian Chronicles move at modern day rate (taking several months between inner planets and year long trips to the outer planets) or if it was intended to reduce flight times to days or weeks by applying constant thrust. A fast military ship (0.7 g) would need 7 days and 20 hours to fly from Earth to Jupiter under constant thrust which is easily within it’s stated deployment range (3,000 hrs). Using the time formula from the books the same ship (appying all 1,000 EBPs) would take 14675.9 hours or 611 days to get there – that’s more than a year and a half and way beyond the stated deployment range.