Travel to 100 Diameters

[Twist]

I was looking at the time to travel to 100 planetary diameters chart in the TNE book, and it says it takes about 10 hours to travel to 100 diameters on a size 8 world (earth size), at a 1 g-hour burn.

Using ½ gt2 to a distance of 100 diameters (12800 * 1000 * 100/4.9) ^.5 / 3600. I get like 4.5 hrs. Even if I assume they only accelerate half way there and decelerate the other half (the book says they accelerate the whole way) I get like 6.35 hrs. Maybe they were taking into the account the gravity of the world, but I though contra gravity was supposed to nullify that. So what am I missing.

Also does anyone else think it's weird trading ship would waste all that space on maneuver fuel when they can go to and from a rather large world with just 20 G-Turns. It seems to me, there would either be a thriving tug business, or there would be a common meeting place 100+ diameters out and solar sail barges or robotic barges operating at low g or some such would take the cargo the rest of the way (especially the low priority cargo)? I just can't see a merchant vessel spending 17-30% of his volume on maneuver drives. Anyway guess that's 2 questions.

 

[aramis]

The TNE isn't doing a continuous burn; it's doing a 35 min or so initial burn, and a 25 min or so decell burn, and coasting the in between.

the D=0.5AT², reparsed for T=√(2D/A) is for a continuous burn the whole trip.

That's the difference. Coasting for 7 hours at 18km/s

 

[MR TEK]

Falling into the (gravity) well...

Personally I always thought there would be a "commercial" high port past the 100D limit. At least the big routed freighters jump close to that platform, so time on their own fuel would be minuets at both ends.
By cutting at least 1/2 day travel time, and at least that much fuel and life support, they can shave the margins that much closer.

Of course I always envisioned that imperial guaranteed shipping rate only applied to the big scheduled commercial haulers, and gypsies of all sorts could charge a higher rate for transport.

That would explain why the 1 mil dt commercial haulers that HAVE TO BE THERE for commerce to be of any volume to occur have never been seen or discussed. The big haulers never come in-system far enough for any but the mega-corp crews to see.

Of course the other side is that there is a steady stream of in system haulers that shuttle back and forth to that far port, but cargo transiting the system really only stays in system for exactly the length of time it takes to refuel.

There are of course other economic repercussions, but I expect only the mega-corps have the resources, and permits to build and traffic through the far ports, so the only effect on players should be to explain why the megas can make a living and the independents have to work so hard to get by.

Assuming the express boats stop way out there, that also cuts half a day per jump from the express boat routes.

So a system with much commerce has a far port where the equivalent of long haul trucks stop long enough to fuel and transfer fuel, and the rest of us indies and feeder lines fall into the high port and have to climb back out to jump.

 

[Twist]

I see what I did wrong, the burn is only for an hour.
Total time – t
Burn time – tb
Coast time – tc

If you ignore the distance traveled while accelerating the formula would be
t = 100D/a(tb). If you calculate that you get the number in the book.

So now were talking 2 G-turns out and 2 G-turns in. Now I'm really not sure why they are carrying all that maneuver fuel. The Free trader carries 280Kl of Jump fuel and 700 Kl of maneuver fuel. A G-turn for it is 12.5 Kl. So you could carry 8 G-turns for 100 Kl. What is the rest of the fuel for? Fighting pirates? You can't out-run or out-gun them anyway, so why not jump away, it's less fuel (I never really understood the pirate thing anyway, but thats another conversation). So 2 complete Jumps with 4 G-turns each and 20% extra jump fuel is only 685 Kl. I may change the fuel thing back to CT in my TNE campaign. Why would anyone ever fight a battle unless they wanted too, it takes less fuel to jump away; so either you dead in space, or you jump away.

But to get back to the formula, if you don't ignore the distance traveled while accelerating:

If the distance to travel is more than what is accomplished during the burn, the formula is the distance traveled during the burn = ½at^2 and the distance traveled after the burn 100D – ½at^2. The time traveled during the burn is of course an hour, and the time after the burn is
(100D – ½a(tb)^2) / (a(tb)) = tc.
100D/a(tb) – ½tb = tc
100*12800*1000 / (9.8*3600) –.5*3600 = tc (in sec)
100*12800*1000 / (9.8*3600*3600) - .5 = tc (in hrs)
128000/(9.8*36*36) - .5
tc = 9.58
tb + tc = 10.58

The errata says 10.14, which I think was an attempt to count the time accelerating. Course I may have done that part wrong.