Travel math

Stormcrow's picture
Stormcrow
January 8, 2014 - 8:22pm
Herein I do the math related to acceleration and Void speed. Just for fun.

Let:
1 hex = 1×10m
1 g = 9.8 m·s-2
3×10m·s-1
1 turn = 600 s
1 day = 7.2×10s

First, we calculate the relationship between 1 ADF and 1 g:

1 ADF = 1 hex·turn-2 = (1×107 m)(600 s)-= (1×107 m)(3.6×105 s2)-1 =~ (28 m·s-2)(9.8 m·s-2)-1g =~ 2.9 g

So the assertion in the rule books that 1 ADF is 1 g is incorrect; 1 ADF is nearly 3 g.

Since the size of a hex is arbitrarily set at 10,000 km across, we can feel free to select a different arbitrary size and call it a "short hex" (sh), in which 1 ADF is 1 g:

d = vt = at2
d[1turn@1g] = (1 g)(1 turn)2 = (9.8 m·s-2)(600 s)2 = (9.8 m·s-2)(3.6×105 s2) = 3.528×10m = 3528 km

Therefore a short hex is 3528 km. You can say "about 3500 km" if you like. This is the new size of a hex in the board game, in which one "short ADF" is equal to 1 g. You're just scaling down the speeds of everything in the game to where you read 1 ADF as equal to 1 g.

Starships traveling between systems spend most of their time accelerating or decelerating at 1 g. Any trip of X light years is supposed to take 0.5·X days of 1 g acceleration and 0.5·X days of 1 g deceleration to reach the destination. Furthermore, astrogators must spend 0.5·X days plotting a jump, unless they perform risk-jumping. To get to a destination faster, a ship must both accelerate faster than 1 g and risk-jump.

Jumping through the Void is supposed to take place at 0.01c. This doesn't work:

v = at
t = va-1
t[Void] = (0.01 c)(1 g)-1 = (0.01)(3×108 m·s)(9.8 m·s-2)-1 = (3×106 m·s)(9.8 m·s-2)-1 =~ 3.06×105 s = 4.25 day

Therefore at 1 g a ship will reach 1% of the speed of light in about 4.25 days, making the shortest trip in the Frontier 8.5 days. This is clearly not the case, as shown on the Frontier map.

So how fast are we going if we travel 1 day at 1 g?

v[1day@1g] = (1 g)(1 day) = (9.8 m·s-2)(7.2×104 s) = (7.056×105 m·s-1)(600 s·turn-1) = (4.2336×108 m·turn-1)(1 sh)(3.528×106 m)-1 = 120 sh·turn-1

We're traveling 120 short hexes per turn. This is equal to

v[1day@1g] = (7.056×105 m·s-1)(3×108 m·s-2)-1c = (2.352×10-3)c = 0.002352c

Thus, 1 day at 1 g brings you to about 0.2% of light speed, a far cry from the 1% of c in the book.

Therefore, it is necessary to drop the 1% of c idea and implement a "jump drive" or "Void field" device to be activated at the requisite 1 day 1 g acceleration per light year.

Summary:
Change hex size to 3528 km ("short hex").
1 short ADF = 1 g.
Traveling to a different system requires total acceleration for a number of days equal to (distance in LY) ÷ ADF ÷ 2.
Traveling to a different system requires a number of days of astrogation calculations equal to (distance in LY) ÷ 2, or less if you're risk-jumping.
When requisite speed is achieved, Void-jumping device must be activated to enter Void and deactivated to leave it.
Deceleration takes (distance in LY) ÷ ADF ÷ 2 days. The astrogator must make his calculations already knowing what the ADF on the far side of the jump will be (or else the ship will arrive too far or too close to the system and have to travel for longer to get there).
Void-speed is not related to the speed of light.
Comments:

TerlObar's picture
TerlObar
January 9, 2014 - 7:29am
I just use 1g=10m/s/s to make range math simpler. Using that makes your short hex 3600 km.That's what used in the vector rules in SFMan issue 11.

And in Star Frontiers, I typically make all jumps take 8.6 days and ignore the distance. I also have a mechanic that i use of I want or to vary by distance but that requires the use of a jump device white isn't in the rules.

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Stormcrow's picture
Stormcrow
January 9, 2014 - 3:03pm
Good idea regarding the value of 1g.

Presumably all starship tickets in your Frontier cost the same regardless of distance?

jedion357's picture
jedion357
January 9, 2014 - 3:46pm
Stormcrow wrote:
Good idea regarding the value of 1g.

Presumably all starship tickets in your Frontier cost the same regardless of distance?
I thought at the end of the AD book it had rates based on the light year traveled?
I might not be a dralasite, vrusk or yazirian but I do play one in Star Frontiers!

Stormcrow's picture
Stormcrow
January 9, 2014 - 6:28pm
Right, but if all trips take 8.6 days in TerlObar's Frontier, starliners have no excuse for charging more for greater distance, unless he's got another reason.

jedion357's picture
jedion357
January 9, 2014 - 9:59pm
Stormcrow wrote:
Right, but if all trips take 8.6 days in TerlObar's Frontier, starliners have no excuse for charging more for greater distance, unless he's got another reason.

they may not have an excuse but they do because they can and that extra carryone luggage has a fee, and so on and on....
I might not be a dralasite, vrusk or yazirian but I do play one in Star Frontiers!

iggy's picture
iggy
January 9, 2014 - 11:04pm
This is another part of how Night Hawks rewrote Alpha Dawn without considering the effects on all published details.  Technically all night hawks jumps should cost the same.  However thinking as an engineer I have problems with the energy expenditure for different distances being the same.  Energy is the item we are consuming here and thus charging more credits for.  My way of reconciling this is to remember that night hawks states that the time in the void is different for the distance traveled by fractions of a second per light year traveled.  These fractions of a second must therefore consume energy to account for the distance traveled.  A one light year jump may be a quarter of a second, a four light year jump 1 second, an eight light year jump 2 seconds, and so forth.  The amount of energy consumed for each successive amount of time in the void is what we are counting here.  If this was just the normal engines continuing to burn the energy would be so infintesimal that it does not count or make sense.  If it was more energy then I would see the engines buring out as the mass of the engine is turned to energy.  Thus I lean toward some jump device consuming the extra energy.

Now we could say that while in the void entire pellets of atomic fuel are converted in an instant but that does not account for other engine types and their fuel.  The amounts of energy consumed needs to be consistantly the same despite engine and fuel type.
-iggy

Tchklinxa's picture
Tchklinxa
January 10, 2014 - 6:25am
I checked out the ticket prices and per book it is so much Cr. per light year depending on class.

Now here are additional reasons a company will charge more: astronavigator costs (it takes more hours to crunch the numbers... think of this like taking your car to the mechanic's we all know he does not get $60.00 an hour but that is on the bill, and it did not take him 2 hours to do the job), costs of maintaining your life support (frozen or not you are using energy), costs of having staff check on you, food and water, quarters maintained, taxes they must pay, and so on. 

I figure that Spaceship Passage on ships actually transporting people regularly for profit is some weird hybrid of airline and cruise ship. The ticket prices are probably what we should consider as average, but if you where going to ride say the Grand Stellar Princess it might be more or at least all 100% First Class because that ship would be set up to entertain you and transport you where as the Blue Star might only offer the deep freeze. 

I think the prices are a guide and are simple to keep the game moving, after all refs can tweak away.

I figure a bunk on a Tramp Freighter that is not a passenger ship is a totally different ride then Journey Class on a Pan-Galactic Passenger Liner. Sort of depends a bit on how you envision people being transported in the RL there are all sorts of rules about passenger transportation. 

You guys would be shocked at the amount of paperwork each person generates, the number of government agencies involved (and I swear they are in a pissing contest), the number of laws and regulations, the way billing has to be done by law, inspections, employee continual education training costs, union costs, contract costs, port or terminal costs and much more. We only see people buying tickets and going for a ride on a train, plane, boat or bus, what we don't see is how it all really works behind the scene. 

Most people think my job requires no training, no continuing educational training, and anyone doing my job is very stupid... they have no clue until they either ride along or decide to get this "easy" job just how hard it is, most never complete training and of those that do only a small % don't quit the first 2 months declaring they can't take the stress, the liability, it is too hard and so on.








 "Never fire a laser at a mirror."

rattraveller's picture
rattraveller
January 10, 2014 - 8:32am
Weird hybrid of airplanes and cruise ships? So you mean a zeppelin like the Hindenburg.
Sounds like a great job but where did you say we had to go?

Tchklinxa's picture
Tchklinxa
January 10, 2014 - 10:53am
No, but interesting, it was a sort of air cruise way of flying once, I might read up on that more. What I actually mean is there is more to passenger travel then we think about, and at times looking at sci-fi and SF it is hard to decide what vision of the future we are seeing... space flight like an airplane or space flight like a cruise ship/sea ship. So I always figure length of travel makes a differnece in the vision... short trips tend to be bus/cab/airplane like, while longer trips remind me of cruise ships or sleeper car/passanger trains more in the way travel is envisioned inside the craft. But the vision of passenger travel in space also affects space station design and life and planetary/lunar star ports as well. Think about everything that is at the airport, or a major port of call, this includes not just buisness but government all that will have a space version.

Also what is the feel of your SF seting: I want mine to be much more "Cowboy". Wagon Train, (1950-1970ish sci-fi), and explorer primative feel. So I am going with most passenger ships being sleeper ships, and only a few ships having extra class options, they exist but are rare or only a few cabins exist per ship. Now can people get a ride on a cargo ship, sure but it will not be a passenger grade trip. The crew is not there to hold your hand or serve you refreshments. 

:)
 "Never fire a laser at a mirror."

TerlObar's picture
TerlObar
January 13, 2014 - 12:23pm
I guess I've never really designed a starliner in the game but thinking about this, you would definitely need a larger crew to handle all the people.  Much like on a cruise ship as the trip takes over a week.  That's kind of how I envision the starliners working (especially now that I've actually been on a cruise).  There may not be all the on-board activities on a cruise ship but there would be more than just a room and a dinning area.  I think maybe looking at the model of the old ocean liners before air transportation is the way to go.  I think the First, Journey, and Storage class berths in the AD rules are modeled something on that.

I've always added a few passenger cabins to my freighters but in those cases, you're just along for the ride.  There's food provided and you have access to the entertainment in the ship's common area but nothing dedicated for the passengers.

The discussion here on the costs for tickets is all good. Yes, based on just resources, you'd expect that all tickets would be the same as it takes the same amount of time regardless.  There is more work for the astrogators to do the longer jump but that is just one person (or maybe a few) so there isn't much overhead there.  iggy's point about extra resources is a good one but isn't supported by the KH rules.  I agree it should be considered in a revision, however.

If anyone is interested in the general idea of how I'd do void jumping (and wants the short version over my novella) check out:  http://starfrontiers.info/docs/voidjump.html  This is the original write-up I did and includes a game mechanic that makes longer jumps take longer.

As for prices in Star Frontiers, I'd probably do the following (it's been so long since I had characters actaully pay for travel that I've never used this, I just used the old rate per ly rules).  I assign a base rate depending on the class of accomodation, basically taking the rates from the AD rules and multiply it by 8 days.  Then I'd add in a small variable bit based on the length of the jump.  Say 1/10th the AD rate times the number of light years.

That of course assumes that the astrogation work can be done ahead of time so that you don't need to be travelling while it is done.  In that is not the case you might consider a flat rate for anything under 9 ly and then adding half a day's rate for every ly above that to represent the extra time the trip will take while the astrogators work things out.  I'd use half a day's rate because your out bound leg will be longer than the standard 4.3 days but deceleration in the target system will still only take 4.3 days and I assume any decent starliner has at least 2 astrogators so the calculations can go around the clock.

Of course there is also the variable of not coming out in the same location each time and fact that the location of the desination planet is going to vary by hundreds of millions of miles depending on the time of travel.  This will all cause the deceleration time to arrive at the destination planet to vary by up to a couple of days.  However, this is inherent in any jump and is probably figured in in the base cost.  In fact, I always assume that any jump takes 10 days on average.  8.6 actually spend accelerating and declerating and the other 1.4 to accomodate the orbital and void exit location variations so I don't have to really think about it.  Alternately, you could say it takes 8.6 days for the jump plus 1d3-1 days for the variations if you want to actually show the variation.

Of course if I really wanted to do it right I'd design a few starliners of various sizes, compute their operating costs for various jump lengths, fold in the the "fill factor" from the KH rules on how many berths are typically fillled and look at the income necessary to cover the costs.  That might be a fun exercise to do at some point.
Ad Astra Per Ardua!
My blog - Expanding Frontier
Webmaster - The Star Frontiers Network & this site
Founding Editor - The Frontier Explorer Magazine
Managing Editor - The Star Frontiersman Magazine

Tchklinxa's picture
Tchklinxa
January 13, 2014 - 7:04pm
Good points.

I think modified cruise ship is probably a good star liner gloss. 

In RL it should be possible for me to get a direct flight from my international airport to another one in the USA... but it is usually not, usually I catch multiple flights. Ticket prices seem to be based on some weird logic that I am sure makes sense to the airlines but baffles me. For instance it might be cheaper for me to fly to Hawaii or Europe, then go from my city to another city in my home state.

So it would not surprise me that some places could be cheaper to get to, or at least easier to get to then others based on business and tourist travel versus mostly cargo/supply ships going there. A person trying to get to someplace in the Frontier might need to get to the right space station to catch the right ship to station B from which they will then need to catch a ride to their final destination... there might not be a direct or even semi-direct route as far as ships go. System travel might be very much like this. 

Now this is all complex, and slows travel down a bit, but if a ref wanted to really flesh out a System and run a System based storyline then all the bases, ports, and stations would be important because the PCs would probably be visiting these places more then once and would probably have adventures on various lunar bases, mining stations, various space stations and some NPC's would be reoccurring. 

Maybe the PC is the dreaded space safety inspector... thus they have to visit lots of places, go in dangerous areas and in the process of making sure say PGC's space facilities are up to spec stuff happens. 

Smile






 "Never fire a laser at a mirror."