Interplanetary Transit Times Table

[Tigleth Pilisar]

I can't replicate the chart for Interplanetary Transit Times

The formula should be:

t = 2 * sqrt ((D / 2) / g)

What formula is being used?

t = time in seconds
D = Total Distance
g = acceleration, or in this case "g"forces, which I think you used the rate of gravity for earth which is 9.81 m per second per second. In traveller, this is called thrust

It is 2 * because a ship accelerates to halfway and then flips and decelerates the second half.

It is D /2 because the ship is in acceleration only for half the distance.

I get within 1% of your answers if I use:

t = 2 * sqrt (D / g)

Plug in 10,000 distance of km which is 10,000,000 meters, divide by thrust of 1 which is 9.81 m per second per second.

Equals 1,019,367.9, the square root of which is 1,009.

2 * 1,009 is 2,018, which is close to your chart which says 2,000 seconds.

The flaw with this is that the ship has travelled double the distance! The 2 * at the beginning is right, but the distance to go half way should be D/2!

And the calculations should be exact. But maybe you rounded the constant for gravity (thrust differently).

Ive heard there is a new chart, but on your Player Aid section on your website it has a reprint of the exact same thing.

 

[Fovean]

The old CT formula was

T = 2*sqrt(D/A)

where T = Time in seconds, D = Distance in meters, A = Acceleration in G's (1G=10 meters per second, 4G=40 meters per second, etc) and assumes deceleration from the midpoint.

For MGT Thrust 1 = 1G, Thrust 4 = 4G, etc

So 10,000km at Thrust 1 =

2 * sqrt (10,000,000/10) = 2 * sqrt(1,000,000) = 2 * 1000 =
2,000 seconds

or for Thrust 4 =

2 * sqrt (10,000,000/40) = 2 * sqrt(250,000) = 2 * 500 =
1,000 seconds

or 400,000km at Thrust 2 =
2 * sqrt(400,000,000/20) = 2 * sqrt(20,000,000) = 2 * 4,472.14 =
8,944.28 seconds = 149.1 minutes

Which seems to match MGT Core.

 

[Chernobyl]

There are errors in the core rulebook chart (see my thread below) for thrust 3 and 4 for the last 3 entries.

I graphed the entries and did a regression to find the formulas, and got
Transit time (seconds) = 20 * sqrt (Distance in km) / sqrt (Thrust)
sqrt = square root.
very simple to do a calculation cell in Excell on a laptop during games.

I've also found some information regarding Jump Masking in a SJgames book, think it was "far trader", essentially, the 100D limit of the star means that the path to your destination may pass through it on the way there, so you have to get outside the 100D masked area of your current Star to make a jump to the next one.

 

[Rikki Tikki Traveller]

Tigleth, your formula should NOT have the D/2, it should be D since the ship DOES accelerate for the entire trip, 1/2 of the trip it is positive acceleration and then the ship flips and you get negative acceleration for the second half of the trip.

 

[hdan]

Tigleth, your formula should NOT have the D/2, it should be D since the ship DOES accelerate for the entire trip, 1/2 of the trip it is positive acceleration and then the ship flips and you get negative acceleration for the second half of the trip.

Right you are RTT. Just to spell it out for posterity, or until the thread gets deleted:

The basic constant acceleration equation is:

D = 1/2*A*T^2 + V0*T + D0
where:
D = position after T seconds of A acceleration
A = acceleration
T = time spent under acceleration
V0 = initial velocity
D0 = initial position

Since V0 and D0 are assumed to be zero in Traveller, we get:

D = 1/2 * A * T^2

Which refactors to:

T = sqrt(2 * D / A)

But since you are effectively making two trips at full acceleration so that you end up at zero velocity (again, a simplification), you are going half the distance each trip, so substituting D/2 for D and canceling out the constants we get:

T = sqrt(D / A)

So for the whole trip we have:

T = 2 * sqrt(D / A)

 

[Rikki Tikki Traveller]

Interestingly, if you go through those formulas and do the unit conversion from Meters and Seconds to Astronomical Units (AU) and Gravities (Gs) and Days of time you get:

T = 2 * sqrt (D/A)

Where:
T is the time in DAYS
D is the distance in AU
A is the acceleration in Gravities

It isn't exact, but it is within about 5% of the correct equation, which since we are ignoring a lot of things within the orbital mechanics, is more than good enough. So, if you need to calculate interplanetary travel times, this formula works as well.

 

[DFW]

Interestingly, if you go through those formulas and do the unit conversion from Meters and Seconds to Astronomical Units (AU) and Gravities (Gs) and Days of time you get:

T = 2 * sqrt (D/A)

Where:
T is the time in DAYS
D is the distance in AU
A is the acceleration in Gravities

It isn't exact, but it is within about 5% of the correct equation, which since we are ignoring a lot of things within the orbital mechanics, is more than good enough. So, if you need to calculate interplanetary travel times, this formula works as well.

Good idea.

 

[DFW]

Here's a good page for your games

http://www.transhuman.talktalk.net/iw/TravTime.htm

 

[captainjack23]

Interestingly, if you go through those formulas and do the unit conversion from Meters and Seconds to Astronomical Units (AU) and Gravities (Gs) and Days of time you get:

T = 2 * sqrt (D/A)

Where:
T is the time in DAYS
D is the distance in AU
A is the acceleration in Gravities

It isn't exact, but it is within about 5% of the correct equation, which since we are ignoring a lot of things within the orbital mechanics, is more than good enough. So, if you need to calculate interplanetary travel times, this formula works as well.

Nice ! And I can run it (mainly) in my head

I generally use a rough approximation of Bodes law* about planetary orbits when it matters.
"we have to go to the gas giant ? How long ?"

"Well, assume its about as far as Jupiter from earth...ummm mars, asteroids and then Jupiter, about 3-4 AU, I guess" so T=2* SQRT(4/2).....3 days at 2G ?"

table lookups are a pain when running games and answering questions about routine stuff...


*Yes, I know it's rubbish...it works well enough for an RPG..http://en.wikipedia.org/wiki/Titius–Bode_law

 

[Tigleth Pilisar]

Thanks guys.

DFW - great site! Right in line with my on calcs, but of course it uses accurate "g" numbers, not the rounded 10 number in the game.

The simplest way to express stop motion/acceleration/deceleration/stop for Traveller is:

Time(seconds) = 2 * SQRT(Distance(km) * 100 / Thrust)

The simplest way to express the time it takes to get somewhere, with constant acceleration and no deceleration is:

Time(seconds) = SQRT(Distance(km) * 200 / Thrust)

In the latter case the speed the ship will be at during the travel is:

Speed(km/s) = Time(seconds) * Thrust /100

A Space Combat turn in Traveller is 6 minutes. The distance covered by a ship in a space turn is the speed at the start of the turn for 360 seconds plus the change in speed from the Thrust in whatever vector the thrust is made:

Distance(km) = Speed(km/s) * 60 min/sec * 6 min
plus/minus
Distance(km) = 60 min/sec * 6 min * Thrust/100
(or the acceleration vector simplified to: Distance(km) = 3.6 * Thrust)

For added simplicity, I like the High Guard vector model, but it hurts the brain a bit sometimes to see how a battle might take place sometimes. For example, consider a thrust 3 ship that has accelerated for an hour has added 3 thrust (30 m/s) to its speed 3,600 times. Its moving at 10,800 thrust points in one vector or 108 km/s (38,800 kms in one 6 minute game round). At this point if another ship isn't going a similar speed on the same vector, not much fighting could happen. For a stationary object, the ship would go from a very long distance to adjacent in 1 round to a very long distance in round 2 and then they would be 70,000km or more apart (distant)! Or if this hour was spent thrusting to get to the safe jump distance away from a planet (which takes about 2.26 hours at thrust 3 from a 10,000 km planet) and another ship was thrusting in towards the planet after jumping to the sector, they would be going at similar speeds but in opposite directions - maybe just one round of combat with no chance of turning the ship around (it would take an hour just to stop going the opposite direction).

Anyway, these formulas get convaluted when people bring in AUs or use days instead of seconds, or don't convert m to kms or use the correct gravity of earth as a g, being 9.8065 meters per second per second instead of the rounded off 10 m/s^2 that the game uses. I like the formula stated in seconds for time - I can convert from there - and distance being in kms.

 

[DFW]

At this point if another ship isn't going a similar speed on the same vector, not much fighting could happen. For a stationary object, the ship would go from a very long distance to adjacent in 1 round to a very long distance in round 2 and then they would be 70,000km or more apart (distant)!

This is probably how many battles would be fought depending on the squadron/ship types.

There is probably something similar to this theory for spaceship combt in the TU.

http://en.wikipedia.org/wiki/Energy-Maneuverability_theory

 

[Fovean]

Its moving at 10,800 thrust points in one vector or 108 km/s (38,800 kms in one 6 minute game round). At this point if another ship isn't going a similar speed on the same vector, not much fighting could happen.

Jack Campbell's The Lost Fleet: Valiant describes several fleet battles where the combatants basically zip past each other at crazy velocities and computers fire at each other because the time the targets are in range is so short that people can't do it. Then they make big lazy arcs in space and zip past each other again... pretty cool book, and one of a series of four I think.

Also, GURPS:Spaceships has variable-length space combat rounds, from 20-second turns up to 10-minute turns, based on acceleration and range to target. I'm playing around with this idea IMTU and I'm liking it a lot - the tension can really ratchet up as those turn lengths get shorter and shorter...

 

[Tigleth Pilisar]

Jack Campbell's The Lost Fleet: Valiant describes several fleet battles where the combatants basically zip past each other at crazy velocities and computers fire at each other because the time the targets are in range is so short that people can't do it. Then they make big lazy arcs in space and zip past each other again... pretty cool book, and one of a series of four I think.

Fovean, Jack Cambell's books are a MUST READ. The series is six books:

DAUNTLESS
FEARLESS
COURAGEOUS
VALIANT (the fourth book)
RELENTLESS
VICTORIUS

About 1800 pages in all. I couldn't put it down! I'd start at the beginning though although he makes it so you could start at any book. I also liked the idea of how light time was taken into account to recognize that positions only reflected where things were when the light from their position was sent. For far distances, this leads to tactical display lags the farther ships are away from each other.