Max ship speed?

[CosmicGamer]

Looking for some input from the math Whiz's

If it's a simple formula, I should probably document it somewhere and just do this myself.

1) With no fuel restrictions or gravitational issues and so on, how fast can a Traveller ship go? Close to the speed of light? How long would it take ships of different thrust to reach this speed?

2) Assuming a situation where a ship is not jumping so has plenty of fuel for, hmm, lets say for simplicity of calculation, about a month, 750 hours of nonstop thrust, how fast could ships of different thrust go in this time and how far?

3) Assuming a situation where a ship is jumping and has about 2 weeks of operational fuel, one week on arrival and half the time used to increase speed as the other half is needed to decelerate, so about 75 hours of nonstop acceleration, how fast could ships of different thrust go in this time and how far?

 

[Matt123]

In space "fast" is relative to your observation point, I'm not sure you want "fast" . Picture two ships ships travelling at 60% of the speed of light, passing in opposite directions. Are the crew of each ship, really seeing the other passing by at 120% of the speed of light? Or take an observer on Earth and and observer on Mars, do they both perceive a ship as having the same speed? They might do if they can agree on some mutually agreeable reference point, but those Martians are pretty argumentative...

If you are after acceleration, distance covered or time taken then Bk2, p10 has three formulas to use.

 

[Ifandbut]

I dont know what version of Traveller you are using, but in the Mongoose Errata there is the following formula:

Time (seconds) = 20 * sqrt(distance in km) / sqrt(thrust)

 

[CosmicGamer]

I dont know what version of Traveller you are using, but in the Mongoose Errata there is the following formula:

Time (seconds) = 20 * sqrt(distance in km) / sqrt(thrust)

So ((Time (seconds))*(sqrt(thrust))/20)squared = distance in km
Did I get that right?

75hr = 4500min = 270,000sec
With Thrust 1, sqrt(thrust) = 1

(270,000/20)squared = distance in km
Did I get that right?

Distance in km = 182,250,000 for ship traveling at constant thrust 1 for 75 hours
Did I get that right?

 

[The Oz]

In TRAVELLER ships are limited in speed by the ability of their hulls to withstand collisions with space dust.

I worked out the math one (slow) day, and unarmored ships can withstand impacts at up to 0.167% of lightspeed, or about 500,000 meters/second. A 1-G ship can reach that speed in 14 hours of acceleration.

A ship with factor-15 armor can reach nearly 60% of lightspeed

 

[GypsyComet]

I know there has been speculation that there are drive physics constraints as well, if only to keep near-C rocks from being a thing.

 

[whulorigan]

I dont know what version of Traveller you are using, but in the Mongoose Errata there is the following formula:

Time (seconds) = 20 * sqrt(distance in km) / sqrt(thrust)

That equation is based on Newtonian Physics, which is an approximation that is excellent for speeds that are not significant fractions of lightspeed. As you approach significant fractions of lightspeed, it is no longer accurate. The travel times involved will be progressively longer.

In space "fast" is relative to your observation point, I'm not sure you want "fast" . Picture two ships ships travelling at 60% of the speed of light, passing in opposite directions. Are the crew of each ship, really seeing the other passing by at 120% of the speed of light? Or take an observer on Earth and and observer on Mars, do they both perceive a ship as having the same speed? They might do if they can agree on some mutually agreeable reference point, but those Martians are pretty argumentative...

Two ships passing each other in opposite directions of travel whose speeds are measured relative to an outside reference frame at 0.6c will not perceive one another as moving at 1.2c relative to each other, as logical as that might seem. Distance and time distortion due to Special Realtivity will cause each ship to perceive the other as moving at 0.73c.

V^' = (v₁ - v₂) / (1 - {v₁v₂}/c²)

V^' = velocity perceived by one ship relative to the other.
v₁ = Ship #1 velocity = 0.6c
v₂ = Ship #2 velocity = -0.6c
​

To the independent observer in the outside reference frame, the passage of time experienced by each ship is slowing down. To an observer on either ship, time seems normal to them, respectively, but the distance between the ships is contracted as compared to the outside reference frame, so that it takes less time (and hence, less velocity) to cross the distance in the specified perceived time.

 

[aramis]

Realistically? About 0.1C relative to the local medium before the abrasion becomes lethal radiation instead.

 

[Timerover51]

So ((Time (seconds))*(sqrt(thrust))/20)squared = distance in km
Did I get that right?

75hr = 4500min = 270,000sec
With Thrust 1, sqrt(thrust) = 1

(270,000/20)squared = distance in km
Did I get that right?

Distance in km = 182,250,000 for ship traveling at constant thrust 1 for 75 hours
Did I get that right?

In the Real World, and also Starter Traveller and The Traveller Book, distance covered by acceleration is equal to 0.5 X Acceleration X (Time of Acceleration Squared). One G of acceleration is equal to 32.174 feet per second per second or 9.8066352 meters per second per second.

The distance covered during the time of 75 hours of constant 1G acceleration is about 222,110,284 miles or about 357,375,447 kilometers. Deceleration at the same 1G would require the same amount of distance. One Astronomical Unit is equal to 149.597,871 kilometers, so the distance covered is about 2.38 AU, on in Terra Solar System terms, from the Asteroid Belt to the Sun.

In the Real World, you also are limited by the deliverable energy contained in your fuel. That does not seem to be a constraint in Traveller.

 

[Ifandbut]

So ((Time (seconds))*(sqrt(thrust))/20)squared = distance in km
Did I get that right?

75hr = 4500min = 270,000sec
With Thrust 1, sqrt(thrust) = 1

(270,000/20)squared = distance in km
Did I get that right?

Distance in km = 182,250,000 for ship traveling at constant thrust 1 for 75 hours
Did I get that right?

Looks right

That equation is based on Newtonian Physics, which is an approximation that is excellent for speeds that are not significant fractions of lightspeed. As you approach significant fractions of lightspeed, it is no longer accurate. The travel times involved will be progressively longer.

Just going by what the book gave me. Thought that would be enough for the OP.

 

[whulorigan]

Looking for some input from the math Whiz's

If it's a simple formula, I should probably document it somewhere and just do this myself.

1) With no fuel restrictions or gravitational issues and so on, how fast can a Traveller ship go? Close to the speed of light? How long would it take ships of different thrust to reach this speed?

2) Assuming a situation where a ship is not jumping so has plenty of fuel for, hmm, lets say for simplicity of calculation, about a month, 750 hours of nonstop thrust, how fast could ships of different thrust go in this time and how far?

3) Assuming a situation where a ship is jumping and has about 2 weeks of operational fuel, one week on arrival and half the time used to increase speed as the other half is needed to decelerate, so about 75 hours of nonstop acceleration, how fast could ships of different thrust go in this time and how far?

For an object accelerating from rest:

t = [ (∆x/c)² + 2∆x/a₀ ]^1/2

∆x = [c²/a₀] _* { [ 1 + (a₀t/c)² ]^1/2 - 1 }

V_f = [a₀t] / [ 1 + (a₀t/c)² ]^1/2


where:

a₀ = rest acceleration of ship
V_f = Final velocity
t = time (as perceived from the external reference frame)
∆x = distance
c = speed of light

​

A interesting webpage dealing with the subject:
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

 

[kilemall]

Re: the upper speed limit, I'm working within CT and with the missile supplement in play.

The missile supplement is important as it gives you a hard number for what 1 hit is re: joules.

The rule states that you add a hit for every multiple of 300mm closing speed between a missile and it's target.

300mm is 3Gs or 30000 km per 1000 seconds, or expressed another way, 30km/s or approximately .0001 C.

Missile supplement missiles are 50 kg total, so I am assuming 10kg of fuel burned on average before impact, 40kg at 30 km/s.

That yields 18 gigajoules, on the boom table something like 9x the power of a TLAM-C Tomahawk warhead. So even our commercial grade starship hulls can shrug off a lot if that is the damage threshold.

http://www.projectrho.com/public_html/rocket/usefultables.php#id--The_Boom_Table

On the other hand it means that even very low pokey 1G accel to jump distance can be fraught with peril if there is debris out there.

In practice I am assuming a rock big enough to be 40kg would show up on radar and ships will simply maneuver to avoid (a primary reason why pilots are on duty). Or in an asteroid field/ring, there is a much greater change of impact and you just go slow, period.

Large rock groups like the ones that generate meteor showers would be the space-going equivalent of reefs, charted and to be avoided. Corollary is unexplored systems will be full of uncharted 'reefs' waiting to wreck fast moving ships that are not prepared.

Further assumption- the threat is likely smaller rocks or debris that is unmapped and unremarkable, coupled with the need to go faster then 3G/.0001 C.

Heh, or maybe Sand fields from ships' sandcasters.

So a more typical issue would be something 1kg or less, what's the speed limit in that scenario?

Assuming the 18GJ per hit limit, something short of that.

Playing around with the joule/impact calculator, I get 189 km/s, or .00063 C, or 18.9Gs or 1890 mm.

Never knew you were playing with death at slow Traveller speeds, did you?

Now for Big Drama and going say .1C, 30000 km/s. The 1kg impact becomes 450 TeraJoules. Divided against the 18GJ hit value, that's 25,000 hits.

Well. Go for it speedy.

The other factor is probability of impact, which should be VERY low but not impossible, rising to near probably in asteroid belts, rings, orbit, rock fields, etc.

I suppose for inner planet space I would roll something like 4D all 6s per week, 5D for outer planet space, 6D for deep space per month, and something like 3D per hour for asteroid belts or 2D for planets with rings or satellite/sentient space debris.

Implementing something like this even if you disagree with my numbers and assumptions can make for very interesting space terrain and a sense of 'no really you are in space and you can die' and drama if you exceed safety limits.

Haven't done it yet, but I expect the numbers are scarier for solar flares.

 

[Timerover51]

Re: the upper speed limit, I'm working within CT and with the missile supplement in play.

The missile supplement is important as it gives you a hard number for what 1 hit is re: joules.

The rule states that you add a hit for every multiple of 300mm closing speed between a missile and it's target.

300mm is 3Gs or 30000 km per 1000 seconds, or expressed another way, 30km/s or approximately .0001 C.

Missile supplement missiles are 50 kg total, so I am assuming 10kg of fuel burned on average before impact, 40kg at 30 km/s.

I am assuming that the Real World physics of the Rocket Equation apply to the missiles in Traveller for the following reply.

The standard Rocket Equation is: Delta(V) = Exhaust Velocity of propellant (or Specific Impulse X Gravity) X Natural log (Initial Mass of Rocket)/(Final Mass of Rocket).

Your initial missile mass is 50 Kilograms, with a final mass of 40 Kilograms, which means the fuel mass was 10 Kilograms. Your final velocity of the Rocket is given as 30 kilometers per second, equal to 30,000 meters per second or 98,425 feet per second. (I still think in terms of English Units). The natural logarithm of 50/40 or 1.25 is equal to 0.2231.

Therefore, 98,425 = Exhaust Velocity X 0.2231. Exhaust Velocity of the propellant is therefore equal to 98,425/ 0.2231, which is equal to 441,170 feet per second. That gives a specific impulse, dividing exhaust velocity by gravity of 32.174, of 13,712. The specific impulse of the Space Shuttle's main engines, running on hydrogen and oxygen, for comparison is 455 in vacuum, if I remember correctly. High energy solid propellents have a specific impulse of somewhere on the order of 300. Therefore, your fuel for the given missile has an energy content far higher than any combination of fuels that can be projected to exist.

Next, you are expending 10 kilograms or 10,000 grams of fuel over a period of 1000 seconds, for a fuel expenditure of 10 grams per second. I am not sure how you would manage that small a fuel expenditure of any form of solid fuel, so some form of either liquid-solid bi-fuel or liquid fuel combination is apparently used. However, the cost of the missile is stated in Starter Traveller as 5,000 Credits, which would be appropriate for a solid fuel missile, but not at all for the more complicated operation of a fully or partially liquid fueled rocket. Five thousand credits is about the same cost as the early version of the Sidewinder Air-to-Air missile, which also weighed about the same as the given missile.

Now, the total distance covered by the missile while powered is 0.5 X Acceleration X Time(squared), so 3G/2 X 1000(squared). Crunching the numbers gives a powered range of 9140 miles or 14,709 Kilometers. That is the distance covered over the distance covered in those 1000 seconds given by the initial launch velocity. If the target is not hit by the time of fuel burnout, then a radical course change by the target will leave the missile without maneuver power, and result in a miss. However, unless the missile has some form of self-destruct mechanism, it will continue to travel on the final velocity vector until it either hits something, exits the sun system that it is launched in, or falls into the sun of the system.

Basically, under Real World Physics, the missiles used in Traveller are not possible. That is why they do not exist in My Traveller Universe.

 

[kilemall]

I am assuming that the Real World physics of the Rocket Equation apply to the missiles in Traveller for the following reply.

The standard Rocket Equation is: Delta(V) = Exhaust Velocity of propellant (or Specific Impulse X Gravity) X Natural log (Initial Mass of Rocket)/(Final Mass of Rocket).

Your initial missile mass is 50 Kilograms, with a final mass of 40 Kilograms, which means the fuel mass was 10 Kilograms. Your final velocity of the Rocket is given as 30 kilometers per second, equal to 30,000 meters per second or 98,425 feet per second. (I still think in terms of English Units). The natural logarithm of 50/40 or 1.25 is equal to 0.2231.

Therefore, 98,425 = Exhaust Velocity X 0.2231. Exhaust Velocity of the propellant is therefore equal to 98,425/ 0.2231, which is equal to 441,170 feet per second. That gives a specific impulse, dividing exhaust velocity by gravity of 32.174, of 13,712. The specific impulse of the Space Shuttle's main engines, running on hydrogen and oxygen, for comparison is 455 in vacuum, if I remember correctly. High energy solid propellents have a specific impulse of somewhere on the order of 300. Therefore, your fuel for the given missile has an energy content far higher than any combination of fuels that can be projected to exist.

Next, you are expending 10 kilograms or 10,000 grams of fuel over a period of 1000 seconds, for a fuel expenditure of 10 grams per second. I am not sure how you would manage that small a fuel expenditure of any form of solid fuel, so some form of either liquid-solid bi-fuel or liquid fuel combination is apparently used. However, the cost of the missile is stated in Starter Traveller as 5,000 Credits, which would be appropriate for a solid fuel missile, but not at all for the more complicated operation of a fully or partially liquid fueled rocket. Five thousand credits is about the same cost as the early version of the Sidewinder Air-to-Air missile, which also weighed about the same as the given missile.

Now, the total distance covered by the missile while powered is 0.5 X Acceleration X Time(squared), so 3G/2 X 1000(squared). Crunching the numbers gives a powered range of 9140 miles or 14,709 Kilometers. That is the distance covered over the distance covered in those 1000 seconds given by the initial launch velocity. If the target is not hit by the time of fuel burnout, then a radical course change by the target will leave the missile without maneuver power, and result in a miss. However, unless the missile has some form of self-destruct mechanism, it will continue to travel on the final velocity vector until it either hits something, exits the sun system that it is launched in, or falls into the sun of the system.

Basically, under Real World Physics, the missiles used in Traveller are not possible. That is why they do not exist in My Traveller Universe.

Heh, best you not read up on the missile supplement then, the actual powered range is expressed by Gs followed by essentially fuel capacity. A 2G12 missile can burn at 2Gs for 6 turns or 1G for 12, and can switch with variable burn features. The CT errata makes it worse for your issue, changing 2G12 to mean 2Gs at 12 turns.

The classic Traveller missile is literally defined as a 5G6 continuous burn mass sensor proximity detonator HE warhead. That means for your purposes a missile that can go 5Gs for 6000 seconds, assuming you apply the errata.

If that missile impacts at the end of it's run, it's packing 30Gs of inertia, which by the impact rules means its going to do 10 hits of damage not counting the warhead.

Who needs nukes?

I had not done the actual energy exchange numbers, but knew it was silly.

My fuel consumption calc BTW assumed impact within the first 1/3 of the flight, the actual fuel package for the standard Traveller missile is 35kg. That would have lowered the joule level of what a 'hit' was, with all manner of ugly for the safe speed limit having to be lowered.

Didn't feel too badly about that, two turns and the missile has picked up 100,000 kms of velocity, in most cases you will either have mutual closing, or a stern chase with a faster ship running down a slower ship so the range will close up pretty quickly.

Then again.

Moving a 10,000 ton warship on paltry levels of fuel for weeks at a time is not exactly hard science either, by our tech standards, just on the reaction mass alone.

I actually went over going alt tech with the maneuver drive AND missiles operating with EmDrive type bubble fields, which would handily solve both the fuel issues AND the very very short detection ranges that are silly with very hot reactors, electrical emissions and reaction drives firing in very very cold space.

I decided it was just too much trouble for play value to figure out energy barrier issues on a bubble ship, I'm trying to give a unique feel without going overboard on redoing the game, and so went with mostly published systems and 'really really efficient ion/reaction mass driver engines' and an integral spoofing system that keeps detection range down.

Kind of the old Star Trek fan 'if its in the series its real' sort of ethos.

Mostly.

Messed with the jump system, hard, but that's another topic.

 

[Timerover51]

Didn't feel too badly about that, two turns and the missile has picked up 100,000 kms of velocity,

So, in two turns, the 50 kilogram missile is moving at 100,000 kilometers per second? That is 0.333 light-speed.

 

[kilemall]

So, in two turns, the 50 kilogram missile is moving at 100,000 kilometers per second? That is 0.333 light-speed.

I am being sloppy in my expression of scales, although the point was to highlight closing speeds in the typical 100,000-500,000 km ranges the game deals in.

That is a 100,000 km vector after two 1000 second turns of 5G acceleration, 50 meters per second times 2000 seconds would yield 100,000 meters per second, which would translate to 100 kps or 10Gs of speed over the initial launch speed imparted by the firing craft.

 

[kilemall]

Hmmm, imprecise expression on my part.

Two 1000 second turns of 5G, a missile or ship has a vector of + 100,000 kms per 1000 second turn after that, over and above initial launch speed.

From a km/s perspective, the vector would be 100,000 m/s, which of course translates to 100 km/s, definitively not a high fractional C speed.

The point is that with just a two turn burn, the average Traveller missile has the capacity to chew up a lot of closing space and still impact with 30kg.

If we want to get all serious about the Traveller missile's physics, the REAL troublesome system is the laser, with attenuation and damage success that doesn't even begin to degrade until 250,000 km.

Back to the OP's issue, I paint an ugly picture, but there are fixes for the frac-C small rock impact issue, notably lasers/energy guns/railguns in an anti-missile 'playing Asteroids' defense gun mode, sand itself (if you maintain speed and position behind the sand cloud, allowing the sand to impact objects just ahead of your craft), and repulsors.

If we look at the single unmapped surprise unavoidable rock or meteor swarm as a 'missile attack' under the HG system, we find that repulsors are your best bet.

At near C speeds, you won't GET that kind of warning for both repulsors and guns, so that leaves sand.

 

[Magnus von Thornwood]

Lasers!

/snip/

If we want to get all serious about the Traveller missile's physics, the REAL troublesome system is the laser, with attenuation and damage success that doesn't even begin to degrade until 250,000 km.

/more snipping/

Interesting how the coversation went from ships to missiles.

Now, as to lasers being too awesome, you are aware we shoot the Moon with lasers currently pretty much every night? Since that is about 300,000 Km, Traveller having long distance lasers never seemed that out of whack to me. Also, you might enjoy T5 since lasers got weak in that edition.

 

[flykiller]

Basically, under Real World Physics, the missiles used in Traveller are not possible.

I just say that missiles are motivated by micro m-drives. an m-drive must be a minimum of 1dton (remember that rule?) to be long-term viable, anything smaller essentially is single use only.

However, unless the missile has some form of self-destruct mechanism, it will continue to travel on the final velocity vector until it either hits something, exits the sun system that it is launched in, or falls into the sun of the system.

there are places in russia that still have the rusted hulls of wwii tanks littering the landscape. imtu there are debris fields from battles centuries past.

by the way, any "self-destruct" mechanism will have to be one that upon loss of target and reaching a certain time limit steers the missile into the local star.

 

[kilemall]

Interesting how the coversation went from ships to missiles.

Now, as to lasers being too awesome, you are aware we shoot the Moon with lasers currently pretty much every night? Since that is about 300,000 Km, Traveller having long distance lasers never seemed that out of whack to me. Also, you might enjoy T5 since lasers got weak in that edition.

I was fully aware that we do that, they did this from a NASA/university office complex that my mother worked at in the 1970s.

BIG difference between a little laser bouncing a ranging shot, and Traveller lasers delivering enough joules to punch through our ship hulls and damage/destroy systems with no effective attenuation across 250,000km.