CT Only: Talking M-Drive Acceleration

[Supplement Four]

Help me with this. I'm sorry with physics.

Using the M-Drive (and provided enough fuel and life support), a character in a Traveller ship with a 1G M-Drive could approach the speed of light while never reaching it.

As the ship accelerates, contact with bits of matter and radiation will be quite dramatic--this drag has an effect slowing the drive.

I'm wondering what the top speed is, measured in light years or light seconds, given standard Traveller craft.



We know that Power Plant fuel is a limiting factor, thus it can be assumed that most Traveller spacecraft/starcraft designed for long distances have power for four weeks. That's a maxium of two weeks of acceleration followed by two weeks of deceleration. Or, that's four weeks of acceleration then drifting at that constant speed from there on out (and no more fuel to decelerate).

Therefore, maximum range for a 1G vessel is (D=AT squared /4) 1,463,132,160,000 meters, or 1,463,132,160 km.

Is that correct? The table on page 54 of TTB says that a 1G vessel can travel 1,000,000,000 km in 7.3 days. It takes 100% more time to travel an additional 50% (less than 50%) distance? Is this the drag effect I cite above?



What I'm really interested in working out, in an easy way (if at all possible), is what it takes for a ship to intercept another ship in a star system. From what i see, that ain't easy.


First off...

The starport picks up detection of a ship entering Normal Space. Let's say that this is easy to detect due to the distortion a ship makes when making entry. Any ship in the system with a passive sensor turned "on" will detect the new vessel.

So, it's a Size 8, Earth type world. The entry point will be somewhere on the sphere 100 diameters out (provided the point isn't masked by a moon or the system's star). The ship will be 1,280,000 km out from the starport, and since detection happens at the speed of light, detection is a delay of just over 4 seconds--nothing to really worry about as far as the game goes. Communication and sensors operate at near real time (4.2 second delay).

The new ship has a 1G M-Drive, so it will take 348 minutes to get to the starport. That's 174 minutes of acceleration and 174 minutes of deceleration (provided the ship jumped in at a relative zero acceleration).

HERE'S A QUESTION: How would you figure travel time had the ship jump into the system at a 1G acceleration after it has built up some velocity? Is there an easy way to do this.

Would this work? The ship builds up 100 min. of acceleration, then jumps, entering this new system with that velocity. I supposed the ship would travel for another 74 minutes before flipping and decelerating?

That's probably not quite right, since the distance to the starport is longer. But, is it close enough for game purposes?




And, back to the other question. What does a ship have to do to intercept the new vessel?

I suppose, after detection is made, that a ship in orbit of the main world (let's say this is a 2G vessel) need only plot the point at which interception is made.

But, what about matching vectors?

So, if the new vessel is taking 174 min. to reach its journey mid-point, and the mid-point is half the distance: 640,000 km, then the 2G vessel can zip on out there in less than 74 min, giving the interceptor an extra 100 min to match vectors with the incoming ship.



Oh (and I've asked this before but didn't the answer didn't stick with me), if fuel is no option, what is the maximum velocity for a ship moving at a 1G acceleration? Near light speed, right? Or, about 300,000 km per second?



Just thinking about this stuff.

What are your comments?

 

[Supplement Four]

A follow up question:

We seem to overlook this in Classic Traveller. Or, rather, we handwave the effect to the inertial compensator.

The question is: How long can a human being endure 2Gs? 3Gs? 6Gs?

An interesting "hit" to add to the starship damage tables is to take out the compensator. This will reduce a vessel's M-Drive effectively to 1G, or to another G rating for a certain period of time.

It would be a neat thing to add to the game.

 

[atpollard]

I don't think there is an official top speed in the CLASSIC Traveller rules, you could go ahead and accelerate and decelerate past the speed of light to travel between stars (in rules as written). If you want to get into real world physics, there is a relativity thing with time and mass that may or may not affect a MD (since we have no idea how it actually works). There are lots of house rule ideas based on armor and impacts.

There may or may not be a top speed in other versions.

***

The math for a 3D intercept will quickly get too ugly for words with variable accelerations and attempting to match velocity. I once used a spreadsheet to calculate accelerations and tweak them based on 15 second time increments and I couldn't get it to work out exactly even at that resolution. I am sure there are equations, I doubt they are user friendly.

 

[Spinward Scout]

The question is: How long can a human being endure 2Gs? 3Gs? 6Gs?

Here's How US Fighter Pilots Learn To Survive Under Inhuman Levels Of G-Force

High-G training

Hope that helps.

 

[Enoki]

While I've never seen an official maximum speed, two things limit it realistically:

1. How far are you going? Interplanetary travel within a system is going to be limited to acceleration for one half the distance at most, with the other half of the trip being slowing down. I doubt you'd ever get to relativistic speeds going from one planet in a system to another, while going to another system without jump capacity means years, if not decades or centuries, in space.

2. Of course, the increasing mass of the ship as you approach C. For this part I'd limit movement to about 100 million kph or .1C. You might allow up to about .25C, but I really doubt that you could go much more than that before mass problems start to appear.

Anyway, that's how I see it.

 

[whulorigan]

. . . or .1C. You might allow up to about .25C, but I really doubt that you could go much more than that before mass problems start to appear.

As as general rule of thumb, relativistic effects start becoming noticeable above about 0.1c, and become significant at about 0.9c or above.

Mass Increase:
M_tot = m₀ / sqrt [1-R²], where R = v/c.

(In other words, a constant force produces a constantly decreasing acceleration with increasing velocity).
​

Time Dilation:
t = t₀ / sqrt [1-R²], where R = v/c.

Distance Contraction:
D = D₀ * sqrt [1-R²], where R = v/c.

 

[Spartan159]

IMTU I have a colony ship that left Earth in 2058 AD using an NAFAL drive from T5 capable of 0.35 m/sec acceleration, taking 51 weeks to reach 0.355 Lightspeed. The target of the colony was Neumann in the Trojan Reach. If my count was right it was a 169-parsec trip that took 1,601 years (1,508 perceived) and another 51 weeks decelerating. Does that look realistic or are my calculations way off?

 

[whulorigan]

IMTU I have a colony ship that left Earth in 2058 AD using an NAFAL drive from T5 capable of 0.35 m/sec acceleration, taking 51 weeks to reach 0.355 Lightspeed. The target of the colony was Neumann in the Trojan Reach. If my count was right it was a 169-parsec trip that took 1,601 years (1,508 perceived) and another 51 weeks decelerating. Does that look realistic or are my calculations way off?

I am about to head off to bed, so I don't want to do any detailed calculations right now. But a quick look at the numbers says that you are in the ballpark.

 

[Carlobrand]

Checking the math:

2 weeks at 1g accelerating:

t=14*24*60*60 = 1,209,600 seconds
t² = 1,463,132,160,000
We'll say a = 10 m/s²
1/2at² = 7,315,660,800,000 m = 7,315,660,800 km

v at turnaround = at = 10*1,209,600 = 12,096,000 m/s = 12,096 k/s
We'll say c=300,000 kps, 'cause I'm lazy
v at turnaround is 0.04032c. Relativistic effects that would be noticed by experimental equipment but trivial on the crew's scale.

Then 2 weeks deceleration, so another 7,315,660,800 km for a total 14,631,321,600 km traveled - 14.6 billionish

It takes almost 81 years to travel a parsec at that speed. Best use radioisotope thermal generators to power your low berths and to keep the computer going during the coast phase.

K.E. = 1/2 mv²; a little 1-gram bit of matter packs 73,156,608,000 joules. At 4.184×10⁹ joules per ton TNT, that's about 17 tons of TNT, which is very roughly equal to a single nuclear missile. (Note also that impact is more a kind of drilling in - and maybe all the way through - than a "boom".) Fortunately, something that big is rather rare in interstellar space - most of what I'm finding is considering "average" to be something around a tenth of a micrometer in diameter, which is to say a few picograms mass, so impact energies in the tenths of a joule range. You'd have to get someone smarter than me to tell you how likely you were to run into something bigger at some point during a trip of time T. I'm not the sharpest cutter in the drawer here by a long shot.

Accelerating for 1 month:

t = 28*24*60*60 = 2,419,200 seconds
t² = 5,852,528,640,000
v(t) = 24,192,000 m/s or 24,192 k/s, twice as fast 'cause you've been accelerating twice as long. So 0.08064c, 8% of light speed.
s(t) = at = 5,852,528,640,000 m or 5,852,528,640 km before you hit the 4-week mark and your power plant dies.

Of course, you can use the jump fuel to extend flight time if you're not jumping, and you can pack the hold with collapsible fuel bladders, so if you're really interested in getting close to C, it's doable, but it's a bit late and my insomnia-fatigued mind is not up to playing with relativistic equations at the moment.

 

[Enoki]

As as general rule of thumb, relativistic effects start becoming noticeable above about 0.1c, and become significant at about 0.9c or above.

Mass Increase:
M_tot = m₀ / sqrt [1-R²], where R = v/c.

(In other words, a constant force produces a constantly decreasing acceleration with increasing velocity).
​

Time Dilation:
t = t₀ / sqrt [1-R²], where R = v/c.

Distance Contraction:
D = D₀ * sqrt [1-R²], where R = v/c.

I figure that in the Traveller universe since they have the ability to control gravity they can mitigate those effects somewhat.

 

[atpollard]

Except MASS (with or without an increase due to relativistic velocity) has no effect on the acceleration of a Maneuver Drive ... does the ship increase in volume as velocity approaches c?

If not, then the formula is T = 2 X Sqrt (D/A) per the rules.

1,000,000,000 km @ 6G = 2xSqrt(1E12m/60 mps) = 258,199 sec = 2.988 days

6 parsecs @ 6G = 2xSqrt(6 X 3.086E16m/60 mps) = 111,103,555 sec = 1286 days = 3.5 years

So interstellar travel via MD requires a fuel scoop to collect Hydrogen, but is possible.

 

[Supplement Four]

So interstellar travel via MD requires a fuel scoop to collect Hydrogen, but is possible.

1. Why isn't top speed the speed of light, or close to it?

2. Could a fuel scoop conceivably collect enough Hydrogen to run the power plant? Could it collect that much?

 

[McPerth]

So interstellar travel via MD requires a fuel scoop to collect Hydrogen, but is possible.

In the game Imperium, Monitors (jumpless ships) can travel sublight at the rate of 1 hex (0.5 Pc) per turn (2 standard Terran years).

2. Could a fuel scoop conceivably collect enough Hydrogen to run the power plant? Could it collect that much?

At MT rates sure not (sorry, I know this is a CT only thread, but I could not resist).

Now more seriously, IIRC it's assumed there's one proton (so 1 hydrogen atom) per m³ on average in vacuum. To collect 1 g of hydrogen, you need 6.023 E23 such atoms (so to collect a ton of it, you'd need 6.023 E32)...

Now calculate the suface collecting it, multiplied by the meters it travel on a week, and see if it compensates for the PP needs...

In any case, again IIRC, in TCS description of the Islands sectors the ships carrying the colonist there worked this way, so hinting that it is possible in CT...

 

[Carlobrand]

Except MASS (with or without an increase due to relativistic velocity) has no effect on the acceleration of a Maneuver Drive ...

If I recall my relativity, mass change due to relativity technically has no effect on the acceleration of any drive, at least not with respect to someone in the same frame as the ship. The drive is affected by relativity as well, and since it's in the same frame as the ship it's on, it behaves as if the ship's mass has not changed. An observer in the frame with the ship will see the drive as performing as well as it ever has. However, with respect to an outside observer, the drive's performance is falling - time dilation means the drive output is decreasing.

 

[aramis]

1. Why isn't top speed the speed of light, or close to it?

2. Could a fuel scoop conceivably collect enough Hydrogen to run the power plant? Could it collect that much?

1: Physical drag force from collecting the hydrogen will exceed thrust generatable at some point below C. Given the mass energy of resting hydrogen (E=MC², and C≅3e8m/s, thus 1kg ≅9e18 J) and the energy cost to accelerate it to current speed (0.5MV²), moving at C, acceleration energy ≅ 4.5e18J per kg. And you have to do this twice for use as reaction mass...

Given that you need to retain it as reaction mass, as well, and fusion efficiency is under 1% in Traveller... E_fusion is under 9e14 J/kg, which means your ramjet cannot get you above 9e7 m/s velocity, as that is the energy cost of accelerating the fuel alone. Above that, the cost of the fuel is more than it provides in Traveller fusion tech.

2: Absolutely!
Avogadro's constant is 6.02e23 atoms per mol, 1 mol masses (1 g * atomic mass)...
Average rate of interstellar hydrogen is 1 atom per cc, or 1e6 atoms per kL
we need 6.02e17 kL per g. If we burn 1000 kg per 28 days (2419200 Sec, or 2.4192e6 s), we need 6.02e20 kl per month. Given a speed of 0.1C, we can obtain 3e7 kL per m² of frontal area per second. times 3.6e3 seconds per hour, 4.08e11 kl per hour, or 9.792e13 kL per day, 2.74176e15 kl per month.
to get the needed 6.02e20, we need a frontal area of (6.02/2.74176)e(20-15)=2.19567e5 m². Roughly a 469m square per Ton of fuel per month at 0.1 C. But note also, that fuel produces a drag due to its lack of relative velocity...

Using tractor technology at TL12+, it's possible that it might be acheived by that means.

 

[atpollard]

1. Why isn't top speed the speed of light, or close to it?

The nut and bolt details of relativity is way outside of my area of competence (Civil Engineers like Newton), but as near as I can follow it, it has something to do with MASS increasing with velocity until one approaches the speed of light where it requires infinite energy to accelerate infinite mass.

We know almost NOTHING about a Maneuver Drive except that in Classic Traveller performance is based on the VOLUME of the ship and not its MASS. A 400 dTon Freighter hauling 200 dTons of Lead Ingots, a 400 dTon Freighter hauling 200 dTons of Farm Tractors, and a 400 dTon Freighter with an empty hold all accelerate with their Maneuver Drive at the same rate in spite of having staggering different masses. The only thing we know for sure about a Classic Traveller Maneuver Drive is that MASS does not matter.

So I don't see any reason to assume that the speed of light is a top speed ... it is a reasonable assumption, but so is the assumption that the the speed of light does not effect the Maneuver Drive. The rules are silent, so both options are equally viable.

Perhaps someone with better math and physics skills can explain some other reason why it is impossible, but it must have NOTHING to do with MASS.

2. Could a fuel scoop conceivably collect enough Hydrogen to run the power plant? Could it collect that much?

Bussard thought so.
Seriously, I have no idea. One thing that will help is that as velocity increases, you will be scooping a HUGE volume of space.

Another option is that a MD just needs power, not Power AND Jump Hydrogen ... so Fission is an option (but not in the CT Core Rules). Is there a JTAS article on Fission Power Plants?

 

[atpollard]

1: Physical drag force from collecting the hydrogen will exceed thrust generatable at some point below C. Given the mass energy of resting hydrogen (E=MC², and C≅3e8m/s, thus 1kg ≅9e18 J) and the energy cost to accelerate it to current speed (0.5MV²), moving at C, acceleration energy ≅ 4.5e18J per kg. And you have to do this twice for use as reaction mass...

Given that you need to retain it as reaction mass, as well, and fusion efficiency is under 1% in Traveller... E_fusion is under 9e14 J/kg, which means your ramjet cannot get you above 9e7 m/s velocity, as that is the energy cost of accelerating the fuel alone. Above that, the cost of the fuel is more than it provides in Traveller fusion tech.

1977 Traveller (Reaction) MD ... Maybe (I am less familiar with these rules).
1980 Traveller (Reactionless) MD ... No.

There is no "thrust" or an empty freighter would have a greater acceleration than a freighter with a hold full of ore. They have EXACTLY the same acceleration, so the mechanics must not be based on any actual 'thrust' and 'drag' may or may not play any part. The rules are silent but clearly a TL 8 trip to the Oort Cloud is possible using the CT RAW. What would the Top Speed be at turnover? What about a trip between distant binaries? Is that further than the Oort Cloud?

 

[whulorigan]

We know almost NOTHING about a Maneuver Drive except that in Classic Traveller performance is based on the VOLUME of the ship and not its MASS. A 400 dTon Freighter hauling 200 dTons of Lead Ingots, a 400 dTon Freighter hauling 200 dTons of Farm Tractors, and a 400 dTon Freighter with an empty hold all accelerate with their Maneuver Drive at the same rate in spite of having staggering different weights. The only thing we know for sure about a Classic Traveller Maneuver Drive is that MASS does not matter.

So I don't see any reason to assume that the speed of light is a top speed ... it is a reasonable assumption, but so is the assumption that the the speed of light does not effect the Maneuver Drive. The rules are silent, so both options are equally viable.

Perhaps someone with better math and physics skills can explain some other reason why it is impossible, but it must have NOTHING to do with MASS.

Even a massless object has lightspeed as its top speed (in fact, it is its unique and only speed - the photon and all other particles with zero rest mass are examples).

A moving object has an intrinsic kinetic energy based on its mass and velocity. Under Relativity, an object's total energy is given by:

E_tot = m₀c² / sqrt[1 - R²], where R = v/c, and m₀ = rest mass.
​

Its rest energy (related to its rest mass) is:

E₀ = m₀c²
​

Since there is a mass-energy equivalency under relativity, an increase in kinetic energy necessarily implies an equivalent increase in mass. The result of this is that as an object accelerates under a constant force, the increasing mass produces a constantly decreasing acceleration, causing the increasing velocity to asymptotically approach a maximum limiting speed (which happens to be the speed of light). *

* Though this is common in physics textbooks on the subject, note that many physicists prefer the interpretation that the mass remains constant and equal to the rest mass, but the apparent change in mass is due to the changing space-time curvature through which the object is moving as a result of increasing velocity.
​

It is not just an issue of increasing mass, however. Since it is an observed property of light that it is always measured at the same velocity regardless of the state of motion of the observer, the necessary consequence for this to be true is that as one moves relative to another object, the spatial distances measured between moving objects change in proportion to the velocity. At lightspeed, distance in the direction of motion for an object has shrunk to zero (or alternatively, to an outside observer time would have stopped aboard the moving ship/object).

Note that I did a brief discussion of this topic (on request) over on the Lightspeed page on the TravellerWiki.

Actual travel FTL through normal-space will necessarily create causality problems, as FTL travel in normal space is the equivalent of moving backward in time.

If one wishes to interpret the M-Drive as a type of "warped-space drive" (similar to an Alcubierre Drive), then FTL travel will still require a source of negative energy in order to achieve FTL pseudo-speed.

 

[whulorigan]

There is no "thrust" or an empty freighter would have a greater acceleration than a freighter with a hold full of ore. They have EXACTLY the same acceleration, so the mechanics must not be based on any actual 'thrust' and 'drag' may or may not play any part.

According to the CT RAW, you are absolutely correct. But I always considered the acceleration-based-on-volume rather than mass as a rule-artifact to simplify both ship-design and actual use during play.

 

[atpollard]

According to the CT RAW, you are absolutely correct. But I always considered the acceleration-based-on-volume rather than mass as a rule-artifact to simplify both ship-design and actual use during play.

For ANY later version I would completely agree, and I would not have brought it up at all excpt the topic is designated (CT Only).

Personally, I also IMTU view the MD as a magic box that produces an actual force and the details of the rules as simplifications. However, that is not the only valid interpretation of the rules. Particularly since how REAL gravity functions is a bit of a debated topic, never mind how imaginary super-tech functions. Perhaps the MD generates slightly imbalanced positive and negative energy/mass/gravity like the Alcubierre Drive requires, but Jump drive is more efficient for interstellar distances. I just do not know.

[Your comments on OTHER massless particles is interesting. It lends credibility to the Speed of light speed limit. It is just not an irrefutable fact of the Rules, and goodness knows that Sci-Fi is all about FTL travel and handwaves.]