question(s) for those with better maths skills than myself

[Elysianknight]

I've been toying with the idea of adapting Alastair Reynolds 'Revelation Space' setting into a Traveller campaign setting, as its my favourite vision of a dark human future. Given the time frames for travelling between star systems (non-FTL), i felt it would best work based in the Yellowstone system, with limited extra-system travel. For those unfamiliar with the the setting, travel between star systems is by Lighthuggers, which accelerate up to near C velocities, then halfway, turn around and decelerate to arrive in the new system.

My questions are:

1) Whats considered the maximum sustained acceleration a human body could tolerate(assuming no future tech adaptations)
2) How long would it take to reach near C speeds (>0.95C) at this rate of acceleration (assume fuel isn't a problem, Reynolds has anti-matter drives on huge ships).

More questions may follow, prompted by the answers.

Thanks in advance

 

[rust]

Whats considered the maximum sustained acceleration a human body could tolerate(assuming no future tech adaptations)

When I served as an airforce medic, 6 G was considered the upper limit
for peacetime maneuvers, and it already included a risk that pilots would
become unconscious. I think that therefore the limit for sustained accele-
ration would probably be rather low, perhaps only 2 G or 3 G.

 

[Vargr]

Even at just 1G acceleration you could reach near-C speed in about a year.

The max sustained acceleration would be the gravity you would be willing to live under during the trip. 2G and above are right out, I don't see anyone wanting to have to support twice their body weight in the same set of muscles and bone structure.

1.2G or 1.3G? Maybe... it would be the same as putting on quite a few pounds but it wouldn't kill you. But IMHO it doesn't cut enough time off the journey to be worth it.

Does "Revelation Space" lack both gravitics and low-berths?

 

[Elysianknight]

Does "Revelation Space" lack both gravitics and low-berths?

No gravitics, but does have low berths, so crews sleep for the decades of travel.

 

[rust]

No gravitics, but does have low berths, so crews sleep for the decades of travel.

Hmm ... if the bodies are in suspended animation and rest in a fluid that
distributes the acceleration pressure equally over the entire body, even
a higher acceleration than 3 G could be possible - but I do not have the
slightest idea how much higher it could be. :?

Edit.:
This article could be interesting for you. I did not read all of it (English
at 3 am is not my specialty ...), but it seems to cover the subject:
http://www.wired.com/wired/archive/11.03/7g.html?pg=1&topic=&topic_set=

 

[iainjcoleman]

The question "how long does it take" is slightly complicated. You can work out two different times: the time measured by the person on the accelerating ship (proper time) and the time as measured by the people back at the starting point (coordinate time). As the ship approaches the speed of light, these two measurements diverge more and more as the time dilation effect means time passes more slowly on board the ship than it does back home.

The general formulae are as follows (assuming the ship experiences constant acceleration):

T = (c/a)arctanh(v/c)

t = (c/a)sinh(arctanh(v/c))

where:

T = proper time (i.e. time measured on the ship)

t = coordinate time (i.e. time measured back home)

a = acceleration

c = speed of light

v= final velocity

sinh = hyperbolic sine function

arctanh = inverse hyperbolic tangent function

I've worked out the numbers for accelerations between 1g and 6g, and for final velocities of 0.95c and 0.99c

a      v              T                 t       

1g	0.95c		1.77 years	      2.95 years
2g	0.95c		0.89 years	      1.47 years
3g	0.95c		0.59 years	      0.98 years
4g	0.95c		0.44 years	      0.74 years
5g	0.95c		0.35 years	      0.59 years
6g	0.95c		0.30 years	      0.49 years

1g	0.99c		2.56 years	      6.8 years
2g	0.99c		1.28 years	      3.4 years
3g	0.99c		0.85 years	      2.27 years
4g	0.99c		0.64 years	      1.7 years
5g	0.99c		0.51 years	      1.36 years
6g	0.99c		0.43 years	      1.13 years

I hope this helps.

 

[Elysianknight]

No gravitics, but does have low berths, so crews sleep for the decades of travel.

Hmm ... if the bodies are in suspended animation and rest in a fluid that
distributes the acceleration pressure equally over the entire body, even
a higher acceleration than 3 G could be possible - but I do not have the
slightest idea how much higher it could be. :?

Edit.:
This article could be interesting for you. I did not read all of it (English
at 3 am is not my specialty ...), but it seems to cover the subject:
http://www.wired.com/wired/archive/11.03/7g.html?pg=1&topic=&topic_set=

Thanks Rust. As i replied to you i was wondered whether this was the handwavium solution to allow relatively quick accelerations up to near C speeds.

The question "how long does it take" is slightly complicated. You can work out two different times: the time measured by the person on the accelerating ship (proper time) and the time as measured by the people back at the starting point (coordinate time). As the ship approaches the speed of light, these two measurements diverge more and more as the time dilation effect means time passes more slowly on board the ship than it does back home.

The general formulae are as follows (assuming the ship experiences constant acceleration):

T = (c/a)arctanh(v/c)

t = (c/a)sinh(arctanh(v/c))

where:

T = proper time (i.e. time measured on the ship)

t = coordinate time (i.e. time measured back home)

a = acceleration

c = speed of light

v= final velocity

sinh = hyperbolic sine function

arctanh = inverse hyperbolic tangent function

I've worked out the numbers for accelerations between 1g and 6g, and for final velocities of 0.95c and 0.99c

a      v              T                 t       

1g	0.95c		1.77 years	      2.95 years
2g	0.95c		0.89 years	      1.47 years
3g	0.95c		0.59 years	      0.98 years
4g	0.95c		0.44 years	      0.74 years
5g	0.95c		0.35 years	      0.59 years
6g	0.95c		0.30 years	      0.49 years

1g	0.99c		2.56 years	      6.8 years
2g	0.99c		1.28 years	      3.4 years
3g	0.99c		0.85 years	      2.27 years
4g	0.99c		0.64 years	      1.7 years
5g	0.99c		0.51 years	      1.36 years
6g	0.99c		0.43 years	      1.13 years

I hope this helps.

Iain, very compehensive, thanks. I'm surprised by how quick you could get up to those speeds.


A follow up question then, if i may. Using:
3g 0.99c 0.85 years 2.27 years

imagine a journey between systems 50 light years apart. What would be the T & t journey times?

My impression over all is trying to roleplay this would involve a lot of complicated time keeping of physiological age and chronological age!

 

[rust]

Assuming constant acceleration to a mid point followed by constant de-
celeration, the travel time in hours is:

T = Square Root of [0.0000508 x (D / A)]

where D is the distance in miles and A is the acceleration in G.

Well, at least that is the formula used in GURPS Space, a bit unwieldy
because one has to convert the 50 light years into miles. But with a
calculator at hand it should enable you to calculate the time required
for different values of acceleration in G.

 

[BP]

...A follow up question then, if i may. Using:
3g 0.99c 0.85 years 2.27 years

imagine a journey between systems 50 light years apart. What would be the T & t journey times?

My impression over all is trying to roleplay this would involve a lot of complicated time keeping of physiological age and chronological age!

Break the problem into 3 parts: Acceleration - coast - deceleration. Calc the distance accelerating and decelerating (use distance = time x final velocity /2 each way) then use the time dilation factor of 1/sqr(1-v*v) times the time coasting.

Note that time dialation occurs regardless of direction (i.e. if v is negative above then the answer is still positive).

In your example the time dialation factor is 1 / sqr (1 - 0.99*0.99) or 7.09.

So the 2.27 yr (reference frame time t above) + 50.27 yr + 2.27 yr is a total trip time t of 54.81 yr 'back home'. With time dialation factor of 7.09 while coasting, our traveller has only 'aged' 9.43 yr ship time.


Of course, we'll ignore the fact that constant accel of 3G to near c will require a non-constant amount of energy... bear in mind that relativistic mass increases exponentially so that 0.99c requires an amount of energy quickly approaching infinite This is part of the basis for the FTL 'limit'!

Speaking of time - its 2am and a long day for me - so I hope I didn't screw this up too much...

 

[Vargr]

iainjcoleman, you obviously have a grasp of time-dilating effects of travelling at relativistic speeds.

I wonder if you could tell me what is speed limit from whence the TD effect becomes a noticeable factor?

 

[Myrm]

1) Whats considered the maximum sustained acceleration a human body could tolerate(assuming no future tech adaptations)

G force tolerance depends upon a number of factors -
1) Magnitude - which you are trying to establish a range for
2) Duration - which you have kind of settled with sustained but are you talking in periods of hours, days or minutes? You see this 2000 paper looks at some aspects and is talking about 140s durations and 5Gs
http://www.ncbi.nlm.nih.gov/pubmed/11051304?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_SingleItemSupl.Pubmed_Discovery_RA&linkpos=2&log$=relatedreviews&logdbfrom=pubmed
Which many would consider sustained but doesn't look like what you are after.
3) Direction of the force - humans handle Gforce very differently horizontally vs vertically - and even +ve/-ve makes a difference)
4) Body posture....thats been known a while
http://www.ncbi.nlm.nih.gov/pubmed/1156299?itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_RVDocSum&ordinalpos=20
It was known even before that with the rocket sled tests from the 50s...

 

[Rikki Tikki Traveller]

iainjcoleman, you obviously have a grasp of time-dilating effects of travelling at relativistic speeds.

I wonder if you could tell me what is speed limit from whence the TD effect becomes a noticeable factor?

It becomes noticeable at about 50% c (c = speed of light) and really noticeable at about 80% c.

I have normally not worried about time dilation effects below those velocities. YMMV

 

[BP]

iainjcoleman, you obviously have a grasp of time-dilating effects of travelling at relativistic speeds.

I wonder if you could tell me what is speed limit from whence the TD effect becomes a noticeable factor?

Time dialation is always a factor - wether it is noticed or not is another story!

Commonly this is said to be .5c, but that is quite arbitrary - since at .4c the difference is about 1 month per year!

Simpy determine the time dilation factor using 1 / sqr(1-v*v). A brief list of factors:

   v	  f
.10c	1.01
.20c	1.02
.30c	1.05
.40c	1.09
.50c	1.15
.60c	1.25
.70c	1.40
.80c	1.67
.90c	2.29
.95c	3.20
.96c	3.57
.97c	4.11
.98c	5.03
.99c	7.09

 

[iainjcoleman]

A follow up question then, if i may. Using:
3g 0.99c 0.85 years 2.27 years

imagine a journey between systems 50 light years apart. What would be the T & t journey times?

My impression over all is trying to roleplay this would involve a lot of complicated time keeping of physiological age and chronological age!

Assuming you mean accelerating uniformly to 0.99c, then coasting, then decelerating uniformly to reach zero velocity at the endpoint:

The distance covered in accelerating to 0.99c is given by

d = (c*c/a)[cosh(aT/c) - 1]

where d is the distance, cosh is the hyperbolic cosine function, and other symbols are as before.

For the case in question, this works out as d = 1.97 light years.

At the end of the trip, it takes another 1.97 light years to slow down.

Traversing the 46.06 light years in between will take 46.53 years of coordinate time. You calculate the proper time by multiplying by the time dilation factor sqrt(1-v*v/c*c), which in this case is 0.141. So the proper time is 6.56 years.

Putting all this together, the whole trip takes 51.07 years of coordinate time, and 8.26 years of proper time.

These are not the same numbers that BP gives above. This is because when calculating the distance travelled while accelerating, you have to bear in mind that the acceleration is only constant in the reference frame of the ship, not in the reference frame of an observer back home. BP treated the acceleration as constant in the latter reference frame, which is incorrect. (My time dilation factor is just the inverse of BP's, but I multiply by it and BP divides by it, so it amounts to exactly the same thing in the end)

As for your last point: yes, if you're going to do SF with near-light-speed travel then you are going to have to keep track of each character's proper time as well as some coordinate time. This will indeed be a pain in the bum. Traveller just handwaves all this away with jump drives, which makes life much simpler.

If you haven't already, I would strongly recommend reading The Forever War, by Joe Haldeman, in which the protagonist's experience of time dilation in interstellar travel is the main focus of the plot.

 

[Vargr]

As for your last point: yes, if you're going to do SF with near-light-speed travel then you are going to have to keep track of each character's proper time as well as some coordinate time. This will indeed be a pain in the bum. Traveller just handwaves all this away with jump drives, which makes life much simpler.

Not exactly a pain. Since "Revelation Space" has cold berths the characters won't age during the trip. Indeed, from their prespective, the trip will be almost instantaneous. Just a dreamless nap and...you're there.

 

[BP]

...These are not the same numbers that BP gives above. This is because when calculating the distance travelled while accelerating, you have to bear in mind that the acceleration is only constant in the reference frame of the ship, not in the reference frame of an observer back home. BP treated the acceleration as constant in the latter reference frame, which is incorrect. ...

Well, that was kinder than I deserved

I definitely took my zest to simplify and avoid reference frames, inertial and non-inertial and trig a bit too far

Thanks for the corrections!