Speed limit in space?

His Divine Shadow · Post by **His Divine Shadow** » 2002-09-17 07:56am

Speed limit in space?
Or a reasonable one given mass/fuel efficency.
We all know that the absolute speed is C, but even when travelling at fractions of C your mass increases.

I wonder, at wich point would one consider further acceleration to be of no use or too inefficient to warrant the cost of the fuel it would take?

I guess it depends on the sublight engines too, but lets say using reaction engines with a 70-80% effiency ratio or something

Post by **haas mark** » 2002-09-17 08:25am

uhhh.......okay.

His Divine Shadow · Post by **His Divine Shadow** » 2002-09-17 08:34am

verilon wrote:uhhh.......okay.

No really, I mean there are talks about speed limits in sci-fi books for ships, logically, what would that be, since there is no speed limit in space except C.

greenmm · Post by **greenmm** » 2002-09-17 11:29am

Um... what do you mean by 70-80% efficiency?

If you're using a reaction engine, the problem is carrying enough fuel. Basically, unless you have a fuel that releases a high amount of energy per mass unit, you end up having massive fuel tanks just to get to extremely slow intrasystem velocities... and the more fuel you need, the more thrust you need to move the fuel you need.

But, let's assume you don't need to worry about fuel (refueling available and/or high thrust-to-mass ratio in your fuel). And let's say that, thanks to an inertial compensator, your reaction drive can accelerate at 100 g's (somewhat slow for a sci-fi ship, but a Porsche's wet dream compared to our spacecraft).

At 100g's, it normally takes the ship 8 h 29 m 31 s to reach 0.1c. Of course, your mass will be slowly increasing the whole time, so let's say it takes about 8 h 31 m to reach that speed. Your ship will also travel about 460 million kilometers, or about 3.1 AU's. Due to time dilation, everyone on the ship will experience 59 m 42 s for every hour that passes outside the ship (loses 18 seconds every hour).

By the time you reach 0.9c, your mass has increased to 2.294 times your rest mass, time dilation means you'll experience only 26.2 seconds for every minute that passes, and your engine thrust is reduced now to 43.6% of its normal capability.

When you reach 0.995c, your drive's effective thrust is about 10% of its base thrust, thanks to the mass increase (mass is 10x rest mass), and time passes really slowly (6 seconds pass for every minute outside the ship).

Crown · Post by **Crown** » 2002-09-17 11:42am

Ahh a topic I know all too well. What defines speed limit in space is the exhaust velocity of a specific rocket. For example a chemical rocket has a top exhaust velocity of 400m/s IIRC (it might actually be 4km/s), and then by using Tsiolkovsky's brillaint rocket equation we see that the final velocity of the rocket is soley dependant upon it's exhaust velocity times the natural log (ln) of the mass fraction of the rocket plus it's starting velocity;

DeltaV = Uex*log(Massfraction)+U

The mass fraction is just total mass of rocket (fuel, structure) divided by final mass of the rocket (for all purposes assume single stage, and you are left with payload and structure).

Now I know you might be saying, okay but where is the speed limit? Well here is the thing, if you rearange the equation to solve for fuel;

Massorig = Massfinal*exp((DeltaV-U/Uex))

And you start plugging in values, you realise that the restriction is in the exhaust velocity. For example plug in values of Uex = 4 km/s and U = 0, and DeltaV =52km/s and Massfinal = 80 000kg, you will get a fuel mass that is larger than the total mass of Earth!!!!!

So now that we know that we are able to sumarise, exhaust velocity sets practical limits on rocket propulsion. So for chemical rockets, 16 ~ 20 km/s DeltaV, Fusion 0.1c, and antimatter about 0.5c. Don't believe me play around with the equation and see for yourslef!

Andrew J. · Post by **Andrew J.** » 2002-09-17 02:40pm

*gawks at the complicated math above*

I feel so inadequate.

Wicked Pilot · Post by **Wicked Pilot** » 2002-09-17 06:54pm

Here is a little speed to mass table I made. I hope the calcucations are accurate. The equation used is: m=(1-(v^2)/(3E8)^2)^(-1/2). My knowledge of Relativity is somewhat limited, so if any of you experts (cough cough Darth Wong) find a problem, feel free to let me know.

Speed - Mass
rest - 100%
0.1c - 101%
0.2c - 102%
0.3c - 105%
0.4c - 109%
0.5c - 115%
0.6c - 125%
0.7c - 140%
0.8c - 167%
0.9c - 229%
0.99c - 709%
0.999c - 2237%
0.9999c - 7071%
0.99999c - 22361%

Asst. Asst. Lt. Cmdr. Smi · Post by **Asst. Asst. Lt. Cmdr. Smi** » 2002-09-17 10:16pm

I think that if you accelerate at 1G, it will take you 3 months to get you to C. I don't know. My dad told it to me years ago. Now, assuming we have a 1,000,000kg ship, how much energy would be used getting it to C, including mass dilation effects. There would be other variables. As fuel is expended, the ship loses mass, but gains reletavistric mass as it approaches relativistic speeds. I'm confused.

Post by **Darth Wong** » 2002-09-17 10:18pm

There's a relativity calculator on my main site, in the "Science" subsection. Not to disrespect your dad or anything, but he's flat wrong about accelerating to c. Your mass increases as you approach c, so it is impossible to accelerate at a constant rate indefinitely.

Post by **haas mark** » 2002-09-17 10:21pm

Andrew J. wrote:*gawks at the complicated math above*

I feel so inadequate.

Ditto.

Crown · Post by **Crown** » 2002-09-17 11:10pm

It's not that complicated, it's just one simple equation;
Tsiolkovsky equation;

Uex/V = ln(Mo/M) + U

Uex = Exhaust velocit of rocket
V = Velocit of rocket (commonly refered to as Delta V, change in velocity)
Mo = Starting mass
M = End mass
U = initial velocity

ln = Natural logarithm

And that's it!

Post by **haas mark** » 2002-09-17 11:43pm

And U can't be Vo, why?

Master of Ossus · Post by **Master of Ossus** » 2002-09-17 11:48pm

verilon wrote:And U can't be Vo, why?

What are you talking about? The U symbol is just used by convention, as are all mathematical symbols.

Post by **haas mark** » 2002-09-17 11:57pm

I'm just beign a bug, that's all...

Crown · Post by **Crown** » 2002-09-18 12:35pm

His Divine Shadow did that help at all?

Andrew J. · Post by **Andrew J.** » 2002-09-18 03:21pm

Crown wrote:It's not that complicated, it's just one simple equation;
Tsiolkovsky equation;

Uex/V = ln(Mo/M) + U

Uex = Exhaust velocit of rocket
V = Velocit of rocket (commonly refered to as Delta V, change in velocity)
Mo = Starting mass
M = End mass
U = initial velocity

ln = Natural logarithm

And that's it!

Fine, except I have no idea what the hell a logarithm is.

Crown · Post by **Crown** » 2002-09-19 12:14am

Andrew J wrote:
Crown wrote:It's not that complicated, it's just one simple equation;
Tsiolkovsky equation;

Uex/V = ln(Mo/M) + U

Uex = Exhaust velocit of rocket
V = Velocit of rocket (commonly refered to as Delta V, change in velocity)
Mo = Starting mass
M = End mass
U = initial velocity

ln = Natural logarithm

And that's it!
Fine, except I have no idea what the hell a logarithm is.

Well a logarithm is defined as...The power to which a base, such as 10, must be raised to produce a given number. If nx = a, the logarithm of a, with n as the base, is x; symbolically, logn a = x. For example, 10^3 = 1,000; therefore, log10 1,000 = 3. The kinds most often used are the common logarithm (base 10), the natural logarithm (base e), and the binary logarithm (base 2).

ln is what is known as the natural logarithm, that is with a base of e which is 2.713 IIRC.

Crown · Post by **Crown** » 2002-09-29 12:32am

Sorry guys! I said 52km/s was about the same mass of propellant of Earth! I had the brackets in MATLAB wrong and it was spitting out insane calculations!!!

I seriously hope that I didn't give anyone false data!