How much energy does it take to reach relativistic speeds?

[schonovic]

I'm trying to make a chart that displays how much energy it takes a rocket with x mass to reach Y factors of relativistic change but do not know how to build the equation that will give me such information. Can anyone help me with this?

 

[Simon Bridge]

You could use work = change in kinetic energy, and use the relativistic kinetic energy equation - or look up the relativistic rocket equation. What have you tried?

 

[schonovic]

What relative rocket equation? What have I tried; well, I've tried calculating the energy it takes to reach a velocity approaching lightspeed without relativity then multiplying that by the relativistic factor for that speed however, that does not include the factor for each velocity previously achieved up to that point. Really, I'm not even up to college level algebra so I really do not know what else to try. I call myself a sci-fi inventor. I'm trying to create a universe where the technology for faster than light travel is based on a machine that converts your relativistic factor into a faster than light factor. So if you want to travel at two times lightspeed you have to accelerate up to a speed where your relativity factor is two and activate the machine. I need an equation that I can use to calculate the energy required to reach a factor of two for ships of various metric tonages. I need an equation that will calculate the energy required for any relativistic factor for any tonage of ship. Is there such an equation? Does anyone know of one?

 

[Bill_K]

What relative rocket equation?

Have you learned how to use Google yet? If so, try Googling "relativistic rocket equation."

 

[Simon Bridge]

Bill is right - you can put the search terms "relativistic rocket equation" or "relativistic kinetic energy" into a search engine and get thousands of hits.

Considering what you want to know for, you'd probably be happy with the quick and dirty KE equation.

 

[HallsofIvy]

The real problem is deciding what you mean by "relativistic speeds"!

 

[ghwellsjr]

What relative rocket equation? What have I tried; well, I've tried calculating the energy it takes to reach a velocity approaching lightspeed without relativity then multiplying that by the relativistic factor for that speed however, that does not include the factor for each velocity previously achieved up to that point. Really, I'm not even up to college level algebra so I really do not know what else to try. I call myself a sci-fi inventor. I'm trying to create a universe where the technology for faster than light travel is based on a machine that converts your relativistic factor into a faster than light factor. So if you want to travel at two times lightspeed you have to accelerate up to a speed where your relativity factor is two and activate the machine. I need an equation that I can use to calculate the energy required to reach a factor of two for ships of various metric tonages. I need an equation that will calculate the energy required for any relativistic factor for any tonage of ship. Is there such an equation? Does anyone know of one?

If you're going to invent your own science (fiction), then why are you asking on a science forum? Just make up anything you want since it violates science anyway.

I guess there must be certain protocols that sci-fi inventors feel compelled to follow in order to be "credible". But I don't understand why your machine would convert relativistic factor, gamma, into a faster than light factor. When gamma equals two, the speed of the ships is 86.6% of c so shouldn't the machine only be capable of converting to 86.6% faster than c? Seems like you are violating a sci-fi protocol and taking advantage of your sci-fi audience's ignorance.

 

[Simon Bridge]

The real problem is deciding what you mean by "relativistic speeds"!

The rule of thumb in SF tends to be that "relativistic" is whenever the plot says - loosly, when the relative speed would be faster than light if Newtonian physics held: when kinetic energy is $\frac{1}{2}mc^2$ or higher.
In SF, the default reference fame for speed also depends on plot - it will be the origin or destination reference point, whichever is important to the development of the story at the time.

When gamma equals two, the speed of the ships is 86.6% of c so shouldn't the machine only be capable of converting to 86.6% faster than c?

By that rule, no ships would be able to make 2c.

If the FTL drive flips the gamma factor into an FTL-factor, then the ships prepared to spend the most time accelerating in e-space (einstein/regular-space) will be the faster in h-space (hyper-space). The idea introduces all sorts of tradeoffs that could be useful to the storyline.

A fugitive being shot at by bounty-hunters may want to escape by flipping to h-space early (avoiding being shot at) at the expense of being slower (the hunters wait a bit before flipping, if they know the destination they may even be able to get there before the fugitive).

It can be handy to have a framework of some kind that references something about known physcs, when writing SF - the usual rule is to allow a one-time breaking one rule. Some just have a "magic" breaking the rules while others like to try to tighten things up, generating a feeling, in the reader, that the World of the story still has rules that get in the characters' way.

To do this it helps to get some idea of how badly an exception violates known physics ... what a lot of SF writers don't realize is just how extreme a breach FTL actually is.

@schonivic: Back of envelope $K=(\gamma-1)mc^{2}$
... m is the mass (~tonnage) of the ship, K is the kinetic energy, and $\small \gamma$ is the relativity factor.

So for a 10 Tonne ship to have gamma-factor 2, E≈3TJ (three tera-Joules) ... i.e. the energy released by anihilating 5T of matter with 5T of antimatter.

Should give you an idea what you are getting yourself and your characters into.

 

[ghwellsjr]

When gamma equals two, the speed of the ships is 86.6% of c so shouldn't the machine only be capable of converting to 86.6% faster than c?

By that rule, no ships would be able to make 2c.
...

So for a 10 Tonne ship to have gamma-factor 2, E≈3TJ (three tera-Joules) ... i.e. the energy released by anihilating 5T of matter with 5T of antimatter.

If the OP is seriously concerned about energy, then no ship will make it to any speed beyond a tiny fraction of c. However, I have a solution, it just takes two of these machines that convert gamma into FTL. You just start your journey in the direction you want to go at the slowest possible speed and flip the switch. Since gamma a slow speeds is ever so slightly greater than 1 your ship with its second machine will be traveling ever so slighter over the speed of light. Now you slow down just a bit (if necessary, who knows?) to get you just below 1c where gamma is an extremely large number and you flip the switch on the second machine. Now you're going billions of times the speed of light and for practically no energy at all!

 

[schonovic]

I guess it is sarcasm when you say "have you learned how to use google?", yeah, thanks for you're input buddy. I kind of figure that if I see some one who needs help that I can give; why not give it to them but I'm no atomic physicist so you have me at a weakness here but you don't need to use that fact to make a mockery of me, and I ask on a science site because I want people to ask, "Is this real because it really sounds like it could work that way?" I'm all for saying that every jump through hyperspace causes every ones stomach to turn and nobody knows why and leave that as the only comment on star travel in the book. And that is great but I also like to work the other side of the fence and say you need to understand the universe as Steven Hawking does to even consider trying to understand hyperspace. Hell I even like saying "We flip this switch and it just works, but you see we have too many people who want all science fiction to be "Hard science fiction" according to what we know now, and I think those kinds of people think they know everything but don't because I really believe there's more out there than we know and maybe that scares people...that's too bad! Also I want to thank Simon Bridge for the handy equation and ghwellsjr for his comments, sounds cool!

 

[Simon Bridge]

I guess it is sarcasm when you say "have you learned how to use google?", yeah, thanks for you're input buddy.

You mean Bill_K right?
It is harsh - yeah - and not etiquette for PF. OTOH: see
http://www.catb.org/esr/faqs/smart-questions.html
particularly the section "how to interpret answers" (at the bottom).

I kind of figure that if I see some one who needs help that I can give; why not give it to them

- you may be misunderstanding what goes on here - you did receive the help you asked for in a way that saves time and typing for us. That way we can help the most people in the time we have.

I ask on a science site because I want people to ask, "Is this real because it really sounds like it could work that way?"

Oh well you should have said! :D
The answer is "no, it is not real and it cannot work that way."

I really believe there's more out there than we know and maybe that scares people...that's too bad!

What we know is alrweady out there scares lots of people already ;)

Also I want to thank Simon Bridge for the handy equation and ghwellsjr for his comments, sounds cool!

No worries :)
Have fun.