World size questions

[kerbiloid]

9 minutes ago, Master39 said:

Kerbal core is in fact in what both of those game lack, orbital mechanics.

But KSP is a game, so it's focused on gameplay. The orbital mechanics is just applied.

9 minutes ago, Master39 said:

you won't replace a comnet sat launch,

Why replace it? I have made it out of old tractor parts and kitchen pots.

9 minutes ago, Master39 said:

a exploration rover to a new planet

No "new planets". No uncrewed rovers. Only moons. You fly there in flesh and drive the car yourself.

9 minutes ago, Master39 said:

Let's use a "the Martian" mission profile as an example, yes, you use a big mothership to move the crew between Kerbin and Duna, but the robot reconnaissance for the landing location

No motherships in rookie phase.  They don't fit your hangar, and you don't have enough spent tractors to build them. Also, you don't have so much Kerbals. And you can fly only to the moons.

9 minutes ago, Master39 said:

And then, when you're bored with the system you're in, you build a huge colonization mothership

By taking "Mothership Head", "Mothership Middle", "Mothership Propulsion" parts, not by attaching every battery. 
The farther you get, the more resources and abilities are integrated in cfg file anyway.

Edited November 17, 2020 by kerbiloid

[Guest]

27 minutes ago, kerbiloid said:

But KSP is a game, so it's focused on gameplay

And, as I said, the core gameplay loop is designing and flying a rockets and spacecrafts to solve a specific problems.

In KSP1 except for a very basic science system and some random contracts you have to make up every single problem and make your own constraints, KSP2 is obviously set to overcome that limitation and replace abstract random contracts with a miriad of actually working secondary gameplay loops, like colonization, resource gathering and offworld ship-building.

The two aspects of the game are meant to work alongside each other, not "rocket building first and then colonisation"

 

30 minutes ago, kerbiloid said:

Why replace it? I have made it out of old tractor parts and kitchen pots.

I'm not talking about replacing a old satellite, but about building the comnet infrastructure for your next exploration target.

 

32 minutes ago, kerbiloid said:

No motherships in rookie phase.  They don't fit your hangar, and you don't have enough spent tractors to build them. Also, you don't have so much Kerbals. And you can fly only to the moons.

A "the Martian" mission profile is a perfect example of something that doesn't quite fit neither of your theorised phases, it's way too early tech to talk about colonization (the HAB lasts for a month or so) but also too advanced for a KSP1 level of tech.

Another example would be wanting to build a Mun colony as early as possible and use it as a launch site to explore the rest of the Kerbol system.

Those are good examples of why a strict 2 phases system is a terrible idea.

 

43 minutes ago, kerbiloid said:

By taking "Mothership Head", "Mothership Middle", "Mothership Propulsion" parts, not by attaching every battery. 
The farther you get, the more resources and abilities are integrated in cfg file anyway.

In the podcast we discovered that the big ship main design gameplay loop will be around balancing the power usage and production in relation to the heat management, something already way more complex than " Ship head + ship middle + engine", but it doesn't stop there, a mothership is just a mean of transportation, it won't be able to land, explore and offer system while communication network capabilities and how you build those? With your old "small parts" system.

Even in the case in which your ship is an all-in-one single part craft you'll want to build smaller more traditional "KSP1-stlyed" crafts all around it to actually do things after your reached your destination.

[MarsUltor]

On 11/16/2020 at 4:25 AM, KerikBalm said:

although 0.5 may be achievable if they have antiatter rockets, avoiding velocity faster than this also has the nice side-effect of making it Ok to ignore time dialation

What?! Half the speed of light will bring in huge time dilation. d(t’)=d(t)/(1-(v^2/c^2))^0.5

At 0.5c it’ll be d(t’)=d(t)/0.86!

 

[KerikBalm]

32 minutes ago, MarsUltor said:

What?! Half the speed of light will bring in huge time dilation. d(t’)=d(t)/(1-(v^2/c^2))^0.5

At 0.5c it’ll be d(t’)=d(t)/0.86!

 

so... 86 seconds on the starship = 100 seconds back at kerbin, I don't consider that huge ... granted, in another thread I mentioned I'd set the cutoff for acceptably ignoring time dialation at a 10% difference which is 0.4c not 0.5c. Atomic rockets on the other hand uses 1%, which would be 0.14c  http://www.projectrho.com/public_html/rocket/slowerlight.php

http://www.projectrho.com/public_html/rocket/slowerlight.php

At .99c though, then its going to make huge differences in terms of time elapsed for the crew, changing the level of life support they'd need by an order of magnitude

[Kryfulli]

That brings a really good question. Will KSP2 implement time dilation at all ?

It is really necessary considering the distances that separates two stars, but with the whole universe size thing, i might see the dev just forgetting this part because it would be really complex to follow (for the game, and the player !) ...

Especially since we know they have some engines that could fire for years, time dilation would change with the actual time. I see some integrations that need to take place, and i could understand if they would just not implement that.

[MarsUltor]

11 hours ago, KerikBalm said:

so... 86 seconds on the starship = 100 seconds back at kerbin, I don't consider that huge ... granted, in another thread I mentioned I'd set the cutoff for acceptably ignoring time dialation at a 10% difference which is 0.4c not 0.5c. Atomic rockets on the other hand uses 1%, which would be 0.14c  http://www.projectrho.com/public_html/rocket/slowerlight.php

http://www.projectrho.com/public_html/rocket/slowerlight.php

At .99c though, then its going to make huge differences in terms of time elapsed for the crew, changing the level of life support they'd need by an order of magnitude

I just remember one of my physics professors saying anything over 0.1c makes Newtonian physics break down... granted, I haven’t thought about this stuff since university, more than 25 years ago... and if it’s an issue for gps satellites in geostationary orbit, seems like it’d start being an issue at high speeds, far distances, etc

Edited November 17, 2020 by MarsUltor

[K^2]

5 minutes ago, MarsUltor said:

I just remember one of my physics professors saying anything over 0.1c makes Newtonian physics all messed up... 

It's all, well, relative. The electrons in wires are barely moving, and you still get magnetism as side effect of relativity, simply because if you were to separate all positive and negative charges, the forces and energies involved would be absolutely enormous, so even a tiny relativistic correction of these gives you an appreciable force. I wouldn't get stuck on any particular value of fraction of c as a cutoff. Just do the quick estimate for any given case. Fortunately, the math for special relativity is super simple.

[MarsUltor]

2 hours ago, K^2 said:

The electrons in wires are barely moving

To be fair, electrons are a pretty bad example, since there is no example of Newtonian physics that can reasonably apply to their behavior... if memory serves, Newtonian physics and quantum mechanics are largely incompatible.

[K^2]

9 minutes ago, MarsUltor said:

To be fair, electrons are a pretty bad example, since there is no example of Newtonian physics that can reasonably apply to their behavior... if memory serves, Newtonian physics and quantum mechanics are largely incompatible.

There's nothing quantum about magnetism. It's all Coulomb's laws + relativity.

Magnets, on the other hand, they're deeply quantum, but that's another story. We're just talking about magnetic fields of current-carrying wires here.

[mattinoz]

On 11/16/2020 at 8:25 PM, KerikBalm said:

I would disagree with your assumptions. I would assume a maximum velocity of around 0.1-0.2c (although 0.5 may be achievable if they have antiatter rockets, avoiding velocity faster than this also has the nice side-effect of making it Ok to ignore time dialation). Given the general 1/10th scale, I would expect the nearest star to be 0.45 light years, not 4.5. I would also expect maximum timewarp ot be at least 10x higher. So assuming 1/10th the velocities, 1/10th the distances, and 10x the time warp, the 20 minutes comes down to just 2 minutes... which seems fine to me.

The standard KSP system is smaller with less bodies than our system. So if our system has 52 "nearby" stars, I would expect the KSP system to have less than 50.

plus, >50 is a lot of work...

So that's my speculation

2minute games time to travel interstellar would negate the need for acceleration on rails while not focused, which has been confirmed as a feature.  Even 20-40minutes seems to short. I think the set-out will be more leading towards multiple play sessions. Say EP1) manage launch colony up to scale, build craft, Ep2) Point and shoot, ..... some time later after doing some stuff....  Ep3) Arrival.

Maybe Sandbox will be different and more like no current KSP that doesn't stop you wasting time. But it sounds like Adventure mode will have the tools and demands to drive the game along as a program.

 

[KerikBalm]

9 hours ago, mattinoz said:

2minute games time to travel interstellar would negate the need for acceleration on rails while not focused,

I disagree, if you want to launch 2 missions simultaneously, then its needed. Some of us care about how much time passes in game and want to do missions in parallel. Not focused or not, KSP1 doesn't allow acceleration on rails. The big improvement is acceleration on rails, and when its on rails, it shouldn't really matter if it is focused or not.

[mattinoz]

19 hours ago, KerikBalm said:

I disagree, if you want to launch 2 missions simultaneously, then its needed. Some of us care about how much time passes in game and want to do missions in parallel. Not focused or not, KSP1 doesn't allow acceleration on rails. The big improvement is acceleration on rails, and when its on rails, it shouldn't really matter if it is focused or not.

Agree personally it's a massive but KSP1 Producers don't, they would (I'd suggest given comments over the years) push for short game transit times and favour playing out missions concurrently.

So if KSP2 team do favour and promote simultaneous flights that is a (to me much welcomed) shift in the games style.  Certainly feels like they are giving a lot of love to making  a progression for the game to tease the player further and further out to space as they get more comfortable with the mechancis of the game.

[vv3k70r]

On 11/15/2020 at 8:43 PM, kerbiloid said:

But this is Kerbal Space Program, so most part of the time is the space gameplay.

Rovers take most of time for now. Planes are second on the list.

Not all stars should have planets?

Complexity of the game make reasonable to split loading into Kerbin+its moons, then other planets and its moons, and then other stars. Most of people ending up somwhere on the first part because of complexity boud to travel to any other celestial body in career mode. If the point of the game is fun - complexity exceed most of the population ability to handle, if point is to make it intresting for a small part of bells curve that can handle it it make a narrow market target (however this target have money for spending on good and intelectualy intresting products).

I suspect that it could be a problem to solve for marketing department who is the target of the game and what are the expectations. Game around Kerbin, game around other planets, and game around other stars sound like three completly diferent games (somthing like making history). Packed in one? Most of people cant get there other way then alt+F12 just to see the content.

Vast content in game cost developing, and someone has to pay for it. Question is if the customer can experience the content in given way att all. There are such complex games for hobbyst, but these games are not made as products for market and as such they are not generating any intresting income to pay devs.

Edited November 23, 2020 by vv3k70r

[MarsUltor]

On 11/17/2020 at 9:15 PM, K^2 said:

There's nothing quantum about magnetism. It's all Coulomb's laws + relativity.

Magnets, on the other hand, they're deeply quantum, but that's another story. We're just talking about magnetic fields of current-carrying wires here.

I think you’re getting a little off point, regardless of how I recall electron physics... I provide a literal example of the need for relativistic recalibration IN SPACE TRAVEL, and you counter with “it’s all relative... electrons in wire...” I’m sorry, but you’re example continues to be bad, considering my example is on topic, whereas yours has no real bearing to space travel.

[K^2]

1 hour ago, MarsUltor said:

I think you’re getting a little off point, regardless of how I recall electron physics... I provide a literal example of the need for relativistic recalibration IN SPACE TRAVEL, and you counter with “it’s all relative... electrons in wire...” I’m sorry, but you’re example continues to be bad, considering my example is on topic, whereas yours has no real bearing to space travel.

The example you quoted immediately after talking about 0.1c is GPS satellites, which, first of all, travel at 0.000014c, and secondly, require a larger correction for Earth's gravity than their orbital speed. Clocks on the GPS satellite actually run faster than on Earth, not slower.

The reason I brought up electricity is because it is the most extreme example of relativistic effects at low speeds, and it highlights that using an arbitrary cutoff point, like 0.1c, is absurd. But the GPS example proves exactly the same point. It just has an inconvenience of having to deal with General Relativity, meaning working out the correction is actually far, far beyond the kind of math that has been discussed in this topic.

The idea that Newtonian physics starts breaking down at a specific threshold is absurd. Newtonian physics is a model. A way to make an estimate. And whether or not it is going to be good enough depends on the purpose. 4km/s is too fast for Newtonian physics to be good enough for GPS, sure. But also 4m/s is too fast for Newtonian physics to be good enough for a length of wire, so big woop. At the same time, if I use classical Rocket formula, derived from Newton's laws, to estimate quantity of nukes I need to get an Orion-style NPP to 0.4c, I'll still be off by a smaller factor than variance I'm likely to get from detonation to detonation. So Newtonian physics is perfectly good here. 

To once again repeat the obvious, relativity is relative. There is no specific point at which Newtonian physics stops making sense if it ever did. If you want to show that something's moving too fast for us to do Newtonian computations for, you'll have to do the work with relativity taken into account and then show that the error is too high for particular purpose. If you want to show something for a particular trip between stars, work it out and show that you have to take relativity into account. Don't just quote an absolutely pointless threshold that has nothing to do with anything.

[vv3k70r]

On 11/18/2020 at 3:15 AM, K^2 said:

There's nothing quantum about magnetism. It's all Coulomb's laws + relativity.

Force is carried by particles that dosent have its own frame of reference as far we konw. It is what relativity is about. It starting to break when two such particles passes ech other because from they point of view they dont.

Newtonian physics is a statistical aproach bound to given experiments. It is a model, not the reality. Usefull and very acurate model, but still.

Relativity is about acceleration, not speed. Accelerating vehicle face particles that other observers do not consider existing att all. And that particles generate forces on the vehicle. Only description of such effects (that we have) are purely numerical, it dosent make sense if translate to common sense. But as far we do not have engines to speed up anything worth of considering (above information) so newtonian for starspace travel is good enough. We do not expect to have such engines in near or far future.

Edited November 24, 2020 by vv3k70r

[K^2]

1 hour ago, vv3k70r said:

Force is carried by particles that dosent have its own frame of reference as far we konw. It is what relativity is about. It starting to break when two such particles passes ech other because from they point of view they dont.

You absolutely can describe interactions from coordinate system of interaction particle. In case of electromagnetic interactions, that yields light cone coordinates, and it's a useful tool in particle physics.

But again, considering particle nature of interactions is entirely unnecessary. If you were still stuck in late 19th century and only understood electrostatics as an effect of electric potential, if somebody came to you and explained to you special relativity, you'd be able to derive magnetic force from it. And in fact, the full set of Maxwell's equations.

[vv3k70r]

1 hour ago, K^2 said:

You absolutely can describe interactions from coordinate system of interaction particle.

Ok - describe it for photon. Start with "what is a direction for timless particle". Because there is no dynamic if there is no timeline. So for photon exist only now1 and now2 in exact same moment, and everything on any direction is never. One now and infinite never is quite small degree of freedom to draw reference frame. And You cannot observe photon from side, so when You seen it - its gone. It dosent interact with photons passing in our other directon (in terms of by carring energy it dosent bend way of passing cousin).

1 hour ago, K^2 said:

that yields light cone coordinates, and it's a useful tool in particle physics.

For not accelerating objects it works. But for accelarating it is far more complicated. And it was statet in some question on topic how would it work. And we do not know, because energy to conduct such experiments are outside our curent abilities. And even outside imagination of our future abilities.

In accelerating coil there be particles "from nowhere" (from this energy of accelation) that are not seen by non accelerating observer. Like this:

https://en.wikipedia.org/wiki/Unruh_effect

And there is more such things. But in case of game - Newton works, we do not have such energies to get in this kind of trouble.

1 hour ago, K^2 said:

But again, considering particle nature of interactions is entirely unnecessary. If you were still stuck in late 19th century and only understood electrostatics as an effect of electric potential, if somebody came to you and explained to you special relativity, you'd be able to derive magnetic force from it. And in fact, the full set of Maxwell's equations.

I completly agree. In case of travel with imaginable mass we do not have such issues, we do not expect to have. I suspect that most of people mismatch speed with accelaration in reference frame. Accelaration is what cause gps corection, not speed.

Edited November 24, 2020 by vv3k70r

[K^2]

31 minutes ago, vv3k70r said:

Ok - describe it for photon.

Light cone coordinates are that description. And yes, a massless particle is emitted and absorbed in the same instance in that particle's proper frame, but the rest of the universe around it still has concept of space and time.

32 minutes ago, vv3k70r said:

For not accelerating objects it works.

And that's all that's needed. A gauge boson is never going to accelerate.

But if we do need to describe dynamics from accelerated coordinate system, that's what General Relativity is for. And while one will run into problems trying to build up Quantum Electrodynamics in a GR setting, you can build a mean field theory that will give you an equivalent of classical electrodynamics in GR setting, and yes, that will include Unhuh radiation once you account for statistical mechanics. None of this is actually a problem, but we are going way, way off track here into deeper math than is necessary for this discussion.

[vv3k70r]

1 hour ago, K^2 said:

Light cone coordinates are that description.

No, they are not. Light cone is Your reference frame. Photon dosent have any cone. Cone is a degree of freedom that You have. Degree of photon is its spin.

1 hour ago, K^2 said:

And yes, a massless particle is emitted and absorbed in the same instance in that particle's proper frame

Its proper frame have only one point. Hard to consider it as frame for any usefull pourposes. More - this frame dosent change even if photon travel from accelerated frame of reference - thats the reason why it is considered to not have any, or any usefull, reasonable or understood for our way of thinking (its purely numerical and lead us nowhere).

1 hour ago, K^2 said:

but the rest of the universe around it still has concept of space and time

Is there any proof that space exist?

Or we measure distance using time reference like "two days by horse" or "three day on foot" and now we get to light years?

I'm quite suspicious because I understund matrix of values for reference frame and there is no diference beetwen spatial and time, we just do not have degree of freedom in one of them so we mark it as time. It is a real issue in technology, because we have spatial free description of 4time and it is simpler that derivate distance. It is just complicated for our brains to set a separate clock on every particle in matrix and derivate observed distance from these values. However it is what our brains do automaticly and unconcious.

I do not suspect universe to have any concept att all, concept could be considered only for conciousnes.

 

1 hour ago, K^2 said:

And that's all that's needed. A gauge boson is never going to accelerate.

Is he about to leave occupied vessel when we start engine?

Of course it is a joke because we do not have any engine to give reasonable accelaration, but it is what Unruh effect is about - unobserved bossons should start appear on the vessel when we accelerate because they are not about to accelerate as well. As far we do not know the answer, there are many questions.

1 hour ago, K^2 said:

But if we do need to describe dynamics from accelerated coordinate system, that's what General Relativity is for.

Yes. But because cone have angle depending on acceleration it is hard to grasp. Most explanations implicate local statis, if we put scewed cone on every accelarating object numerical matrix is to be considered, and derivate from it what we observe gives counterintuitive results. I suspect it is why this disscusion has started. It was about speed, but from gps system we already know that object accelerating more (we on earth) have separate future from accelarating less (satelite) and we have to send the message to corect its clock like the time they experienced never happened, because in our past it didnt.

1 hour ago, K^2 said:

None of this is actually a problem, but we are going way, way off track here into deeper math than is necessary for this discussion.

Agree. We do not have energy dense fuel to even considered engines that gonna trouble us on such a subject.

Lets hope there be not much space opera energy density in the magic can in KSP2 to cause time dilation, because in such a case they gonna mine squeezed stars to use them as fuel.

Edited November 24, 2020 by vv3k70r

[K^2]

8 hours ago, vv3k70r said:

No, they are not. Light cone is Your reference frame. Photon dosent have any cone. Cone is a degree of freedom that You have. Degree of photon is its spin.

If that was the case, light would be unaffected by gravity. In addition to having U(1) DoF corresponding to phase, which has spin as it's conserved current, photon, just like any other particle, has the R(1, 3)xO(1, 3) DoF corresponding to normal transformations in space-time, and which give energy, momentum, and angular momentum as conserved currents. Moreover, a photon, even a virtual one, has a world line, and therefore, a proper frame, that being light cone coordinates.

8 hours ago, vv3k70r said:

Is there any proof that space exist?

And now you're just being obnoxious. I was giving you discount for the language, but I'm starting to think that's not the problem at all here.

[vv3k70r]

9 hours ago, K^2 said:

If that was the case, light would be unaffected by gravity.

Gravity is statistical imagination. For the photon path is always stright. There is only one path and time to pass it is exact zero.

9 hours ago, K^2 said:

which has spin as it's conserved current, photon

Is there any experiment that prove it or is it just assumption on same basis as "there is no prefered direction in space" (so why do we have time?).

If photon "carry" any energi we can derivate mass from it. So photon pasing ech other sould bend they way because of gravity. Is there any observation of this "bending" of light beams? Or it is just action on distance that is not spooky because we can catch the photon and stop the action? And if we cant stop the cerrier we call it spooky?

If photon has reference frame that is corect it includes other, passing by photons and we can assume there be a carrier to transfer interactions between them.  Not observed - we assume there is no such frame of reference for already stated reason.

9 hours ago, K^2 said:

just like any other particle, has the R(1, 3)xO(1, 3) DoF corresponding to normal transformations in space-time, and which give energy, momentum, and angular momentum as conserved currents

Momentum is force*pathlength/time, time for a whoole path for photon is none for its "frame" of reference. This "frame" is not corect. If we are about to split by zero (if we asume that none is in fact zero which is doubtfull if these axis even cross each other in any point - specialy in zero) we have to go deep to field (math meaning) over sets that has rings and to make it comply with SU could be a rough and far terrain - at least not aplicable for our understanding. It could be just numerical fantasy. Or meybe not if there is aplication.

You refer to world transformation on photon, not to photon itself. You transforming its imaginable matrix by world matrix. Remove world and find its corect frame of reference.

Which basis on a pile of assumptions because of all this variables (energy, momentum, and specialy angular) are our statistical point of view that we made to describe it for us. But it is not world, it is our description. Picture we painted for oureselfs. We making this picture more reliable by performing experiments. Is there no experiment so it is our imagination - I do not trust my imagination, I test.

9 hours ago, K^2 said:

Moreover, a photon, even a virtual one, has a world line, and therefore, a proper frame, that being light cone coordinates.

How to prove this with virtual one?

If something dosent affect us it dosent exist in our world line. It dosent mean it has its own - its just an assumption.

9 hours ago, K^2 said:

And now you're just being obnoxious.

No, I stated this question long before on profesional ground. Subject looks deep, but Mr Arkani already did geometrical workaorund long before. I just take it here because its relevant to space statement. Degrees of freedom for spatial vs time looks to be nothing more then our interpretation. It could be exact the same phenomen and no more then one, meybe we found a use for this.

9 hours ago, K^2 said:

I was giving you discount for the language

Not in tech. In human interatcion only. Someone ask (on one of programing forum) for next derivate of velocity and accelaration, I stated obvious answer "jerk" and found that this word has other meaning which he took personaly. So I make longer explanation about meanings.

If we are here (on small letters with 64nm star) - star under the horizon of BH could bequite normal star just so energy dense that it become made of strange matter which keep its pressure under given cirmustances between given multipler of sun mass of what we see in our reference frame as BH horizon. Way there for photon is, and way back is hard to describe as infinite, its never.

I preffer to stop this disscution if You agree. It is very intresting as always, but there is no such engine and energy denisty to trouble us with aplication of time delay to space travel on this Kardashev levelin KSP2(it would give tiny value). Before we even get near there be more experiments stating more questions that we propably could not even imagine today.

Edited November 25, 2020 by vv3k70r

[K^2]

20 minutes ago, vv3k70r said:

Not in tech. In human interatcion only.

Your understanding of physics is at high school level at best, but you seem to be under an impression that it gives you ability to listen to some pop-sci talk and understand the subject. Case in point:

22 minutes ago, vv3k70r said:

Momentum is force*pathlength/time

First of all, check your units. Nm/s is Watts - units of power. Units of momentum are same as these of impulse - Ns. It's an integral of force over time.

More crucially, we aren't discussing high school kinematics. Therefore, relevant definition of  momentum is spatial component of stress-energy tensor projected into a reference frame.

You are using your high school definitions of concepts, incorrectly at that, and are then confused that they don't apply to serious physics.

 

I'm happy to explain concepts in relativity, particle physics, and everything in between in as simple terms as necessary. But you need to stop pretending like you have an actual scientific understanding of any of it if all you know is what you got from TV shows.

[vv3k70r]

49 minutes ago, K^2 said:

First of all, check your units. Nm/s is Watts - units of power. Units of momentum are same as these of impulse - Ns. It's an integral of force over time.

Time is still zero whatever You transform the unit.

54 minutes ago, K^2 said:

More crucially, we aren't discussing high school kinematics.

Yes we are. Time dilation stated in topic came from idea of ever accelerating vessel powered by energy it cannot carry. It is one of the story about relativity they teach them in school.

[K^2]

12 minutes ago, vv3k70r said:

Time dilation stated in topic came from idea of ever accelerating vessel powered by energy it cannot carry. It is one of the story about relativity they teach them in school.

I recommend you study this article on proper acceleration to get you started. And while I do not expect you to follow all of the math, it comes with this nice graphic. This is for a 1g torch ship, which is far more extreme than anything discussed in this topic, and it quotes the energy you actually need to reach nearby stars at relativistic speeds, which are very reasonable amounts. Feel free to provide your own mathematical derivation if you disagree with any part of this.