This is a very popular question!
The conventional logic of past sci-fi authors who have written about trips to Alpha Centauri in various ways has been that you can go at 10% light-speed as an absolute minimum. Since Alpha Centauri is only 4.3 light years away, you get there in 43 years. It's as simple as that, end of story.
Now, my concept is based on a vastly different timescale of 50,000 years

for no simpler reason than the fact that this ark happens to be a gargantuan, super-heavy, super tanker.
Please see this thread:-
Escape time lines for my interstellar ark The 50,000 year long voyage duration I am projecting is what I like to call a "least-propulsive energy requirement versus most-safe, optimisation". If the ark moves much slower and it takes any longer than this order of timescale, you can see that Alpha Centauri will soon start to drift out of range, and the vehicle will be playing 'catch up' with its destination. If it speeds much faster, and aims to reach Alpha Centauri in say just 5,000 or 10,000 years from now, then the craft will need a lot more propulsive energy on its way out of our Solar System, suffer major impacts from any Oort cloud bodies encountered en-route and also require excessive delta-v at the other end in order to slow right down and successfully rendezvous with New Earth.
Alpha Centauri is 4.3 light years away from the Earth and our Solar System. Light travels at a speed of 186,282 miles per second, or about 5.9 trillion miles in one year. This means in normal every day distance measure, Alpha Centauri is roughly 25.3 trillion miles away from us.
The Centauri Princess ark has spent several decades within our own Solar System, doing a series of
speed-gaining maneouvers to achieve a final Sun-relative escape velocity of circa 60,000 miles per hour:-

At that speed it will take just under 50,000 years to cross the 25.3 trillion miles of interstellar space to reach New Earth at Alpha Centauri. Simple arithmetic!
Let us compare my concept with a couple of others. In Sid Meier's Alpha Centauri strategy games series, a ship called the Unity reaches Alpha Centauri in just 40 years

In Mary Doria Russel's world renowned novel 'The Sparrow' another fantasy ship gets to a planet called Rakhat at Alpha Centauri in just 17 years

Well, I certainly wont be stopping anybody if they want to bypass my interstellar ark and settle on New Earth at their faster-invented speeds,
if they can demonstrate how they will slow down at the other end. "... If you have the power to pass beyond the zones of the heavens and the earth, then pass beyond them! But you will never be able to pass them, except with authority (from God)!" - Qur'an (55:33) Mine's is a massive 200-trillion kilogramme vehicle that is going to accelerate using planetary gravity-assisted slingshots from our Solar System and decelerate using similar means at the destination. The world's *first* blueprint for the safest way that humanity will eventually reach another Solar System beyond our own...
At first glance, people are quick to point out: "Oh, but our technology would improve vastly in the future... we'll find newer and faster ways...". Yes I accept that we'll have improved technology in the future, there's no question about it, but my argument is that the fundamental laws of nature, the physical distances and the dynamical constraints will never ever alter. Not now, not in a thousand years from now.
One study concluded that a solar sail craft of (249 foot by 249 foot) could theoretically propel a tiny 3-kg probe to the stars in... wait for it.... 100,000 years!
It seems to me that the
only way humanity will ever hope to bridge the gulf to the stars is via a multi-generational mission concept of this type. The
asteroid belt is there to provide material for us to utilise to build our interstellar arks and the two primary suns of Alpha Centauri are there to serve as our first stop destination. Human interstellar travel is no longer a fantasy-filled dream! "Warp drives" from Star Trek may never happen in the real world...
Abdul Ahad