At a constant 1G acceleration it takes a little less than a year to reach near light speed speeds. Time would dilate locally on the ship slowing time for them. Could the time dilation be pushed to 12 times faster than normal time, so 1 light year of travel is only 1 month of local spaceship time? If possible, A star 10 light years away would only take 2 years 9 months to reach from the spaceships perspective. 1 year to accelerate, 9 months in dilation, 1 year to decelerate. It would of course still take 11 normal year to reach.
The closer you get the the speed of light a kind of drag effects the ship stopping it from getting faster and reaching the speed of light, so only so much speed and time dilation is possible with a limited amount of thrusting power. What would be the time dilation for a space craft with 1G thrusting power going max speed? If the engines were turned off at fastest possible speed, would that dragging force slow the ship down or lessen the time dilation or would it coast at the same speed and dilation to save fuel? If the engines were still on, pushing with 1G but the ship was at max possible speed, would the crew still feel the 1G on the ship even if it is not accelerating anymore?
Would the ship measuring the distance to it's destination at 12 times dilation seem like it is traveling 12 times faster then the speed of light from the ships perspective?
Could you go fast enough that the dilation would be 52 times normal so 1 week a light year? or 365 times for 1 day a light year? Is there a limit to the time dilation? do we need faster then light tech to explore space at all? Sure it would take a really long time out side the ship in real time, but to the people on the ship it would be doable.