Relativistic calculations

That's very cool but way over my head ;-)

...being one of those individuals who still counts on their fingers!

This is over my head but also eminently useful for my WIP. Can I assume your Bobbiverse eschews FTL travel?

Without derailing your thread, I would love to hear more about propulsion methods.

I'm calling mine a good 'ol metric drive, sometimes referred to as an Inheritor Drive. Is the SURGE front-mounted, or at the back?

So that's Bob, huh?



I'm gonna keep these formulas on hand & thank you again. I've been hitting the same roadblock with trying to figure out some relativistic timeframes. This much math is kind of panic-inducing to me, fortunately I only have get to a broad estimate.

I tend to keep to the level of Terry Pratchett's troll arithmetic: One, two, three, many. Ultimately, lots.

caw

Would work great as a calculator. (Project Rho might have done one already, they've got all sorts of good resources.)

http://www.orionsarm.com/fm_store/RTTCalc.htm

http://convertalot.com/relativistic_star_ship_calculator.html

http://nathangeffen.webfactional.com/spacetravel/spacetravel.php

There are others, don't ask me how well they work because I'm about as well-versed in actual science as the Insane Clown Posse.

Nice set of equations, but there's more worth adding. Let's define alpha as acceleration in gees. So if alpha=1, the passengers on the spaceship will feel an effective gravity like on Earth.

Measuring T in years, the ratio of the payload to the spacecraft's total initial mass will be
R = exp[1.03*alpha*T*c/ve]
where ve is the speed of the rocket exhaust relative to the spacecraft itself. In order to get a reasonable R, you'll need a ve that's a substantial fraction of c. Even then, R is liable to get quite large. The vast majority of the initial mass will have to consist of fuel.

It will be a bit more efficient if, instead of having constant acceleration, the spacecraft has periods of hard acceleration at the beginning and hard deceleration at the end, with a longer period of coasting in between. On the assumption that the periods of acceleration and deceleration have equal subjective time, I've derived an equation for T. It's pretty complicated, so I won't try to post it here. But I find that if ve=0.5c and R is 400 (which is about the most I could believe in for a spacecraft with any significant number of passengers),
T = 0.47D + 1.15T_1
where D is the distance to the destination in light-years and T_1 is the subjective time in the initial acceleration period, measured in years. During the acceleration and deceleration, the effective gravity as felt on board will be
alpha = 1.5*0.97/T_1

Incidentally, the factors of 1.03 and 0.97 pop up because the gravitational acceleration felt at the surface of the Earth, g=9.8 m/s2, is 1.03 light-years per year squared.