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Comment by ubermonkey | Hacker News Reader

Check my thinking here, from a lay perspective:

So the fastest way to point B in space (Mars, Europa, whatever) would be to accelerate constantly until you're halfway there, and then flip around and start slowing down, right?

OTOH, a more efficient approach is to achieve some velocity V via an initial burn and/or gravity assist, and cruise along via Newton with no additional burn until time to slow down and drop into orbit at your destination.

I further assume that, if you live passengers you'd prefer not to render into soup, you must labor under an acceleration limit.

Realistically, what IS that limit? And would would the acceleration plan look like for a long flight like Mars with people aboard?

Lots of hard-ish SF (notably the Expanse) handwaves this away with drugs or whatever, which is fine for storytelling, but I'm sort of curious what we could actually tolerate.

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You're describing a brachistochrone trajectory. The "magic" in sci-fi isn't the drugs, it's rocket engines that are actually that efficient. If you accelerate/decel at a sustained 1 g, you can make it to Mars in about 2 days.

> If you accelerate/decel at a sustained 1 g, you can make it to Mars in about 2 days.

This is the key calculation where you realize that quick inter-planetary travel is totally within the realm of physics.

> Using Days and AU (astronomical units) we can see 3 days will get about 2.5 AU (halfway to Jupiter). 4.5 days will get you 5 AU (halfway to Saturn). 9 days will get you 20 AU (more than halfway to the Kuiper belt)

Obviously inter-stellar travel seems like a totally different matter, but actually at 1g constant acceleration it works out to about “1 year + the number of light years” to an outside observer. Less time passes for the traveler.

Invent an engine efficient enough to allow constant 1g acceleration for years at a time and humans really could become interstellar.

The best ion engines get around 200,000 Isp. If you had a 500t ship burning 1t of mass per day, you would need an Isp of ~4.5m to achieve 1g over that first day (it gets easier as you get lighter).

The theoretical limit (ejecting mass out the back at 1c) for specific impulse is 300 million.

https://space.stackexchange.com/questions/840/how-fast-will-...

At first I was like: Nah, it can't be right...

High-school math, napkin, and 5 minutes later: Wow, it's only 42 hours!

Thanks for providing that term. I did not know it.

I'm surprised to learn that Mars is (or can be) so "close" in terms of a sustained 1g acceleration.

We just need to work some more on the dark matter repulsion drive, or the parallel universe reaction mass extraction drive. Or, the "belch of god". Still figuring out what the belch or the god part of that one actually are.

Or you fire off refueling packs ahead of the trip.

Continuous acceleration on the order of 1G is solidly in the realm of fiction today (see: The Expanse series). The actual engines we have today capable of continuous thrust for weeks at a time only produce less than a Newton of thrust. The practical approach is starved for both energy and propellant to achieve such levels of acceleration.

We don't have good data for long term high G tolerance, but estimates I've seen are usually around 1.5 G maximum. However, engine efficiency usually comes at the expense of thrust; there are few theoretical designs even that could provide 1.5 G for the amount of time needed to get to Mars.

For this engine, for example, the specific impulse is twice that of a chemical rocket - so around 800. At an acceleration of 1.5 G, this engine could only run for around forty minutes before exhausting all the fuel in the vessel.

So we are not yet at the technology level necessary for Brachistochrone trajectories (accelerate halfway there, flip over, decelerate the rest of the way); this would merely allow for a shorter Newtonian transfer orbit.

Hard to say with the G limit. Fighter pilots routinely tolerate 9 Gs with training and pressure suits (or more, for very short periods of time). That's extreme, but if you're strapped on your back, the Gs don't pull blood down out of your skull as much (but you also don't want to send too much pressure IN to the head). I think for a while at least, one can assume astronauts are comparable in physical shape and training to elite pilots. Previous spacecraft and roller coasters routinely do around half that. If the required acceleration would take a very long time, even at 9 Gs, you'd need to lessen the force.

Edit: Some back of the napkin math: It's It's between 30 and 250 million miles to Mars. Let's call it 100 million on average. And let's say we want to make the trip in about 3 months. That means we need about 20km/s of velocity, and at 9Gs that only takes you around 4 minutes. I would probably lower the acceleration and just stretch it out longer. The bigger acceleration might be needing to match Mars's velocity once you get there. But I think those are all pretty reasonable numbers for humans to tolerate. The really hard problem is still the landing, rendezvous, and launching a spacecraft big enough to do all that and then come back.

When we say "something accelerates" what we mean is "its velocity increases over time". Its acceleration could also increase over time, but that is not a requirement. When you ask "what is the acceleration limit" it seems like you are not clear on that fact. The velocity of the rocket relative to the Sun could be increasing for the first half of the journey, while its acceleration (or deceleration, on the second half) could remain constant. At 9.8 m/s² the crew would cruise at a comfortable 1G.

But let's consider that the acceleration increases over time. The maximum number of Gs the human body can withstand has been studied in astronauts and fighter pilots. They can withstand 8 or 9 Gs for some time with special training and compressive clothing. That puts the biggest acceleration at about 99.8 = 88 m/s², but this would have to be done in bursts, with special clothing and training. The maximum acceleration for being able to perform regular human tasks like walking or taking readings would be much less however. I don't have figures for that, but I think the risk of accidental bone fracture increases dramatically when we go above our specs. 2Gs would already be too much.

All these questions are kind of moot for now because with the fuels we currently have we can only sustain acceleration for a very limited amount of time.

I also want to point out that the fastest point from A to B in space must* take into account that space is not always empty. A third object C can be used to give a "gravitational assist" to a spacecraft. Or its influence might have to be counteracted by spending extra fuel (making an alternative to the straight line between A and B preferable).

What I meant was "what sustained acceleration could humans tolerate? Others have answered that question, and also provided the surprising (to me, at least) bit of data that a 1G constant acceleration -- currently not remotely possible -- would put the entire solar system within easy reach.

And yes, I understand about gravity assists and the like.

High accelerations require bigger heavier engines, or more engines, so they chew through fuel quickly. Essentially your trading away some of your payload for the luxury of burning your engines for a shorter period.

Burning your engines continuously during a long journey isn’t practical with most of our propulsion technologies as they can’t carry enough fuel for that long a burn. The exceptions are mostly electric propulsion systems such as Hall Thrusters, which are very low thrust and aren’t useful for quick transits.

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