# Thread: Constant Acceleration at 1G and Beyond

1. Established Member
Join Date
Feb 2011
Posts
487

## Constant Acceleration at 1G and Beyond

Exactly what kind of technological leap and how much energy would be needed to accelerate/decelerate at 1g on a trip to another star system? I understand that, barring wormholes, constant 1g acceleration is the only way to achieve relativistic effects and get a spacecraft across significant distances in a human lifetime as measured aboard the spacecraft.

2. Banned
Join Date
Dec 2004
Posts
14,782
There should be online calculators that will allow you to input
one or more of the following, and then calculate the others:

- Distance you want to go

- Acceleration

- Maximum speed

- Time for the voyage by your clock

- Specific impulse of your engines

- Propellant mass

- Structural mass

For specific impulse, you would probably choose one of
a few different propulsion options.

Many combinations of inputs aren't possible. You could
not specify a large distance, large payload and short trip
time but a small propellant mass, for example.

I'm hoping that someone will know of and link to such a
calculator. Or make one.

With such a calculator you will be able to see how much
propellant is required to move a given payload a given
distance in a given time.

Somehow you should also have a choice of whether to
accelerate continuously (for shortest time) or just at the
start (and optionally end, if you don't want to just whizz
past the destination) of your trip, to minimize propellant
mass and save wear on the engines.

The amount of propellant required, the duration of engine
operation, and the duration of the trip as a whole should
give pretty good indications of what technological leaps
are needed.

-- Jeff, in Minneapolis

3. Exactly what kind of technological leap and how much energy would be needed to accelerate/decelerate at 1g on a trip to another star system?
Just using Newtonian math to keep it simple, let's imagine that you want to get something about twice the mass of the ISS (on the small side for interstellar flight, but lets start there), so 1 million kilograms to accelerate at 1G (10 meters/second(squared)) for 30 years (a billion seconds).

F=ma so the Force required is 106 * 10 Newtons.
Distance in the first second is 5 meters
Energy per second = FD = 50,000,000 Joules per second.
Energy stored for the whole trip: 5x1016 Joules.
This is roughly the amount of energy stored in a kilogram of antimatter.

Currently we can store about one atom of antimatter, so we need to improve that by a factor of 1027.
We also need to create a process for efficiently converting antimatter energy into acceleration, preferably using as little reaction mass as possible. Failing that we might need to increase the mass of the ship by six to ten orders of magnitude, so as to have a less dense method of storing energy and converting it to accelerating your vessel.

So, I can't say exactly what kind of technical leap we'd need, because we are so far from it that no clarity is really possible.

4. Established Member
Join Date
Sep 2005
Posts
1,679
You'd definitely need a new form of propulsion; no chemical rocket has burned for more than about 10 minutes.

5. Banned
Join Date
Dec 2004
Posts
14,782
Originally Posted by antoniseb
Just using Newtonian math to keep it simple, let's
imagine that you want to get something about twice
the mass of the ISS (on the small side for interstellar
flight, but lets start there), so 1 million kilograms to
accelerate at 1G (10 meters/second(squared)) for
30 years (a billion seconds).
That's an awfully long time. Just one year at 1 g will
get you close to the speed of light. When relativistic
time dilation is taken into account, 30 years should
permit travel to distances of hundreds of light-years.

Originally Posted by antoniseb
F=ma so the Force required is 106 * 10 Newtons.
Distance in the first second is 5 meters
Energy per second = FD = 50,000,000 Joules per second.
Energy stored for the whole trip: 5x1016 Joules.
This is roughly the amount of energy stored in a kilogram
of antimatter.
Wow! That's several orders of magnitude less than I
would have guessed! Starts out sounding pretty good!

Originally Posted by antoniseb
Currently we can store about one atom of antimatter, so
we need to improve that by a factor of 1027.
I have no idea how it might be done, but I'm a little bit
optimistic that a way can be found to do that.

Originally Posted by antoniseb
We also need to create a process for efficiently converting
antimatter energy into acceleration, preferably using as
little reaction mass as possible.
The problem is that mixing antimatter and ordinary matter
produces gamma rays, which go right through everything.
You want a gamma-ray mirror. Neutronium, maybe? I'm
not optimistic about that at all. Something to absorb the
gamma rays and turn them into heat? Lots of mass for all
known materials. Lots of shielding for the payload. Huge
problem to solve.

-- Jeff, in Minneapolis

6. You might try pre-positioning fuel on route to reduce ship mass.

7. Originally Posted by Ara Pacis
You might try pre-positioning fuel on route to reduce ship mass.
How do you propose delivering the fuel to those pre-positioning stations?

8. Originally Posted by Hornblower
How do you propose delivering the fuel to those pre-positioning stations?
Not only that, but how do you rendezvous with them to refuel without slowing down?

9. Originally Posted by Hornblower
How do you propose delivering the fuel to those pre-positioning stations?
Originally Posted by NEOWatcher
Not only that, but how do you rendezvous with them to refuel without slowing down?
Seriously guys? How do you think?

10. Banned
Join Date
Dec 2004
Posts
14,782
Have them placed there, moving in the right directions, at
the right speeds, by friendly alien time-travellers. Obviously.

If God wanted man to travel to the stars, He would have
surrounded us with friendly space aliens. With fuel tanks.

-- Jeff, in Minneapolis

11. Originally Posted by Ara Pacis
Seriously guys? How do you think?
I was being serious. I don't see the advantage.

Getting the fuel there, and then up to speed to match your craft, or slowing down the craft to pick them up is going to use nearly the same fuel since the weight requirements of such a craft is going to be almost all fuel anyway.

The only way you can be ahead is if those fuel depots collected fuel from local sources after they got in position.

12. Originally Posted by NEOWatcher
I was being serious. I don't see the advantage.

Getting the fuel there, and then up to speed to match your craft, or slowing down the craft to pick them up is going to use nearly the same fuel since the weight requirements of such a craft is going to be almost all fuel anyway.
Sure, but that depends on what propulsion method you're using.

The only way you can be ahead is if those fuel depots collected fuel from local sources after they got in position.
By "ahead", do you mean efficiency or position?

13. Banned
Join Date
Dec 2004
Posts
14,782
He means efficiency. The reason you gave for "pre-positioning"
fuel along the route was to reduce ship mass. It might reduce
the mass of that ship, but at the cost of requiring additional
ships with a far larger total mass. Getting them to rendezvous
without slowing the ship whose mass you are trying to reduce
would be at the expense of sending the fuel out ahead of time,
slowing it down, and speeding it back up again for rendezvous.
Wasteful, pointless, and kinda goofy.

-- Jeff, in Minneapolis

14. Is anyone including the resistance from plowing through the interstellar medium?

15. Originally Posted by Jeff Root
That's an awfully long time. Just one year at 1 g will
get you close to the speed of light. When relativistic
time dilation is taken into account, 30 years should
permit travel to distances of hundreds of light-years.
1g for 1 year is 3% more than the speed of light ( (acceleration of gravity)*(1 year) at wolframalpha.com ), and since the ship can not exceed light speed, the occupants may feel 1g, but their acceleration relative to the universe would be less, right?

16. Banned
Join Date
Dec 2004
Posts
14,782
The radiation would be terrible at really high speeds.
Aside from that, and maybe running into a few rocks,
the interstellar medium shouldn't be significant.

No forward-looking windows. Just cameras that can be
poked out the side when you want to see what's ahead.

-- Jeff, in Minneapolis

17. Banned
Join Date
Dec 2004
Posts
14,782
grapes,

I don't think I've ever calculated a relativistic acceleration
in anyone's frame but that of the one accelerating. It must
depend on how you define "acceleration". A change in speed,
or force per unit mass. Although continuing to accelerate
doesn't increase speed much relative to outside observers,
in addition to providing artificial gravity for passengers, it
gets them to their destination a lot faster by their clocks.
So I think it would be worth it if you can afford it, and can
deal with relativistic collisions.

-- Jeff, in Minneapolis

18. Banned
Join Date
Dec 2004
Posts
14,782
Some fraction of all starships moving at near-light speeds
must be totalled when they run into an object comparable
in size to the front bumper. I hope it's a small fraction.

-- Jeff, in Minneapolis

19. Originally Posted by grapes
1g for 1 year is 3% more than the speed of light ( (acceleration of gravity)*(1 year) at wolframalpha.com ), and since the ship can not exceed light speed, the occupants may feel 1g, but their acceleration relative to the universe would be less, right?
Originally Posted by Jeff Root
I don't think I've ever calculated a relativistic acceleration
in anyone's frame but that of the one accelerating.
Yes; it gets complicated considering the frames of reference. A linear calculation based on 9.8m/s2 just doesn't do it.
As the traveler is accelerating, their 1g is not our measurement of what we would see as their 1g. Our view of their 1g becomes less and less over time because of length contraction.

I have no clue how to compute this, but I know its not t=c/g.

20. Order of Kilopi
Join Date
Jan 2010
Posts
5,065
Originally Posted by NEOWatcher
I have no clue how to compute this, but I know its not t=c/g.
Use relativistic kinetic energy (c=1), so given a certain amount of energy expended to accelerate the craft its velocity will be

21. Order of Kilopi
Join Date
Jan 2010
Posts
5,065
But if you're using constant acceleration you can simplify a little, such as given here. That link also includes some example calculations for accelerating constantly at 1g.

22. Originally Posted by caveman1917
But if you're using constant acceleration you can simplify a little, such as given here. That link also includes some example calculations for accelerating constantly at 1g.
Thanks for the link. It helps to see it when someone else does the math and gives several values along the way (particularly that first table)

23. Originally Posted by cjackson
Exactly what kind of technological leap and how much energy would be needed to accelerate/decelerate at 1g on a trip to another star system? I understand that, barring wormholes, constant 1g acceleration is the only way to achieve relativistic effects and get a spacecraft across significant distances in a human lifetime as measured aboard the spacecraft.
First off, a human lifetime interstellar journey is possible with "only" a fraction of c. The Alpha Centauri system is arguably the most interesting star system to visit in our neck of the woods, and it is conveniently also the closest. At "only" 0.09c, it would take less than 50 years to reach. That's less than a human lifetime.

My usual assumptions for a manned interstellar mission include a return journey, so I look for a baseline mission of .30c going there (about 1.5 decades), 1 decade of study in situ, and then .25c returning (about 2 decades). That's a total of 4.5 decades, a good scientific career for someone in their early 30s to retire in their late 70s.

To reach .30c, with an acceleration of 10m/s/s, would only take around 3.5 months.

So basically, constant acceleration is not necessary. Even so, 1gee acceleration for 3.5 months is an extreme technical challenge. No existing propulsion systems can come within orders of magnitude of doing it. The only method demonstrated in the lab which could do it is microwave sail propulsion (demonstrated multi-gee acceleration of decimeter scale sail by James Benford).

One method which I used to like is "bombtrack" propulsion, which uses nuclear bombs to push against the magnetic field of a large superconducting magnetic loop. This is similar to the Mag-Orion concept, except that these bombs are not carried by the starship. Instead, they are pre-positioned drones that form a "track". The bombs detonate as the starship passes by--the starship consists of the magnetic loop along with payload modules strung on the loop like beads on a necklace.

There are numerous problems with the bombtrack proposal, which I won't detail. The key concept, though, that is relevant to questions in this thread is that you do not have to pick up "fuel" along the way. Rather than rendezvous with fuel supplies, you merely interact with them in passing.

In fact, the methods of interstellar propulsion I favor now use the high relative speed between the "supplies" and the starship as the entire source of energy. The sheer violence of relativistic kinetic impacts is so great that they exceed the energy density of nuclear bombs (with no annoying neutron radiation or minimum critical mass requirements!). Rather than try to pick up an incoming relativistic "fuel" packet, the starship merely puffs a bit of on board propellant, which instantly explodes upon impact with the "fuel" packet. This explosion of charged particles is deflected by the mag-loop's magnetic field, producing thrust.

This relativistic kinetic impact powered rocket/ramjet is, I think, the most practical method of achieving the sorts of sustained accelerations you're asking about.

24. Order of Kilopi
Join Date
Jan 2010
Posts
5,065
Originally Posted by IsaacKuo
There are numerous problems with the bombtrack proposal, which I won't detail. The key concept, though, that is relevant to questions in this thread is that you do not have to pick up "fuel" along the way. Rather than rendezvous with fuel supplies, you merely interact with them in passing.
Does that make much of a difference? If the bomb is just sitting there and you pass by at a decent fraction of c then the energy imparted on the ship by the bomb will be significantly lowered. This also requires energy for the bombs to slow down again when they reach their destination, so it looks like a double loss to have them stationary waiting on a track.

25. Originally Posted by IsaacKuo
That's a total of 4.5 decades, a good scientific career for someone in their early 30s to retire in their late 70s.
I would worry about someones health in a mission that long. It would take a boatload of "in case" medical supplies, or a boatload of spare researchers as a risk mitigation plan.

Originally Posted by IsaacKuo
There are numerous problems with the bombtrack proposal, which I won't detail.
The biggest I see is the nearly instantaneous accelerations. That's high g impacts and a lot of them.

Originally Posted by caveman1917
Does that make much of a difference? If the bomb is just sitting there and you pass by at a decent fraction of c then the energy imparted on the ship by the bomb will be significantly lowered.
It's better than nothing.

Originally Posted by caveman1917
This also requires energy for the bombs to slow down again when they reach their destination, so it looks like a double loss to have them stationary waiting on a track.
Or, if they were sent out long before the craft, then we have the bombs at a closer speed and no need to slow down.

But; how long would it take to put this "infrastructure" in place. Without a relativistic way to place the bombs, you're wait for setup seems to be as long as a non-relativistic trip would be in the first place.
It just gains you less "man-time" in space.

26. Order of Kilopi
Join Date
Jan 2010
Posts
5,065
Originally Posted by NEOWatcher
Or, if they were sent out long before the craft, then we have the bombs at a closer speed and no need to slow down.
Yes, that was my point, if you're going to do it with bombs prelaunched then it seems to be a lot better to keep them at top speed. The more i think about it, the more the idea of having the bombs slow down again and being stationary for when the ship passes seems like a huge efficiency loss.

27. Originally Posted by caveman1917
Does that make much of a difference? If the bomb is just sitting there and you pass by at a decent fraction of c then the energy imparted on the ship by the bomb will be significantly lowered.
It is indeed lowered--there is no free lunch--but that's simply part of the design. The key requirement for "bombtrack" propulsion is that some useful fraction of the bomb's charged particle products are moving fast enough to usefully push against the starship's magnetic field.
This also requires energy for the bombs to slow down again when they reach their destination, so it looks like a double loss to have them stationary waiting on a track.
No, there is no requirement to slow down the bombs at all. The track can be moving at whatever speed was suitable for deployment. For example, you might use high performance solar sails for track deployment, resulting in bomb units heading away from the Sun at 100km/s. This speed is far too slow for interstellar travel, but it's fast enough to deploy the bomb track in a reasonable length of time. The bomb units never brake at all...they just keep on coasting away from the Sun at 100km/s until detonated.

28. Originally Posted by NEOWatcher
But; how long would it take to put this "infrastructure" in place. Without a relativistic way to place the bombs, you're wait for setup seems to be as long as a non-relativistic trip would be in the first place.
It just gains you less "man-time" in space.
For the initial acceleration track, relativistic deployment is not required. An acceleration run of 3.5 months up to .3c requires an acceleration track only a few light weeks long.

For the deceleration track, things get more complicated to explain.

Maybe the simplest way to explain it would be to have the starship itself hold the deceleration bombtrack as cargo. Shortly after completing the acceleration run, the starship starts spitting out bomb drones behind it. This is not simply a matter of tossing them overboard; there is no drag in space. Rather, the bombs themselves have thrusters and/or a mass driver is used to impart a relative velocity. The goal is to deploy a bombtrack behind the starship, so that it reaches the desired length when the starship arrives at Alpha Centauri.

Then, when Alpha Centauri is reached, the starship uses this bombtrack to decelerate. In the frame of reference of Alpha Centauri, the starship and bombtrack both starts off moving at .3c; the starship slows down as the bombtrack screams onward at .3c. In the frame of reference of the bombtrack, the starship starts off moving at 0c and it accelerates up to .3c.

This balloons the mass requirements of the initial starship geometrically. But the mass growth is still only quadratic, which can be a win against the rocket equation. The rocket equation's mass growth is exponential.

29. Originally Posted by IsaacKuo
For the initial acceleration track, relativistic deployment is not required. An acceleration run of 3.5 months up to .3c requires an acceleration track only a few light weeks long.
Which means that the farthest one will take over 150 years to be in place for your ship (assuming 20 light days long) at 100km/s.

Originally Posted by IsaacKuo
Maybe the simplest way to explain it would be to have the starship itself hold the deceleration bombtrack as cargo. Shortly after completing the acceleration run, the starship starts spitting out bomb drones behind it.
That's pretty much the same as carrying all the fuel you need to decelerate.

30. Originally Posted by Jeff Root
He means efficiency. The reason you gave for "pre-positioning"
fuel along the route was to reduce ship mass. It might reduce
the mass of that ship, but at the cost of requiring additional
ships with a far larger total mass. Getting them to rendezvous
without slowing the ship whose mass you are trying to reduce
would be at the expense of sending the fuel out ahead of time,
slowing it down, and speeding it back up again for rendezvous.
Wasteful, pointless, and kinda goofy.

-- Jeff, in Minneapolis
Yes, it is less efficient, but that can't be helped, not if you want to complete a realistic mission in a suitable amount of time. The key is to establish an infrastructure that does a lot of the heavy lifting. And then, use non-chemical propulsion systems where you can, in order to reduce mass. See Isaac Kuo's posts in this thread for something close to what I'm thinking.

The bomblets (and other pods, possibly reactor fuel or food containers) in advance of the vehicle are accelerated by an extending laser relay station track. These laser relay stations push the bomblets and other pods to higher speeds along the track. The laser station also push each other, and then are pushed by some of the impactors and bomblets. The vehicle itself has a propulsion laser to help increase the speed of the bomblets to match velocity and position for capturing. However, yes, at some point the vehicle may over take them. The trajectories are design such that the reduction of speed from maneuvering/capturing those bomblets is towards the part of the mission where the ship is intended to decelerate. After using them for momentum transfer, the vehicle uses them for pulse propulsion to decelerate into the target star system. Then, the vehicle may loop around the target star and then interact with the follow-on impactors to further reduce its speed. The pulse system might use a pusher plate or a magnetic system, whichever is most efficient.

The initial launch might be a combination of solar sail dive, laser sail or magnetic sail, whatever works best for the laser station and bomblets and pods. The vehicle is launched later, years, perhaps decades later. Depending on mass and efficiency, it might make a solar dive and perform an Oberth maneuver as close to the sun as possible. It may use drop-off boosters/tanks using a short duration high thrust fuel (NSWR or similar) then it might drop those and switch to an electric drive. It might use solar/laser sails or mag sails too at some point, depending on efficiency. At some point it may also use pulse propulsion from inert object impacts caused by objects that take solar dives and receive propulsion from lasers and/or from objects that are fires from electromagnetic catapults. These pulse propulsion events may be periodic depending on infrastructure, at which point it switches back to electric drive (unless it didn't need to turn it off). Eventually, the vehicle's speed will be close enough to that of the impactors that it's no longer advantageous, at which point it may switch to the bomblets that were with it at launch. The vehicle uses these and then coasts until it gets to the point where it starts picking up more and prepares for deceleration (which might take years or decades).

I have to give Isaac Kuo props for a lot of this, from previous threads.
Last edited by Ara Pacis; 2014-Jun-12 at 06:49 PM.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•