Offcentre thrust, spinning spaceship

[B.E.M]

This isn't really an aerospace problem, just basic physics. Been thinking about hardSF spaceship designs. Could someone comment on my logic and maths?

The basic plan has a nuclear powerplant and a habitable section connected by a long tether. the whole contraption spins to provide cetrifugal artificial gravity and the length of the tether provides radiation protection.

The direction of thrust is the same as the axis of rotation.

Originally I had an ion drive at the centre of mass, but more recently I've preferred the idea of a nuclear thermal engine. However for a nuclear thermal engine, the thrust would come from the power plant, not the center of mass.

This seems ok to me(although bizarre) because the engine is only meant to give a weak thrust compared to gravity. Think of spinning a frisbee on your finger. The force will average out over a full rotation. The only effect will be to change the angle of the tether slightly off 90 degrees to the direction of travel, against the restoring force from the spin.

Suppose we assume the power plant and habitable sections are both the same mass, so both are under 1g force, and we decide we only want to allow 1 degree twisting. I think the restoring force (as a fraction of the centrifugal force) is very nearly sine(1 degree) or 0.017, implying the engine could provide almost 2% of 1g acceleration and change the tether angle by only 1 degree. Thats plenty for travel within the solar system if we could maintain it for long periods.

In conclusion, an off center thrust is perfectly reasonable for my spinning interplanetary craft.

 

[DaveC426913]

It seems to me you're ignoring some critical factors, but I'm no engineer.

1] The moment you start up your drive, the craft is going to tilt out of the line of travel. It will pivot, not merely around the axis of rotation, but around the centre of mass, thus pointing the drive out of your line of desired travel.

2] Is the tether rigid? You are applying stresses to it on its weakest axis. Why wouldn't it just fold?

 

[technobot]

Assuming he starts up the rotation before he fires the engine, the centifugal force would keep the tether rigid even if it is flexible by default. And then when he does fire the engine, the thrust should distribute evenly around the center of rotation, giving a net forward thrust. Admittedly though, I'm not so sure about that second part - but it sounds reasonable to me..

 

[DaveC426913]

Assuming he starts up the rotation before he fires the engine, the centifugal force would keep the tether rigid even if it is flexible by default.

I'm not concerned about its rigidity lengthwise, I'm concerned about its rigidity crosswise. The moment he fires up the rocket, spinning or no, bending forces are put on the tether.

Ever tried to see how long you can extend a tape measure without it collapsing?

 

[technobot]

The moment he fires up the rocket, spinning or no, bending forces are put on the tether.

True, but the point is that the centrifugal force would resist that bending. Because the moment the tether bends a bit, the centrifugal force is no longer completely aligned with the tether, so you get a component that acts to straighten the tether back. Not to mention that with the centifugal force pulling at the edges, the tether will try to be as straight as it can be (to keep the edges as far apart as possible). So instead of a bend, you'll get a tilt. At least that's how I understand the problem...

What may happen though, is that instead of a net forward thrust, you'd get a complex rotation around the center of mass. But here someone else would need to step into clear this up for us.

 

[Danger]

I think that I'm going to have to just do up a diagram or 3 to visualize what's going on. If I understand the concept correctly, I can't see it possibly working. Even if the modules were connected with a rigid tube rather than a tether, the whole thing would just start pinwheeling. There's also the gyroscopic effect. Thrust from one point of the 'rim' of the assembly would cause precession.
On the other hand, 2 balanced modules on the ends of a rigid tube would work just fine with the engine mounted half-way between them. I need a couple days to think on this.

 

[DaveC426913]

So instead of a bend, you'll get a tilt...What may happen though, is that instead of a net forward thrust, you'd get a complex rotation around the center of mass.

This is what I was saying would be the net result, yes.



Me, I'm thinknig there should be a way to simulate this in a scale model.

2 balanced modules on the ends of a rigid tube would work just fine with the engine mounted half-way between them.

It would, but that is a complete corruption of the OP's design. Also, you've got an extra mass and nothing to do with it. Cold storage? Pantry?

 

[Danger]

Septic tank.
Hey, it's a long trip...

 

[B.E.M]

I have attached a beautiful diagram to explain the set up :)

Even if I can convince you it works, I might go for a different design simply because if everybodies first gut reaction is 'thats silly!'.. it sort of breaks the illusion. Personally I like the bizarro aspect. It says to me "Here is a ship design that must be practical.. because it obviously doesn't give a damn about asthetics!" ;)

 

[B.E.M]

Another way of looking at this is to consider that trick where someone spins a plate on the top of a stick.. I am pretty sure I have seen them 'spin up' the plate some more by twirling the stick a bit, ie moving its end in a small circle that is slightly offcenter to the plate, but the plate is kept horisontal by its spin.

Btw, I've considered that other configuration. having the engine in the middle is certainly more intuitive. It has however halved the distance to the habitable section and halved the mass we could have placed between the engine and the habitable section. And yes there is the question of what we want to keep even further from the crew than an unsheilded overpowered fission reactor. Their Inlaws, perhaps? :)

If I decide I need the engine in the center, Ill probably go back to the iondrive idea instead of the nuclearthermal engine. Then the powerplant could still be as far as possible from the habitable section with the drive inbetween, helping to block the radiation. Ion drive just doesn't feel as grunty though. Also the engine would need more radiators I expect. To get lots of energy you don't just need lots of heat, you need a large temperature difference. I expect a nuclearthermal engine can lose a lot of its heat directly through its exhaust.

 

[BobG]

The concept is correct. In fact, that's why spacecraft are usually spinning when they fire the booster to go from a parking orbit to a transfer orbit and a tansfer orbit to a drift or final orbit. The torque created by an unbalanced thrust (and it's not possible to get a perfectly balanced thrust) is canceled out one half rotation later.

You overlooked one important point. When you fire a rocket, part of the thrust is usually applied to moving the center of mass and part of the thrust creates torque. How much is applied to each type of motion depends on the location of the thruster. If the thruster is perfectly aligned with the center of mass along the axis you're aiming for, all of the thrust is applied to moving the spacecraft 's center of mass and there is no torque. If the thruster is aligned perpendicular to its radius, all of the thrust goes into creating torque and none into moving the center of mass.

Your spacecraft will barely have any net movement at all. It will just be creating and cancelling torque.

 

[B.E.M]

Interesting note about spacecraft spinning when they fire their boosters. I didnt know that.

Thrust perpendicular to a radius doesn't purely go into rotation though.
When the engine is pushed forwards, the habitable section is not pushed backwards.

Another way of looking at it is to ask what has happened to all the propellent. If we are agreed that it has all been expelled backwards then something must be moving forwards to conserve the momentum of the entire system (propellent + craft).

 

[Danger]

Think of a pinwheel (Catherine wheel, if you prefer). It's essentially just a couple of rockets mounted on the opposite ends of a stick with an axle in the middle of the stick. It will work the same way with only one motor.
Now look at your spaceship as if the centre of mass was the pinwheel axle.

 

[DaveC426913]

Septic tank.
Hey, it's a long trip...

True, true. But that's a long hop to the loo. On the plus side, your toilet would not have to be all the way at the other end ... only far enough...

 

[Danger]

Exactly.

 

[B.E.M]

I might be reading your message wrong.. you are arguing it will just spin faster and faster?

Think of a pinwheel (Catherine wheel, if you prefer). It's essentially just a couple of rockets mounted on the opposite ends of a stick with an axle in the middle of the stick. It will work the same way with only one motor.
Now look at your spaceship as if the centre of mass was the pinwheel axle.

Absolutely. If my ship was not spinning, then the thrust would merely start it spinning, creating an axis of spin perpendicular to the direction of thrust. It would not gain velocity because the drive would be aimed forwards for half of its rotation. It would simply gain more and more spin.

What I am talk about though is first spinning up the ship (probably through the above method) to gain a 1g centrifugal gravity for comfort and health of the crew but then changing the direction of thrust by 90degrees to be inline with the axis of the spin. Notice that the direction of thrust is no longer changing during a rotation.

Now if you average the thrust over an entire rotation there is no tendency to twist in anyone direction.

This is like my plate spinning example, the booster example mentioned by bob, and also like a rodeo cowboy spinning a lasso above his head against the force of gravity. Note that his noose is supported against gravity at only one point, but this point is spinning around him rapidly.

Here is the only decent picture I could find of someone spinning a lasso
http://www.bbc.co.uk/derby/content/image_galleries/features_derby_juggling_club_2004_gallery.shtml?13

 

[Danger]

Thanks for the link, but believe me, I don't need to see some twerp in a hat twirling a rope. I live a few km's away from Cowtown, in the heart of cattle country.
Anyhow, neither the spinning plate nor the lasso analogies are applicable here, because in both cases the impetus is from a central source. The fact that the direction varies is irrelevant. In your ship design, the impulse is totally off centre to start with, and remains that way.

 

[B.E.M]

Ok, but consider that loop, floating horisontal to the ground. It doesn't know that it is connected to a rope that is connected to a funny guy in a hat.

Now consider just the knot where the rope connects to the loop. As we can see from the picture, the rope is applying a force to just that point in an inwards and upwards direction.

Now delete the rope and replace the knot with a thruster aiming in the exact same inwards-upwards direction. adjust your throttle to the right value and again you have a hovering loop. If there were no gravity the loop would be accelerating upwards.

This is pretty much the situation of my craft, except you don't need to waste propellent on the inwards component of the thrust. A simple tether to the other side provides the same effect, although even that is not necessary.

(also if you look more closely at the plate example you will note I was also describing a case where the stick was slightly offcentre during a spin-up procedure. You might have missed my original note)

 

[B.E.M]

Hi, if there is any doubt remaining, I just thought of another example you can try at home that I think demonstrates the viability.

(A) take a one meter length of fishing line and attach two lead weights as in the diagram. We can pretty much ignore the effects of the weight of the line.

(B) you'll find you can spin up the contraption as in diagram (B) by holding the top end and spinning it around. How you spin it up doesn't really matter, the point is that when you stop, it will remain spinning in this manner for a while.

(C) In this diagram I have replaced the top segment of line with a hypothetical thruster that provides force in the exact same direction. This is pretty much the same argument as for the lasso above but I think the relationship is much more obvious with this example.

Anyway, I have managed to convince myself. Another interesting note is that crew in the habitable section will always feel gravity as being exactly vertical regardless of how thrust is adjusted.

 

[Danger]

There's something severely wrong with that, but I've had too much beer to figure out what it is specifically. I'll get back to you tomorrow.

 

[B.E.M]

But that's the best time to try this type of experiment! Use two full beercans and a length of string. You can tie it to their tabs. See how close you can get them to spinning horisontally before the g forces open the tabs :)

 

[Danger]

Sure... and who'll be the first to open one of those cans afterwards to be greeted by a faceful of beer?