Truss frame Vs. frame made of cables, who is better?

[someone_else]

Ok, I'm not talking about magitech like my last thread, this is mostly an engineering question.
I want to build a (hard sci-fi) starship and I can choose between a conventional truss structure like most realistic NASA designs or a frame made by an engine towing the rest of the ship with cables, like the Valkyrie, or the ISS Venture Star of Cameron's Avatar (apparently both designed by the same guy).

I read Atomic Rocket's and I know that the ship made of cables has some nice advantages like the reduced mass, allowing the crew to stay faaaaaaaar away (kms or more) from the highly radioactive engine and power plant, and can help in generating decent gravity if I decide to spin the ship like a bola.

But then I hit a wall of bricks. 'Cause I'm not an engineer and figuring out some numbers (to get a ballpark estimate of the things in play and make some comparisons) without any experience in that field is hard.

I assume a not very powerful engine, so the thing will be at best under 0.5 gravities of acceleration, and obviously must be made of materials that aren't damaged by vacuum.

Can you point me in the right direction to get some numbers?

[someone_else]

I forgot to add a linkie to Charles' Pellegrino's Valkyrie
and one to the ISV Venture Star

both from Atomic Rockets.

[Korvan]

I think some first year physics can help here, and if not you'll have to find someone else! We'll take a look at the case where you have an engine towing the ship with say a single 100m cable. To keep things easy at first, we'll neglect the mass of the cable, assuming it is small compared to the mass of the ship. You want to start with a free body diagram of the two objects, the engine and the ship. A free body diagram just shows the isolated object with forces acting on it. For the engine, the two forces acting on it are the thrust which pushes the engine forward and the tension from the cable which is holding the engine back somewhat. For the ship, the only only force on it is from the cable, pulling it forward. We will need to know the masses of the engine and the ship, we'll just use 10 tons for the engine and 100 tons for the ship. (1.00-e^4 kgs and 1.00-e^5 kgs). These numbers are just made up, so you'll need to do a big of research to get more reasonable ones.

Now, for an object, the net force acting on it = the objects mass times the objects acceleration. You've given 0.5g as a max acceleration, so we'll use that.
For the engine, F = ma, but the net force is also equal to the thrust - the tension from the cable, so Th - T = ma. We don't know what the thrust is, so we can't calculate the cable's tension (T) here, but we're not done yet.
For the ship, F=ma and the net force is also equal to the cable's tension, so T=ma, T = (1.00-e^5 kg)(0.5(9.81m/s^2)) = 490500 N (newtons).
If your cable can handle that tension, you're fine with a max acceleration of 0.5g.

I haven't really studied stresses and strains, but I think I can work something out here. My text shows that steel has a tensile strength of 520 MN/m^2. That is a piece of steel with a cross sectional area of 1 square meter can be stretched out with a force of 520 million Newtons before it breaks. We'll give ourselves a nice 20% safety margin and go with a tensile strength of 416 MN/m^2.
So Ts = F/A so A = F/Ts, A = 490500N / 416 MNm^-2, A = 0.00118 m^2. Since we're dealing with a cable, A = (pi)r^2, r = (A/pi)^1/2, r = 0.019 m or 1.9 cm.
So it looks like in our case a steel cable with a diameter of 3.8 cm (or 1.5 inches) will do the trick. Since the tension in the cable depends only on the acceleration and mass of the ship (not the engine), if you keep a = 0.5g and just increase the mass of the ship, the radius of the cable will increase in proportion to the square root of the increase in mass. In other words, you can increase the mass of the ship by 4 and the cable will just double in radius.

A final check will be to make sure the mass of the cable is not significant when compared to the mass of the ship. Volume of cable = Length X Area = (100m)pi(0.019m)^2 = 0.1134 m^3 (cubic meters).
I get the Density of high carbon steel = 7820 kg/m^3 so Mass cable = Density * volume, M = Dn * v, M = (7820 kg/m^3)(0.1134m^3), M = 887 kg. That's heavy for you or me, but it's only 0.89% of the ships mass, so we can ignore it.

It looks like current materials are sufficient for small ships at least. I just looked up the mass of the space shuttle which is about 20x heavy as the ship we used. Multiplying our 1.9 cm by the square root of 20 gives us a cable radius of 8.6 cm or about 7 inches in diameter. Still feasible, but at some point you will want to use multiple cables.

[sericks]

I have studied some structural mechanics, though I'm no structural engineer by any means. Korvan's got much of it down, but it's important to put maneuvering thrusters on both the engine and the main ship part. Otherwise you'll have to bend the cable to actually maneuver or even slow down, meaning a wide turning radius or stronger cabling or both. If you try to turn too sharply with just the engine you'll effectively be trying to push the ship with the cabling on the inside of the curve while pulling with only the outer edge. Naturally, cables have little compressive strength (otherwise it's a beam, not a cable). This will give you a badly damaged single cable or snap the cables/wires on the outer edge of the curve, as they now bear all the force in the turn.

[Darth Wong]

You know, you really should keep in mind that if the ship contains a livable habitat area, that structure must be rigid regardless of which design you go with, and if it's connected to the engine by a cable, then that rigid structure must withstand the exact same force that it would sustain in a conventional design (albeit now applying on a single point, where the cable connects to the livable section) without deforming beyond tolerance.

The only real weight savings you get are from eliminating whatever structure you need in order to suspend the engine farther away from the ship (keeping in mind that you would probably fill much of that structure with fuel anyway), so it depends on just how much isolation you decide you need. Also keep in mind that in-flight maintenance (if necessary) will be far more difficult with that strung-out design.

Of course, you might simply decide that in-flight maintenance is impossible; I don't know how advanced your ship is supposed to be, and how long it's supposed to be in space. The Apollo 13 astronauts didn't have an option to go outside the capsule to fix anything, but that was a short mission. Presumably, a ship which is intended to operate for years must have been designed with the possibility of something going wrong in mind.

[Simon_Jester]

The only real weight savings you get are from eliminating whatever structure you need in order to suspend the engine farther away from the ship (keeping in mind that you would probably fill much of that structure with fuel anyway), so it depends on just how much isolation you decide you need.

For engines with radioactive cores or exhaust, that can add up very quickly. Distance is a very appealing form of radiation shield, especially in space where you don't want to slow down your spaceship by carting around several thousand tons of lead.

The maintenance problem is serious, and I have a sneaking suspicion that most would-be starship designers to date have underestimated it.

[someone_else]

Nice take on the cable Korvan! (and the wit ) Now I can put the equations in a spreadsheet to play with the different materials and cable strenght and weight.

Now I just need a similar thing for a truss structure. Or for a beam. Or for whatever structure that must withstand both compression and tension (although I think that a truss is more lighweight of a beam of the same strenght). Maybe your analysis works for compression too, after all it is just a force applied in a different direction. I just want to be sure.

Still, anyone wants to add is free to do so.

Korvan's got much of it down, but it's important to put maneuvering thrusters on both the engine and the main ship part. Otherwise you'll have to bend the cable to actually maneuver or even slow down, meaning a wide turning radius or stronger cabling or both. If you try to turn too sharply with just the engine you'll effectively be trying to push the ship with the cabling on the inside of the curve while pulling with only the outer edge.

The valkyirie designer got around this problem by placing two different engines at each end of the cable (and making the payload section able to climb the cable to change position when the other engine is turned on).
I find this rather stupid to do on a interplanetary craft that will not get at a significant fraction of c (i.e. that is not threatened by dust or particles slamming on it at a significant fraction of c while rotates around to start the deceleration burn).
But I don't know engine mass, so he may be right for interplanetary ships too.

Still, I think that if you angle the maneuvering thrusters well on the engine section you don't need to place them on the payload too. If the thrust from the thrusters is angled in a way that a fraction of it pulls "forward" and the rest of it pulls in the direction of rotation desidered, it should keep the cable always under tension.
This way you have the engine section that "spins around" the payload while accelerating it forward by a minuscule amount. Theoretically it would be a spiral.
Otherwise you just need to keep thrusting with the main engines while you use the thrusters to rotate.

This means that the crew section is not spinning around the ship's barycenter, but that the engine is spinning around it. So would be rather useless for artifical (rotation) gravity while the ship is coasting. So I would need thrusters on it too if i want gravity.

You know, you really should keep in mind that if the ship contains a livable habitat area, that structure must be rigid regardless of which design you go with

Yep. But that would be the payload, and any rocket no matter the engine has a very small payload mass if compared to the reaction mass tanks, the fuel and engines and whatnot.

Also keep in mind that in-flight maintenance (if necessary) will be far more difficult with that strung-out design.

Considering that most kinds of engines are radioactive (by fuel for fission or by neutron activation for fusion and antimatter) and EVA work is tiring and hazardous, there will be the need to use waldos anyway.
Atomic Rockets talks about Canadarm 2, the arm that is used to perform maintenence on the ISS as a good example of waldo. Its main feature is the ability of move around all the ISS by attaching itself to dedicated slots placed in different spots of the station. One arm, multiple slots.

Yes, the amount of repairs would be limited though. Will probably depend on the size of the replacement part storage of the ship.

The maintenance problem is serious, and I have a sneaking suspicion that most would-be starship designers to date have underestimated it.

I think that the main problem with it is the mass of the spare parts (that cuts down the overall payload mass). And the fact that something cannot be possibly repaired (melted nuclear reactor or NERVA engine).
But the sail ships of the old times were not stopped by these same concerns.
It's just a more risky ride and, just like with the Space Shuttle, the reward for failure is death.