Ringworld (thing)

For the Ringworld as written by Niven, this is true. But there are ways to design around the problem.

First off, you could pick a smaller and/or less luminous star and build a smaller Ringworld. You could also reduce the amount of gravity. Earth-chauvinists will object to both of these solutions on aesthetic grounds, and I must say I agree that having a red sun would be kinda weird.

But we can still fix things if you keep the Ringworld around a Sun-like star and give it 1g of gravity. We just need to come up with some way of supplementing/replacing the compressional force currently provided by the scrith to balance the centripetal force provided by the Ringworld's rotation.

Any given area of Ringworld floor has a certain force pushing it outward, given by F=ma, with a in this case equaling ~9.7m/s^2 (one Ringworld gravity). If we look up the mass of the Ringworld, multiply by one Ringworld gravity to get its weight, and divide by the area, we can calculate the average force exerted over a unit area of the floor (the outward pressure exerted on the scrith). That is how much force must be balanced to keep the Rignworld from tearing apart, and all of that balancing is currently done by the tensile strength of the scrith.

Next, given the size of the Ringworld and the mass of the star, we can use a=GM/r^2 to calculate the acceleration due to the star's gravity at the Ringworld floor. If we take the outward force on the Ringworld floor, and plug that and our new value for acceleration into the F=ma equation, we can solve for mass with m=F/a.

If we position exactly that much mass outside the Ringworld with zero orbital velocity, the inward force of its weight will exactly cancel the outward force on the Ringworld. Less, and there will still be some net outward force for the scrith to handle, but it will still be reduced. More, and we'll have to start worrying about compressional strength.

The scrith is supposedly frictionless, or nearly so, so we could concievably rest all of that mass right on the bottom of the Ringworld. On the other hand, we're trying to do this with the minimum of magical materials, so let's say that the counter-ring is coupled to the main ring via electromagnets.

Once the counter-ring is in place, the tensile strength of the Ringworld floor material is irrelevant. If we really needed to, we could concievably construct the Ringworld out of such low-tech material as stainless steel, plus the superconductors to build the magnets to hold it all up. Note, however, that we'll need a whole heckuvalotavit, whatever material is used, as the counter-ring will be orders of magnitude more massive than the main ring, itself already the mass of Jupiter.

Time to run some numbers and see just how much a heckuvalotavit really is. In order to make things simple I'll use as my given area the total surface area of the Ringworld. Ringworld surface gravity is .992g or ~9.7m/s^2, and its total mass is 2E²⁷ kilograms, so the outward force is

F=9.7(2E²⁷)=1.940352E²⁸newtons

The star is noted as being just smaller than the Sun, which masses 1.989E30 kilograms, so I'll round that down to 1.95E30 as a rough estimate of the Ringworld star's mass. The Ringworld's radius is 1.52E11 meters, and at that distance from the star inward gravitational acceleration is

a=1.95E30/1.52E11²=.028733726 m/s^2

We now know the force we need to balance and the acceleration we have available, and so can solve for the mass:

1.940352E²⁸=m*.028733726
m=1.940352E²⁸/.028733726
m=675287291317527006417476104560.891 kilograms
m=~6.753E29 kilograms

As expected, dividing a large number by a small number gives a very large number for the mass of the counter-ring, a little shy of 6 hundredths the mass of the star, or ~338 times more massive than the original main ring.

If we're willing to (almost) completely abandon Niven's vision, we can construct a Ringworld much more economically. First, lets flip it inside out and kill its rotation- now, the livable surface is on the outside, and the gravity is the star's own. In order to get it up to reasonable levels, you'll either need to make the star bigger or the Ringworld smaller. Rather than shadow squares on the inside, this version of the Ringworld would have mirror squares on the outside to create day/night cycles. Filters and phosphors could be used to color the sunlight however you want, so almost any star would be suitable, and power collectors could still be orbited inside the ring.

Now, the strength we need to hold it up is compressional, rather than tensional. If we look at this as a case of the counter-ring becoming the main ring, it's obvious that what we need is a counter-ring spinning on the inside to create outward centripetal force to hold the Ringworld up. And, in fact, just as the outer counter-ring described above is more massive than its associated inner main ring, the inner counter-ring in this case can be made as thin as desired, and simply spun faster to make up the difference. There are two ways to set this up.

First, a single counter-ring could span the entire underside of the main ring. The main ring would be flat, and would still have walls at the edges to hold in the atmosphere. This is the most obvious set up.

Second, you could have two counter-rotating counter-rings, one at each edge. This way, if you use the main ring as a reaction surface for spin-up, the net angular force imparted on it will by zero. If they are each half the width of the main ring, they'll still span the entire underside, and the main ring will still be flat. If they're thinner, however, only the edges would be supported directly, and the main ring would be curved into a catenary cross-section for strength. The curve will hold in the atmosphere, with pressure decreasing as you approach the edges, eliminating the need for heavy rimwalls.