[Spaceships] Interstellar Magsail Deceleration
 

I'm hoping someone who has actually used calculus in the last two decades can check my thinking here.

The Dirac-class Exploration Cruiser (p. SS5:11) says that it can use its magsail to decelerate from 23% light-speed. I was curious to see how much distance it required to perform this deceleration.

GURPS Spaceships says to use a ship's average distance from the sun to determine the acceleration provided by a magsail (p. 39). This didn't seem to make sense to me when you're coming in from an interstellar trip at some non-negligible fraction of light-speed -- do you use the mid-point distance between the two stars where the magsail's acceleration will be negligible? Three-quarters the distance as half of the deceleration phase, where the magsail's acceleration is still negligible? Neither seemed right, so I decided to try real math instead of the explicit simplification.

Using an energy balance equation similar to a derivation of escape velocity (conceptually you can think of this as a magsail-equipped spacecraft starting at the sun's surface, seeing what kinetic energy it will have after a specific distance of acceleration, and what velocity that produces -- and then reversing it to find the distance needed for a deceleration from a specific velocity):

1/2 * m * v^2 = INTEGRATE (a * m * (u/x)^2 * dx) FROM r0 TO r

where: m is the spacecraft's mass (which quickly cancels out of the equation); a = 0.001 * 9.81 m/s^2 (0.001G for a magsail); u = 1.50e11 m (1 AU); r0 = 7.00e8 m (our sun's radius); and r is the resulting distance from the sun's center and v is the resulting velocity. All units are meters and seconds.

Solving for r in terms of v, I get:

r = (2 * a * u^2 * r0)/(2 * a * u^2 - v^2 * r0)

Obviously, there are some values of v which will produce a negative result for r, which wouldn't make sense. Like the escape velocity derivation, v converges on a finite value even as r goes to infinity -- in this case, when v = (2 * a * u^2 / r0)^1/2 = 7.94e5 m/s = 494 mps (miles per second).

So it seems like, realistically, the most a single magsail could reduce your velocity by is 494 mps (0.27% light-speed), even if decelerating from infinity all the way down to the sun's surface (though actually 98% of the deceleration is done in the last 0.1 AU). You'd need 14 magsails just to get down from ramscoop velocity (1,800 mps) and effectively 7,500 magsails to decelerate from 0.23c (magsails to mps is non-linear).

Is this correct, or have I screwed up my math, or simply taken the wrong approach?

Re: [Spaceships] Interstellar Magsail Deceleration
 

There's a fault in your approach. Magsails can be used to accelerate on solar wind, but that's not the basis of their 'parachute' effect. In interstellar space the solar wind is negligible (in fact, I think it essentially cuts off at a distance from the sun). But there's still interstellar medium, and in quite a lot of space that medium is ionized. Thus a craft moving through the ISM and c-fractional velocities naturally sees a headwind of charged particles that a magsail can use to break.

Re: [Spaceships] Interstellar Magsail Deceleration
 

It *should* but where keeps moving out as we look for it. Both Voyagers finally did pass through the termination shock (where the solar wind goes subsonic, which is about 100 km/s in the interstellar medium, vs the 400 km/s down here in the inner system) so they are probably getting close, but there still could be surprises.

Also, as long as the sail is moving relative to the ISM faster than that 400 km/s speed of the solar wind (.00013 c), it would generate more thrust than it would even in that wind in the inner system - the system is actually a much more effective parachute than it is a sail. Though of course you might not be able to take advantage of the full thrust if the physical part of the sail isn't strong enough to take the resulting tensions. Still as long as you are moving faster than that relative to the ISM, at you can decelerate as fast as you can ever accelerate on the solar wind *at a minimum*.

The performance of magsails is *vastly* simplified for any of the GURPS treatments anyway, so applying sophisticated mathematical analysis to those simplifications is pretty pointless.

Re: [Spaceships] Interstellar Magsail Deceleration
 

So what deceleration can a magsail generate in the interstellar medium? The same as the distance-corrected acceleration of a magsail at the heliopause?

Re: [Spaceships] Interstellar Magsail Deceleration
 

Like I say, at least as great as the maximum acceleration it can ever achieve on the solar wind, as long as the craft is currently above the velocity of the solar wind you are comparing it too. You shouldn't be doing any distance correcting at all.

Re: [Spaceships] Interstellar Magsail Deceleration
 

I'm not sure I'm following. A GURPS Spaceships magsail produces 0.001G at 1 AU from the sun. Right down next to the sun it could produce almost 46G. You're saying that a magsail could use the ISM to produce 46G deceleration?

Re: [Spaceships] Interstellar Magsail Deceleration
 

A magsail almost certainly couldn't produce 46G anywhere, since it'd be anihilated by the stresses involved.

Also, I don't think the Spaceships magsail says anything about 'at 1 AU'. The light-sail's acceleration varies as the inverse square of distance, but there is no similar statement for the magsail. Probably because it's a plasma sail, which (by means I don't understand) expands its effective area as the solar wind thins. In any case, it states a constant acceleration. I'd use that for the parachute effect as well as everywhere else.

Re: [Spaceships] Interstellar Magsail Deceleration
 

The lightsail mentions distance correction in its description and the magsail doesn't, but it's mentioned for both of them on p. 39.

Re: [Spaceships] Interstellar Magsail Deceleration
 

So it is. Well, I don't know how much peak acceleration the magsail is supposed to be able to manage. If you find your magsail accelerating faster than a chemical rocket, though, you can probably assume that you've gone beyond structural capabilities.

Re: [Spaceships] Interstellar Magsail Deceleration
 

A magsail's acceleration doesn't change with distance from the sun up to the heliopause - the way they work, the sail automatically grows as the ship goes farther and farther away from the sun and the solar wind becomes less dense, leading to greater acceleration. I remember reading a pretty decent description of how this works, but I can't find it anywhere:/