MDMs should last a little longer than they do

Due to relativistic effects. David has done an awesome job talking about how time dilation affects ships travelling in hyper at 0.6c. But missiles in n-space are also affected. And the math is a more difficult because the dilation factor does not grow linearly, even under constant acceleration. It grows hyperbolically, which is why this is called "hyperbolic motion".

After 60 seconds of α=92000 gravities, ignoring relativity, a missile would be moving at 0.180c. So a 3-stage MDM under max power would top out at 0.542c and would have travelled 14.62 million km. However, at that point, the time dilation factor reaches γ=1.1897, so relativity can't be ignored.

Recalculating to account for relativity, we get that the final speed is c*tanh(α * τ / c) = 0.494c but will have flown 14.98 million km (+2.5%). This is possible because the flight time is 188.9 seconds (+5%).

Now, what happens if we step down to half power? 9 minutes at 46000 gravities makes us think that the missiles reach 0.81c and travel 65.77 million km. With relativity, it only reaches 0.671c, but travels 69.47 million km (+5.6%), having lasted 10 minutes and 1.4 seconds (+11.4%).

This would allow a 4-stage MDM to still top out at 0.794c, which is well within the particle shield capability. It could fly for 128.82 Gm or 7.16 light minutes (+10%), lasting not 12 minutes, but 14m29.3s (+20%).

The problem is that this calculation contradicts information on the books. It's clearly established that a 3-stage MDM lasts 9 minutes from the rest frame of reference and do reach 0.8c. Almost everything else could be simply rounding, but this one is over 10% error in time and 17% in the final speed...

See equations at https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)#Worldline

Interesting points raised. Just to complicate things further, by the time you get up there the mass of the missile is also growing due to relativistic effects, so can the acceleration be maintained at the same rate?

Daryl wrote:Interesting points raised. Just to complicate things further, by the time you get up there the mass of the missile is also growing due to relativistic effects, so can the acceleration be maintained at the same rate?

Well, not exactly. From its own frame of reference, the missile's mass is not increased. In a coasting phase between drive activations, the missile is in a fully inertial frame of reference and you can calculate everything as if it were at rest and everything else in the stellar system were moving.

However, and this is where the particle shielding comes in, the solar wind becomes less diffuse, more thick. So you lose speed due to collisions. Like an aircraft or submarine, you need a source of power to just keep the same speed. Though I don't expect this to have any appreciable effects below a substantial fraction of c.

The problem is we don't know how impeller drives work. We know they extract a portion of their power from the hyperspace band above, though the ship needs still to have fusion or fission generators to power everything, including impeller activation. We know the shape of the wedge influences how the craft inside it accelerates, so it might be the wedge and space within it that accelerate, in which case even our current Physics say that inertial mass does not apply. And then there are the inertial compensators: missiles must have them too, as not even electronics can survive 1000 gravities of acceleration.

ThinksMarkedly wrote:The problem is we don't know how impeller drives work. We know they extract a portion of their power from the hyperspace band above, though the ship needs still to have fusion or fission generators to power everything, including impeller activation. We know the shape of the wedge influences how the craft inside it accelerates, so it might be the wedge and space within it that accelerate, in which case even our current Physics say that inertial mass does not apply. And then there are the inertial compensators: missiles must have them too, as not even electronics can survive 1000 gravities of acceleration.

For whatever reason (probably in no small part because it makes the math simpler) no ship or missile under impeller drive has ever paid attention to relativistic effects on acceleration.


My personal handwave is that somehow - magically - the energy siphon effect that helps power the wedges by stealing power from hyperspace manages to scale up its power and the node's output perfectly matched to retarding effect of increased relativistic mass. So the two "just happen" to cancel out and give you the same numbers that Newtonian physics would have if it applied to those operating regimes.

Jonathan_S wrote:For whatever reason (probably in no small part because it makes the math simpler) no ship or missile under impeller drive has ever paid attention to relativistic effects on acceleration.


My personal handwave is that somehow - magically - the energy siphon effect that helps power the wedges by stealing power from hyperspace manages to scale up its power and the node's output perfectly matched to retarding effect of increased relativistic mass. So the two "just happen" to cancel out and give you the same numbers that Newtonian physics would have if it applied to those operating regimes.

The Math isn't that difficult. I didn't know it yesterday, so I looked up on a few sites and the Wikipedia link above. It's not obvious to a layman, but you can easily make a spreadsheet to calculate the values given some inputs.

I don't know if I'm right, though. I had Special Relativity at the University, but never got to learn General Relativity, which is required for an accelerating motion. But I do know that Special doesn't suffice. I'm just applying the formulae that I'm finding at the pages plus what I remember from those classes 20 years ago. The whole reason I thought of this was that I was reading Alastair Reynolds and his ships are high sublight ships, which got me thinking of the Muon Dilemma (see [1] and [2]): cosmic rays impacting our upper atmosphere create muons, but those should be too short lived to reach the ground. Yet they do. And if muons lived longer than expected due to relativity, so should missiles.

Unfortunately, you can't be right either, at least not completely. We know relativistic effects do happen because David mentioned them more than once, for ships travelling for a long time. I suspect his calculations were approximations assuming that the time spent accelerating was negligible compared to the trip itself. (Without Relativity, it takes 12 hours to go from zero to 0.7c at 500 gravities, which is 2.5% of a 20-day trip; with it, it's 15 hours)

Here's the kink: if the missile accelerated constantly at 46000 gravities (451.11 km/s²) as seen from the ship that launched it, we can make the same exercise for a ship-to-ship. If one ship coasts and the other accelerates at 700 gravities (6.86 km/s²) for 6 hours, we'd classically expect it to have reached a relative speed of 0.495c. If in the next second the coasting ship still measured a change of 6.86 km/s, then the accelerating ship itself must have measured its own change of speed as 10.45 km/s. Not 700 G, but 1066 G.

This is the kind of thing that would have been mentioned, since it blows way past the compensator safety margins...

[1] http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html
[2] https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation#Theory

I'm pretty sure that the series predates Wikipedia and possibly ubiquitous spreadsheets. Which might help explain why the math was kept simpler.

Don´t forget that missles with fusion reactors consume fuel, so they get lighter during the flight.

Maldorian wrote:Don´t forget that missles with fusion reactors consume fuel, so they get lighter during the flight.

They do, but it seems like the fuel is used to supply power, not for reaction mass. That is, there's no accelerated exhaust to provide thrust: that's what the wedge is for. So the loss of mass due to fusion is negligible: the fusion products are slightly lighter than the reactants, as the difference is converted to energy. But fusion converts less than 1% of the mass of hydrogen to energy.

Anyway, there's one thing that may provide a hint: upwards and downwards hyperspace translations losing speed. When a ship translates from alpha to n-space, it loses 92% of its speed. And it can't translate up at more than 0.3c. One of the fundamental aspects of Relativity (one very one that gives it its name!) is that any inertial frame of reference is equal to any other. But if a non-accelerating ship loses speed as it translates and if there's a speed limit, that means there is a preferential frame of reference, the one where the "at rest" is measured. It need not be Universally the same, but it's likely to be very close to be rest relative to the star that creates the hyperlimit in question.

So maybe wedges and compensators work relative to this frame of reference, in violation of what we know of Relativity. So yes, the missiles and ships under wedge do measure a higher acceleration in their own frame of reference as they go faster relative to the star, but it doesn't matter since the compensator limits are also relative to it.

As another Sci-Fi author wrote, "Einstein wept, but Newton is a rightful bastard" (J.A. Sutherland, Alexis Carew series)

[Though I still think missiles should last a bit longer, since the lifetime of the components is measured in the missile's frame of reference]

I still remember a decades old quote from an Analog Magazine.
If it takes infinite energy to accelerate up to exactly C, and at that point the space ship relative to the stationary reference is infinitely heavy, all would be attracted to it, possibly forming a pin point big bang source.
Thus while it may be true that a space ship could attain C, it would only be one per universe.

Daryl wrote:I still remember a decades old quote from an Analog Magazine.
If it takes infinite energy to accelerate up to exactly C, and at that point the space ship relative to the stationary reference is infinitely heavy, all would be attracted to it, possibly forming a pin point big bang source.
Thus while it may be true that a space ship could attain C, it would only be one per universe.

Paul Andrson.
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