It would appear the author ignored lightspeed restrictions entirely.
The choice of wording is a clue of a lack of regard for basic physics -- the speed of light being a fixed speed in your medium of choice, rather than acceleration which is the rate at which your speed changes.
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In the first book they are held to normal human accelerations with the engine pushing the ship, but in Skylark Three they find a way to accelerate everything at the same rate with no side effects.
They also get artificial gravity from it as well.
Early inertial compensation, I guess.
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IIRC I think the first book said that the drive acted on every particle of the ship, though I'm not sure exactly what that drive did physics-wise but initially, they were going five times light speed.
Later on in the Lensman books Doc Smith came up with first,the partial neutralization of inertia, and then the complete cancellation of inertia.
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I interpret the accelerations as being per second.
Thus, an acceleration of five times light speed would be 5 * 186,000 miles /second
/ second.
This was the acceleration of the Fenachrone ships.
Warning: spoilers below!
The Skylark Three had a Fenachrone style drive, which accelerated every particle in the ship and its contents equally, so no sense of acceleration was felt; the first two Skylarks did not, so their acceleration was limited by what the inhabitants could stand.
But Skylark Three actually had a higher acceleration than the Fenachrone ships -- 3.9186 times as high, according to the novel -- or it could never have gotten close enough to Ravindau's ship to fight it.
As for Einstein, relativity was ignored as being "just a theory".
Basically, special relativity says that an object's mass increases as the object moves at faster and faster speeds, so it would take an infinite amount of energy to accelerate an object up to the speed of light.
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And do remember that Einstein doesn't postulate the speed of light as a speed that cannot be exceeded.
All the theory of relativity does is indicate that it's a speed that cannot be attained, it says nothing about what would happen if you found a way to reach a speed faster than light without first reaching the speed of light itself (thus some sort of discontinuity drive that would make you jump from say 0.8c to 1.2c without passing through c itself while accellerating).I've had in the past some interesting discussions with my university physics teacher about this subject, including what it would mean for accelleration and braking in an FTL environment.
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In  Skylark Three  by E.E. "Doc" Smith, the  Skylark  has an acceleration of five times the speed of light, and in  The Skylark of Valeron , it has nearly unlimited acceleration. Is there any indication of how the light speed limit was overcome? It seems to have been ignored entirely.
How did the Skylark deal with the Einstein light-speed limit?
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<ftl-drive><e-e-doc-smith><skylark-series>
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It would appear the author ignored lightspeed restrictions entirely. Lightspeed restrictions were ignored by the author.
Lightspeed restrictions were ignored by the author.