The
TNG Technical Manual says that impulse drives are "required" to be able to provide an acceleration of 10km/sec²... that's about 1000g! However, in fact from what we see on screen some impulse engines must be capable of
substantially higher acceleration than this. In
Star Trek: The Motion Picture the
Enterprise travels from Earth to Jupiter in 1.8 hours at "warp 0.5". During this time its warp drive is explicitly offline, so we know it must be entirely running on impulse here, and that therefore "warp 0.5" must be a sublight speed. It's not clear what the relative positions of Earth and Jupiter were in
ST:TMP but their closest approach is 590 million kilometres and their furthest distance is around 960 million kilometres, with the average distance between them being 778 million kilometres; this gives us an upper and lower limit of the distance travelled and therefore the acceleration achieved.
If Jupiter is at its closest approach to Earth, the acceleration the
Enterprise sustains is around 28.1km/s².
If Jupiter is at its furthest distance from Earth, the acceleration the
Enterprise sustains is around 45.7km/s².
Assuming the average distance between Jupiter and Earth, the acceleration the
Enterprise sustains is around 37.1km/s².
In even the slowest case, this is somewhat greater than
the acceleration of a bullet in the barrel of a rifle when it is fired. And the
Enterprise is sustaining this rate of acceleration for
almost two hours 
The acceleration, assuming that it's 10 km/s² is significantly above Earth's 9.80665 m/s² average gravity.
That's a acceleration factor of 1,019.7162129779282425700927431896 g
That's ~= 1,019.717 g
The CST (Constant Space Time) coils that give you the extra acceleration necessary to meet the acceleration times that we see on screen, it basically acts as a multiplier for the Base minimum listed Acceleration factor by ALOT more.
1.00 c = 299,792,458.0 m/s
0.25 c = _74,948,114.5 m/s
Why Star Trek's Impulse Speeds Are Totally Impractical
To accelerate to 0.23c w/o CST Driver Coils to enhance performance using 10 km/sec²:
Wow! It would take almost two hours and 1.6 times the distance from the Earth to the Sun!
Time to Accelerate to 0.23c = 6895.227 seconds
___________________________ = _ 114.920 minutes
___________________________ =
____ 1.915 hrs
Time to Accelerate to 0.25c = 7494.81145 seconds
___________________________ = _ 124.91352416… minutes
___________________________ =
___ 2.0818920694… hrs
- The Constant Acceleration Limit w/o CST, would be due to Inertial Dampeners not working; so limit to ~3g which should be similar to NASA's STS Space Shuttle's Maximum Acceleration factor. However that would be piss slow.
- Handling ~1,019.7g's is very do-able once you have Inertial Dampeners working, even then, that would still be slow.
- This is why Impulse Engines need the CST coils & Inertial Dampeners to work together; otherwise you just have a Fusion Rocket that has it's thrust output severely handicapped due to lack of Inertial Dampeners or CST.
- Which is why the CST coils needs to have a "Multiplier Effect" on acceleration output to match the acceleration factors we see on screen to match modern day Jet Fighter (Accel to Mach 1) or Automobile (0-60) acceleration times that we see on screen.
https://www.quora.com/How-fast-can-...-What-is-the-fastest-accelerating-fighter-jet
Normal Fighter Jet Acceleration to Mach ~1.0 usually takes about:
- Usually takes about 17-22 seconds to Mach 1.0 @ Minimum Mass/Payload
- Usually takes about 28-36 seconds to Mach 1.0 @ Maximum Mass/Payload
For a StarShip, depending on it's mass your acceleration times could be up to 65.535 seconds, in a worst case scenario, it would usually be at 99.999 seconds at the absolute worst case scenario for largest heaviest StarShip. The slower you make your acceleration the easier it is for other vessels to catch up to it at STL, so you want to setup a reasonable acceleration performance target when you design your vessels. Obviously faster is better, but don't go crazy to over-compensate and add more STL Impulse Exhausts to the point that a giant chunk of your mass / volume budget gets dedicated to Impulse Exhaust drives.
To have Fighter-Jet like acceleration to 0.25c from stand-still, you need to accomplish the acceleration in 2-digit seconds.
Not rated in hours.
CST Driver Coil 'Acceleration-factor' Multiplier from Classical Newtonian Exhaust @ 10 km/s² =
- 114.36349202716105897611963073167× ~= 114.364× for taking up to 65.535 seconds to accelerate to 0.25c
- Obviously the 'Acceleration-factor' Multiplier will change based on how fast/slow you want to accelerate up to the top speeds.
That's how much the CST would need to multiply the traditional Newtonian Exhaust to get to 0.25c to match IRL Fighter-Jet like acceleration times to that accelerate to Mach 1.0.
- Smaller & Lighter vessels like Small Shuttles can accelerate to 0.25c in less time due to smaller mass
- Obviously Larger vessels like a StarShip would be slower to accelerate unless you have REALLY PowerFul Impulse Drives.
