Many times on this site, it was shown that Impulse Power/Engines generate Faster Than Light (FTL) speeds in TOS episodes. Analyses are scattered over this site, but the key episodes are
WNMHGB,
Balance of Terror, and
The Doomsday Machine. (Numerous posts associated to Balance of Terror are in
[URL="https://www.trekbbs.com/threads/the-romulans.297364/"]The Romulans[/URL].)
My head canon: Impulse is an alternative drive system that burns fuel reserves and does not involve any space/time warp technology. The fuel is not a rocket propellent, rather it is used as an energy source (in fusion reactors) to generate some unknown force which provides thrust (probably a gravity drive; the ship has artificial gravity and inertial dampening, so, why not a drive system, too?). For the TOS Enterprise, the gravity drive emitters will need to be physically mounted to structural hard points on the saucer. The obvious ship feature puts the main gravity emitters associated to the extended rear housing at the rear of the saucer. These gravity emitters are
the impulse engines which provide the forward and reverse propulsion. Another prominent ship feature is the top spine above the impulse drive. The entire spine itself can be another elongated gravity emitter, or a series of smaller emitters along its length, primarily used for maneuvering the ship in a straight line, or up, down, side-to-side, plus rotate and pivot in any direction (e.g. Pitch, Roll and Yaw).
The spine feature acts as the ship’s impulse rudder and keel.
Additionally, an anti-gravity field around the ship results in a mass elimination effect. With mass elimination, all Einstein and Newtonian physics that involve mass are circumvented, so, no increase in mass with high speed hence no speed limit of c and no time dilation. This field also eliminates the effects of inertia and acceleration inside the field, so, high acceleration maneuvers are possible. I suspect that the field is the ship's
inertial dampening system.
One more powerful gravity emitter array is present on the TOS E, this is the main deflector which generates a powerful long range, cone of force (reverse gravity) to push all matter away from and around the front of the ship as it moves though space. This effect is comparable to a
bow wake.
Together, mass elimination and directional gravity thrust, you have the impulse drive. The strength of the drive is directly related to the energy levels supplied from the different power systems, i.e. main power (M/AM reactors or “warp” power), auxiliary power (fusion reactors or “impulse” power) and emergency power (capacitor banks or batteries). Regardless of the power source, the top speed of the system is somehow limited by the gravity force used for thrust (speed of gravity?) which in TOS is about 5 to 10 c or equivalent to about Warp 1.8 to Warp 2.