If you're going to a higher inclination than your launch latitude (for example, going from Cape Canaveral at 28º to ISS at 51º), you'll want to do it as early as possible, while your horizontal velocity is minimal -- essentially immediately when you start your gravity turn. The velocity you start with from Earth's rotation is less than that of even a very high orbit, so the inclination change is nearly free.
If you're going to a high altitude, lower inclination orbit, for example to equatorial GSO, there are two options:
- Option A: Combine the plane change with the circularization/"apogee kick" burn, which makes the total burn requirement equal to the hypotenuse of the triangle made by the normal (plane change) and prograde (circularization) components of the burn, potentially yielding large savings;
or
- Option B: Launch into a orbit higher than the destination orbit and do the plane change at apogee when you're going very slow. This writeup claims (without citation or derivation) this is more efficient than the first option for plane changes of more than 45 degrees.
The tricky case is when you're trying to reach a low orbit at lower inclination than your launch latitude, like equatorial LEO. In this case, to minimize the size of the plane change, you want to launch into the minimum inclination reachable from the launch site (i.e. fly a due-East initial ascent, making your inclination equal to your launch latitude). Circularization for LEO has to be done some 10-15 minutes into flight, but the descending node where you need to make the plane change is a quarter-orbit (23-30 minutes) from the launch site, so the burns can't be combined for efficiency. By launching into a more steeply inclined orbit (e.g. flying southeast instead of east from Canaveral) you can arrange for the circularization and plane change to coincide, but the plane change will have to be greater; I'm not sure how it optimizes.
