In case you didn't know: You can Circle jump with forward only
Every circle jump tutorial that I've seen tells you that you have to press up and strafe key (depending which side you're turning). This is not actually true. It doesn't matter which keys you are pressing as long as you get the turning motion right. However, it just so happens that pressing up+strafe keys makes it easier to continue with air acceleration, because your fingers are on the right keys and the mouse angle is correct the instant jump off the ground. You instantly transfer from circle jump to strafe jumping and we all know strafe jumping is the best way to gain speed. Which is why up+strafes is the most preferred technique for circle jumping. I might be biased to which technique is the easiest, because I'm the most used to the traditional way of doing it.
Experimenting with different techniques might open new routes and angles for your trick jumps! It might also come in handy in situations where you need to circle jump and at the same time look somewhere else where you can't whilst doing the traditional circle jump technique.
I decided to make this "guide" in the off chance that this stuff about ground/air acceleration is not a widely known fact. Mainly because I've come across several high skill QL/CPM players who had it come as a surprise and because several tutorials have failed to mention it. It's safe to assume that the new(ish) players who recently followed those tutorials are oblivious as well. Note I put guide under quotes earlier, because I feel like it's more trivia than a helpful guide. Tricks in this video were made with default Quake Live physics (whatever default is ever since QL became paywall'd on steam).
Song: Sonic Mayhem - The Prophecy