Hello,
There are lots of things that can effect the speed of the swing. Perhaps the most common reason for having a slow swing would be because a person takes off under, which wrecks just about everything that comes after it. I would even go as far as saying that taking off under is the pole vault equivalent of smoking. Nasty habit, extremely difficult to get away from and it's just about the worst thing you can legally do for your health (no offense to any smokers out there)
Anyway in a literal sense, the swing starts after the take off is finished. But in a less pragmatic sense, the swing is "built" on the ground. If you don't do the ground elements well (run, plant and take off), your swing will not be as good as it can be. Plain and simple.
A video of your jumps would be very helpful in sorting out your problem since there are literally a million things that could slow the swing down. Heck, the taller you are, the slower your swing would naturally be!
Also, I'm not sure what you mean by "keep my left leg back in a stronger position" - you shouldn't be really trying to "keep" your left leg back. The focus is more on to finish the take off jump which will naturally bring your leg back to a good position to start the swing. IMO, the whole notion of cranking your leg back as far as possible before letting the swing rip can be a bit detrimental to the swing. There are goods and bads in the whole thing. It is good to get the leg back (to a point) because it will create a more powerful swing. However, making a huge effort to bring the leg back will invariably delay the timing of the swing so you won't get inverted in time. As a result, your swing will be slow because you didn't start on time! And if you bring the leg back far enough you will also have to break good body posture. In order to bring the the leg any further back past a certain point you will have to release muscular tension from the quads, hips and stomach which will actually make your swing significantly slower. You need that muscle tension in your front side muscles to get the stretch-contraction reaction on the front side of your body which will make the swing much better. You also need that tension to keep a strong body position while swinging. You swing slower when you're floppy - just try swinging a baseball bat vs a slinky, a bit of a silly comparison but you know what I mean. To put it simply if you let your stomach, hips and leg go loose in order to bring your leg back, you are losing power and speed in your swing. Just because the leg is further back doesn't mean the swing will be necessarily stronger/faster. In fact, making a huge effort to bring the leg back will probably result in a swing that is slower than what it could be. A good way of looking out for this is to see how arched the back is just before the swing starts. Invariably, there will be degrees arching due to the forces involved but you can really see the difference if there is too much arching and the vaulter has completely lost posture. Also look for a delay between the take off and the swing in your videos.
Think of the swing as a giant swing on a high bar. In fact, do your best to learn that - especially the gymnastic 'tap swing' (just google/youtube it if you don't know what it is). It is not so much an effort of pumping muscles really hard to get upside-down. I see it as more of a little game with physics:
You're running into a jump
You jump up and then the pole starts bending (hopefully!)
As the pole bends and ultimately stops, your upper body which is connected to the pole decreases in horizontal velocity along with the pole. However your lower body will be carrying momentum forward.
Since your lower body is moving forward relative to your upper body, you are effectively rotating - much like swinging on a high bar.
So to accelerate further you need to tap swing
To accelerate even more you break at the hips after the tap swing and bring you legs out to 90 degrees in front of you (one knee is still kept bent). This is going to be like a figure skater bringing their arms in while spinning, the spin gets even faster.
Do this and trust me, the swing will be very fast.
You can try and work to get your knee up and in more but past 90 degrees it won't make much of a difference and the extra effort may be taking away focus from more important things.
Think high bar swing and figure skater more than ab-crunch-machine. Though the more core strength you have the better, getting the technique right will get you more drastic results!
-Andrew
