If you really want to read up on g forces, then this Wikipedia page covers it.
First of all, "g force" isn't really a force, rather it's a measure of a rate of acceleration. It's one of those slightly confusing expressions.
g force is a way to "normalise" accelerations relative to that we experience every day due to gravity on the surface of the Earth. It's a way to gauge how much we'd "weigh" when experiencing an acceleration that's more or less than 1g.
When we are standing on the ground, we experience 1g (units are usually expressed a "g", not to be confused with grams). We are not actually accelerating, since the ground is there to stop us from falling, so instead we feel a force we call weight.
While we normally use standard international unit of metres per second squared (m/s^2) to express accelerations, it's common to express accelerations relative to that we experience on the surface of the Earth, which is defined a 1g.
If you have a mass of 80kg and are standing on the ground then you'll weigh 1g x 80kg. That's why many confuse weight with mass. They are not really the same thing, mass is an intrinsic property of an object, weight is the force it pushes down on the ground with. It's just that on when sitting on the surface of the Earth, an object with a mass of 80kg will also weigh 80kg.
However if you are accelerating upwards away from the Earth's surface (imagine you're travelling upwards in a rapidly accelerating elevator or rocket), then you'll experience more than 1g.
How much more depends on the rate of acceleration. If you happens to be accelerating upwards at 9.81 metres per second per second (which equals 1g), then you'd experience 2g, being acceleration due to gravity + the extra acceleration of the elevator or rocket. If you were able to stand on some bathroom scales while that acceleration is happening, then you'll "weigh" 80kg x 2g or feel like you now weigh 160kg. ugh.
Now keep in mind that an acceleration can be a change in speed and/or direction.
e.g. when a travelling in a car that turns around a corner, even through the road speed of the car may not change, we experience what feels like a force pressing us towards the opposite side of the car. Such lateral accelerations can also be expressed relative to 1g. Modern Formula 1 racing cars for example are capable of generating lateral corning accelerations of up to 6g.
g force on a velodrome
So whenever we are riding around the curved path on the turns of a velodrome, we are constantly accelerating towards the centre of the track, even though we may not be changing the bike's forward speed. As a result, we experience some lateral g forces when riding on velodrome, as well as the downward 1g due to gravity. What this means is the total g force we experience will be more than 1g. How much higher depends on our speed and the turn radius.
Calculating the rate of lateral acceleration when riding around a track is a pretty simple:
Estimating rider turn radius
To estimate a rider's turn radius, we start by estimating the track's turn radius.
First an overhead shot of a velodrome to get a sense of the general shape of a track (thanks to Google maps). This one happens to be a local outdoor track not far from where I live. It's a 333.33m concrete track. You can make out the faint blue band around the inside of the track, which is just inside of the track's black measurement line, the inner edge of which = 333.33 metres in length.
Like I said, it won't be exactly that as in reality tracks have a variable turn radius but it's close enough for the purposes of this discussion. OK, that's great, we have the track's turn radius.
Now back to our lateral g force formula:
The rider's speed and turn radius is based on the position of their centre of mass (COM). Since a rider leans over when riding around the banked turn of a velodrome, then their COM speed and turn radius is less than the wheel's speed and the turn radius at the track where the tyre is rolling along.
Another diagram to help explain. You might need to look at a larger version - so click or right click on it to view a larger pic. ('The pic of a leaning rider I found on this blog item. Hope they don't mind me borrowing it - I can't however vouch for the physics discussed in that item).
To calculate COM radius and speed, you then need to know the rider's COM height and their lean angle (from the vertical). It's a little basic trigonometry.
That then brings us to the question of how do we calculate the rider's lean angle? Well I'm going to leave that one for now because I'm getting further away from the issue of g forces than I'd really like. Suffice to say that we can reduce the estimated track turn radius and wheel speed by a couple of percent to estimate rider turn radius and rider COM speed.
Are you still with me?
How much g force does a rider feel in the turns?
There is a physiological question to be considered, namely does this higher g force, which occurs twice per lap and lasts for about 2/3rds of the total time on track, cause any problems with blood circulation, is it sufficient to hamper performance?
I don't know, and I'm not sure if there's been anything more than speculation on this question. 1.3-1.4g doesn't sound like it'd cause too much of a problem to me, but who knows?
This is why track sprint bikes and wheels have to be made extra strong, and also partly why track sprinters run extra high pressure in their specialist tubular tyres.
Would you put a 200kg rider on your bike?