How can I estimate the minimum runway needed to take off with a hang glider?
What you need is enough lift to remain in the air. For that, the maximum lift of your hang glider needs to exceed the total weight. 

When you know the total weight of the glider (you included), you can derive the theoretical minimum airspeed from the lift formula:

$$L_{max}=\frac12{\rho}V^2C_{max}S$$
$$V_{min}=\sqrt{\frac{2W}{{\rho}C_{max}S}}$$

Where:


$L$ = lift
$\rho$ = air density
$V$ = air speed
$C_{max}$ = maximum lift coefficient
$S$ = wing surface
$W$ = weight




Now you have to know your maximum lift coefficient. Suppose this is 1.2, and for safety and initial manoeuvring, let's add a margin of 40% to the weight.

Let's say your mass is 85 kg, and the glider has a mass of 35 kg. The total weight would be 120 kg &mdash; that is about 1,177N weight, which for the sake of safety margin is increased to 1,650N.

I'll estimate the surface of the wing to be $16m^2$. Assume a normal day, the air density will be about $1.225kg/m^3$.

Filling in the numbers is the formula:

$$V_{min}=\sqrt{\frac{2\times1650}{1.225\times1.2\times16}}\approx 12 \textrm{ m/s}$$

Any wind speed you get you can subtract from this figure: what is left you have to achieve by pushing, running or diving.