In the picture above you see that the discharge of buffer capacitor C1 starts at t=T1. Now assume that T1=0. The rectified sine wave will now be a rectified cosine. At t=T2 V_C1=-V_topcos(2∙π∙f∙T2). (Note the minus sign. At t=T2, the original transformer output is negative.)

So cos(2∙π∙f∙T2)=-V_C1/V_top. This means

When you discharge a capacitor with current I, V_C(t) = V_C(0)-I∙t/C. In our case:

V_C1(t) = V_C1(0)-I∙t/C1, so at t=T2: V_C1 = V_top-I∙T2/C1. Since V_C1=V_top-V_r, we can also say V_top-V_r = V_top-I∙T2/C1. So V_r = I∙T2/C1. This means

If f=50Hz and V_top=20V and we want a 2V ripple voltage, we need a 4.3mF capacitor per ampere load current.

Note: Make sure your calculator uses radians!