Assuming that the angle can be anywhere from 0 to 90 degrees, uniformly distributed, using a bit of calculus we get that the ratio is on average pi/4, or .785398. 11/14 is a sufficient approximation for this. So (abs(V)+abs(W))*11/14 provides a fairly good approximation, erring at most by 10% for angles between 10 and 80 degrees.
If you need a linear approximation that reduces the error necessary, the constant that you are looking for is e^(2C/pi-ln(2)/2) (C being Catalan's constant), or about .789348. 15/19 is a sufficient approximation for this.
