collinear antenna with phasing coil

i would like to construct collinear antenna with phasing coils then stacking for higher gain .So I've searched on many website but i don't find the formula for designing . anybody can guide me about these formulas , i am very new for antenna and I have some questions.

1st : What is difference between 1/2 lambda and 5/8 lambda of monopole ? Just radiation pattern and gain ?

2nd : What is the function of phasing coil and What is the meaning of number of coils ? All i know it is about changing phase.


Thank you so much
dd