Coaxial Collinear (CoCo) Antenna - Hyps & Facts.

(1) I fully agree with views of Devonian (Nigel). You should fist make a 1/4 wave groundplane antenna and establish your system by running it for at least few days (or better few weeks), before attempting to make a Coco.

Please see this thread for how to make a 1/4 wavelength groundplane antenna (Spider or Cantenna):

Three Easy DIY Antennas for Beginners

(2) One of the most important thing in making a Coco is to accurately know the Velocity Factor (VF) of the coax used for making the Coco. This can be achieved by using a Coax of known brand & model whose Specs or Data Sheet is avaiilable on internet, from which you can find exact value of VF.

Once you know VF, the length of element is simply 138 mm x VF. For example if your RG6 coax has a VF of 0.85, then its element length will be 138 x 0.85 = 117 mm.