Whipped up many of those collinears over the years, unless you have a good grid dipper for 1090 you probably won't get enough precision in the cutting to get the +6 or +9 db gain out of an 8 or 16 element, and the BW gets narrower the more elements you've got, meaning your match could be well off target. HOWEVER, if you get your hands on some plain old RG-11, RG-8, RG-9 or RG-213/214 (non-foam) with copper conductor and shield you can broaden the BW and it is much easier to solder than trying to solder aluminum and messing around with foil. I also note that in the original construction article he uses a 50 or 75 ohm terminator at the end of a 1/2 wave element... even though it will work, that is not correct. What you do is add one more coax element (to the four, eight or sixteen 1/2 wave stack) that is 1/4 wave instead of 1/2 wave and add a 1/4 wave (in air) radiator to the end of that, which will provide the proper radiation resistance as well as provide a DC circuit to ground to protect against static. You short the end of the last (now 1/4 wave) element, and the radiator is attached to the short... meaning you simply extend the center conductor of the last element by 1/4 wave and short the shield at its base. With a little loop on the end of the radiator you can hang it with some fishing line. You can also decouple the feed line and improve the match by adding another 1/4 wave coax section below the first 1/2 wave element feed point with either some radials around its base or a shorting stub from the bottom of its shield ("it being the 1/4 wave section) to point on the feed line shield 1/4 wave in air below.
But the most important thing is to check the actual velocity factor of the cable you are using. Do not use generic or manufacturers' specifications, my own experience is that they simply are not good enough when working at UHF and above, in fact rarely at VHF. Cable changes over time and from batch to batch, and the higher the frequency the more critical these changes become. This can be done either with a grid dipper or an analyzer like an MFJ 259. It is not necessary to dip the 1/2 wave elements at 1090 (though nice if you can), just get the actual, measured wavelength at 136.25 for your chunk of coax and divide by 16 to get the length of your 1/2 wave elements.
A quick search found this article which is about as good as any on the subject...http://www.angelfire.com/extreme/sideband/collinear.html
HAMs have been building these for decades, in fact I knew guys who made them to work 1296 back in the early 70's when very few had the equipment, skill or technology to get "up" there, let alone buy any antennas on the market. They'd just string them together and hang them from an outrigger on their towers.