NERD ALERT
Just a fair warning, my brain gets obsessed with the "planning" part of projects. So much so that I usually start out with a spreadsheet and instead of just keeping track of where my money went, it's trying to figure out math problems to get the results that I have pictured in my brain.
An example of this obsessive behavior was choosing a manual transmission for my '40 Ford coupe, based on the rear end gear ratios, RPMs at take off and shift points, and the resulting RPM points after the shift has been made, just so I know what to expect when it's time to drive them. Turns out sometimes that works perfectly, and in the case of my '40 Ford panel truck, it resulted in me needing to change the rear gear ratios to get the RPMs in a range that shifting from 3rd to 4th didn't drop me below the power band of the 85HP flathead.
Today's mathing problem involved a z50 that's in KCMO, me in Springfield, a measurement from a stock and a 5cm extended swingarm, and an educated guess of the stock shock length of 280mm. (I HATED 8th grade geometry, and don't remember much, so I am thankful for online calculator tools for stuff like this.)
I actually kind of already knew the answer from having read a BUNCH of threads on the topic, so the answer is 12 to 12 1/2" or in the neighborhood of 305-315mm, but I had to solve the problem for myself.
Keeping the angle from the swingarm pivot to upper shock mount the same, results in needing the longer shock. It also will result in a slightly raised back end of the bike without any rider weight on it, which I am definitely a fan of since I will need that room since I am now a long time member of the "Tenth of a ton" club.
By using the protractor on the image of my z50 sitting in my driveway, I was able to calculate the approximate angle from the axle to the swingarm pivot, and up to the shock mount.
Using the known length of 280mm shock, and the 9" between the shock mount and pivot bushing center, and the 73degree angle of the swingarm to pivot and upper shock mount, it gave me a measurement for the distance between the upper shock mount to the pivot bolt.
I was able to change the formula to use the extended length of the new swingarm, and it gave me a measurement of 311.
The result of this? Well, I chose to spend some Amazon credits on a pair of 1.5" shock extensions to see how my maths prove out before dropping money on the final shocks that will appropriately support my lard butt. LOL
(Oh, and just for funzies, the bottom of the triangle should be pointed down at about a 21 degree angle to make it look right.)