Hello, new to the board. As to carbon arrows and tuning, if you buy a 500 spine arrow @ 32 inches and cut it to your desired length say, 28 inches, Do you still have a 500 spine arrow or are you approaching a 450 or 400? And, If you replace the now missing GPI with added insert weight will you negate the spine change in cutting the arrow? Hope that makes sense. Thanks

Spine on carbon arrows is measured at 28 inches so you still have a 500 (static) spine if you shorten them to 28 inches.  However, the arrow will act dynamically stiffer at 28 inches than it will at 32 inches. 

If you add weight to the front, it will soften the dynamic spine.  Whether it negates/balances the stiffness gained by shortening the staff depends on how much weight you add.  Since most carbon arrows weigh about 8 grains per inch, give or take a gpi, cutting off 4 inches of shaft would reduce the overall weight by about 35 grains.  You would have to add a lot more weight up front (my guess 150 to 200 grains) to "balance" four inches less shaft, i.e., soften the dynamic spine enough to equal the full length shaft.   

The static spine stays the same after cutting the arrow, because that is a characteristic of the shaft itself.  The dynamic spine of the arrow changes with it's length, point weight, and less commonly with its tail weight.

While the static spine has a number, e.g. .500, I have never heard of a number associated with dynamic spine.  It is described instead as a change from a previous condition, e.g. the dynamic spine increases as the shaft is cut shorter, or the point weight is reduced.

My experience is that an insert (without considering the weight of the insert) effectively shortens the shaft by the length of the insert, because it essentially eliminates the bend in that part of the shaft.  As the weight of the insert increases, the additional weight begins to offset the effect the insert itself has in reducing the effective length of the shaft, and at some point may become heavy enough to reduce the dynamic spine of the arrow.  My experience is that if the purpose of the additional weight is to reduce the dynamic spine of the arrow, that is best accomplished by increasing the point weight.  If the purpose is to increase the weight of the arrow with as little effect on dynamic spine as possible, that is best accomplished by using a weighted insert.

Dynamic spine changes dramatically with arrow length, and more gradually with point weight.  I have had cases where I have increased insert weight to attempt to reduce dynamic spine with little result, and in one case, the dynamic spine actually increased when the additional weight went behind the existing insert, thus effectively reducing the effective shaft length .

Thank you guys. Yes that answers my question. Your post helped me much in understanding the complexities of the  arrow. To sum it up, archery, especially Traditional archery is a bit complicated from the shooters perspective. I suspect if a fly poops on my shoulder just prior to release, yep, It's going to throw off my shot.

Here is a good read on tuning.

https://www.fenderarchery.com/blogs/archery-info/basic-tuning

Yup that is a good article, Gery.