How do we define a pyramid bow? And what does "bend evenly" mean? Is a pyramid bow any type of bow that has the limbs tapering in a straight line? Would an English longbow, tapering from 1¼" wide at the handle to ½" wide at the tips, be called a pyramid bow then? And what about 4" wide at the fade, tapering to ½" nocks in a straight line? Or 3" wide tapering to 2" wide nocks? Or how about 1" wide fades, tapering to 4" wide tips? That's (part of) a pyramid as well, right? Just an upside down pyramid. And how about a bow tapering from 2" wide fades to ½" wide tips, that is 90" long? How much of a pyramid can we actually achieve in a bow that will always have nocks wider than zero inches (the tip of an actual pyramid)?
And how about "bend evenly". A circular tiller is "evenly"? And an elliptical tiller is not? Depending on the width of the bow, an elliptical tiller can still be the correct tiller that spreads out the load as evenly as possible.
In my opinion, a "pyramid bow" is a stiff-handled bow that has a more or less uniform limb thickness, with a straight line width taper from fade to tip resulting in a circular tiller. I call the thickness "more or less uniform", since you preferably want the tips to be a little bit thicker in most cases, to provide enough rigidity with the string grooves filed in.
A bow tapering from 1½" wide fades to ½" wide tips does still meet the pyramid width taper rule, but it will not have a more or less uniform thickness if you want to achieve a circular tiller. You would have to decrease the thickness towards the tips, if you still want this circular tiller, which is what we do in ELBs. A bow tapering from 4" wide fades to ½" wide tips will be quite the contrary. It will bend too much near the tips and the fades will be too stiff. So you would need to reduce the thickness near the fades.
In my opinion, a sensible pyramid bow will be tapering from 2½" wide fades (maybe 2¼" works as well) to ½" wide tips. The thickness could then probably be machine made with a thickness planer/sander to about 3/8" for a 40-50 pound bow. Then you would just have to glue down a thicker handle, while you could use powertools for the width taper (circular saw or band saw) and thickness (planer/sander). Only minor tillering would be necessary to create a circular tiller then.
So does "a pyramid bow of equal thickness always bend evenly regardless of starting width"? No, it doesn't. I've given several weird bow designs where Badger's intuition would probably feel that there's something wrong in that statement. The starting width at the fades would have to be around 2½" wide in my opinion to create a sensible pyramid bow. With other widths the bow would not have an equal thickness if you're looking for a circular tiller.
