http://www.lasc.us/Fryxell_Book_Chapter_11_Wadcutter.htm

The typical 38 Special HBWC match ammo traveling at 650 fps or so, does start to yaw a little past 50 yards. Push a solid base wadcutter 850 and it flies straighter for a greater distance. Put that same wadcutter in a 357 Mag going 1,100 fps and it will do great work at 80 yards and beyond. I have not shot them and farther so I don't know.

The instability of the wadcutter depends on how fast it is going when it hits the target. Higher speed means greater distance.

Years ago there was an egg stealing bitch what would come over from the next farm over to steal eggs and chickens to feed the pups she'd whelped. Her people didn't feed her so it was understandable - but inexcusable. One afternoon I looked out and saw her sneaking up the trail, keeping low and heading for where the chickens (true free range birds) usually hung out. The 6" Rossi was handy and loaded with 148 gr Lyman (or was it Ideal?) wadcutters crimped over a 22 LR case full of Especial de Caça (about the same burn rate as Bullseye). It was a decently accurate load in this sixgun. I didn't expect to hit her as she was 50 meters or more out there, but figured I'd let her know it wasn't healthy around there. I held right at the base of her ear as she paused to sniff and get her bearings - and it was like I'd reached out and placed the slug with my hand, it hit exactly where I was holding. She hit the ground as the shot and then began to howl. As I ran up to her she was trying to drag herself towards home. Two rounds into her neck did no good so I got around and managed to get one into her head. That one shut her down completely, game over. So it's not just about getting there accurately, it's about having enough OOMPH when it gets there. I've NO idea what speed those slugs were going, but it wasn't enough to do a clean job of it. A faster moving bullet where I placed the first one would have shut her down right there.

Below about Mach 0.8 (~850 fps), one observes a conformal slipstream around a projectile. In other words, the air flowing past the bullet conforms to the bullet's shape and is flowing more or less parallel to the surface. That conformal slipstream starts to get distorted above about Mach 0.8, with a larger turbulent boundary layer forming along with a vestigial bow wave. By Mach 1.0 (~1080 fps) one observes a well defined separate bow wave in front of the bullet, and emanating backwards at an angle.

In part, a bullet's stability is influenced by how well the bullet's ogive interacts with this bow wave and turbulent boundary layer.

One of the issues facing a true cylindrical wadcutter is the complete lack of an ogive, so any yaw (precession) is destabilizing. For a round-nose or spitzer bullet shape, the ogive fits inside this, and the bow wave serves as damping agent to dampen the yaw. For a true cylindrical wadcutter, there is only an edge, and a large flat face, so not only is there nothing to dampen the yaw, the large flat face can actually amplify the yaw, leading to instability (and ultimately tumbling).

Nowadays, most people associate the term wadcutter with what used to be called "button-nosed wadcutter". The purpose of the "button-nose" is to provide kind of a "false ogive" and generate a little bit of stability, and extend the useful range.

I did some testing with an ogival wadcutter in .44 Magnum a number of years ago. It weighed 365 grains and I was shooting them at about 1125 fps from my 7 1/2" Ruger SBH, as I recall (I was looking for a short range hog thumper load). Groups were good at 25 yards, and still pretty good at 50 yards. Shooting at impromptu targets on the hillside at about 80-90 yards was an eye opener for me -- about half of my shots hit close to the point of aim (within a few inches), and about half of my shots missed by 10-20 FEET. Clearly, some of those bullets were starting to tumble somewhere around 60-70 yards or so.