Dear Tigersimmo,
The basic idea of the vertically radiused putter face has been around quite a while, and is usually associated these days with the Tear Drop putter design. The basic idea is to promote an impact modelled after a no-skid, all-roll billiards shot with a cue stick. In physics, imparting a level blow with a stick thru the top quadrant of a ball 5/7th the way up the ball's diameter matches the rotational motion with the translational motion, so there is roll matching the sidewise motion, and hence no "skid" at the start. Tear Drop designed a putter with the face radiused vertically, like putting with a tube sideways on a stick, so that the forward-most edge of the tube shape met the ball at the 5/7th height on the ball, moving level.
The usual trouble with these designs in that the golfer is not that consistent in the "level" delivery thru impact, so you still get variable results notwithstanding the basic general concept. When the golfer delivers the putter head too high, you really get bad results, as the putter's shape both tops the ball and punches it down into the turf at the start. It's not very easy to hit the ball too low with one of these putters. Tear Drop eventually reassessed the trade-off of trying to reduce a little initial skid versus inconsistent impacts and loss of energy and redesigned the shape of their putters with a drastically milder radiusing. The last one I saw had such a mild radius that extending the curvature into a complete circle would make a circle with a 40-foot diameter.
Other models include the Benson putter and the Rolo putter. Today, all these putters appear to have given up on the 5/7th level blow idea in favor of something simpler -- just send the putter COG on a rising path above the ball's COG and be content with impact near the equator.
Recent Tear Drop theory:
Benson Putter:
Rolo Putter:
A mild radiusing can be a good thing, and I have a knock-off putter like this that works very well. Whether it is better than a standard "slab" design is another question. The variability in the golfer's movement probably swamps any minute difference attributable solely to the design.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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