Well that formula - 1/4 wavelength -0.61r is as close as you can get in my experience. A couple of things to think about if it doesn't seem to match reality. 1. measure the actual frequency of your bars - bars are not always in tune so can drift away from resonators. 2. Be sure to consider both tuning standard (ie A440? 442?) and temperature/humidity. Remember W=V/F where F=frequency and V=velocity of sound - but that will differ depending on the air temp and humidity. Plugs can have a "seal point" that is not quite as it seems. Ideally we are looking for a perfect flat resonator floor that seals at the exact boundary - but that is often not the case. That top surface of the plug closest to the bar is where we are measuring to of course - but if the shape is slightly concave or convex or has a bump or if the seal point is a bit further down in the middle of the plug... it will make the direct measurement inaccurate.
My best advise if you are making new plugs, is to make adjustable ones so you can move it till you get it working well with the bar. The simplest way is to use a holesaw to cut out 2 SLIGHTLY undersize disks of 3/4" plywood - find an O ring that is pretty much a perfect OD fit to the ID of your tube (thicker is better like about 3/16" or 1/4" rubber diam) Insert and glue in a nut to your top disk - bolt with a couple of locked nuts from the bottom so tightening the bolt squeezes the O ring to lock position and enough bolt protruding to use as a handle. That's about the simplest and cheapest way.
My best advise if you are making new plugs, is to make adjustable ones so you can move it till you get it working well with the bar. The simplest way is to use a holesaw to cut out 2 SLIGHTLY undersize disks of 3/4" plywood - find an O ring that is pretty much a perfect OD fit to the ID of your tube (thicker is better like about 3/16" or 1/4" rubber diam) Insert and glue in a nut to your top disk - bolt with a couple of locked nuts from the bottom so tightening the bolt squeezes the O ring to lock position and enough bolt protruding to use as a handle. That's about the simplest and cheapest way.
