A proposal suggesting how hits could be quantified and evaluated more objectively.
How momentum is transferred
When an object is swung or thrusted, it has momentum - a mass and a velocity (linear or angular). Because of the compressive foam/other flexible materials in the weapon, not all of that momentum is transferred to the body instantaneously. That energy can be spread out over a longer time, or dissipated as sound or heat. The longer the transfer takes, the softer the hit will feel.
The other element that affects how momentum is transferred is the surface area of the weapon's contact area. The foam will greatly affect this, as the surface area may change during compression. It's possible that the foam compresses so much that the core of the weapon ends up transferring the momentum, which is referred to as the "core being felt." 4.2.1 The larger the surface area, the softer the hit will feel, but this doesn't mean we should make wider striking surfaces to make it hit softer - generally, when more foam is exposed in this way, it decreases how much the foam compresses, which changes our calculations in foam selection, making it hit harder.
The goal in constructing a weapon is to fine-tune this transfer "to prevent excessive stinging or bruising during a full-force swing," 4.2.1.1 while still letting the hit be felt, and allowing the weapon to return to its owner in a way that doesn't affect gameplay.
How a hit could be measured
If you think about someone's bare, open back being hit with a boffer weapon, it's easy to imagine it leaving a temporary red spot where it contacted their body. A device could be built that would record this image using an array of sensors, along with the total force over time, represented as a graph.
The image may just be a circle of a certain size, or a more complicated shape, similar to a heatmap, showing a concentrated area that would represent where a harder impact was felt - this could be used to determine if the core was felt.
The combination of this image and the maximum point on this graph could represent how hard the hit felt. A particular hit may affect different people in different ways, as well as feel harder on different parts of their body, so it may be interesting to look at both the size and maximum force of the hit, and correlate it with body parts, but also total weight, height, etc. of the individual.
How this could be used in boffer sports
If enough data could be collected with calibrated, repeatable hits on willing people and their various body parts, boffer rules/guidelines could specify a range of values allowed (possibly for each weapon type), preventing the subjectivity of weapon-checkers and whoever the weapons are being tested on. We could also systematically record values for various construction techniques, foams, and swing types, and track the behavior of the degradation of the materials over time.
To implement something like this, these measuring devices would either need to be easy and inexpensive to construct or buy, or a cheaper litmus test would need to be developed around the maximum value(s) specified in the rules, such as not being able to break a material with a standard/tolerated strength, which would correlate to a specific hit's measurement.
Some existing tests used in foam production
Usually these sorts of tests are very specific to the intended use of the material, so they may not be entirely relevant, but could supply some feedback on how a material might feel.
ASTM D3574
To conduct an IFD test, a circular flat indenter with a surface area of 323 square centimeters (50 sq. inches - 8" in diameter) is pressed against a foam sample usually 100 mm thick and with an area of 500 mm by 500 mm (ASTM standard D3574). The foam sample is first placed on a flat table perforated with holes to allow the passage of air. It is then "warmed up" by being compressed twice to 75% "strain", and then allowed to recover for six minutes. The force is measured 60 seconds after achieving 25% indentation with the indenter. Lower scores correspond with less firmness; higher scores with greater firmness.