^ So, basically more volume for same weight will perform better?
Two bats of similar weight One is concaved and the other isn’t..Both middles from low to High go give or take equally well.. however, the ‘low density’ bat enables me to have off middled shots still go miles.. the other bat however, if you don’t Middle it just clanks and doesn’t go.No science involved.. quite simply the bigger bats allow for more error in ball striking. In the modern game of white ball that’s immensely important as slogging means you won’t Middle everything
I'm pretty sure it has something to do with the coefficient of restitution (newtons laws) and there will be variability in the wood changing this (think of why golf clubs are now metal to reduce the variability and increase the trampoline effects. How much density changes this I do not know, but will certainly have an effect.I think it is worth considering it close to a golf club where the forces generated are also partly due to speed (so heavier clubs vs lighter clubs changes the ability to deliver speed of impact and in turn the forces generated) so lighter bats generate more speed, heavier bats need less speed to generate the same force. Adding a better rebound effect will in effect make the efficiency much higher as less energy is lost but not sure on what proportion that would account for compared with the effects of weight and speed.
I dont think the F=ma kind of equations can accurately/fully apply to cricket bats (unlike in baseball) since there is the "response" specific to the bat based on the "pressing" that is not accounted for in any of the equations. Two cricket bats with same weight and thickness but different pressing will rebound the ball differently. This is not accounted by any of known physics equations I think .That is also what makes the cricket bats so mysterious and make people want to buy more and more in search of that elusive perfect bat . Maybe we should research to come up with an accurate equation to apply to cricket bats. I am guessing it will have some coefficient like TK/SK or SS anonymous batmaker coefficient etc to account for the response introduced into the bat by the pressing of the corresponding batmaker, some way to account for handle materials/flex etc. etc.
That reasoning only works if you are assuming that the two bats are made to different profiles with the low density bat distributing more weight to the edges and the high density bat distributing more weight to the centre. The question is whether a low density bat of the same profile would perform better
F=MA will always be the right equation to apply except at speeds close to the speed of light (only applies when Sir Ben is batting 😂😂) . Problem is, it's really complicated to apply it correctly to a system as complex as this. More importantly, total momentum = mv is conserved in a bat ball collision, and this can be used to make equations. The physics equations do account for the pressing and response at different hitting points through the Coefficient of Restitution (CoR). The CoR is exactly the 'pinginess' of the materials, on a scale from 0 (ultimate dead plank! ) to 1 (most pingy). At the moment though I think this has to be measured by firing balls at different striking positions and measuring speed after the collision. Maybe materials scientists could suggest a formula for this based on density, pressing, age, etc. but I doubt it would be accurate.
It would never be the same as they would weight different weights
Yes, totally agree that it is personal choice and very complex in the end. There won't be a formula that solves the whole problem. But, don't agree about momentum. Total momentum is always conserved in a collision. Energy is also conserved, but some of it is used up in collision sound, bending /vibrating of the bat/deforming the ball, etc.
Momentum is only conserved in an isolated system from memory (so the effects of deforming of the ball, deforming the bat and the resistance etc are not included in an isolated system and assumes perfect elasticity). Those elements in effect all effect the outcome but i do agree it is more about energy loss as you say. Density is only a benefit if it changes the trampoline effect (COR) as mass remains constant based on the question. So no effect of high vs low density in my (slightly scientific) view as all about mass.With regards to the effect of swing speed vs mass I think there is limited difference with the numbers being quotes as around 1% benefit overall for heavier bats (heavier and slower swing speed), vs lighter and higher swing speed as you also have to swing your arms so effect of the extra weight is actually pretty negligible overall.
This the interesting question to me: whether a heavier bat but slower bat swing or a lighter bat and faster swing generates more power