Simple Calculation Showing a Small Increase in Size HA Body Size Could Lead to a Big Relative Increase in Rechargeable Battery Capacity.
Our perception of size is ~1-dimensional. If asked to compare HA body sizes between two HA’s (it’s been done on this forum before), we might compare the two lengths vs. each other, the two widths, the two thicknesses. If one HA body was 10% bigger in all dimensions, would that be a big deal? Maybe not. But it could significantly increase relative battery capacity. Because battery capacity is a function of volume (dimensions cubed) - the increased mass or space occupied by battery material.
If every dimension increases 10%, the volume of the hearing aid (length x width x depth) is 1.1 cubed greater, i.e., 1.1 x 1.1 x 1.1. That’s a 1.331 times increase in overall volume of the HA body. What if this 33.1% increase in volume was all devoted to adding more Li-polymer battery to the HA body? Is the HA to begin with 100% battery? Certainly not. If the battery occupied 50% of the original HA body and you increased its size by 33.1% of the original body size, the battery is now 33.1% increase in original body size to HA battery increase/50% of original body size is battery = 60% increase in HA battery size for only a 10% increase in each dimension.
OK. Let’s get extreme. Let’s say the original HA battery size was 75% of the original body. Then 33.1% increase in body size to increased battery size / 75% original body size is battery = 44.4% increase in HA battery size for only a 10% increase in each dimensions.
I think both these thought experiments overestimate the original size of the battery as a proportion of the overall HA body size so a 33.1% increase in body size entirely devoted to more battery likely would be an even bigger increase in relative battery size-if the battery were 33% of the original body, 33%/33% would be a 100% increase in battery size for a 10% increase in each dimension. But the point of these calculations is that even if the Li-ion battery already occupies a substantial portion of a rechargeable HA body, with a very modest 10% increase in each linear dimension, you can significantly increase the relative volume of the rechargeable battery and get enough extra battery capacity not to have to go between 0% charged and 100% charged in using the Li-ion battery. But users want small hearing aids and HA OEMs want to sell them new HA’s every so often so who wants to make a hearing aid bigger than the competition’s and one that lasts much longer so there’s less inducement to upgrade every few years.