Coppertops vs. Car Batteries
        1. Voltage Comparison

This is very simple. Our triple A cell has a nominal voltage of 1.5V, meaning eight AAA cells can approximately equal the voltage supply of a car battery. This is a strong initial note to start the analysis on, because if voltage supply was the only remarkable issue preventing the replacement of car batteries with copperheads, we have addressed the problem. But it is plainly evident that this is not the case.

        2. Lifespan

Here, it is uncertain what the effective amperage hour rating of our 8 AAA cell arrangement would be. They are intolerant of increased current, but, if we assume each battery supplies 100 mA, we might see a service life of ~nine hours at 800 mA, idyllically, or, about 7.2 amp hours.

This, compared to the ~45 amp hours you might draw from a car battery, is immediately lackluster. But, it would merit saying that. while we have technically matched the voltage output of a car battery, I did so without considering the raw volume of that single cell versus our eight AAA cells. For reference, our 8 cell substitute weighs 88 grams.

The solution to this problem is to lay the cells in parallel, reducing the current run through each individual battery and improving their performance, while also drastically increasing lifespan. To match a car battery, I work with my initial flawed assumption and divide (car cell amp hours/AAA amp hour estimate) which equals 4.5. Rounding down, we now have an 8x4 arrangement, and if we assume a current of 2 amps, with each individual battery bearing a current of 500 mA, we now see that the arrangement should last about one hour when we take into account the performance of a AAA at various currents versus 22.5 from the car battery. Fortunately, adjusting this to a practical performance level from here is simple.

We start with two knowns. Our cell arrangement must be able to provide ~2 amps for about 22.5 hours. This means our current through any one of the parallel cells should not exceed 50 mA. dividing 2000/50 we get 40. So, an 8x5x8 cell arrangement, about 320 AAA cells weighing 3.52 kg, will comfortably match.

        3. Amperage draw

A perhaps too modest car battery draws maybe 300 amps, shorted. This performance is substantial, for the operation of the spark plug, so our AAA amalgam must be able to roughly match this.

A single AAA with an impedence of 250 mO has a shorting potential of about six amps, which, like the car battery, it can briefly tolerate. Each of our forty eight battery cells has a gross impedence of 2 ohms, for a total resistivity of 1/((1/2)*40) ohms, which is 50 mO. 12V/.05O equals 240 amps of draw, idyllically. So, we are about sixty amps short of our ideal. The relationship here is plain. to match ~300 amps of maximum draw, we increase the number of 8 AAA cells to fifty, bringing our total 400 AAA batteries, in a 5x10x8 arrangement.

       4. Temperature tolerances

This is mostly a footnote. AAA cells and car batteries actually have temperature performances that are not shockingly dissimilar. Both suffer badly below 0 C, and both can encounter issues at extremes over 50 C. Nominally, a person could handle day to day life with either the AAA amalgam or a standard battery.

        5. Recharging

Of course, anyone could have seen this issue approaching my analysis like a derailed train. What they may not have known is that, actually, AAA coppertops are rechargable, and, although this is still a crippling flaw in the performance of my AAA amalgam, there is still a way to make this work.

The reason AAA coppertops fail is that, by the nature of the solution they use to make them, they will generate insoluble compounds as they discharge, and the principle difference between copperheads and rechargable batteries of the same fundamental alkaline/manganese solution is that compounds are added to avoid this. Once a battery is fully discharged it has lost all potential for recharging. Past the 1/3 discharge mark it is at risk of failure if you recharge it. But, it has been observed that these batteries can still be charged between full charge and the 1/3 discharge mark, speaking loosely.

Coppertops are also very susceptible to overcharging. This means, essentially, that the alternator must be disabled to accommodate the AAA amalgam safely. As a consequence the amalgam must be manually charged after each use and carefully checked for unsafe discharge.

        Summary of Analysis
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