Why are car batteries still so heavy?
So, obvious answer first:
why do batteries still weigh 20kg?
Because they're still the same lead-acid batteries. Simple as that. No other technology came near the low cost per Ampere (and ampere-hour) of those, near the reliability and near the ease of handling. 20kg isn't that heavy, if you consider that "fuel economy" still means your average new car carries around dozens of kilogram of "comfort" functionality, and weighs around 1 Mg for the metal parts alone.
45 years later, car batteries still look the same and weigh the same.
45? More like 120 years... but yeah. We still build bridges out of steel, our concrete has gotten better, but still is essentially concrete, we use Asphalt for roads, copper is still our favourite conductor, the most commonly found amplifier technology in everything that isn't basically low-frequency is a bipolar-transistor based class A/B amplifier, and our refrigerators still aren't based on more efficient means of heat transport, but on compressing more or less dangerous fluids.
So, now after the answer to your literal questionto your real question, that you sadly didn't ask
Battery technology has moved so far in the last 100 years. The lead-acid starter battery became common in cars in 1920, lead is essentially poison, and sulphuric/lead acid isn't any less dangerous. They tend to fail in cold temperatures, especially if not regularly maintained, and even though they're obviously cheap as hell to produce, the whole handling of them, including legal requirements to take back old batteries, must be a nightmare.
Why hasn't the industry just drawn a line and switched to things like LiIon or good ol' NiCd or NiMH batteries, now that electric cars have shown you can reliably drive years based on those?
The NiCd batteries are simply worse in every aspect but energy density than lead acid. NiMH is better, but much more expensive, and still has a higher rate of discharge, typically (unless you make them even more expensive). And still pretty hard to properly dispose of.
Lithium batteries aren't that easy handle. You need to protect them against all sorts of failures, and some of them are pretty fatal: don't overheat your lithium Battery. It will explode. And heat is a serious problem inside a motor compartment (in fairness, a battery doesn't have to be in there, but it's pretty handy).
The main reason really is cost. The battery in my last car, a 1999 Fiat Punto, supplied max 100 A (when I tried to estimate the actual short circuit current, around 43 A, but still a lot. Let's say P=U·I=12V·40A=480W) current, and had a nominal capacity of around 30 Ah (that's an energy of 12V·30Ah = 360Wh). It cost me 25€. So, rough guess, it's cheaper than 10€ to produce.
So, let's take a lithium battery type that is mass-produced and hence cheap. The commonly found round cells that make up many laptop battery packs are around 3€ each (let's say 1€ in production) for around 3Ah (11.1Wh), supplying up to 5A (tops, don't do that for long) at some 3.7 V. That says a single cell of these can supply 18.5W. So to reach the estimated 480W of my cheapo car battery, you'd need 26 of them. They'd cost 26€ in production, not counting the Euros you spend on control, charge and protection circuitry, on encasing them in something rigid and safe, and the fact that the minerals needed to produce some of the rare-metal components in Lithium batteries aren't currently getting cheaper, and equipping cars all over the world with those will definitely speed up that market mechanism.
Let's assume cost scales with capacity. My 26-cell lithium battery has 26·11.1Wh=288.6Wh energy. So we need to scale that by 1.25 to achieve the same 360Wh as the lead-acid battery.
Such a cell weighs around 90g. So the weight of the cells is 26·90 g = 2.34 kg. Ok, I don't have the exact weight of my cheap car battery in my head, but let's say it was 15 kg. So we saved weight by a factor of about 6.3, if our casing, and electronics are lightweight (they're not – as far as I can tell, you'll need a hefty switch mode power supply to be able to efficiently charge these using your car's generator, and those mainly consist of a pretty bulky coil of copper, and maybe some ferrite core that isn't exactly lightweight, either).
That leads to a cost factor of about 3.5 between component A and component alternative B, with handling disadvantages, lesser reliability and supply chain changes. No wonder the car industry isn't pushing in that direction. (And, by the way, they have excellent lobbying.)
The latest batteries are much lighter and cost less over a vehicle lifetime than ones of yore. But they do not use LA (lead acid) chemistry.
A LiFePO4 (Lithium Ferro Phosphate) battery will do what is required at acceptable whole of life cost BUT at higher initial capital cost - which makes it unattractive to car manufacturers.
Low initial capital cost seems to be the main reason to prefer lead-acid to LiFeO4 and it's not obvious that there are any other really good reasons.
Cycle life is very much greater than that of Lead Acid, which allows whole of life cost to be lower than lead acid.
Unlike LiIon (Lithium Ion) a "spike through the heart" will not cause the issues a LiIon has.
Charging control is "easy enough".
Compared to lead-acid:
Allowed depth of discharge, & max acceptable charge rates are higher,
Temperature range is better
Recharge efficiency is better.
Self discharge performance is better.
____________________________________________
Lithium Ion / LiIon:
It's worth commenting on LiIon batteries as they often get "bad press" with respect to safety.
Compared to lead-acid, LiIon chemistry offer substantially better mass and energy densities (lighter & smaller), somewhat longer cycle life, higher capital cost and probably somewhat superior whole of life cost. Properly managed, charging control is easier. Temperature ranges are better, charge/discharge efficiency is somewhat superior. Disdavantages relating to safety are largely not an issue - see below.
In many applications LiIon batteries are the battery of choice - from Dreamliners to Samsung phones to "Hoverboards", Mars Rovers to laptops and smartphones to MP3 players and more. The first three applications above were selected for their known spectacular failures. But anything used in a Mars Rover is chosen for its suitability in a long life, hostile environment, must not fail task. And there are hundreds of millions of LiIon batteries in everyday use in people's pockets and homes and cars and more.
Given the ways in which LiIon batteries CAN fail, the numbers that DO fail in a spectacular manner are very rare. Failures that are widely reported are quite often due to some systemic failure that affects a batch or model of battery that has been produced and distributed in vast quantities OR lower volume bu high profile applications. In such cases a design or manufacturing fault or shortcoming causes or allows failures whose consequences are exacerbated by the LiIon chemistry's unforgiving behaviors.
Examples are well publicised "vent with flame" events in some past Apple laptops, Samsung phones, self-balancing "hoverboards" and similar. In the 1st two examples usually competent manufacturers allowed a design fault to exist uncorrected and/or unnoticed or cut corners in manufacturing to the extent that safety margins caught up with them. In the case of the "hoverboards" the cause is unknown to me but is as liable to be low quality low cost manufacture and poor charge control as anything else. In consumer equipment LiIon battery failures often result from a short circuit occurring in a cell due to inadequate clearances and either consequent impact sensitivity or hitting the far end of statistical manufacturing tolerance variations. These are design and manufacturing errors that can be avoided at the cost of extra $ - something high volume manufacturers would love to avoid.
In the case of the Boeing Dreamliner battery failures I've not seen a final root-cause report BUT while a number of well publicised failures occurred (and maybe a few unpublicised ones) in a very small product volume, the consequences were astoundingly well contained.
A detailed examination of LiIon failures and modes and consequences shows that they are almost invariably nowhere near as violent as popular 'myth' suggests and that while the energy release is substantial, containment is relatively easy in engineering terms. Containment adds weight and volume and cost and is unlikley to be found in laptops or pocketable / portable devices. It IS found in Dreamliners and could easily be used in automotive single battery (ie non-EV) applications while keeping weight and volume still well below lead-acid levels and at modest extra cost. In electric vehicle applications the problems seem to have been solved or accommodated "well enough". I have ni expertise in vehiclar safety regulatory areas, but am confident that the regulations that bring us spectacular crash-dummy footage and allow the catting of high volatility petroleum fuels in passenger vehicles also address the safety issues around LiIon power sources. I have not heard of a 'Tesla' car being immolated through battery failure - although it may have happened - and I imagine that Musk and co believe they have this risk area "adequately in hand".
I have never, somewhat to my disappointment, seen a LiIon vent-with-flame event and do not personally know anyone who has. Occurrences are common enough to occasionally make the NZ news (NZ population is under 5 million).
LiIon versus LiFePO4:
Compared to LiFePO4, LiIon chemistry offers somewhat better mass and energy densities (somewhat lighter & smaller), substantially LOWER cycle life, slightly lower capital cost (per energy capacity), and substantially inferior whole of life cost. Charging control is about the same but LiFePO4 are significantly harder to damage in marginal cases. Temperature ranges are not as good, charge/discharge efficiency is about the same. LiFePO4 are far less subject to safety issues.
In areas where smallest size and weight and lowest capital cost matter (with electric vehicle use being a good example) LiIon are superior to LiFePO4.
In almost all other areas and applications, LiFePO4 are better or much better than LiIon and I'd consider them the current battery technology of choice for high energy long lifetime, high cycle count energy storage.