1st I think we also need to recognize some of the choices being made.
BEV fires like those seen in some Tesla video's are a result of deliberate choices .. not necessarily a requirement of having a BEV.
Rich on rich rebuild , his fire (linked to above) was not about the Tesla battery system .. Rich was extremely negligent .. he disabled the Tesla safety systems .. he had no BMS .. no balancing .. no thermal regulation .. the charger didn't turn off when the battery was fully charged .. then instead of leaving it alone or using ABC dry/foam fire extinguishers they started sprayed the burning Li batteries with water .. any rookie fire fighter knows you don't spray water on a live electrical fire , but the rich video did just that , causing more electrical short-circuits on other cells .. any rookie fire fighter knows you don't spray water on a burning puddle/pool of floating flammable liquid .. like a large tank of gasoline .. the floating flammable liquid will just float on the water surface and spreads the fire .. but that's what they did in the rich fire video .. the venting liquid flammable electrolyte spread by the water , the already over heated and fully charged battery short circuited by the water .. it was almost like they deliberately went out of their way to cause the fire , and make it worse .. the enormous number of video camera angles they had setup in advance , also make it further suspect .. for people who supposedly knew better they seemed to go out of their way to deliberately do many things wrong .. all while having lots of cameras in place to catch the whole thing on video.
For instance (one such example) the Toshiba SCiB LTO battery does not have a thermal run away condition .. Even if you puncture short-circuit it with nail .. it doesn't burst into flames like some of the other battery chemistry choices currently being used in BEVs .. sure it isn't a super conductor so there are is IR heating from the discharge .. but no fire from events that would cause a Tesla battery to burst into flames ..
.. It also lasts about 3-4x more cycles / years than the other battery chemistry choices currently be used in BEVs .. .. but .. this choice is currently deliberate .. It is currently more expensive $/wh , and lower energy density wh/kg .. So the same size and weight Tesla Pack that got ~300miles of range new with a ~8year ~80% of marketed Capacity warranty .. would for a little more money only get ~150 miles using that Toshiba LTO , and be like ~24 years to ~80% of marketed capacity , and the added fire safety thing too .. the market value (consumer choice preference) for 24yrs or for the increased fire safety is too small to counter the market value of ~300 miles range for less out of pocket $ .. sure I drive a 19 year old car , but most people don't.
The same potential to 'swap' to a safer energy carrier , is not possible for gasoline or diesel to a 'non-flamible' safer energy carrier fuel .. gasoline and diesel fuels have to be the high energy flammable dangerous products they are in order for the ICE to work.
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As to your question:
NTSHA already studied it .. back when the 1st gen Volt caught fire after it was in one of their crash tests.
When an accident happens ICE or BEV .. at that time .. the BEV is not any more likely to have a fire than a ICE .. nor is there any greater chance of injury from a fire when it happens.
Given the reports of improvements to BEV safety in the years after that .. but no such reports of any fire safety improvements to ICE vehicles .. it stands to reason it is at worst , still no more dangerous or likely BEV or ICE .. and .. at best , less likely/dangerous in BEV than ICE.
Thus we do reasonably know .. it's no greater risk to happen (might be less) .. and we know we can make the energy carrier (batteries) more safe in the BEV (if we want to) .. but we can't make the ICE energy carrier more safe (even if we wanted to) , the ICE depends on it being the high energy flammable product it is .. and the BEV is very likely to bring with it far less energy to do any work (like burn or melt things) .. the 1st Gen Leaf (fully charged) had what , less than 1 gallon worth of ICE fuel energy.
Of course .. as was already posted .. we will have to wait many more years to see how things shake out for aging BEVs vs aging ICE .. and as the % of BEVs on the road increases .. but .. the old BEV reduces it's kwh of fammable potential over time .. has even less energy kwh than the new BEV .. soo , it seems to me to be pretty unlikely that trend/tide will flip directions.
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To the thread topic .. I agree with the previously posted position .. I expect it will be a slow transition .. 50-100 years .. and even then .. like horses and wagons .. there will be hold outs still using ICEs long after the vast majority of society no longer does.
Mobile fossil fuel use will not be as efficient as a stationary facility could be.
But even the stationary facilities are starting to buckle to RE.
RE has been getting cheaper $/wh over time .. and in many places it is already cheaper than it's fossil fuel counter part .. and that trend continues.
Sure there is RE ICE fuel .. but it just has not been keeping pace with the efficiency gains nor cost reductions of other RE options like Solar/Wind.
That RE side of the ICE to BEV equation will also take a long time .. it's a big job .. I suspect 50-100 years .. but the numbers are already there today in allot of places , and the trend to continue to improve the numbers only continues to push the others further and further.