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The FiA institute founded in 2004 spends many millions of € for motor sport safety and F1 naturally is the most advanced.
The FiA regulations for track safety are making the building of new F1 tracks a costly exercise. You can assume that 25% of the cost of a venue is caused by safety. $60m will not be far off. Old circuits like Spa or Silverstone had to invest heavily over many years to meet the increasing safety standards.
You can't be too far off if you assume that teams spend 10% of their operating budget in order to satisfy all the hundreds of safety requirements in car design, test and race operations. Their combined budget is close to $1bn so this would put their annual safety costs close to $100m. Those figures may be bigger or smaller but at least the magnitude is established.
Race and test venues have to have expensive medical and safety services on site. You basically have hundreds of marshals, a fleet of emergency vehicles, an operating theatre, a team of physicians, air med evacuation facilities and specialists on stand by in near hospitals. It comes to at least $10m per event. If I add all that up the cost for safety in F1 is probably over $300m per annum today.
This situation has steadily grown up over the years. In the 60ties there was literally no significant amount of money spend. The first big push came with Jackie Stewart in the seventies as copperkipper already said. Then in the eighties we had a steady increase in car design safety efforts in order to make cars fire safe and the monocoque stronger with carbon sandwich technology. At that time the cost of safety was probably less than 10% of what we have now.
In the second half of the nineties after the deaths of Roland Ratzenberger and Ayrton Senna safety was massively ramped up. It is fair to say that we probably had a linear increase in cost between 1994 and now. The FiA had no budget on safety research and team budgets were only 20% of what they spend now. It is fair to assume that the cost of safety was also on a proportional level. That would put the total figure perhaps to $50m a year.
1965 $ 1m
1975 $ 10m
1985 $ 25m
1995 $ 50m
2005 $150m
1012 $300m
If you add up the cost over five decades you find a massive amount of money being spend just to make F1 racing safer. The total is probably exceeding $3bn. No other racing series on earth would invest so much into safety as F1 has over the years. If you are shocked by the explosion of safety cost from 2000 you have to consider that more than one new track has been build per year during that time frame. Also the upgrades to the existing tracks have been substantial. This btw includes tens of tracks that are not being in use for GPs but have been upgraded to F1 standards. Just think of A1-Ring, Imola, Turkey, Indianapolis, Magny Cours, Jerez, Portimao, Paul Ricard, Fuji and many others.