The graph below shows relative change compared to a reference point of rho=1.2041kg/m3 at sea level and 20°C (from wikipedia). Every color change represents a 1% change relative to that. I have also marked the conditions of last year's races. This includes only the two overwhelming factors: altitude and temperature. For pressure changes I have interpolated from data of air pressure at 0 and 1000m altitude. This is not perfect but the errors seemed small enough, of the magnitude of errors caused by local weather (0.2%-0.3%). The rest of the numbers came by applying the ideal gas law. I figured out the effect of humidity would be equally small. This is not true (see at the end of the post), but I leave it out of the graph for simplicity.
Flags represent the conditions of all 2012 races (some had to move a bit as they overlapped). There were no races held at extreme air temperatures this year, yet the spread due to temperature changes is much more important than that caused by altitude, Brazil excluded. We have a 10% change between China and Brazil but already a 5% change between races held at sea level. In a year with more extreme weather those numbers could easily be 15% total with 7% due just to temperature changes.
One always hears that the engine power suffers in Brazil due to the altitude, but Hungary, held in what I would call typical temperatures, is not that far away. Also interesting how Spa, normally considered an engine circuit, has 4% less air density than it could if it were at sea level.
Back to the original subject: with a more or less typical May weather and 20°C, the race in Barcelona registered 98% in this graph (the EU flag is for Valencia). Last year's tests were held predominantly between 10°C and 15°C, often a tad colder in the morning and at sunset (Jerez's altitude is 40m). With an air temperature of 10°C, the air density would have been 102% of the reference or 4% higher than in the race. So as a general rule, for any one place, 10°C temperature difference equals a 4% difference in air density. That's half the effect of Interlagos' altitude.
Most of this has been talked about in some threads in the past, like here , here , here or here.
A little compilation of the most obvious effects of air density on F1 cars (in all sentences one should add "at a first approximation"):
a) Engine power: Power increases linearly with air density as the same volume of air contains more oxygen (this will get more complicated with turbos).
b) Drag: Increases with air density, linearly.
c) Downforce: Increases with air density, linearly.
d) Cooling: Air of higher density has a greater cooling ability (does it scale up linearly?), but the engine is also putting down more power and hence producing more heat. Still, cooling scales with deltaT to a fixed maximum water and oil temperature, so cooling gets better at low air temperatures but not directly related to air density. Better cooling allows less air intake in the car, reducing drag.
e) Air temperature and track temperature: Normally track temperature will be air temperature plus 10-20°C. Tyre grip generally increases with temperature, but not directly related to air density.
The interplay can get complicated. For example: drag and engine power change linearly in opposite directions, so the ultimate top speed remains unchanged (at first approximation). Still, these effects make the car faster at lower altitudes and temperatures (higher density), as the car if often power limited but rarely drag limited, and it will get faster to speeds where it is also drag limited.
Of course we all get the impression that downforce trumps most other effects, affecting braking ability, cornering ability and the initial acceleration phase, with all the extra carried speed implied.
@Machin, any chance that your lap simulator can break down the individual effects?
Some interesting facts:
The concentration of oxygen in interlagos, while 21% at the local density, would be comparable to 19.3% at sea level. This is below 19.5%, the official limit for an oxygen deficient environment, not dangerous but unpleasant if the change was sudden.
Taking a 1.5m2 frontal section, a F1 car at 300km/h comes across 150kg of air every second.
The water content of air also has an effect as the molar mass of water is 18Da compared to about 29Da for dry air. At 20°C saturated air contains 1.5% of water by mass. This reduces the density of said air by about 0.6% but the oxygen content by 2.4% (as in from 21% to 20.5%). At 30°C those numbers almost double, something to think about next time the air in your shower doesn't feel very oxygen rich.
So, what other effects am I forgetting here?
For example: air viscosity increases with air temperature. Correlated to, but not directly a function of air density. This affects things like boundary layer and vortex formation, but its exact effects on car performance are beyond me.
Pitch in please.
