Air density \rho (kg/m^3) is given to a *very* good approximation by the ideal gas law,
\rho = p/(R T),
where p is the pressure in pascals, R the specific gas constant (about 287 J/kg/K for dry air and slightly larger by maybe up to 2% for very humid air), and T the temperature in Kelvins.
Because the power lost to drag scales linearly with air density but as the cube of the ground speed (in still air), it will take about a 3% decrease in air density to give a 1% increase in speed, if power is held fixed.
Typically, as noted by another J7, (in mid-latitudes) temperature affects air density more than pressure at a given altitude, with humidity in third place. Temperatures vary by ~20 C seasonally, which is a ~7% impact on air density. Pressures might vary by 20-30 hPa between strong high and low pressure systems, which is a 2-3% impact on density since reference sea-level pressure is about 1000 hPa (Higher wind speeds encountered in strong low-pressure systems tend to make this less effective at increasing speed though!).
Also J7’s 1”/km/6C rule of thumb can be tested by this logic but probably is a bit high. 6C warming would be about a 2% decrease in density, which would be give a 2/3% increase in speed at constant power. At 40kph or 90”/km, 2/3% is 0.6"/km -- but 1"/mile faster for each 10F warming at 24 mph would be about right.
(edited to correct a dumb math error and revise the rule of thumb down a bit!)
\rho = p/(R T),
where p is the pressure in pascals, R the specific gas constant (about 287 J/kg/K for dry air and slightly larger by maybe up to 2% for very humid air), and T the temperature in Kelvins.
Because the power lost to drag scales linearly with air density but as the cube of the ground speed (in still air), it will take about a 3% decrease in air density to give a 1% increase in speed, if power is held fixed.
Typically, as noted by another J7, (in mid-latitudes) temperature affects air density more than pressure at a given altitude, with humidity in third place. Temperatures vary by ~20 C seasonally, which is a ~7% impact on air density. Pressures might vary by 20-30 hPa between strong high and low pressure systems, which is a 2-3% impact on density since reference sea-level pressure is about 1000 hPa (Higher wind speeds encountered in strong low-pressure systems tend to make this less effective at increasing speed though!).
Also J7’s 1”/km/6C rule of thumb can be tested by this logic but probably is a bit high. 6C warming would be about a 2% decrease in density, which would be give a 2/3% increase in speed at constant power. At 40kph or 90”/km, 2/3% is 0.6"/km -- but 1"/mile faster for each 10F warming at 24 mph would be about right.
(edited to correct a dumb math error and revise the rule of thumb down a bit!)