[CTcard]

I am happy to defer to the engineers among us, but I believe density (of the fluid(air)) is only one factor affecting the drag on the baseball.  Viscosity also matters, so I thought I'd look at that.  

Density goes down as the humidity goes up (30deg C: 0%RH: 1.164  100%RH: 1.116 (down 0.41%).  units: Kg/m3
Density also goes down as the temperature goes up. (0% RH: 20deg C: 1.205; 30deg C: 1.164; 40 deg C: 1.127)
  For density, going from 30C 0%RH to 30C 100%RH is about the same as going from 30C 0%RH to 47C 0%RH

Viscosity also goes down as humidity goes up. (30deg C: 0% RH: 18.647; 92%: 18.569; down 0.42%)  units: 1e-??3?? Kg/m s
Viscosity goes up as the temperature goes up. (0% RH: 20deg C: 18.176; 30deg C 18.647; 40deg C: 19.111)
  For viscosity,  28C 0% RH is about the same as 30C 100% RH

NASA has a page on the drag on the baseball.
  https://www.grc.nasa.gov/WWW/K-12/airpla...ldrag.html
The drag coefficient (C_d) is generally inversely related to the Reynolds number
Per the NASA page, The equation for the Reynolds number is: Re = rho * V *  2 * b / mu
where rho is the air density , V is the velocity, b is the radius of the ball, and mu is the air viscosity.

At 30C, the Reynolds number would hardly change at all going from 0% to 100% RH.
RE(30C 0RH) * 0.9959/0.9958 = RE(30C 100RH)

... Unless the humidity changes the drag crisis significantly, it would seem the warmer temperatures would be a bigger effect than humidity on the ball's aerodynamics (when pitched & hit).

Surprised myself that I haven't chimed in previously as I am one of a couple of resident physicists on this board.

Friction/drag is a complicated subject that tends to not lend itself to clean mathematics. 
That NASA page sure doesn't clear much up, in my opinion.

Yes, temperature and humidity both affect air density (and viscosity) but so does atmospheric pressure. My back of the envelope calculation roughly matched yours that temperature would be a much bigger effect than humidity, with pressure inbetween.


However, the actual temperature differernce between Starkville and Palo Alto on an early June day is unlikely to be large, and at least this coming Saturday Palo Alto is forecast to be 4 degrees warmer. However, pressure will be a solid 0.3 inches of Hg lower in Starkville and humidity will be about 20-30% higher (right now it's only 13% higher in Starkville, and I cannot find a humidity forecast).

I'd guess the biggest difference from Palo Alto on the ball carrying would be the pressure.

-------------
Here is a NASA page where you can download an ap to simulate the flight of a hit baseball under different weather conditions.
https://www.grc.nasa.gov/WWW/K-12/Intera...sdown.html
(scroll to "HitModeler Weather" about 2/3rds of the way down)

It may be fun to play with, but I would be suspicious of its accuracy until proven. Drag is hard to model well.

[CTcard]

I am happy to defer to the engineers among us, but I believe density (of the fluid(air)) is only one factor affecting the drag on the baseball.  Viscosity also matters, so I thought I'd look at that.  

Density goes down as the humidity goes up (30deg C: 0%RH: 1.164  100%RH: 1.116 (down 0.41%).  units: Kg/m3
Density also goes down as the temperature goes up. (0% RH: 20deg C: 1.205; 30deg C: 1.164; 40 deg C: 1.127)
  For density, going from 30C 0%RH to 30C 100%RH is about the same as going from 30C 0%RH to 47C 0%RH

Viscosity also goes down as humidity goes up. (30deg C: 0% RH: 18.647; 92%: 18.569; down 0.42%)  units: 1e-??3?? Kg/m s
Viscosity goes up as the temperature goes up. (0% RH: 20deg C: 18.176; 30deg C 18.647; 40deg C: 19.111)
  For viscosity,  28C 0% RH is about the same as 30C 100% RH

NASA has a page on the drag on the baseball.
  https://www.grc.nasa.gov/WWW/K-12/airpla...ldrag.html
The drag coefficient (C_d) is generally inversely related to the Reynolds number
Per the NASA page, The equation for the Reynolds number is: Re = rho * V *  2 * b / mu
where rho is the air density , V is the velocity, b is the radius of the ball, and mu is the air viscosity.

At 30C, the Reynolds number would hardly change at all going from 0% to 100% RH.
RE(30C 0RH) * 0.9959/0.9958 = RE(30C 100RH)

... Unless the humidity changes the drag crisis significantly, it would seem the warmer temperatures would be a bigger effect than humidity on the ball's aerodynamics (when pitched & hit).

Surprised myself that I haven't chimed in previously as I am one of a couple of resident physicists on this board.

Friction/drag is a complicated subject that tends to not lend itself to clean mathematics. 
That NASA page sure doesn't clear much up, in my opinion.

Yes, temperature and humidity both affect air density (and viscosity) but so does atmospheric pressure. My back of the envelope calculation roughly matched yours that temperature would be a much bigger effect than humidity, with pressure inbetween.


However, the actual temperature differernce between Starkville and Palo Alto on an early June day is unlikely to be large, and at least this coming Saturday Palo Alto is forecast to be 4 degrees warmer. However, pressure will be a solid 0.3 inches of Hg lower in Starkville and humidity will be about 20-30% higher (right now it's only 13% higher in Starkville, and I cannot find a humidity forecast).

I'd guess the biggest difference from Palo Alto on the ball carrying would be the pressure.

-------------
Here is a NASA page where you can download an ap to simulate the flight of a hit baseball under different weather conditions.
https://www.grc.nasa.gov/WWW/K-12/Intera...sdown.html
(scroll to "HitModeler Weather" about 2/3rds of the way down)

It may be fun to play with, but I would be suspicious of its accuracy until proven. Drag is hard to model well.