06-05-2019, 12:29 PM
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)
The drag coefficient does change significantly when the flow of the air around the ball changes its nature (between laminar and turbulent). This region is referred to as the drag crisis. 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).
Links you may find interesting:
More on drag crisis in baseball. (suggested reading)
Aerodynamics of baseball.
In situ measurements of drag on sports balls.
A study of baseball and softball aerodynamics.
Effect of air on pitches.
NASA's baseball pages.
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)
The drag coefficient does change significantly when the flow of the air around the ball changes its nature (between laminar and turbulent). This region is referred to as the drag crisis. 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).
Links you may find interesting:
More on drag crisis in baseball. (suggested reading)
Aerodynamics of baseball.
In situ measurements of drag on sports balls.
A study of baseball and softball aerodynamics.
Effect of air on pitches.
NASA's baseball pages.
