Please help settle a bet

[mike rico]

[SOLVED] Please help settle a bet!

A friend and I were debating about wether a base ball travels further in hot air or cold air. For example 60 degrees versus 90 degrees. Can someone please shed some light on the subject.

 

[chroot]

The 90 degree air would be less dense than the 60 degree air (all other atmospheric features being held the same). As a result, 90 degree air imparts less wind resistance on the ball. The ball will fly further in 90 degree air.

- Warren

 

[enigma]

chroot is right,

Although, it would be really difficult to do any sort of test for this in real life. There are just too many variables which would be difficult to impossible to isolate.

The difference in density between 60 and 90 Fahrenheit is also pretty small, so even if you were able to isolate everything else (spin of the ball, force of the throw, angle of the throw, pressure the same throughout the path, etc. etc. etc.) you're not talking about a really appreciable change in distance.

 

[Bystander]

Viscosities of gases increase with increasing temperature --- hence, the ball travels farther in cold air if density is held constant.

 

[climbhi]

Originally posted by Bystander
Viscosities of gases increase with increasing temperature --- hence, the ball travels farther in cold air if density is held constant.

Couldn't you argue that if it became too cold the viscosity of the gas would see a sudden jump upwards (i.e. gas condenses to liquid cuases viscosity to skyrocket...)

 

[Bystander]

Depends on how many nits you want to pick --- gases are not liquids, and vice versa --- however, cooling along the critical isochore might get to a rather weird region around the critical point while still arguably in the gas phase.

 

[Njorl]

I assume you mean a baseball hit by a bat. You must also consider the elasticity of the ball and bat. I believe both increase with temperature.

I suppose this all relates to why you see fewer home runs in April and October than in other months of the season. The biggest reason is not physics, it's biology. Pitchers work harder than anyone else on the field. In hot weather, they tire more easily. Tired pitchers make mistakes. Mistakes are hit for home runs. All the physics stuff might make for a differences of a few inches on a hit ball. Those few inches are rarely significant.

Njorl

 

[climbhi]

Originally posted by Bystander
Viscosities of gases increase with increasing temperature --- hence, the ball travels farther in cold air if density is held constant.

Are you sure that viscosity increases with temperature? I don't think it does, rather I think it decreases with temperature. And my prof stated the same in class today so... My previous point was me trying to say this more subtly. Could someone settle this for us.

 

[Bystander]

Originally posted by climbhi
Are you sure that viscosity increases with temperature?

"...of gases..."

I don't think it does, rather I think it decreases with temperature.

This is the case for liquids; what people wish to think, or intuit, has very little to do with observed physical behaviors.

And my prof stated the same in class today so... My previous point was me trying to say this more subtly. Could someone settle this for us.

 

[Andre]

Now the free moving ball is subject to drag. the standard basic drag formula is D=0.5*Cd*A*R*v^2

Cd is considered a "constant" value
R is the air density,
A is the size or area
V is speed
So basically air density and temperature are inverted proportional so less drag with higher temperatures, unless Cd has a surprise.

Now Cd is dependent on the shape of the subject (form drag), possible interference with air flow due to other parts of the object (interference drag) and skin friction. In all cases viscosity is a basic variable. Viscosity has a dimension of force*time/area. Force translates to mass and mass to density so viscosity should decrease with density.

So basically higher temperature is less density and less viscosity resulting in less drag and the ball should fly further.

Did I win?

 

[Artman]

Andre is very close. The Cd value in the equation he gave is selected from a chart that is created from wind tunnel data. The value that you use is determined by the Reynolds Number of the object. Here is where the viscosity comes into play. The kinematic viscosity of the air is used to calculate the reynolds number. The calculation for that is Re = v* L / ([mu] /[rho] ). v=velocity in m/s, L = the length of the longest cross-sectional side in m and ([mu] /[rho] ) is the kinematic viscosity.

Kinematic viscosity of air rises slightly when the air gets warmer, but not enough to make a noticable difference on the drag experienced by a hit baseball. Viscosity goes from 1.5E-5 at 20 deg C to 1.79E-5 at 50 deg C.

With the speed of the baseball being about 165 mph or 73.8 m/s when hit (approx) and the size of a baseball at about .076 meters the Re is high enough (Re > 3 x 10E5 each) that neither viscosity changes the value for Cd used in the calculation, which is 0.1 for a sphere

Density of air plays a bigger roll. It changes approximately 6% from the 60 deg F air to 90 Deg F air. and directly effects the calculation for drag as noted by Andre.

 

[russ_watters]

Lets not forget humidity too...

 

[Artman]

Originally posted by russ_watters
Lets not forget humidity too...

I considered mentioning the effects of humidity. There is a relationship between relative humidity and density. If we start off at 60 degF and 50 % relative humidity (RH) the specific volume of the air is 13.2 Cu Ft per lb of dry air. If we just heat the air to 90 degrees and don't add humidity the RH drops to below 20% and the specific volume is 14.0. However if the RH stays 50% when the temperature rises to 90 Deg F then the specific volume becomes 14.2. changing from a 6% increase to a 7% increase in the specific volume (a 6% to a 7% decrease in density).

 

[ObsessiveMathsFreak]

So is the drag greater in hot air or cold air?

 

[Artman]

Originally posted by ObsessiveMathsFreak
So is the drag greater in hot air or cold air?

Let's plug in the numbers and see.

Calculation for drag from Andre's post...

D=0.5*Cd*A*R*v^2

Cd is considered a "constant" value
R is the air density,
A is the size or area
V is speed

Cd for both temperatures = .1

R = Density = .076 at 60 Deg F (50% RH)

R = Density = .070 at 90 Deg F (50% RH)

A = Area of the baseball (projected area normal to the flow or the cross-section will work for our use) standard baseball = 9" circumference approximately 2.86" diameter, .072 meters / 2 = .036 meters Radius. Pi x R^2 = .004 sqr meters.

V = Velocity in m/s = 73.8 (approx 165 mph)

I get .144875 using R= .076 (60 deg F) and .133438 using R= .070 (90 deg F). I think you will find that there is more drag on the ball in colder weather.