baseball.frink

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// Baseball calculations
//
// Alan Eliasen, eliasen@mindspring.com
//
// The rules of Major League Baseball, section 1.09 states:
// "The ball shall be a sphere formed by yarn wound around a small core of
// cork, rubber or similar material, covered with two stripes of white
// horsehide or cowhide, tightly stitched together. It shall weigh not less
// than five nor more than 5 1/4 ounces avoirdupois and measure not less than
// nine nor more than 9 1/4 inches in circumference."
//
// http://mlb.mlb.com/NASApp/mlb/mlb/baseball_basics/mlb_basics_objectives.jsp

circ = 9.25 in
mass = 5.25 oz

circ = new interval[9, 9 + 1/4] inches
mass = new interval[5, 5 + 1/4] ounces

radius[circ] := circ/(2 pi)
volume[radius] := 4/3 pi radius^3

density[mass, volume] := mass / volume

vol = volume[radius[circ]]
println["The volume is " + formatSig[vol,"in^3",5]]

dens = density[mass, vol]
println["The density is " + formatSig[dens,"g/cm^3",3]]

x[v0, alpha, h0 = 1 meter, hw = 10 feet, g=gravity] := 
{
   v0 cos[alpha] tw[v0, alpha, h0, hw, g]@1
}

// Drag force on a baseball.  See:
//
// http://farside.ph.utexas.edu/teaching/329/lectures/node42.html#fcd
// http://webusers.npl.illinois.edu/~a-nathan/pob/ppt/SABR36_June06.ppt
//
//  It's unclear what the units are of these equations, though!
//  For the 
F[v] :=
{
   vd = 35 m/s
   delta = 5 m/s
   return 0.0039 m^-1 + 0.0058 m^-1 / (1 + e^((v-vd)/delta))
}

// Reynolds number of a sphere.
// See: http://baseball.physics.illinois.edu/KensrudThesis.pdf , eq. 2.3
// viscosity is *kinematic* viscosity of air.
ReynoldsNumber[velocity is velocity, diameter is length, viscosity is kinematic_viscosity] := velocity * diameter / viscosity


/* This is the drag coefficient for a MLB baseball, non-rotating.

   See: http://baseball.physics.illinois.edu/KensrudThesis.pdf ,
   Fig. 4.37.  

   This probably needs to only go up to about 120 mph, as that
   appears to be an upper limit for batted ball exit velocity
   according to the PitchFX database:

   http://baseballsavant.com/pitchfx_search.php
*/

Cd[velocity] :=
{
   if velocity < 91.82 mph
      return -0.0033 velocity/mph + 0.5883
   else
      return -7e-5 velocity/mph + 0.2917
}
      


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This is a program written in the programming language Frink.
For more information, view the Frink Documentation or see More Sample Frink Programs.

Alan Eliasen was born 20203 days, 11 hours, 19 minutes ago.