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Physics · Grades 11–12 · about 50 minutes

Thin Air at Coors Field: air density and fly balls

Students model air density at Denver's mile-high ballpark and estimate how much less drag a baseball feels than at a sea-level park.

Students will: Use an exponential model of air density; Relate drag force to air density; Explain a real-world effect with physics.

Free to print and share with your class. Includes an answer key.

Thin Air at Coors Field: air density and fly balls

Name: ______________________

Coors Field in Denver sits about 5,200 feet (about 1,580 m) above sea level, while San Francisco's Oracle Park is right at sea level. Thinner air means less drag on a batted ball.

Model and data
QuantityValue
Coors Field elevation≈ 1,580 m
Oracle Park elevation≈ 0 m
Air density modelρ(h) = ρ₀ · e^(−h / H)
Scale height H≈ 8,500 m
Drag forceF = ½ · ρ · C · A · v²

A standard textbook approximation; real density also depends on temperature and humidity.

  1. Find ρ/ρ₀ at Coors Field. Round to three decimal places.
  2. By what percent is the drag force lower at Coors Field than at sea level, for the same speed?
  3. Why does lower drag let fly balls travel farther?
  4. Breaking balls also curve less at altitude. Using the same model, explain why.
  5. The Rockies store game balls in a humidor. Why would extra moisture in the ball reduce how far it travels?

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🔑 Answer key (for teachers)
  1. Find ρ/ρ₀ at Coors Field. Round to three decimal places.
    e^(−1580/8500) ≈ 0.830
  2. By what percent is the drag force lower at Coors Field than at sea level, for the same speed?
    About 17% (drag is proportional to ρ)
  3. Why does lower drag let fly balls travel farther?
    Less air resistance means less deceleration, so the ball keeps more speed and stays in the air longer.
  4. Breaking balls also curve less at altitude. Using the same model, explain why.
    The Magnus force that makes a spinning ball curve is also proportional to air density, so it is weaker in thinner air.
  5. The Rockies store game balls in a humidor. Why would extra moisture in the ball reduce how far it travels?
    A slightly heavier, less bouncy ball leaves the bat with less speed, offsetting some of the thin-air effect.

Teacher notes

  • The Rockies began storing baseballs in a humidor in 2002; all MLB teams have used humidors since 2022.
  • Extension: compute ρ/ρ₀ for Chase Field in Phoenix (about 330 m).

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