Calculating Putt Break Over Distance w/ Friction

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SUMMARY

Calculating the break of a putt over distance while accounting for friction involves using the surface equation f(x,y) and the friction equation F = -kv². The process requires computing the gradient ∇f to determine slope behavior, which helps in assessing the force acting on the ball. Ultimately, solving the resulting differential equations with initial conditions, such as the ball's starting position and initial velocity, is essential. However, applying this in real-life scenarios is challenging due to the unknown nature of f(x,y) on actual greens.

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  • Understanding of differential equations
  • Familiarity with gradient calculations in multivariable calculus
  • Knowledge of friction models, specifically the quadratic friction model F = -kv²
  • Basic principles of physics related to motion and forces
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  • Learn about gradient vectors and their significance in slope analysis
  • Research friction models and their impact on motion
  • Explore practical methods for estimating surface equations f(x,y) on golf greens
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Mathematicians, physicists, golf course designers, and anyone interested in the physics of sports, particularly in optimizing putt performance on varying surfaces.

DylanB
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How would you go about calculating how much a putt would break over a given distance without neglecting friction?

EDIT: I've realized this would be more appropriate in the coursework section, unforunately it's too late now.
 
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You'd need the equation of the surface [tex]f(x,y)[/tex] along with the equation for friction in terms of velocity, like [tex]F = -kv^{2}[/tex]. You'd compute [tex]\nabla f[/tex] which would give you the slope behaviour (so you can work out the force on the ball) and then it's just solving differential equations, including your initial conditions (where the ball starts and it's initial velocity).

For a real life green this isn't practical since you don't know f(x,y).
 

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