Magnus Effect Calculator: Sideways Lift Force on a Spinning Ball

The sideways force on a spinning object moving through air or water.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose whether to find the force, the lift coefficient or the speed.

Choose the fluid, give the ball radius or the area, the speed and the lift coefficient.

The calculator gives the Magnus force with the working, the sideways acceleration, the spin ratio and how far a ball of that mass curves over the distance.

Formulas used

  • F_L = \frac{1}{2}\rho v^2 A C_L
  • C_L = \frac{2F_L}{\rho v^2 A}
  • v = \sqrt{\frac{2F_L}{\rho A C_L}}
  • S = \frac{\omega r}{v}

Worked example

With the default numbers in the calculator above:

  1. Reference area of the ball: 0.0380 m2
  2. Magnus (lift) force: 1.86 N
  3. Sideways acceleration: 4.33 m/s2 (0.44 g)
  4. Sideways curve over the distance: 2.17 m after 20.00 m
  5. Spin ratio: 0.35

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Fluid Another fluid: enter the density below; Fluid density (used when the fluid is another fluid) 1.2 kg/m3; How do you give the reference area? Enter the reference area directly; Reference area (used when you enter the area directly) 0.04 m2; Speed of the object relative to the fluid 10 m/s; Lift coefficient CL 0.5.

  1. Magnus (lift) force: 1.20 N
  2. Sideways acceleration: 2.79 m/s2 (0.28 g)
  3. Sideways curve over the distance: 5.58 m after 20.00 m

Common questions

What is the Magnus effect?

The sideways force on a spinning object moving through a fluid. The spin makes the flow faster on one side and slower on the other, and the pressure difference pushes the object off its straight path.

Which way does the force act?

At right angles to the motion, towards the side where the surface moves with the flow. Top spin pushes a ball down and back spin lifts it.

What is the lift coefficient?

A number that says how much sideways force the spin gives for the speed and the size. It changes with the spin, the surface and the shape, so take it from a test or a reference.

Where is it used?

Curving kicks and serves in football, tennis, cricket and golf, rotor ships (Flettner rotors), and some ballistics and wind engineering problems.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics or physics text (Magnus effect and the lift equation).

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