4GOLF BALL AERODYNAMICS Large Wake of Separated Flow, High Pressure DragLaminar B.L. Separation PointReduced Size Wake of Separated Flow, Lower Pressure DragTurbulent B.L. Separation Point
5GOLF BALL AERODYNAMICS Laminar B.L.Turbulent B.L.Laminar B.L.Turbulent B.L.Pressure drag dominates sphereDimples encourage formation of turbulent B.L.Turbulent B.L. less susceptible to separationDelayed separation → Less drag
6LIFTING FLOW OVER A CYLINDER Kutta-Joukowski Theorem
7SUMMARY OF ROTATING CYLINDER IN CROSS-FLOW Rotating Cylinder Generates LiftVelocity is faster over the top of the cylinder than bottomPressure is higher on the bottom than over the toplifting force is directed perpendicular to the cylinder velocity (or the free stream velocity if the cylinder is stationary)Predicts Zero DragNotice vertical plane symmetryInviscid flow approximation does not model drag physics
9SUMMARY OF STREAM AND POTENTIAL FUNCTIONS TABLE 3.1
10IMPLICATIONSLift theorem applies in general to cylindrical bodies of any cross-sectionLift per unit span of airfoil is directly proportional to circulation around bodyCirculation also defined from pressure distributionCirculation is an alternate way of thinking about generation of lift on bodyPhysical source of lift is pressure distribution
12FLETTNER ROTOR SHIP Length: 100 ft Displacement: 800 tons Rotors: 50 ft high, 9ft diameter
13FLETTNER SHIP Flettner rotor ship in NYC harbor, May 9, 1926 Since power to propel a ship varies as cube of its speed, 50 hp used for this auxiliary propulsion system represented a large increase in fuel efficiency
14FLETTNER ROTOR SHIP: EXAMPLE Flettner Rotor Ship Data:Approximately 100 ft long, displaced 800 tons and wetted area of 3,500 ft2Two rotors each 50 ft tall and 9 ft diameter rotating at approximately 750 RPMMeasured ‘lift’ coefficient was 10 and measured ‘drag’ coefficient was 4Water drag resistance coefficient of boat CD = 0.005Question 1:If the ship is moored (tied to a dock) and subject to a 25 ft/s cross-wind what forces parallel and normal to the ship’s center line are generated?Question 2:How fast will the ship ‘sail’ in open water if the keel aligns itself with the resulting force of the rotors?Note: Keep in mind that boat is now moving and there is a relative velocity that rotors see, which is combination of wind and motion of boat
15OTHER EXAMPLES OF MAGNUS EFFECTS Spin-damping and Magnus dynamic effects are important when determining targeting accuracy of missiles, artillery rounds, and re-entry vehiclesEnergy waves strike proton on underside and because of its spin are forced around it, result is a difference of pressure between each side of proton.
18CURVE BALL BATTER PERCEPTION Perception plays a big role in the curve ball: The typical curveball goes through only 3.4 inches of deviation from a straight line drawn between the pitcher’s hand and the catcher’s glove. However, from the perspective of the pitcher and batter, the ball moves 14.4 inches. This proves that a curve ball really curves.
21EXAMPLE: FOOTBALLFluent 5 Simulation of Football in Flight (Sliding Mesh Geometry)Forward velocity: 40 MPHRotation rate: 300 RPMHigh pressure region in front of ball, long trailing wakeLaces cause B.L. to separate and rotates with callEven if ball is thrown straight, ultimately will begin to wobble