Drag Forces Like friction, the drag force always opposes the motion of an object. Unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid. This functionality is complicated and depends upon the shape of the object, its size, its velocity, and the fluid it is in. For most large objects such as cyclists, cars, and baseballs not moving too slowly, the magnitude of the drag force FD is proportional to the square of the speed of the object. We can write this relationship mathematically as FD ox U2. When taking into account other factors, this relationship becomes FD = 2CpAv2, where C is the drag coefficient, A is the area of the object facing the fluid, and p is the density of the fluid. (Recall that density is mass per unit volume.) This equation can also be written in a more generalized fashion as FD = bu^, where b is a constant equivalent to 0.5CpA. We have set the exponent n for these equations as 2 because when an object is moving at high velocity through air, the magnitude of the drag force is proportional to the square of the speed. For small particles moving at low speeds in a fluid, the exponent n is equal to 1. Drag Force Drag force Fp is proportional to the square of the speed of the object. Mathematically. FD = Cp AU2, where C is the drag coefficient, A is the area of the object facing the fluid, and p is the density of the fluid. Athletes as well as car designers seek to reduce the drag force to lower their race times. Aerodynamic shaping of an automobile can reduce the drag force and thus increase a car's gas mileage. USA From racing cars to bobsled racers, aerodynamic shaping is crucial to achieving top speeds. Bobsleds are designed for speed and are shaped like a bullet with tapered fins. (credit: "U.S. Army"/Wikimedia Commons) The value of the drag coefficient C is determined empirically, usually with the use of a wind tunnel (see figure below).
NASA researchers test a model plane in a wind tunnel. (credit: NASA/Ames) The drag coefficient can depend upon velocity, but we assume that it is a constant here. The table lists some typical drag coefficients for a variety of objects. Notice that the drag coefficient is a dimensionless quantity. At highway speeds, over 50% of the power of a car is used to overcome air drag. The most fuel-efficient cruising speed is about 70-80 km/h (about 45-50 mi/h). For this reason, during the 1970s oil crisis in the United States, maximum speeds on highways were set at about 90 km/h (55 mi/h).
Object C Typical Values of Drag Coefficient C Airfoil 0.05 Toyota Camry 0.28 Ford Focus 0.32 Honda Civic 0.36 Ferrari Testarossa 0.37 Dodge Ram Pickup 0.43 Sphere 0.45 Hummer H2 SUV 0.64 Skydiver (feet first) 0.70 Bicycle 0.90 Skydiver (horizontal) 1.0 Circular flat plate 1.12 Substantial research