After understanding the drag equation, I wanted to figure out the history behind drag forces and how they were discovered. The equation was conceived by Lord Rayleigh, and has uses in many fields across the world. Car designers, scientists, top professors and astronauts alike all rely on the drag equation for applicable circumstances. I realized that so far, I have failed to define exactly what the drag force is. So: the drag force is a resistive force on an object by a fluid in the direction opposite to the object’s movement. A skydiver, for example, will feel the drag force in the opposite direction of his downward velocity (upwards). Some of the time this is hard to observe, but with lighter objects, we see it every day. Something light like a whiffle ball or a beach ball will slow down quickly due to drag forces. The reason lighter objects are more affected is because the drag equation does not take mass into account. Two equally shaped objects with the same drag coefficient, velocity, and reference area but with different masses will each experience the exact same drag force. Because F = ma, or a = F/m, a lighter object will have a much greater acceleration (or rather, deceleration) with the same force. This is why a beach ball doesn’t get very far, but a baseball does.
With that said, now I can go back to where and why the drag equation is used. Car designers use it to design the most aerodynamic cars possible – a drop in the drag coefficient of a vehicle by just 0.01 can boost the fuel economy of the car by up to 0.2 MPG. Certain cars, like the Toyota Prius, take advantage of this and produce much better mileage than cars with larger drag coeffcients (truck, SUVs, Hummers, etc). Someone at NASA might use the equation to determine the forces on a rocket as it leaves the earth’s atmosphere into space, or a physicist might use the equation in an experiment to discover the most aerodynamic surfaces and shapes. The equation has many, many uses.
Now I’d liketo return to skydiving, and how it is impacted by drag forces. When we think of an object or person in free-fall, what we might think of is someoneor something falling and accerelating for a long, long time. In a vacuum with infinite depth, this would be true, but in real life, it is not. Because we live on earth, an object in free-fall will eventually crash into the earth and stop moving due to the normal force exerted by the earth onto the object. And because we don’t live in a vacuum, we have air surrounding us at all times. This presence of air (a fluid) causes a drag force on any object moving through it. Because of this, objects free-falling in the earth’s atmosphere will not accelerate and accelerate until they hit the ground. Instead, they will reach a terminal velocity, where their acceleration is zero because the net force acting on them is zero as well.
But the skydiver was accelerating when he hopped out of the plane! What happened? Well, even though the drag force is independent of ths skydiver’s mass, it is entirely dependant on the skydiver’s velocity. As the diver picks up more and more speed, the drag force rises and rises. Eventually, the skydiver has enough velocity so that the drag force is equal to the force of gravity. This means that the sum of the forces acting on the diver is zero, and that the skydiver’s acceleration is zero as well. When an object or skydiver has reached this point, it has reached its terminal velocity. See this picture for further exaplanation:
Now you might ask: how do you calculate the terminal velocity of an object? It’s pretty simple really, using Newton’s 2nd law and the drag equation:
Anyways, that’s all I’m going to look at for today. I’ve really cemented my understanding of drag forces, the drag equation, and terminal velocity, and I think I’m going to start looking into solving some simple problems tomorrow. I’m getting close to completing the conceptual aspects of my learning objectives, but I’m not quite there with the quantitative stuff yet.
Sources:
http://auto.howstuffworks.com/fuel-efficiency/fuel-economy/aerodynamics2.htm
http://cnx.org/content/m42080/latest/?collection=col11406/latest
Physics of Skydiving 