I see you went to visit the big rat. Hope he didn’t gnaw too big a hole in your wallet. Looks like Jimbo is among the ever growing number of people who have realized that lift is just simple Newtonian physics. My sail puts a force on the air that passes by it and the air puts an equal and opposite force on my sail. That’s all, nothing more. I’ve been struggling with this concept of lift for about 15 years (since college) and I would have to say that I didn’t come to this conclusion until about a year ago. Sometimes the simplest answer is the correct one.
I’m so glad you have discovered 10 OF THE 12 steps to enlightenment. I hate to tell you Steve but once you start drawing diagrams, you can’t help but see the flaw in the circulation theory. To start out let’s place your diagram in front of you with the flow from left to right and the circulation clockwise. Now to the right of your diagram lets put a velocity vector to represent the flow after interacting with the circulation. If you add your 4 resulting vectors together and divide by 4 to get an average velocity vector after circulation, you will notice that the circulation cancels itself out. The flow before is exactly the same as the flow after and the circulation has no net effect on the flow. This was probably obvious to you before you started since circulation has no net direction of flow. If you sit down with the diagram you just drew and the flow diagrams from the actual experiment and ask yourself 1. Why is the flow in my diagram different from the actual flow? 2 If there is a pressure difference then why don’t I see a net change in my velocity vectors indicating an equal and opposite force being placed on the air? Why don’t my forces balance out?
Let’s start with the flow diagrams. First you are using a pure circulation with no physical object in the middle, where as a spinning rod is used in the actual experiment. Not a big problem. It’s not the flow around a stationary rod that is important, it’s the circulation created by spinning the rod and how it reacts with the flow that we want to look at. Look at the velocity vector on the left and right of your diagram then look at the flow lines from the actual experiment. Do you notice anything? In your diagram the flow has no net change in velocity after interacting with the circulation. In the actual experiment you will notice that the flow lines have changed directions after interacting with the circulation. How could we make your diagram more accurately depict the true flow? Go back in to your cad drawing and let’s make a change to your circulation. On the left side of your circle your circulation vector has a length of 0.5 pointing up. Let’s change it to 0.2. Now let’s change the circulation vector on the right to 0.8. Notice that I didn’t change the vector on top or bottom that gave you the pressure difference. Now redraw the resulting vectors and the vector that represents the flow after interacting with the circulation. Now you will notice that there is a change in the direction of the velocity vector of the flow after interacting with the “circulation” and it is in the same direction of the flow line depicted from the actual experiment. Now your diagram agrees much more accurately with actual flow lines. Now let’s look at the force balance. Sum the resultant vectors around your circulation. You will notice that there is a component that is now pointing down. The change in the direction of the velocity vector was caused by a force. You will notice that the direction of force on the flow is down and an equal but opposite force is applied to the circulation. The direction of the force on the circulation coincides with the difference in pressure. Now your diagram agrees with the actual flow lines and the forces balance out correctly not to mention that the pressure difference above and below the “circulation” agrees with the forces indicated by the velocity vectors. Everything agrees except you no longer have pure circulation. In fact you will notice that there can’t be any forces on the wing or rod if there is pure circulation because no forces can be transmitted to the flow. The original diagram that you drew with pure circulation won’t ever exist without another component introduced into the flow to force that condition but we can go into that in the future. It may take a few days, a few beers and lots of paper to digest all of this.