+1 on the comments above. As BBerson points process might be helpful. TOWS, in typical engineering textbook fashion, just jumps right into "this is how to calculate this", sometimes with only a modest basis for the work. Hmm.
Data in appendix IV of TOWS is based upon wind tunnel work. By the time the data cited in TOWS was taken, a whole bunch of stuff had become known and was taken into account in doing the work. Knowledge included:
- Reynolds number matters;
- Turbulence in the air matters;
- Moment changes very little if you capture forces at 0.25c;
- Boundary layer of the model matters;
- Wing tip effects matter;
- Boundary layer on the walls matter;
- The tunnel is restricted by the presence of the model;
- Forces vary linearly with projected wing area S and with dynamic pressure q. Moment varies with S, q, and chord;
So, they set out to control for these issues in order to define the characteristics of the foil, not the characteristics of the tunnel, the model, the air temp, density, velocity, and turbulence of the air. So what did they do about them?
- Reynolds number - is a dimensionless ratio of dynamic to viscous forces in the air. Dana cited it for foils above. The researchers found that most subsonic airplanes of the day used Re between about 1M and 6M, and that behaviour was fairly smooth between these numbers, so those were the Re they tested and reported;
- Turbulence - you get the wind in a wind tunnel by running a big propellor, and that can cause all sorts of burbles in the air that can poison the data. So much effort was spent to smooth flows and reduce turbulence;
- Moment changes very little if you capture forces at 0.25c - so they attached the foil to the precise balances at 0.25c;
- Boundary layer of the model matters - Very smooth models were generated with very low chordwise waviness so that turbuence in the boundary layer would be due to the airfoil shape and not the quality of the model. Then to show effects of surfaces less than perfect, they had runs with artificially roughened surfaces;
- Wing tip effects matter - in a real airplane, the wings end, and air rushes around the tips under the effects of lowered pressure on one side and raised pressure on the other side. Also, we know that the lift vs alpha curve is steepest at high aspect ratio, and flatter as aspect ratio gets smaller. To beat this, the model is constant chord and runs from one wall to the other wall;
- Boundary layer on the walls matter - a layer of air sticks to any solid in the tunnel, with air moving zero speed at the surface and speeding up towards free stream speed some distance away. This is boundary layer, and it can become quite thick. So they apply suction along the walls just upstream of the model. Boundary layer must form again, and it is just getting started at the model, minimizing this effect;
- The tunnel is restricted by the presence of the model - the model reduces the tunnel cross section, slightly choking the tunnel at this point. There are rules of thumb for how much reduction is allowed, computational approaches to correcting data for the choke, etc.
Then they deliberately run from well into stall at negative alpha through stall at positive alpha, at a variety of Re and model surface roughness, with and without split flaps. Lift, drag, and pitching moment are all carefully measured during these runs. Most runs are repeated multiple times, data reviewed for anomolies, and averaged. Then Cl, Cd, and Cm is solved for out of the well known equations of the form F = q*S*C. For lift, C is Cl, for drag, C is Cd, and for moment C is c*Cm. Data is reviewed and plotted.
Standard roughness was selected at a way overdone level. It is about the texture of anti-skid surfaces you will find on a boat deck or wing walk or maybe in your shower. This is way over the top compared to any bug accretion on leading edges, irregularities from rain drops, and really only represents the wing walk surfaces. But it does give you an upper bound on how bad the perfect shape but rough surface can be.
There is no attempt at showing you the effects of rivets, seams, and other irregularities. In so-called turbulent flow airfoils, these effects are modest, mostly adding a couple thousandths to Cd. In airfoils designed as laminar flow foils, the flow over the forward portion of the foils stays laminar at low alphas, and the drag has a low region through there called the laminar bucket. In these foils, waviness, bugs, water drops, seams, paint stripes, trip the boundary layer to turbulent. In your mind's eye, just pull the parabola looking curve from higher and lower Cl across the laminar bucket to get your new Cd...
What about the other appendices in TOWS?
Appendix I is theoretical velocity ratio of air flowing over airfoil thickness distributions known to be useful in airplanes at zero Cl and at some non-zero Cl.
Appendix II is the theoretical pressure ratio of air flowing over airfoil camber curves. We can assemble thickness distributions and camber curves to make a huge variety of airfoils. Likewise we can assemble the velocity profile of any of those foils from this information. Through Bernoulli's well known equation, velocity over a spot predicts pressure at that spot, so you can do detail resolution of forces and thus predict loads in structures.
Appendix III is the unitless coordinates of the airfoils discussed in the book.
Billski