Originally Posted by
danandrews
Theholdingpoint Thank you I appreciate this reply, took me a while to get it at first. My incorrect assumption I believe was thinking that the rest of the equation was representative of all of the energy that could be extracted from the air. And that the co-efficient was simply the proportion that was extracted.
I think I see your point. When the relationship between some factor (wing size, velocity etc) to lift created, is simply observed, or rather, easily derived, it makes sense to put that into the equation. Nice simple relationships. The multitude of other contributing factors to the final value of lift are too complicated to measure and/or express simply. Thus they take the form of a dimensionless co-efficient? Am I getting that right?
I must say this has troubled me since I started my flying training many moons ago. So thank you!
And apologies for the late reply to all who took the time to answer my question in this thread.
Holdingpoint made it complicated and only applied it for the same wing area, but an entirely different weight of the airplane and different airfoil, so an entirely different airplane.
The first use of Cl is to characterize an airfoil for its performance as if it has an infinite wing span. For most small aircraft this will not need a correction for compressibility or Mach number effects - the presumption is the plane isn't traveling fast enough to cause the density of the air to change by moving through it. For a range of angle of attack there will be a chart relating the angle of attack to Cl. Pretty much every useful airfoil will have a chart, so every airfoil over it's unstalled range can have some arbitrary Cl.
When a plane is designed the first factor, after expected airspeed for take-off fully fueled and cruise with some fuel burned off, is an estimate of weight. Next an estimate of wing area is made - and poof there is the design range for the Cl - a high number for takeoff and a lower one for cruise. Then one goes to the big book of airfoil data and chooses an airfoil that covers that range with an eye to generating a minimum of drag while also being thick enough for a first estimate of the bending loads.
In any case, once the weight, speed, and wing area are chosen, then all airfoils for level flight have to operate at exactly the same Cl. What shifts with airfoil shape change is the amount of drag and the extra protection for staying away from stall. If the wing area is distributed in a stubby planform then the induced drag is high. If the wing area is long span and narrow chord, then flex is a potential problem. And so the trade-offs go. It will take a number of cycles where the weight is closer, the wing strength is changed based on the weight. If the structure weight goes down, then maybe bigger fuel tanks are designed for increased range or maybe not - the lower weight can result in lower structure weight, which in turn reduces the structure weight a little more - to some minimum amount of material for a minimum amount of raw material cost.
Many aircraft factors are dimensionless to cancel out the various contributors. The first airfoil data that the Wright brothers depended on was only useful for the exact airplane weight and speed and could not be used anywhere else. They lost nearly a year of development because of this and had to obtain their own data. By balancing the dynamic pressure term against the area, leaving just force, and then dividing that by the force due to lift/weight, then any size airplane (within reasonable limits**) could be designed using that airfoil data. It's possible to predict how an airfoil will perform on Mars, with 0.1% of the air pressure as at sea level on Earth using the same data as was used for a Piper Cub, even accounting for the fact that the weight of a plane is far less on Mars. No special correction to the airfoil data is required.
The other factor that sneaks in is that when the Cl is chosen for a particular cruise speed for a particular airfoil it is choosing the angle of attack, which affects the required pitch of the airfoil relative to the fuselage, which sets whether the fuselage is level in flight - a nice thing in a super-stretch commercial airliner to minimize fuel burn from drag and the slog uphill and downhill for the drink cart and bathroom users. Consider that at low speed, high Cl during takeoff, how slanted the plane is. One could operate the plane that way the entire flight- but it would burn too much fuel and be hard to move around in and be slow.
For the original question - it's a matter of leverage. The dynamic pressure is a measure of the momentum of the air heading towards the airfoil. If that was the only factor it's true that the maximum would be 1. However, there are also usually engines shoving the airfoil through the air, increasing the energy available to cause the air to change direction. High Cl is also a high drag condition. The additional push is either from the engines or by putting the weight of the plane on a steep slope. Look for a chart called the "drag polar" for airfoils. en.wikipedia.org/wiki/Drag_curve
**Reasonable limits involves Reynold's number, the ratio of dynamic properties to viscous properties. For very low speeds and over very short distances the Reynolds number is very low - this is where flies and dust particles operate. Most small aircraft operate at moderate Reynolds numbers and for supersonic aircraft the viscous properties almost don't matter. However almost all airfoil data is suitable for almost all small aircraft - less than 300 mph,