Gliders are airplanes without engines, and they have been commonplace in the aviation industry for more than 120 years. Indeed, gliders predated the 1903 Wright Flyer. They are also nice, relatively simple planes that freshmen aerospace engineering students can investigate.
My Introduction to Aerospace Engineering class had its own glider project last semester, and I think I can take some time right now to provide an overview of it. For more than one month, we built a wooden glider from scratch in the new Baum Family Maker Space. This glider was quite large, with dimensions of roughly 3ft by 3 ft. Then, one morning at 5 AM, my entire class went out to the USC baseball field and we flew our gliders. We measured their initial velocities and the total distances they traveled to make further computations about their performances. In our final project write up, we leveraged several concepts about gliding flight that we will explore below.
When a glider flies through the air, its nose is pointed slightly downward with respect to the horizon. Accordingly, we can label the angle that the glider’s flight path makes with the horizon as γ. By evaluating some force-balancing equations and making some small angle approximations, we can determine that
tan(γ) = 1/(L/D).
Once again, we see the lift-to-drag ratio pop up. We can also notice that the glide angle is minimized, and in turn, our glider’s range is maximized, if we fly at (L/D)max. This fact is completely consistent with the range equation for propeller-driven aircraft that we briefly explored last week.
In particular, for gliders, we can also write that
R = h (L/D),
further solidifying the direct relationship between range and the lift-to-drag ratio.
Furthermore, we can utilize some detailed equations from flight mechanics to write an equation (which we will call Equation (*)) for the speed, umax range, at which range is maximized and the glide angle γ is minimized:
u 2max range = 2W/ (ρS) * sqrt(K / CD,0). (*)
In this equation, “sqrt” is short for “the square root of,” W represents the glider’s weight, S is the planform area of the glider’s wings, ρ is the density of air at the altitude the glider is flying at, CD,0 is the zero-lift drag coefficient, and K is the same airplane-specific constant that can be found in the equation
CD = CD,0 + KCL2.
Equation (*) can illustrate several important characteristics of gliding flight. For example, the higher a glider flies, the smaller the density of air becomes, which in turn leads the plane to fly faster. We also see the quantity W/S, often referred to as “wing loading” appear in Equation (*).Wing loading can be fascinating in its own right, and I hope to explore it more in future posts. If we treat this quantity W/S as one singular variable, we can see that as wing loading increases, so does umax range.
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