RC Soaring
Mike Garton, 2733 NE 95th Ave., Ankeny IA 50021; E-mail: [email protected]
THIS MONTH I'll describe the Airfoil Comparison Tool. It is an Internet-based utility for plotting wind-tunnel data. The tool has easy-to-understand inputs, and it can be accessed for free. It accesses data from Michael Selig's wind-tunnel tests.
Given the size and weight of a glider, the tool preprocesses the data and makes a single Cl vs. Cd curve for the airfoil. This single processed curve is much easier to interpret than a bunch of constant Reynolds-number curves from typical wind-tunnel data. I created the engine of the software, and Dave Orman created the Web interface.
To use the program, go to the Internet site http://eiss.cnde.iastate.edu/calcs/frames.shtml. Enter estimates of a glider's wing area, wingspan, and weight, then select one or more airfoils from the list. You can select multiple airfoils by holding down the control key on a personal computer.
Hit the "compare polars" button, and a graph should appear. It is that simple. No math or other aeronautics skills are required. There are instructions and technical details online too.
For those of you who have not seen Cl vs. Cd plots, here is a one-paragraph basic primer: Cl stands for coefficient of lift. Cd stands for coefficient of drag. Low Cd is always a good thing. High-speed glider flight takes place at Cls less than 0.2.
Most gliders have their best glide ratios with a Cl between 0.3 and 0.6. The minimum sink Cl is often between 0.7 and 0.9. If you want a floater, find an airfoil with a low drag at high lift coefficients. Racers need low drag at the low lift coefficients. The glider airfoils on modern thermal duration gliders are pretty good in all phases of flight.
I want to stress that the relative performance of the airfoils varies with the size and speed of the airplane. Airfoil "A" may have lower drag than airfoil "B" on a small glider. The reverse may be true on a large glider. This kind of reversal is common in the data.
That is why the airfoil-comparison tool needs size and weight information. The performance will all come out in the wash when you run this tool.
What could you use this tool for?
- Choosing an airfoil for an airplane.
- Comparing multiple airfoils.
- Observing the effects of size on an airfoil.
- Observing the effect of different turbulence treatments.
- Observing the sensitivity of an airfoil to building inaccuracies.
- Planning a flap budget (when and how much to lower your flaps).
I used the tool to make some example graphs. Look at the effect of model-building errors on the SD7037 airfoil. Michael Selig digitized the profiles of his wind-tunnel models to check their accuracy. (See table.)
The least accurate model—the SD7037_C—has the highest drag. The most accurate airfoil—the SD7037_B—had the lowest average drag. In some cases, building errors made the airfoil better at one Cl range and worse in another. These errors probably changed the camber of the airfoil a little.
A second example shows the effect of turbulence on the Eppler 214 airfoil. The 214 is very good on large Thermal duration gliders. It is a very poor choice for a small glider. The airfoil-comparison tool confirms what I had learned through experience.
The third example shows a comparison between the SA7035 airfoil and the MH32 airfoil. They are very similar. The MH32 differences are small enough that they might get washed out by building error.
Pilots may not be able to tell the difference either. The SA7035 may have an edge in high-speed cruise. The MH32 appears to have an edge at moderately high Cls for minimum sink. There was no flap data on these airfoils.
With the airfoil-comparison tool, you can do "what if" studies like these very quickly. It sure beats trial and error. I have included some more technical information in a question-and-answer-format which follows. More complete information is on the Web site.
What does this tool tell me?
You should be able to compare the drag characteristics of as many as five airfoils at a time. This is subject to the availability of the data. If data only exists at high Reynolds numbers for a particular airfoil, the program will only give output when you simulate a large glider. The absence of data makes no statement about the quality of that airfoil—just that there is no data.
What is a "Reynolds number"?
It is a nondimensional quantity that represents the ratio of the momentum forces over the viscous forces for fluid flowing past a body. It is calculated by the formula rho*V*x/µ, where rho is the density of the fluid, V is the velocity of the body relative to the fluid, x is the length of the body, and µ is the viscosity of the fluid.
At sea level (commonly used for design calculations), rho is 0.00237 slugs/ft^3, and the viscosity is 3.737e-7 lb sec/ft^2. This means that the Reynolds-number equation in English units can be written as 6,360 x velocity x chord where velocity is in feet/second and chord is in feet.
You might imagine that the flow around a golf ball flying through the air is very different from the flow around the same golf ball sinking into a vat of motor oil. These two situations have two very different Reynolds numbers.
If you changed the speed of the ball flying through air until the Reynolds number matched the motor-oil situation, you could expect to find the shape of the streamlines in the flow field to be the same.
High Reynolds numbers mean that the air has a great deal of momentum relative to its viscosity. Fat airfoils (15-18% thick) work well on large models and full-scale gliders. The high Reynolds number of the large airplane means that the air has lots of momentum, thus it can navigate around the fat airfoil without slowing and separating.
Near the other end of the spectrum, thin airfoils are needed for good performance on a Hand-Launch Glider. The momentum of the air is relatively small. If you try a fat airfoil in this circumstance, the viscosity will slow the air trying to get around the airfoil, and it will separate. Turbulation often helps when an airfoil is marginal at a particular Reynolds number.
What is a "reduced Reynolds number'?
There is a way to "factor out" the velocity dependence of a Reynolds number in order to simplify plotting.
From the equation of the Reynolds number we know that it is directly proportional to velocity. The equation for velocity of a glider in steady-state gliding flight can be written as velocity = (2 x weight/rho/S/Cl)^0.5, where rho is the density of air, S is the wing area, and Cl is the average lift coefficient.
We see that velocity is proportional to one divided by the square root of the lift coefficient. Combining equations, we can show that a glider's Reynolds number is proportional to one over the square root of the lift coefficient. Rearranging terms we can show that for a given glider, the Reynolds number multiplied by the square root of Cl will be a constant. This constant is called a reduced Reynolds number.
At a lift coefficient of one, the reduced Reynolds number is easiest to calculate.
Let's use a 78-inch wingspan glider with 600 square inches of wing and a weight of 32 ounces. We must convert everything to consistent units: 600 square inches = 4.17 square feet, 32 ounces = 2 pounds, and the sea level density of air is .00237 slugs/ft^3, so we get a velocity of (2 x 2/.00237/4.17)^0.5 = 20.1 feet/second.
A Cl of 1.0 is roughly the maximum for most airfoils, so this is a fair estimate of the stall speed.
The average chord is 600/78/12 = 0.64 feet. The reduced Reynolds number for this glider, then, is 6,360 x 20.1 x 0.64 = 81,800 (rounded). Now you can easily find the typical Reynolds number for the average chord of this airplane at any lift coefficient. The Reynolds number will be 81,800 divided by the square root of the lift coefficient.
Where did you get the data for this program? Are there restrictions on the data use?
The wind-tunnel data used in this tool was produced under the UIUC Low-Speed Airfoil Test program and the Princeton wind-tunnel tests, both overseen by Michael Selig.
The data is covered by the General Public License. Also see the copyright notice and the UIUC Low-Speed Airfoil Tests Manifesto.
Sources:
Airfoil Comparison Tool http://eiss.cnde.iastate.edu/calcs/frames.shtml
Michael Selig's UIUC Low-Speed Airfoil Tests site (includes General Public License information) http://amber.aae.uiuc.edu/~mselig/uiuc_last.html
Transcribed from original scans by AI. Minor OCR errors may remain.
