Lift to drag ratio for a given glider

Question

I have data from three wind tunnel tests of a glide bomb at three different pitch angles. For each test, I have graphs showing the drag coefficient, lift coefficient, and pitching moment coefficient as a function of the angle of attack. Additionally, I have the mass, dynamic pressure, and reference area for the configuration. I was asked to determine the lift-to-drag ratio under glide conditions based on the given data. How should I find it? and why it's not simply the ratio of the coefficients founded in the experiments?

Answer 1

This feels suspiciously like a homework problem -- we generally don't like being asked to do someone's homework.

When you are having trouble with a homework problem, you can ask, but you should make clear that it is a homework, you should tell us what you've tried, and we will try to give you some direction without taking away the learning opportunity of figuring it out for yourself.

In this case, I'll go ahead and answer as if it is not a homework.

Assuming the center of gravity is in a location such that the glide bomb is statically stable, it will glide at a point where the pitching moment is zero.

That will imply a particular angle of attack -- which will correspond to a particular $C_L$ and $C_D$ -- and therefore a particular $\frac{L}{D}$. It will also (given the wing loading of the bomb) correspond to a particular dynamic pressure (equivalent airspeed).

Start by plotting $C_M$ vs. $C_L$ ($C_M$ on the vertical, $C_L$ on the horizontal). This should hopefully be close to a straight line with a negative slope.

Either fit a straight line to those points, or interpolate between the data points to find where the chart crosses $C_M=0$ -- you want to know the $C_L$ value. This is $C_L^*$ -- your cruising CL.

Next. plot $C_D$ vs. $C_L$ (Normally we would plot $C_L$ vs. $C_D$). Fit a parabola to the data $C_D=f(C_L)$. If you are doing this by hand, you will need to solve for the coefficients that match the data $C_D(C_L)=a C_L^2+b C_L + c$ -- you have three data points, so you can do it. (Here I am writing $C_D$ as a function of $C_L$, $C_D(C_L)$).

Once you have that parabola, we will treat it as a drag polar. Evaluate the drag coefficient at $C_L^*$ -- this is your cruising drag coefficient.

Then divide $\frac{C_L^*}{C_D(C_L^*)}$ -- that is your cruise L/D (again, in the denominator $C_D$ is a function of $C_L$.)

If you have the wing area and weight (or the wing loading), then you can solve for the speed. Remember

$C_L=\frac{W}{q S}$

and

$q=\frac{1}{2}\rho V^2$

or

$q=\frac{1}{2}\rho_0 V_e^2$

Ignore the dynamic pressure of the wind tunnel (assuming the data has been presented in coefficient form). The whole point of using coefficients is that you can re-use the data at a different dynamic pressure later.

You can do all of this by hand (including the plotting) or with Excel or any other appropriate computer program. If you are doing it by hand, you may be tempted to skip the steps where I say to plot the data. Don't -- go ahead and take the time to draw a plot with the data, it will help the whole process make sense in your head.