# How does the glide ratio change with velocity in a glider with air brakes deployed?

I'm interested in how the glide ratio steepens when increasing velocity, starting from the best slope (best L/D) velocity, in a high drag configuration (air brakes fully extended on a glider).

I've seen several graphs of how L/D changes with AOA for various powered aircraft (and not in a high drag configuration), but couldn't find a relevant one.

Will be happy to see a L/D vs AOA graph and/or a sample polar in clean vs dirty configuration.

• One good graph to answer the question would be a speed polar curve with and without airbrakes deployed – Manu H Sep 3 '19 at 11:26
• @Manu H since an airbrake is parasitic it might drop Vbg down a few knots, which is why flaps are widely used, since they also lower stall speed. Since the airbrake is mainly used to either steepen glide at approach speed or slow the aircraft after touchdown I'm not seeing any other application. The L/D graph would simply show similar lift with much more drag, maybe a little more as a flap, a little less as a spoiler. – Robert DiGiovanni Sep 3 '19 at 23:14
• @RobertDiGiovanni What I meant is that it should be nice to see polar modification. When I learned to fly a glider, seeing this modification with balasts as helpful, I think the same with airbrakes could be interesting. The polar show more than just speeds for max L/D ratio or min V/S. – Manu H Sep 4 '19 at 4:55
• @Manu H definitely a legit question that could be tested with a variety of drag increase systems. Would enjoy developing data points for comparison. Amazing how much of this validates good old flaps. – Robert DiGiovanni Sep 4 '19 at 10:53

This can be easily answered with a spreadsheet. Start with speed $$v$$ going from 20 m/s to 50 m/s. Add a column for the zero-lift drag coefficient and keep in mind that the increasing Reynolds number will change that value over speed, like that: $$c_{D0}=c_{D0_{Ref.}}\cdot\left(\frac{v_{Ref.}}{v}\right)^{-0.3}$$ I picked as reference values $$c_{D0_{Ref.}}$$ = 0.01 and $$v_{Ref.}$$ = 25 m/s. Adjust as required. Next, add a column for the zero-lift drag coefficient with speed brakes deployed and add a constant value. I picked 0.015 for the example plot below.

Now we need to add induced drag and start with a new column for the lift coefficient $$c_L$$. Since weight does not change with speed brake setting, one will do for both configurations:$$c_L=\frac{2\cdot m\cdot g}{\rho\cdot v^2\cdot S}$$ I used 350 kg for the mass $$m$$, 1.225 for air density $$\rho$$ and 10 m² for wing area $$S$$. The induced drag coefficient $$c_{Di}$$ will be $$c_{Di}=\frac{c_L^2}{\pi\cdot AR\cdot\epsilon}$$ My sample glider has an aspect ratio $$AR$$ of 20 and an Oswald factor $$\epsilon$$ of 0.98. Again, adjust as required. For extra correctness you might want to add an extra column for the real-life lift coefficient with beginning stall. Keep the "clean" lift coefficient for induced drag but plot all drag coefficients over that extra column where the lift coefficient grows less than the linear value once it is above the threshold where flow separation starts on the wing, say 1.25. Now your speed will not be correct for lift coefficients above that threshold, but your induced drag will become very realistic.

Now add another column for induced drag with speed brakes deployed. In oder to model the distorted lift distribution over span with speed brakes, reduce the Oswald factor to maybe 0.7. Add both drag coefficients for the total drag coefficient: $$c_D=c_{D0}+c{Di}$$

The result should look something like that. The index wF is for the configuration with speed brakes deployed:

The glide ratio E is the ratio $$\frac{c_L}{c_D}$$ and plotted on the right Y axis. Note that the best glide is cut almost in half and moves from $$c_L$$ = 0.7 to about $$c_L$$ = 1.0 for speed brakes deployed. I did not add the extra drag at high lift, so your result might look slightly different.

• Since flaps increase lift coefficient and spoilers decrease lift coefficient, they surely affect the graph of sink rate versus airspeed somewhat differently, don't they? – quiet flyer Sep 4 '19 at 1:33
• @quietflyer: When I wrote "flaps" I meant speed brakes. Thanks for spotting this – Corrected. Regarding lift loss: Yes, AoA will be a bit higher with speed brakes, but lift will not change. – Peter Kämpf Sep 4 '19 at 7:42
• I don't think we have the same definition of "easily" :) . After reading the whole answer, it seems easier but I still won't call that easy (maybe I should reread again and make the described computations by myself to find it easy) – Manu H Sep 4 '19 at 8:02
• @PeterKämpf this is very interesting, but how does this answer the question? How can I understand from the graph the change to L/D with change in velocity? I suppose the L/D vs AOA (not L vs D) or a polar (at least for a very dirty configuration) could give a good idea for the how sensitive the slope is to changes in airspeed. – GJ. Sep 10 '19 at 8:29
• @GJ: Lift coefficient changes with velocity, so you need to correlate both. Since I do not know the mass of your glider, you need to do that yourself. Generally, the faster you fly the more L/D moves down from the optimum. Due to the high zero-lift drag and high aspect ratio this optimum is very close to stall speed for a glider with speed brakes out. – Peter Kämpf Sep 11 '19 at 5:00