Jan 19, 2013, 04:39 PM person Joined Dec 2012 176 Posts Discussion Figuring out L/D ratio and drag coefficients Hey all, I recently did some flight tests for an aircraft I built to try to figure out the minimum thrust required to keep it in the sky. If I'm not mistaken this minimum-throttle speed is L/D max. Here's my issue, though. My airplane is fairly streamlined, it's basically a wing, two very skinny booms, a small tail section, and a flat, short, streamlined pod suspended off the wing that carries the battery/engine. Very flat, smooth airplane. Here's my issue though- Like I said, I did several flight tests at minimum throttle to determine flight time (and thereby amperage). I then took the averages of all the flights, and then measured the thrust produced by that amperage - the results left me scratching my head. At absolute minimum power for flight, the motor is producing 245g of thrust. The weight of the aircraft, however, is 470g. That's where I'm confused. See, when I divide out all the other factors to get the drag coefficient, it's something crazy high like 0.32 or something. I thought I did my math wrong, but this checks out. The L/D ratio for this this is about 2:1 - horrendous compared to even some of the "draggiest" aircraft out there. Like I said, this is a fairly streamlined aircraft, and has far less of a frontal profile than something like a cessna 150 (Which has a L/D ratio of 7:1 and a drag coefficient of ~0.03). So I'm just scratching my head trying to figure out why my airplane has a drag coefficient 10x higher than modestly-streamlined general aviation aircraft. I realize induced drag also plays a part in this - the aspect ratio is about 6:1, which means the plane isn't so great at the back of the power curve. But a tenfold increase in coefficient? What could be the cause of this? Even a flying squirrel has a higher L/D ratio than this! LOL! Here are the specs for aero purposes: AGW: 470g Wingspan = 30" Chord = 5" Area = 150" A/R = 6 Coefficient of lift at 0 AOA = ~0.3 CG is at 20% MAC Regards, -DE
 Jan 19, 2013, 04:58 PM Needs brain lubrication Aachen, very western Germany Joined Dec 2004 1,391 Posts I guess you mean 245 g static thrust? If so, that does not say much about the in flight thrust, almost nothing at all, actually. Edit: If L/D is close to 2:1, you will be able to see it during power off. However, you can streamline it or not, you will have to pay the AR of mere 6 with a fair share of induced drag, anyway. In addition to that you have a small chord and thus smallish Re numbers, that lead to rather mediocre drag coefficients by itself. Still, I'd expect at least a 5:1 to be reasonably possible. biber Last edited by biber; Jan 19, 2013 at 05:14 PM.
 Jan 19, 2013, 05:03 PM Semi-domesticated primate Joined Jan 2007 3,811 Posts Minimum power required will be at a slower speed than best L/D speed. Minimum sink speed will be the airspeed for for minimum power required, which will be very close to stall speed. L/D gets much worse at low Reynolds number. The small size and low speeds of models means the Re is quite low, and the L/D will be lower than full-size airplanes. Your model is quite small, so the Re will be low. It looks like you have a constant chord wing, so the efficiency at slow speeds will be a bit lower than a tapered wing. Even so, the best L/D should be much higher than 2:1. How did you measure the thrust? If you measured static thrust, that will not be the same as the thrust when flying. Depending on the prop and motor characteristics, the thrust should be much lower as the prop unloads with speed. I'm also not clear how you measured the amperage? Without measuring the in-flight watts, you will only be able to get a very rough idea of the power from how much you have to put back into the battery. You have also ignored all the power system losses. The watts into the motor probably only end up 50% thrust or less. The motor efficiency may be 60% or less at low power, the ESC efficiency is lower at low power settings, the propeller efficiency may be anywhere from 30% to maybe 60%. If you multiply all the power systems efficiencies together, it is the amount of power that actually gets converted into thrust may be 20%. Measuring airplane performance is not easy, and I think the method you tried to use has big errors and has missed a lot of the power losses. Kevin Edit: Here are some good articles on how to do performance measurements on a full-size airplane: http://www.eaa.org/experimenter/arti...09-08_drag.asp https://engineering.purdue.edu/~andr...-46372-872.pdf It isn't easy! Last edited by kcaldwel; Jan 19, 2013 at 05:41 PM.
 Jan 19, 2013, 05:43 PM person Joined Dec 2012 176 Posts The thrust measurements are static. I suspected that there might be a difference between static and dynamic thrust, and that maybe that was the issue, although I didn't realize how the magnitude of the difference. All these numbers are rough approximations, yes. I determined that my average amp draw across a couple endurance flights was 5, by taking the MaH of the battery and diving it by the averages of the time aloft, which came out to ~0.5 hr. This gave me about 5A, which I then checked the thrust of by connecting the motor to a power meter and a scale, which is where I got the 245. While my calculations are admittedly very rough, I'm willing to bet the issue is just static vs moving thrust, and the static thrust is making me think the aircraft has a tremendous drag coefficient. As far as reynolds numbers are concerned, how severely does that impact a tiny, slow flying model's efficiency vs a large airplane?
 Jan 19, 2013, 07:27 PM Ascended Master Palmdale, CA Joined Oct 2000 13,621 Posts Use one of the watt meters available to see how many amps you put back into the battery after a flight. Fly the same pattern all the time for flight duration. But it really all comes down to how does the plane look to you when you think it's doing what you want. There's a whole herd of unmeasureable variables involved with models beginning with the effects of wind.
Jan 19, 2013, 07:39 PM
Semi-domesticated primate
Joined Jan 2007
3,811 Posts
Since you brought up the Cessna 150, I'll use it's airfoil as an example. The NACA 2412 works reasonably well at low Re, so this shows how much the performance changes just because of Re.

At an airspeed of 100kph, which would be near minimum power required for a 150, the Re would be about 2.8M. A scale model with a 30" span would be flying at about an Re = 90k. For the airfoil alone (infinite span), the best L/D goes from about 118:1 down to about 48:1. So the best L/D decreases by a factor of about 2.5. That would be reasonably representative of the whole airplane. So if the full-sized Cessna 150 had a glide ratio of 7:1, a scale model with a 30" span might have a best L/D of about 2.8:1.

Your model sounds much cleaner than a scale Cessna 150 so it might have a best L/D of 6:1 as a wild guess, not even having seen a photo.

Kevin