|Jan 19, 2013, 04:39 PM|
Figuring out L/D ratio and drag coefficients
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:
Wingspan = 30"
Chord = 5"
Area = 150"
A/R = 6
Coefficient of lift at 0 AOA = ~0.3
CG is at 20% MAC
|Jan 19, 2013, 04:58 PM|
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.
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.
|Jan 19, 2013, 05:03 PM|
Joined Jan 2007
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.
Edit: Here are some good articles on how to do performance measurements on a full-size airplane:
It isn't easy!
|Jan 19, 2013, 05:43 PM|
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|
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|
Joined Jan 2007
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.
|Jan 19, 2013, 07:41 PM|
I'm also trying to make some kind of in flight measurement of drag. Not easy !
Here's what I do :
I have the eagle tree data logger, OSD, FVP,... so I can have readings in flight of RPM, speed by the pitot tube, speed by the GPS, speed by simply measuring the time to travel a known distance.
RPM can give you an idea of the thrust using the UIUC propeller database. But it needs to know airspeed and air density. Speed is uneasy to know, pitot tube isn't accurate at low speeds and is influenced by air density, GPS speed can't be very accurate too because of the wind (even only 5 km/h of wind, when a slow flying speed can be down to 30 km/h), same for direct measurement.
BTW, in flight thrust can be only 30 to 50 % of the static thrust at the same throttle level, just to give an idea, so your L/D = 2 can if fact be L/D = 6 !
Making things carefully, you can still have an idea of the drag coefficient, +/- 0.005, something like that.
I have a 1/12 Yak-3, with a dirty finish... I estimate it's drag coefficient around 0.04, when the full scale Yak-3 should be around 0.026.
My FPV plane with camera, antennas, various things almost everywhere should have a drag coefficient in the 0.05 / 0.055 range, low climb rate suggest high induced drag, max L/D might be a bit more than 6.
Here is Mathieu Scherrer's Jibe 2 wind tunnel test results :
Less than 0.015 for the drag coefficient of this skinny sailplane !
Here, if I recall correctly, the Ultra Stick 120 has a minimum drag coefficient close to 0.03 :
|Jan 19, 2013, 08:06 PM|
Alright, it's making a lot more sense to me now. Dynamic thrust being less than static by a factor of 2-3 pretty much explains that mystery. As for the reynolds number, that seems to be the big thing in determining how differently a model performs from the real thing. I've always wondered why if you take a scale model that has the precise same wing loading, drag/lift coefficients, etc it still flies differently than a full size one - and that answers it.
I guess my question now is what measures can be taken to increase L/D to a reasonable level? The obvious factors that come to mind are:
- Larger wing area (lower wing loading)
- Higher aspect wing for a given area
- Best attempts to streamline
What are some other factors than can contribute to L/D?
My long term goal is to make a long-endurance FPV platform that can cruise for a long time at low power, and I'm aiming for something very floaty and efficient in the same category as high-aspect ratio aircraft like the U-2, or even more extreme like the rutan voyager. What are some design considerations for such a plane besides the massive aspect ratio?
Big picture - Larger scale, higher speed = more efficient due to Reynolds number?
|Jan 19, 2013, 09:13 PM|
Joined Jan 2007
Again, minimum power does not occur at best L/D. It happens at a considerably lower speed, in sailplane terms called minimum sink rate speed.
Light weight will decrease the power requirements, but hurts the best L/D at model scales.
Larger wing area doesn't help L/D, except that the longer chord will have a higher Re. L/D is independent of wing loading, except for the Re effect of a higher wing loading flying faster, and increasing the Re. Minimum power depends on the span loading, not the aspect ratio - lower the weight per unit span, either by increasing the span or decreasing the weight, and you will decrease the power required.
A big span and a low zero lift drag coefficient are what you want, except because of Re effects there is an optimum AR for a given Re.
Wing planform has an effect - you want a near elliptical lift distribution, not necessarily an elliptical wing.
Good low Re airfoils, appropriate for the Re at each wing station help quite a lot. Dr. Drela's AG series are very good. Camber changing flaps can increase the performance at other speeds than best L/D.
Larger will always fly better than smaller, all else being equal.
Low drag of all the other components is very important.
If max L/D is really your goal, you want to copy a very good sailplane in the size you want. The AG airfoils and excellent sailplane designs are on the CR site:
Power system efficiency is a huge variable. selecting the right motor and propeller for the speed and power required can make a huge difference to the overall efficiency.
Full scale airplanes such as the U2 had different mission requirements (very high altitude, high Mach number) at a different Re. They won't be optimum for low Re and different requirements.
|Jan 20, 2013, 12:50 AM|
Joined Jan 2009
Juste a note here: endurance and range are not driving the variables the same way when designing an airframe. The power plant (engine + propeller + alternator) has to be optimized for the requirement as well. Once again, the optimal point is not the same for endurance or for range.
Any design is a compromise and as long as a clear requirement doesn't exist on paper it is hard to define de best "tool"to achieve it (or come close to it).
|Jan 28, 2013, 03:06 PM|
Joined Mar 2010
The best way to work out L/D is to do glide tests.
Remember L/D changes with airspeed, you need to do several tests at different airspeeds to find maximum L/D, which is the one that allows your plane to glide the furthest distance without motor, from a given altitude.
You will need some data logging/telemetry equipment with GPS and airspeed sensors - if you are patient enough to log enough airspeed vs sink rate data, you can plot the polar curve of the airplane.
From there, you will know at each given airspeed, how much drag the plane is generating - hence how much thrust you need to overcome it.
For any given value of thrust - you can ESTIMATE power but it gets even trickier - as some people correctly suggested, thrust in the air and on a bench is not the same, since the actual angle of attack between propeller blade and airspeed decreases when airspeed increases - the prop "unloads".
My 2 cents
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