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Old Feb 26, 2013, 01:19 PM
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Joined Feb 2013
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Finding drag coefficient w/o wind tunnel

Hi there! First of all let me introduce myself because this is my post in this community, although I've been reading a lot! My name is Joan, I'm an engineering student from Catalonia, Spain and I'm really interested in aerodynamics, airplanes and airmodels. With this said, I'd like you to help me with a project I have in mind:

The objective is to find the drag coefficient for my MPX Funcub running in straight line with the help of some telemetry instruments. So here comes the science I've been thinking about:

Considering: Drag = 0.5 * airdensity * S * Cx * v^2

And: Thrust - Drag = mass * acc

Airdensity, S(surface) and mass are constant.

The idea is to:
measure: v, rpm, and acc
using: gps, rpm sensor and triaxial accelerometer

With the help of the APC prop's manufacturers dynamic thrust chart find an aproximate value for thrust given values of rpm and v. Then find the Cx for as many cases as possible and find an average value.

So, my question is! First of all if there is something you spot I am saying wrong here or if you think it's going to be a fiasco and I'm just wasting my time... (hope not xD)

Second, what telemetry material I should be getting for the job. What I have in this moment is a Spektrum dx6i tx and orangerx receiver which as I have read are not up for the job.. So what do you think I should get (I've read maybe about turnigy 9xr + frsky). Keep in mind I need the data to be recorded so that I can study it on my laptop later!

Thank you all very much in advance!
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Old Feb 26, 2013, 02:43 PM
HerkS's Avatar
Virginia USA
Joined Jun 2007
1,650 Posts
Hi Joan,

You can find a lot of high quality wind tunnel performance tests of the sort of propellers you will be using at this website.

You could use a force sensor to measure thrust directly.

You could do glide testing. This is much simpler and cleaner than measuring while under power. Plus - propeller slipstream flowing over model increases total drag.

No wind glide ratio is equal to lift/drag. Lift ~weight for shallow glide angles. So if the advance is equal to ten units forward for each one unit of descent, then drag ~ weight/10 Speed and glide angle measurements can be easily documented and analyzed photographically.

Of course once you have drag and flight speed measured, the coefficient is calculated as you indicated.
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Old Feb 26, 2013, 02:44 PM
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Germany, BW, Stuttgart
Joined Mar 2012
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What you are suggesting is not too different from how "Specific Excess Power" is measured in full-scale flight testing. In full-scale you do what's called a level acceleration. The steps for this are:

1. Establish the aircraft in a steady climb at as slow an airspeed as you can maintain with the throttle stabilized at the desired setting for the run.
2. Once at the desired altitude, quickly (but smoothly) pitch over to level flight (without touching the throttle).
3. Accelerate in level flight while recording true airspeed and altitude as a function of time.
4. Smoothly maintain level flight (minimizing any "g-bumps").
5. As you stabilize near maximum airspeed for your throttle setting, smoothly initiate a shallow descent to accelerate just slightly.

Your data will allow you to calculate your total energy (E_total = mgh + 1/2mv^2) as a function of time. The rate of change of your total energy is:

(d/dt)E_total = (Thrust*cos(AOA) - Drag)*V_true


Drag = Thrust*cos(AOA) - (d/dt)E_total / V_true

If your AOA is small, cos(AOA) is about 1.

Any time you differentiate data, you are asking for trouble. That said, if you are very smooth, this can give good results. Some potential problems doing this with R/C:

- To get reliable results you need to fly a long straightaway (often tens of miles if your top end speed is supersonic ). Keeping your model in sight could be a challenge.
- You have to be very careful to avoid g-bumps, or you data will not be any good. This could be very difficult (your accelerometer could tell you how well you did).

Good luck!
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Old Feb 26, 2013, 03:12 PM
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Joined Jan 2007
3,655 Posts
You are missing the induced drag, the drag due to lift. You will be measuring the sum of the parasitic drag and the induced drag - I'm not sure that is what you want? There will also be losses in the propeller efficiency from the fuselage behind a tractor prop, or everything ahead if it is a pusher. The higher speed of the propeller slipstream also affects the results.

You could get a good measure of the zero lift parasitic drag from an airspeed measurement in a terminal velocity dive.

F = m*a = m *9.81 m/sec^2

It would be best to do it without a propeller, which would require some other method of getting it aloft - or perhaps just a folding propeller for a reasonable approximation.

The FrSky telemetry and HK Tx seems to be very good, with lots of flexibility for storing telemetry, etc.

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Old Feb 26, 2013, 03:56 PM
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yomgui's Avatar
France, RA, Cormaranche-en-Bugey
Joined Feb 2011
550 Posts
Hi !

I've also tried to get an idea of the drag coefficient of a model airplane, from rpm and propeller data considering thrust = drag in steady flight at constant altitude.

It's not easy !!

I use the eagle tree data logger with GPS, pitot tube, rpm, altitude, etc.

First of all, it's difficult to maintain a long enough steady flight at constant altitude, the plane is nearly always climbing or diving a bit, or in a slow turn, etc. The GPS data can give you the course, the speed, the altitude so what I've done is selected the most "steady data" with the help of excel --> selecting only the data showing for 3sec upstream the less variations in rpm, course, altitude and speed.
This gave me something like 150 data points out of 13000 !

The only two parameters that's interested me were speed and rpm.

Then I had a look at the UIUC prop database (in fact I have a spreadsheet that allow to use it easily). Knowing speed and rpm you should be able to deduce thrust. The prop data, for each prop, have been made at various rpm (because reynolds and other ? rpm related effects), in my case the APC 9x6E was tested at 4000, 5000, 6000 and 6700 rpm.

I've made a macro that send the rpm and speed data into my spreadsheet, thrust is then calculated from the 4000, 6000 and 6700 rpm prop data. The thrust at the current rpm is deduced from those 3 cases.

At the end, I've got this kind of polar :

See... not perfect at all !! but for me just enough...

Of course, you have to consider the big margin of error due to interference of prop and airframe, GPS speed measurement error due to wind, etc. etc.

Accuracy is poor, but with this I can predict the speed and rate of climb of my plane with other prop and motor, with good results...

Of course, just trying was funny enough !

EDIT : what's the % of speed variation due to a 10 % variation of the drag coeff ?? 10 % also ? 5 % ? 2 % ...
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Old Feb 26, 2013, 06:08 PM
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United Kingdom, Glos
Joined Feb 2009
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Have a look at the sensors and data logger from SM-Modelbau for the Multiplex M Link, Graupner Hott and Jeti radio control systems I've just bought one of the Unisens E multisensors to work with my Multiplex M Link telemetry set up, I haven't used it yet but it's a very neat package. The Unisens E and GPS logger may give all the information you are requiring, have a read up on it, it maybe that you can use it as standalone with your existing equipment and just read it out after you've landed.
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Old Feb 26, 2013, 06:24 PM
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First of all, thank you all very much for your responses! They're truely helpfull!

I'd like to discuss some of the things you've considered!

First of all HerkS i did think about measuring thrust directly with a dynamometer but I could only work out how to measure static thrust not dynamic thrust, maybe there is some way to do that? About the glide ratio being equal to L/D is something definitely to consider, maybe do both experiments and compare results? Truely one of the main issues of the experiment is the effect of the slipstream, which will increase drag at higher rpm, don't really know how to avoid that in the other experiment.

ShoeDLG, very interesting to know this method is used in full-scale. This is more or less one of the methods of testing I was thinking about. Thrust shouldn't change much during the process and that may make things easier. But I truely doubt I'll actually manage to get to maximum speed for any throttle config, dunno.

kcaldwel you definitely puzzled me here, I thought it was common practice to use a single drag coefficient that considers both effects, not that this isn't correct but there's more to it just like you sugested! So ok I've had to do some research for a while and now I'm wiser hehe, just like you said drag coefficient is the sum of the zero-lift and lift-induced drag coefficients Cd = Cd0 + Cdi and the thing is the Cdi varies with lift, therefore Cd is obviously not constant but depends on the lift's value. It shouldn't be too hard to calculate the Cdi in a constant altitude flight though (where Lift=Weight). A terminal velocity dive is a great idea! Correct me if I'm wrong but if the operation was done right, simply measuring altitude and how it varies (total speed if vertical drop) should do the trick right? Wouldn't there still appear some kind of "lift" as to say, I mean if there is an airflow through the wings shouldn't there still be a force perpendicular to the wing's surface which would therefore induce drag though?
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Old Feb 26, 2013, 08:42 PM
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Joined Jan 2007
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If the dive is truly vertical, with the wing developing no lift, there would be basically no induced drag. Every airfoil has an angle of attack where it produces zero lift. Think of pushing over into an outside loop - the lift of the airplane must reduce until it goes to zero, and then continues on into negative lift.

The zero lift angle of a cambered airfoil will not be when the chord line is parallel to the airflow though. Cambered airfoils need to have the chord line at a negative angle to the airflow to be at zero lift, approximately 1 degree per 1% of camber.

Symmetrical airfoils will be at zero lift with the chord line at zero degrees.

Of course things get more complicated with an entire airplane. Some wings have twist, so the zero lft angle of the wing will be with the root and tip airfoils creating a small amount of lift in opposite directions, so the wing as a whole has zero lift. And the tail will likely not be at zero lift when the wing is, so again the zero lift condition of the airplane will be with the tail and wing developing small amounts of lift in opposite directions.

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Old Feb 27, 2013, 07:36 AM
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Germany, BW, Stuttgart
Joined Mar 2012
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We often tend to think of Thrust and Drag as independent quantities. The reality is that they are not completely independent. As Kevin points out, airplane structure in the wake of a tractor propeller affects the Thrust produced by the propeller, and the wake of a tractor propeller affects the Drag acting on the airplane. The Thrust and Drag of a pusher propeller have similar connections.

If you took the propeller off the airplane and put the airplane in a “perfect” wind tunnel (one with no wall effects, no freestream turbulence, etc.), you could precisely measure the Drag acting on it at a given airspeed. You could also put the propeller in the wind tunnel and measure the Thrust it produces for a given airspeed and RPM. In a sense, you could use a wind tunnel to measure “pure” Drag and “pure” Thrust.

What if you were to use the values from the wind tunnel to predict the airplane’s acceleration:

Thrust*cos(AOA) – Drag = airplane_mass * (d/dt)V_true -or-

acceleration = (Thrust*cos(AOA) – Drag)/airplane_mass

Would these values accurately predict the acceleration? In general, the answer is “no”. The airplane’s influence on the Thrust and the propeller’s influence on the Drag will have a very real effect on the airplane’s acceleration. In order to accurately predict the acceleration you would need to adjust the Thrust for the presence of the airplane and the Drag for the presence of the propeller. The quantities measured in the wind tunnel may be “pure”, but they are not directly useful.

The distinction between Thrust and Drag starts to get particularly murky when the thrust is integrated into the airframe. Imagine you wanted to measure the Drag of an F-15 in a wind tunnel. In this case you couldn’t simply remove a prop. How would you treat the inlets/exhaust? Remove the engines and leave the ducts open? Block them off with some kind of fairing? Leave the engines in and let them windmill? Leave the engines in but stop them from spinning? It should be clear that there is no single correct value for the Drag. The value you measure for the Drag depends on the strategy you use to “eliminate” the Thrust. Thrust and Drag cannot be separated to arbitrary precision.

Given that the Thrust and Drag are not completely well-defined, independent quantities, is there value in trying to measure them? The answer is often “yes”. If you have measured an airplane’s performance under one condition and you want to use that data to predict it under another condition, having separate models for the Thrust and Drag can be of great help. In many cases, Thrust/Drag interaction is small enough that you can ignore it or account for it using simple approximations.

I think a good question to ask would be: is it worth trying to set up an experiment where I can measure “pure” Drag in flight test? Knowing that “pure” drag will not directly allow you to predict airplane performance, what would this buy you? Are you trying to develop Thrust/Drag models that will allow you to predict performance for a variety of conditions beyond where you are testing? If the answer is “no” then I wouldn’t bother to try to measure “pure” Drag.

Unless you are trying to develop Thrust/Drag models, it seems entirely backwards to try to measure an airplane’s performance in order to determine the Drag you would measure in a wind tunnel. The whole point of measuring Drag in a wind tunnel is to predict an airplane’s performance in flight!
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