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Saturday, October 17, 2009

Drag explained for model aeroplanes

This is my attempt to provide a simple explanation of drag for the model builder.

DRAG is the force that resists the forward motion of an object through the air. For model aircraft, there are essentially two types of drag (refer to Figure 1 which is a plot of Drag force against air speed, v):

1. PARASITE DRAG is the resisting force that is due to the shape, roughness and form of the aeroplane. As the model moves through the air, the flow is disrupted by the shape and texture of the model. Its magnitude is given by the expression shown in Figure 1 (red, think of A as a constant). Parasite drag increases as the plane speeds up. Think of it as "High speed drag".

2. INDUCED DRAG is simply the drag force caused by the circular flow of air around the tips of the wing, that is, the vortex. An alternative name is "vortex drag". To get an idea of what it "looks" like, just search on wake turbulence or wing vortex in Google Image Search. Notice also the dependency with the lift force squared, L^2. That is why it is also known as "drag due to lift". So, the induced drag also increases with lift, for example with increasing angle of attack. Its magnitude is given by the expression shown in Figure 1 above (black, think of B as a constant). Since it is inversely proportional to v^2 it means that as the model speeds up, the induced drag decreases. Conversely, as the plane slows down, induced drag increases. Think of it as "Slow speed drag".

The total drag is the sum of the parasite drag and the induced drag (see blue curve in Figure 1 and Equation (1)).

Note for readers who like a bit of mathematics: Equation (2) is the "drag polar". To understand where it comes from you would need to look at an aerodynamics book (see References). The full expression for Equation (1) is Equation (6). You can easily derive Equation (6) by substituting equations (3) and (4) into (2) and recalling the relationship between aspect ratio (AR), span (b) and area (S). Equation (5) is the usual expression for dynamic pressure (q).

So much for the theory...

What does this mean for model aircraft performance and design?

1. It is generally desirable to reduce drag. Lower drag means a flatter glide (see the discussion of glide angle in a previous blog post here). In other words a higher L/D, which is a key performance indicator. Modern open class gliders can achieve L/D of 60 or better. In contrast, the Wright Flyer of 1903 had L/D of 5.7.

2. Mathematically, Equation (1) means that the total drag is a minimum at the air speed where the parasite drag equals the induced drag. That is the air speed where the best L/D is achieved. So if one of these drag contributors (parasite or induced) is low at that speed, then the total drag will be two times that low number. While that's a good thing, the plane's behaviour may suffer at one or other extreme of speed.

3. Take for example a small span pylon racer model. It has a small cross section area, smooth, clean, polished surfaces and therefore low parasite drag. Due to its high wing loading, it will have a high induced drag (this will be explained further below). Since it is fast, it will generally fly on the right hand side of the drag-speed curve shown in Figure 1. The good news is that parasite drag is lowish for this model, so it will perform fine under normal operating conditions; it is not impaired by the high induced drag.

4. For slow flyers for example, thermalling gliders and free flight rubber planes, induced drag is much more important. At low air speeds, parasite drag does not have any appreciable influence - this is the left hand side of Figure 1.

5. For many types of aircraft however, both parasite drag and induced drag should be minimised, for instance hand launched gliders and catapult launched gliders. These travel quite fast on release, so low parasite drag means a higher launch. After the transition to glide, they fly slowly, so low induced drag is required for a flatter glide. Another example is the RC glider. It needs to glide well at slow speed in order to climb in thermals. Then after the climb, it needs to be able to glide at shallow angle to cover lots of ground with little loss of height, in order to catch the next thermal. Induced drag is very important for free flight models too, including rubber power.

Reducing Induced Drag and Parasite Drag

6. The wing is the biggest contributor to both induced drag and parasite drag. So concentrate on the wing before the fuselage and tail feathers!

7. The biggest factor for reducing induced drag is the span loading W/b. This comes from Equation (6), noting that L~W, and see also previous blog. It is not as simple as just increasing AR for reasons explained in that blog post. (The over-emphasis sometimes placed on increasing AR to reduce induced drag probably arises from the dimensionless expression in Equation (2) above).

8. That means keep her light and make her span as big as allowed!

9. Another factor to reduce induced drag is wing planform design (elliptical and similar shapes are good). Non-planar surfaces can also reduce induced drag compared to a same span planar wing. For example, winglets, polyhedral configurations and span-wise camber. Some efficiencies can also be gained from multi-surfaces (e.g. boxplanes), but there is obviously a parasite drag and weight penalty.

10. For reducing parasite drag the biggest factors are the apparent cross section area and the wetted area (the area of the plane that is in contact with the air). Keeping the fuselage as narrow and small as possible is a good start. Sharp corners and junctions between wing and fuselage could be smoothed or "filleted" to reduce the drag. Surface roughness also plays a part (but its not as simple as smoother the better: sometimes a rough surface can keep air flow attached to the wing - "turbulators" are a PhD study on their own!).

11. Note that adding weighty fairings and cowlings in an effort to reduce parasite drag could be counter productive because it may increase induced drag! Fairings and such like may help the high speed flight, but could ruin the low speed glide.

CONCLUSION

I hope this blog has helped you to understand drag. Think about what your plane will be doing most of the time. Flying fast or flying slow? What kind of drag would be most relevant to your model? Having decided that, work to reduce the predominant source of drag. However, concentrate on the wing first. As ever, weight is a major factor especially for induced drag.

REFERENCES

1. Anderson J D (2005) Introduction to Flight, McGraw Hill, 5th edition

2. Simons M (1999) Model Aircraft Aerodynamics, Special Interest Model Books, 4th edition

3. Kroo I (2001) Drag due to lift: Concepts for prediction and reduction, Ann. Rev. Fluid. Mech 33:587-617

2 comments:

The probligo said...

"However, concentrate on the wing first. As ever, weight is a major factor especially for induced drag."

That just about says it all. There is another factor that does need to be considered.

Airspeed (V) is (as you point out) directly related to mass. Reduce mass = flying slower.

In that equation it is also essential that the polars of the airfoil are considered. Reducing airspeed also reduces Rn (Reynolds Number) and that can have a massive effect on the performance of an airfoil that is already (with the heavier aircraft) flying at its critical limit.

As an instance, I built several Lulu towline gliders for vintage duration ("improvements" along the way :) ). The second last was the lightest. It was also a total dog. It would not glide. It SANK. The last (off the same templates and jigs) was 15% heavier. It performed, simply because the model was flying that little bit faster.

For that reason, classes with minimum weight requirements (like F1A) require careful airfoil selection - and that is also the reason why particular airfoils become "popular" as they provide consistent performance in the wing-loading range for the class.

Another very good example is the difference between indoor and outdoor HLG airfoils. Totally different environments need very different stability and airspeed requirements resulting in quite different V and airfoils.

Your comments about AR and tip circulation are right on - I must dig out the old old notes on winglets.

Chuck Glider said...

Thanks probligo. You are absolutely right about the importance of choosing the right aerofoil section for the particular model and the effect of Reynolds number. The aerodynamics books that I referenced cover it well.