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

Get a Load of this! Glide Angle, Wing Loading & Span Loading

You wanna fly model planes, so why bother with all this glide angle and loading mumbo jumbo? Well, because it is helpful and, as Mr Spock famously said, "fascinating". Glide angle is a fundamental concept. Wing Loading and Span Loading are important design considerations that affect the model's performance. In this post, I will explain the terminology and try to describe what it means. There is some maths, but don't let that put you off!

GLIDE ANGLE

Figure 1. Showing a plane in steady glide and how the lift force and drag force relate to the glide angle.

L is the lift force generated by the wing.

D is the drag force experienced by the model.

W is the model's flying weight.

h is the height above ground.

x is the distance travelled.

Glide Angle or L/D (pronounced "ell over dee") is an indicator of a glider's performance. From the geometry of the forces acting on a glider in steady flight, you can see that the glide angle relates directly to the ratio of the lift force over the drag force, regardless of the weight of the plane. The maths is set out in Figure 1 (above). High lift and low drag means a flatter (more horizontal) glide. The plane flies forwards, not down like a brick!

WING LOADING & SPAN LOADING

Wing Loading is simply the weight of the plane divided by the wing area. Span Loading comes in two "flavours". The first is the weight of the plane divided by the span. The second is the weight of the plane divided by the span squared. Unfortunately, both are referred to as "span loading". For convenience, I will call these Span Loading v.1 and Span Loading v.2 respectively.

Referring to Figure 2 (below):

• Wing Loading or WL = W / S
• Span Loading v.1 = W / b
• Span Loading v.2 = W / b^2

Figure 2. Showing the important areas for Wing Loading and Span Loading

where:

W is the flying weight of the model.

S is the area of the wing (in blue in Figure 2).

b is the span, and S = ab, where a is the mean chord of the wing. The red area in Figure 2 above is b^2.

Qualitatively speaking, lower Wing Loading means that the model:

• climbs better, both under power and when gliding: it has a "floatier" glide
• flies slower with respect to the air
• requires a shorter take off and landing for rise off ground models
• is more prone to being bumped around by turbulence

Lower Span Loading v.1 means:

• less drag at lower flying speeds, that is less "induced drag

Lower Span Loading v.2 means:

• better glide performance, that is, a flatter more horizontal glide angle

Taken all together, the above indicates that a light weight plane with big span would be ideal. Just consider a typical full-size soaring glider (or 'sailplane' for readers in the USA). For example, the famous and beautiful Duo Discus. I've flown one of these and it was absolutely lovely. In these glass ships, when you push the stick forward, the plane just whooshes forwards (not downwards!).

Note that you can also reduce the Wing Loading (WL) of a given design by increasing the wing area while trying to keep the weight increase to a minimum. However, if you do this by increasing the wing chord alone while keeping the span the same this may not result in a flatter glide. Hopefully, these intricacies will become clearer after you've read the rest of this post.

LEARNING FROM MATHEMATICS!

I suggest that there are three equations worth considering, playing with and understanding. This is quite rewarding and helps to develop a feel for some basics of aerodynamics generally. They are:

Or, when limited by my keyboard:

L = q S CL ......(1)

Di = q S CDi ......(2)

CDi = (CL^2)/(pi AR E) .....(3)

where:

L is the lift force. For a decent model in a steady glide it is essentially equal to the weight.

q is 1/2(rho v^2), also called the "dynamic pressure". Rho is the air density, v is the airspeed.

CL is the coefficient of lift (which depends on angle of attack of the wing).

S is the area of the wing (see above).

Di is the induced drag force. The total drag is this plus the drag from other sources (skin friction and form drag). At lower speeds, the induced drag dominates.

CDi is the induced drag coefficient.

pi is its usual 3.14...

AR is the aspect ratio, that is the span over chord: AR = b/a = b^2/S.

E is a factor relating to the efficiency of the wing. It depends on the design and shape of the wing, 1 for perfect shape, otherwise less than 1, 0.7 is typical for a rectangular planform.

Eeek! What does all this mean?

First, there are some basic ideas contained in these three relationships.

The lift force depends directly on the wing area. Bigger wing, more lift. When the plane goes faster, the lift increases as the square of the airspeed. That's why jet airliners look as if they have smallish wings in relation to the size of the whole plane. Lift from the wing is greater at sea level than in the mountains, where density is lower. So your model may not fly well if you move to a flying location at a different altitude. The drag increases if you decrease the aspect ratio while keeping all else the same (which goes part of the way in explaining why increasing chord to reduce Wing Loading as discussed above, may not lead to a flatter glide).

Substituting (1) and (2) into (3) gives the induced drag:

Di = L^2 / (q pi E S AR) = (L/b)^2 / (q pi E)

This tells you that the induced drag depends on the quantity L/b squared. As mentioned above, in a steady glide, L is essentially the weight of the plane, W, so L/b is the same as Span Loading v.1. A small increase in Span Loading v.1 increases the induced drag significantly because of the squared relationship.

Dividing both sides by L gives the very important Di/L ratio (often referred to the other way round as L/Di):

Di/L = (L/b^2) / (q pi E)

From the geometry of the forces acting on a gliding aircraft, it is a measure of the glide angle (please see Figure 1 to see why). The above relationship shows that Span Loading v.2 is a key determinant of the glide angle (again using the relationship that L ~ W in a steady glide). The smaller Span Loading v.2, the flatter (more horizontal) the glide angle. Also, the more efficient the wing design (E gets closer to 1.0) and the flatter the glide angle.

Another thing to note from the above equations is that Span Loading v.2 = W/b^2 is just the same as WL/AR (just divide top and bottom by wing area S). This explains the point that I made above that reducing the Wing Loading by increasing the chord alone and not the span, may not flatten the glide because although the Wing Loading reduces, the AR decreases as well. We can now see that it will not flatten the glide unless the ratio WL/AR decreases overall.

CONCLUSION

Summing up, if you want to improve the Glide Angle of your model, then concentrate on reducing Span Loading v.2 and on improving the wing's design and efficiency (airfoil, planform, etc). In free flight, good models also tend to have low Wing Loading, at least for calm conditions.

I hope this gives a flavour of how powerful this stuff can be!

Jargon Busting!

Ah, Jargon! Love it or hate it, there is a lot of it. Some is really important to know. For example, bits and pieces of information that relate to "trimming", that is, getting the best performance out of your model. Other terminology is more esoteric, and arguably, not necessary for you to enjoy the sport of Free Flight (and it is officially a "sport" in the UK). I'm not proposing to explain all of the jargon. Instead, I'll list a whole raft of it now. Later, I'll explain some of the important terms, or at least give you a link to more information. So, in no particular order, here's a list:

1. Lift
2. Drag
3. Best L/D
4. Min Sink
5. Polar
   
6. Centre of Gravity
7. Centre of Pressure and Aerodynamic Centre
   
8. Angle of Attack
9. Angle of Incidence
10. Dihedral
11. Decalage (sometimes called Longitudinal Dihedral) - great diagram here
12. Moment Balance
13. Stab Up, Stab Down
14. Stab Tilt
15. Stab Twist
16. Stall
17. Sideslip
18. Dutch Roll
19. Wash Out
20. Wash In
21. Tip Weight
22. Wing Offset
23. Wing Planform
24. Aspect Ratio
25. Wing Area
26. Wing Loading
    
27. Chord and Mean Aerodynamic Chord (MAC)
    
28. Aerofoil section
29. Camber
30. Thickness
31. Winglet
32. Dethermaliser, or DT, or Dethermalizer
33. Span Loading (two flavours)