The ‘P’ Factor

Cast your mind back to the last time you went flying. Poised at the threshold you performed a quick run through your final checks, then with a smooth application of power and a dab of rudder your craft surged forward and off into the wild blue yonder.

Now I’m willing to bet that, for most of us at least, applying the aforementioned dab of rudder is so hard-coded into our subconscious that we’re barely even aware that we do it. And if I asked you why you do it? Other than the obvious answer, “To keep the nose straight”, a hazy recollection of “propeller effects” may come to mind… It’s time to refresh our collective memories and talk about the P-factor.

Mirror Mirror

At first glance most aeroplanes appear to be symmetrical, and when they are obviously not, such as in the Rutan Boomerang, they tend to attract a fair amount of attention. However, the reality is that, despite appearances, all single propeller aircraft are inherently asymmetrical. If you cut a plane in half along the centreline and place it against a mirror a major problem with the prop will be immediately apparent. Propellers are definitely not symmetrical. This leads to a whole host of propeller effects, requiring adjustments in both design and piloting technique to accommodate the quirks this asymmetry introduces.

Quite often all the “P-effects” get lumped together as a single thing, but they actually come from a whole variety of different sources so I’m going to separate them out and look at them individually, starting with why we have to apply rudder when we power up for take-off.

Slipstream

For those of us that fly relatively low powered aircraft – which is virtually all of us given the shortage of Rolls-Royce Merlin powered craft in the ultralight fleet – slipstream effect is the most noticeable of the prop effects. The airflow passing through the propeller is not just accelerated backwards but also develops a helical motion matching the direction of the propeller rotation, causing the air to flow around the fuselage in a corkscrew path. When this airflow arrives at the vertical stabiliser the resulting angle of attack generates a side force causing the aircraft to yaw, unless opposite rudder is applied to cancel the effect. This slipstream effect is strongest at high power settings and low speeds so is most noticeable during take-off and climb out. The pilot is simply expected to apply an appropriate amount of rudder to correct the yaw, but the designer does have the option of making the pilots life easier by offsetting the vertical tail to a slight angle; using a cambered aerofoil; or adding a fixed trim tab to the rudder to minimise the effect at cruise power and speeds.

PropEffect Fig1.png Figure 1 – Propellers add vorticity to the airflow causing Slipstream and Torque Effects. (click for larger image)

Torque Effect

At this point the more thoughtful (or argumentative!) of you will probably be thinking, “Hold on a minute! If the airflow hitting the fin makes the plane yaw, why doesn’t the same airflow hitting the two halves of the horizontal stabiliser cause the plane to roll?”

This is a very good question, and answer is, “It does”, or at least it would, if it wasn’t for the Torque Effect which is more powerful and acts in the opposite direction.

If the propeller is forcing the air to rotate clockwise our old friend Newton tells us the air must be reacting by trying to rotate the aeroplane anticlockwise – think of ‘cartoon physics’ where grabbing a propeller causes the whole aeroplane to spin in the opposite direction! Torque effect is constantly trying to make the aeroplane roll in the opposite direction to the propeller’s rotation, but it is usually easily counteracted with an application of opposite aileron. However, for aircraft with thousands of horsepower travelling slowly, torque effect can be lethal. During WWII there were several accidents attributed to pilots rapidly applying full-power for a go-around at low airspeeds only to have the torque-roll overpower the ailerons and flip the aircraft inverted with fatal consequences. Thankfully in an ultralight with 100hp or so the effect is much more manageable, to the point that it may not even be noticeable, being easily trimmed out or countered with a fixed tab on one of the ailerons.

Asymmetric Yaw Effect and Propeller Normal Force

Whenever the prop disk is not perpendicular to the incoming airflow, such as when an aircraft is operating at high angles of attack or when yawed, the relative motion of the blades and airflow will cause thrust to be generated asymmetricly. As an example, in a nose high attitude a downward travelling blade will also be moving forward and an upward travelling blade travelling rearward relative to the airflow. This affects both the airspeed and angle of attack of the blades as they rotate, with a downward travelling blade seeing increased airspeed and angle of attack and an upward travelling blade seeing reduced airspeed and angle of attack. This leads to two outcomes:

For a clockwise spinning prop the right hand side of the prop will generate increased thrust whilst the left hand side thrust will be reduced, this force imbalance results in a yaw to the left and is called the Asymmetric Yaw Effect.

Prop Effects Fig2 AsymmFigure 2- A propeller which is not aligned with the incoming airflow generates asymmetric yawing forces in addition to thrust.

Secondly, there will be a change in the direction of the force generated by the prop blades as they rotate. The downward travelling blade will incur more drag along with its increased lift whilst the upward travelling blade will incur less, when these two effects are combined the result is a net force acting upwards in the plane of the prop disk, known as the Propeller Normal Force. For tractor configured aircraft the propeller normal force will be destabilising – pitching up produces a force that induces further pitch up – for pusher aircraft where the prop is located behind the C of G the effect is opposite improving the stability. Either way the effect has implications for stability and needs to be considered when sizing tail surfaces.Prop Effects Fig3

Fig3 – The Propeller Normal Force is a result of the incoming airflow not being perpendicular to the propeller disk. (click for larger image)

 

Gyroscopic Effects

Last of all, not all propeller effects are a result of aerodynamics. As a rapidly spinning mass a propeller also acts as a gyroscope and so, like all gyroscopes, it experiences precession when a torque is applied to tilt its axis of rotation. Precession takes an applied torque and precesses it 90 degrees in the direction of rotation of the propeller. Gyroscopic precession is far from intuitive, so I’ll give you an example:

When a tail-dragger with a conventional clockwise rotating propeller (as seen from the cockpit) raises its tail during the take-off run it pitches the nose down. Precession rotates this applied nose down torque 90 degrees in the direction of prop rotation, so as the tail comes up the aircraft also yaws left requiring the pilot to counter with rudder. Unfortunately this behaviour is a perfect recipe for a ground-loop. If the tail is raised quickly early in the take-off run (before there is enough airspeed for the rudder to become effective), the yaw can be more powerful than the rudder can counteract. Of course the same thing may happen at any time if the pilot happens to have slow feet!

Prop Effects Fig4 Gyro

Figure 4 – The propeller is a spinning mass and so acts as a gyroscope. (click for larger image)

So What Does It All Mean?

Fortunately for low powered aircraft with small lightweight propellers most of the effects just described are small in magnitude and can be easily trimmed out, that is assuming they are large enough to actually be noticed; even in the worst cases the controls are highly unlikely to be overpowered so all that is required in most situations is correct piloting technique.

As a pilot you don’t need to know in detail why you have to counter an application of power with rudder, but you do need to press with the correct foot at the right moment, so understanding prop effects will at least save you some embarrassment when you find yourself piloting a plane with an anticlockwise spinning prop for the first time!

 

 

 

 

 

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Short & Sweet

When was the last time you heard a pilot bemoaning his or her aircraft’s incredibly short take-off run, or lamenting its ability to land in a ploughed field the size of a postage stamp? I’m willing to bet never, because given the chance everyone would like a STOL capable aeroplane. The drawbacks with STOL aeroplanes are not their awesome take-off and landing performance, it’s the sacrifices that have to be made in order to achieve them, (and I’m not just talking about their looks, despite most of them being decidedly unattractive! – STOL owners please forward your enraged feedback entitled, “My Plane Looks Best in IMC”, to the editor.) Joking aside, there is obviously good reasons why STOL aircraft look the way they do, so let’s dig a bit deeper.

More Power

First up, any aeroplane can achieve impressive short field performance if you give it enough power. The military have been aware of this fact for a long time with RATO (Rocket  Assisted Take-Off) being first developed in the 1920s. Unfortunately, strapping rocket boosters to the sides of your ultralight would probably fall foul of the “single engine” requirement in the regulations, not to mention causing quite a stir in the RA-Aus Ops department. So as a rather more practical alternative you could just install a more powerful engine. It’ll get you off the ground quicker and may even shorten your landings by allowing you to sit right on the back of the power curve. However, big engines are expensive, heavy and thirsty, so most designers look for other ways of achieving the STOL goal.

More Lift

Clearly if you want to get on and off the ground in the shortest possible distance a low stall speed is essential, which in turn means a high stalling angle-of-attack and a wing capable of large lift coefficients. If you are looking for plenty of lift at low airspeeds a glider style high aspect ratio wing is aerodynamically tempting. Unfortunately a fifteen metre wing span is not a good fit with the rugged ‘go anywhere’ requirements of your average bush plane, so a more practical solution is required. Given that low drag is not vital for STOL performance, short wing spans and high lift devices are the order of the day. Large flaps or flaperons are pretty much essential, but if you want to achieve a really low stall speed then you need to maximise the stall angle-of-attack as well, and that means slats or slots in the wing leading edge. In keeping with the need for rugged simplicity fixed slots are a tempting solution, giving the best of both worlds by increasing the stall angle-of-attack without requiring any sort of activating mechanism, a small drag penalty during cruise being the only real drawback. Automatically deploying leading edge slats are also an alternative, and can give slightly better cruise performance, but require a mechanism to ensure they will only deploy symmetrically and so come with some added weight and complexity.

More Control

It’s all well and good having an extremely low stall speed, but there’s no point being able to fly slowly if the aircraft is uncontrollable. At low airspeeds plain ailerons tend to become ineffective operating in the sluggish and disturbed airflow at the rear of the wing. A common solution to this problem, as seen on both the Savannah and CH701, is to use junker flaperons. Positioned below the wing trailing edge and separated from the main wing aerofoil the control surfaces fly in clean air away from the disturbance of the main wing which improves their effectiveness, especially at low airspeeds. In addition combining the flaps and ailerons into flaperons allows the control surfaces to extend over the full span improving control authority whilst a mixer mechanism allows both ailerons to be drooped together to give the same effect as flaps.

More Attitude

Adding wing slats or slots is highly effective at reducing the stall speed but they also push up the stalling angle-of-attack, this introduces some significant challenges for the rest of the aircraft design. Firstly the horizontal tail must have enough authority to pull the aircraft into an extremely nose high attitude, which can be more than double the usual fifteen degrees or so required to stall a conventional aircraft wing. Simply installing a larger tail will do the job and there’s certainly nothing fancy about the tail of a Piper Cub or it’s many clones, but Zenith aircraft go a step further by using a cambered aerofoil mounted  “upside down”. This allows the tail to produce significantly more downforce for it’s size compared to a conventional symmetrical tail section.

Probably the most visible impact of an extremely high stalling angle of attack is the constraints it puts on the overall shape of the plane. In order to fully utilise the available lift the aircraft must be able to achieve a high angle-of-attack whilst in contact with the ground. This is not too much of an issue for planes with conventional landing gear as they naturally adopt a fairly nose-high attitude – with the extra long landing gear legs seen on the Storch variants taking this to an extreme. However for tricycle gear aircraft the only solution is to include a strongly upswept rear fuselage to ensure adequate ground clearance and avoid a tailstrike when the plane is rotated for take-off. This tends to give these aircraft the appearance of a flying banana and may explain why I have never seen a Savannah painted yellow!

More Landing Gear Travel

Strictly speaking landing gear travel does not affect the STOL performance of an aircraft. However, if you are going to be landing on short, unprepared strips with any degree of regularity you are going to want landing gear which is both rugged and good at soaking up abuse. Long landing gear travel allows the deceleration of a heavy landing to be spread over a longer period of time which decreases the load on the rest of the aircraft structure. Plus giant tundra tyres are not only good for soft surfaces, they also add a significant level of extra shock absorption into the system. Of course heavy landings are not obligatory for STOL performance but a steeper descent will get you into a tighter spot, and given the choice between a heavy stalled landing bang on target or a greased landing 100m into a 150m long strip, the thumper is going to be preferred!

More Drag

My final point may be a little controversial, but I would argue that a draggy airframe is definitely beneficial to STOL performance. If you are a god-like pilot at the peak of his (or her) game then having a slippery aircraft that refuses to slow down is not going to be a problem. After all, your approaches will be perfect and not require any but the subtlest adjustments to arrive at exactly the intended spot at precisely the intended airspeed. For the rest of us mere mortals precision landings require a lot of tweaking and that is a whole lot easier in a draggy aeroplane. In addition, for the experts, a draggy aircraft permits getting well back on the power curve and then bleeding off excess speed quickly at the last possible moment. This allows for a margin of safety on the approach whilst still arriving at the threshold just above stall speed for the shortest possible landing roll.

In Short

They may lack the sweeping curves and fine lines of a thoroughbred but there’s a lot more to owning a plane than looks and while sports cars may be nice to look at, most people would rather own a Toyota Landcruiser. The reality is that STOL aircraft may be quirky looking but in terms of pure utility they can’t be matched. Besides if you really want to make people’s jaws drop, just wait for a stiff breeze and take off with no ground roll – that should get their attention!

 

STOL - CH701

Fig 1 – CH701 showing inverted tail aerofoil section and main wing leading edge slot and junker flaperon. (Photograph by Jerry Gunner CC-BY-2.0)

The Path To Enlightenment

In case you’re wondering, no, I haven’t abandoned engineering and opted instead for a life of meditation. I do firmly believe, however, that weight reduction should be pursued with an almost religious fervor, so I wholeheartedly recommend putting some serious thought into the load paths within the structures you design, after all, the potential weight savings are massive, but I’m getting ahead of myself. Before you can optimise load paths you need to know what a load path is, and what constitutes a good or bad one, so let’s start at the beginning.

A Positive Reaction

Newton’s third law tells us that for an object to be in equilibrium (i.e. not accelerating), all the forces acting on it must be balanced, or to use the famous phrase, “Every action must have an equal and opposite reaction”. The great thing about structures is that they allow the aforementioned ‘actions’ and ‘reactions’ to be physically separated from each other. They do this by providing a ‘load path’ between them. As an example, the wall of a house takes the load imposed by the weight of the roof and transfers that load to the ground via the foundations. In this way the wall provides a load path connecting the ‘action’ created by the weight of the roof to the supporting ‘reaction’ of the ground under the house. It’s clear then that the basic purpose of pretty much every structure ever built is to provide a load path to transfer forces from one place to another, but, as we shall see, not all load paths are created equal.

Short and Sweet

If you are designing a structure for minimum weight it pays to make the load paths as short, straight and continuous as possible. To see why, let’s start with the obvious. The left hand side of Figure 1 shows a rod in tension. Doubling the length of the rod doubles the material required and so doubles the weight. Thus short load paths are lighter simply because they require less material.

This is even more true of structures which have to carry bending loads. The right hand side of Figure 1 shows an ‘I’ beam loaded in bending. Keeping the same force applied to the end of the beam but doubling the beam’s length doubles the bending moment (that is the applied force multiplied by the length of the beam) at the fixed end. To keep the peak stresses in the two beams the same requires an increase in the cross section of the longer beam of approximately 25%, which, when combined with the doubling in length results in a weight more than triple that of the short beam. Now I must admit that simply increasing the cross section is not the most efficient solution to doubling a beam’s length – a tapered beam would be a lighter solution – but even so, when designing for bending, doubling the length always more than doubles the weight.LoadPath Fig1Figure 1 – The effect of increasing load path length

In a similar vein, straight load paths are preferred simply because the shortest path between two points will be a straight line, but there is more to it than that. Looking at Figure 2 it can be seen that a push pull rod with a dogleg will not only be heavier because of the extra material required, it will also have to be more heavily built to cope with the bending stresses the corners introduce, or else be weaker and much less stiff.LoadPath Fig2

Figure 2 – Straight load paths are more efficient

Finally, load paths should be contiguous. In other words, joints and connections should be avoided wherever possible. A single piece structure will always be more weight-efficient than one with lots of connectors; this is one of the primary reasons why composite construction is appealing for aircraft. The major issue is that joining components mechanically requires the loading to be concentrated into a small area around the attachment point, this in turn requires local reinforcement of the structure to control the stresses and heavy fittings capable of carrying the concentrated loads.

So how do we apply this knowledge to practical aircraft design? Consider a tractor aeroplane with nose-wheel landing gear. If the nose gear is aligned with the firewall then it can be mounted directly to what is already a robust part of the structure using only a short bracket, however, if it needs to be mounted 300mm in front of the firewall a large and heavy mounting bracket will be required to bridge the gap – incurring a significant weight penalty. In this case a more optimal solution may be to attach the nose gear directly to the engine mount; given the primary load on the nose wheel will be the weight of the engine, this will provide a short and direct load path with minimal fittings.

Aircraft design is full of these sorts of problems. Next time you go flying have a look at the structure of your plane and you’ll find optimised load paths everywhere. High wing pushers where the engine is mounted right on top of the wing, or low wing craft where the landing gear is bolted directly to the wing spars. There’s plenty of designs where the wing box carry-through forms the seat base, allowing the weight of the pilot and passenger to bypass the fuselage altogether and there’s more than one good reason why modern airliners mount the engines on the wings.LoadPath Fig3

Figure 3 – A Simplified visualisation of the load paths around a wing spar fitting loaded in bending. The top spar cap carries compression, the bottom spar cap carries tension and the web carries shear.

Keeping It Simple?

Simple load paths are appealing. A structure with a single load path, such as a bracket secured with a single bolt, is both easy to analyse (it’s pretty obvious where the loads are going!) and cheap to produce. The drawback is that it ‘puts all your eggs in one basket’ and a single failure will fail the whole structure. Multiple load paths, in comparison, have a distinct safety advantage as they can be designed with redundancy – think of a plate secured by a pattern of rivets where a single rivet failure will not fail the structure. Redundancy of this type protects against single points of failure, but comes at a cost of increased complexity and in many cases increased weight. In addition, when it comes to multiple load paths, things can really start to get complicated on the design and analysis front. You are now forced to figure out where the loads (and therefore stresses) are going within the structure and also how they are being shared between parts.

Analysing redundant structures is complicated, but there are two key factors which determining load distribution: How the external loads are applied, and how stiff the different parts of the structure are. This point is illustrated in Figure 4 with some simple examples, but it is important to realise that many real-life structures will fall outside the ideals shown. Structures like those in Figure 4 where the stiffness and external loading don’t interact are nice, but not all that common, and I’m sure you’ll be relieved to hear that more complex structures are beyond the scope of a short article, but there are still some useful insights to be had, so let’s take a look at a couple of examples and see how failing to understand stiffness and load paths can get you into trouble!

LoadPath Fig4Figure 4 – The effect of stiffness and external loading on load distribution within a structure (Click Image for Larger Version)

Setting a Bad Example

One of the best ways to get a grasp of load paths is to take some bad examples and look at what is wrong with them:

First up is the classic case of mixing up strength and stiffness. I was recently party to a discussion where it was suggested an existing aircraft design could be ‘beefed up’ by simply laminating a layer of carbon fibre onto the outside of the wooden spars. The key point to appreciate here is that carbon fibre composites are very stiff, and wood really isn’t. In fact the ratio is in the ballpark of 20:1 so for every 200kg the carbon fibre spar caps carried, the wood would carry about 10kg. Now the actual amount of carbon fibre wasn’t specified, so one of two outcomes was possible. If a small amount of carbon fibre were to be added, the strength of the wing would not be increased as the stiff carbon fibre would take nearly all of the load and then fail well before the strength of the wooden spar was exceeded. This wouldn’t be dangerous as the wooden spars would still function just fine, but it would be expensive, and provide no discernible benefit.  Alternatively if enough carbon fibre were to be added to significantly increase the strength above that of the underlying wood spar, then the aircraft would be carrying around a heavy wooden spar with almost no structural purpose. Not what most people would consider an optimum design.

My second example is why building a plane ‘stronger’ than the plans call for is not necessarily a good idea. The top half of Figure 5 shows how a two spar wing is usually designed to behave. A vertical gust loads will cause the wing to bend up, but also simultaneously twist nose-down. This reduces the angle-of-attack and sheds some of the load, thus protecting the structure. Compare this to the lower half of figure 5, which  shows what can happen if the rear spar is reinforced or overbuilt, increasing its stiffness. In this case the stiff rear spar bends much less under load so a gust now causes the wing to twist nose-up. This initiates what is called ‘divergence’. The increased twist increases the angle-of-attack, which in turn increases the load, which further increases the twist and so on until, a fraction of a second later, the wing twists itself off. Not a good result from a modification intended to make the wing stronger!

LoadPath Fig5

Figure 5 – Why increased stiffness is not always a good thing (Click Image for Larger Version)

That’s it for load paths, next time I’ll give you a break from structures and look at what it takes to make a STOL aircraft.

 

Biscuits, Jelly, Nylon & Steel

I had planned to dive headlong into the mysteries of load paths this post. But after a moment’s consideration it quickly dawned on me that there are some, far more fundamental, concepts that have to be understood first, and given the trouble which the misunderstanding of these basic concepts regularly causes, I’m going to devote this article to them instead. So without further ado let me introduce the four pillars of engineering: Stress, Strain, Strength and Stiffness. None of which is particularly complicated or difficult to understand, but all of which seem to cause endless problems, mostly stemming from the fact that in engineering they each have very specific meanings, whereas in general usage they are loosely defined and all too often abused.

Let’s start with stress and strain. These two are intimately connected – you simply cannot have one without the other – but this certainly does not mean that they are the same thing! A fact which is easiest to grasp if we imagine how a material behaves at a microscopic level.

Taking the Strain

Solid materials are made up of billions of atoms and/or molecules all held together by chemical bonds. These bonds are extremely stiff, but nonetheless if a force is applied to them they will stretch or compress ever so slightly under the load. The stretch in each individual bond is minuscule but combined over the entire length of a structure will produce a measurable deflection. This is the fundamental basis of strain, and it occurs wherever there is loading, it may be too small to measure – such as a fly landing on a block of concrete, but it will always exist. Strain-Fig1Figure 1 – Strain

As can be seen in Fig 1, strain is a measure of how much an object deforms under load and is given as a ratio of the amount an object has stretched (its extension) divided by its original undeformed length. As strain is a ratio it doesn’t have any units, but strains are usually numerically very small so they are typically converted into a percentage or even multiplied by a million to give units of “micro strain”, thus avoiding numbers with lots of leading zeros which can be easily misread.

Don’t Stress

Getting back to our imaginary microscope, because chemical bonds really don’t like being stretched they respond much like a spring and generate considerable forces in an attempt to return to their original length. It is this behaviour that embodies stress. Stress basically represents how ‘hard’ the bonds within the material are having to pull or push in order to hold the material together and maintain its shape. As can be seen in Fig 2, Stress is calculated by taking an imaginary slice through a structure and dividing the load acting at right angles to the slice over its surface area. The result is the stress and is given in units of ‘force per unit area’.

Stress-Fig2Figure 2 – Stress

Both the location and direction in which stress and strain are measured in is important because, unlike pressure, stress and strain are directional. This is easy to visualise if you imagine a weight hanging on the end of a steel rod, the strain will obviously be much higher along the direction the rod is being loaded and the stresses highest over a surface at right angles to the load

It is important to note that stress and strain describe the conditions at a specific point within a material, they are not a global property of a structure as a whole. Figure 2 shows a wire supporting a load of 100N (or roughly 10kg). Dividing the load by the cross sectional area gives the average tensile stress over the cross section. But what happens if the wire is not of uniform thickness? Figure 2 shows how halving the area, doubles the stress and also illustrates how stresses can vary enormously within a single structure, purely as a result of its shape. Under load one part of a structure may be close to breaking, whilst another part is hardly stressed at all. This variation in stress explains why lightening holes in the web of a beam do not significantly weaken the structure – removing lightly stressed material where it is not required saves weight without reducing strength.

The Agony of Units

As I mentioned before, stress is measured in units of ‘force per unit area’ which should be simple enough i.e. Pounds per square inch (lbf/in² or psi) in imperial or Newtons per square metre N/m² (i.e. Pascals) in SI units. Unfortunately for practical design purposes stress values are usually large in magnitude so the units get scaled up to avoid long numbers with lots of zeros. So we get imperial units of kilopounds per square inch (ksi) and SI units of megapascals (MPa) or its equivalent N/mm² which is sometimes preferred if you are working in millimetres. Plus if you’re really unlucky you may even find some older references to Kilograms force per square centimetre (kgf/cm²)… whoever said metric is easier?!

Putting up a stiff resistance

Now let’s move on to the other two, Stiffness and Strength, and let’s be very clear about this, ‘Stiffness’ and ‘Strength’ are not the same thing. Stiff objects are not necessarily strong, and strong objects are not necessarily stiff. Anyone who disagrees with this should be forced to bungee jump using a steel cable from a bridge made of rice crackers – the bridge will be plenty stiff enough and the cable will have more than enough strength!

Stiffness is a measure of how much something will deflect under a given load, but there is potential for confusion because it comes in two flavours. On the one hand stiffness is a material property: Apply a certain stress and you will get a certain strain (see Fig 3 below). On the other hand stiffness is also used as a description of a structure’s resistance to deflection under load. Puritans will tell you that the material property “stiffness” should be properly referred to as the “Elastic Modulus” but if most professional engineers aren’t inclined to make this distinction I doubt anyone else will be!

Stress_Strain_Ductile_Material Fig3Figure 3 – A Typical Stress-Strain Curve for Steel

Material stiffness is determined by taking a test specimen of uniform dimensions and gradually applying an increasing load whilst measuring the extension. For a ductile metal like steel a plot of the results will give a graph much like Figure 3. The gradient of the straight portion of this graph is known as Young’s modulus (Elastic Modulus) and is a measure of the material’s stiffness. Young’s modulus is a very large number for most materials, it conceptually represents the stress level required to make the material double in length (i.e. achieve 100% strain), which of course ignores the fact that virtually all engineering materials will break at well below 3% strain.

Stiffness-Fig4

Figure 4 – Stiffness

Stiffness of a structure tells you how much it will deflect if you apply a given load and is a result of both the material and its geometry. If your structure is too flexible (that is lacking stiffness) you can either change the geometry, usually making it thicker, or change to a stiffer material.

To illustrate the difference between the two types of stiffnesses, imagine bending a steel rule. If you grasp it ‘flat’ and attempt to bend it you will discover it is fairly flexible. However, rotate the rule 90° along its long axis and hold it by its edges and it becomes very stiff and will hardly bend across it’s width at all, in fact it will probably try and twist or bend away sideways – (but that is a subject for a whole different article!). Clearly the stiffness of the material is the same whichever way you try and bend it, (the rule is made of steel in both directions!!), but the stiffness of the structure is heavily dependent on its geometry and how it is loaded.

Coming on Strong

Last but not least we come to Strength. Much like stiffness an important distinction needs to be made between strength as a material property and the strength of a structure. The strength of a material is independent of geometry and represents the stress level at which a given material will fail… or at least that’s the idea. In reality material strength is inextricably linked to geometry, loading conditions, operating environment and many, many other factors so conservative strength data is instead statistically determined based on the results of collections of standardised tests. This allows us to conveniently design stuff without having to worry too much about the properties of the exact batch of material used… with the extra protection of an appropriate factor-of-safety!

The primary published strengths are tensile, compressive and shear – representing the stress at which a material will yield or fail when being stretched, squashed or sheared respectively. For ductile materials such as Aluminium and Steel, both yield strengths and ultimate strengths are available. The yield strength is the stress beyond which permanent deformation will occur, below the yield strength the material is said to behave elastically and will return to its original shape if the load is removed. Above the yield strength the material will deform permanently, retaining a “set” even if the load is removed. Ultimate strength is the maximum stress the material can support, and any attempt to increase the stress beyond this point simply leads to the material stretching to reduce the load, finally leading to fracture. The typical stress-strain graph for steel given in Figure 3 has these significant points highlighted.

The Strength of a structure is the load at which the structure will no longer be able to perform its designed purpose i.e. it has either broken because some portion of the structure has exceeded its ultimate strength or it has deflected to the point of permanent deformation and so can no longer do its job. The strength of a structure depends on both its geometry and the materials it’s constructed from. It is extremely difficult to build a strong structure from weak materials, but entirely possible to build a weak structure from strong materials, as many engineers have learnt to their cost!

Biscuits, Jelly, Nylon and Steel

It is fairly easy to see how strength and stiffness get confused or even lumped together as meaning essentially the same thing. Very often it is stiffness and not strength that is critical for a design, so many objects end up being vastly stronger than they need to be to be in order to achieve adequate stiffness. In turn this leads to people equating stiffness to strength, both because stiff structures are frequently also strong, and because increasing a weak structure’s strength through adding more material also increases its stiffness. Unfortunately these generalisations are misleading, and in some circumstances reducing stiffness can actually increase a structure’s overall strength, by allowing the loads within the structure to redistribute themselves resulting in reduced stress

Hopefully by now we are clear that strength and stiffness are not the same thing, but you may still be wondering about the title of this article, so I’ll leave you with a quote about stiffness and strength from J. E. Gordon, arguably the father of materials science:

“A biscuit is stiff but weak, steel is stiff and strong, nylon is flexible and strong, raspberry jelly is flexible and weak. The two properties together describe a solid about as well as you can reasonably expect two figures to do.”

Aircraft design is an exercise in optimisation, providing the right amount of stiffness at the minimum possible weight and providing just enough strength to meet the design requirements, but certainly no more than necessary. Unfortunately this also makes aircraft structures unforgiving and beefing up one part may even prove disastrous for another, a problem we will examine next time when we look at load paths.

 

Gone With The Wind

We’ve all had one of those days. The forecast said it was going to be a hot one so you expected to get bounced around a bit, but once airborne it was like flying in a tumble dryer. You may even have discovered your shoulder straps were not quite tight enough, courtesy of a particularly punchy downdraft unceremoniously cracking your head on the cabin roof. It goes without saying then that gusts are a force to be reckoned with, but when it comes to designing for gust loading there are one or two surprises in store.

Gusts Fig1 Gust1

Figure 1 – A Simplified Gust Response (click for larger image)

An aeroplane’s gust response is, superficially at least, pretty simple. An updraft increases the wing’s angle-of-attack, and so generates additional lift (as shown in fig.1) whilst a downdraft has the opposite effect, reducing the angle-of-attack and decreasing the lift force, or even generating a negative lift force in the more extreme cases. The magnitude of the lift change due to a gust is directly proportional to the gust’s strength. That is to say if you double the gust strength you double the change in lift.

Now, the different regulating authorities don’t all agree on how gust strength should be calculated, but the usual approach is to pretend a gust is ‘sharp edged’ for calculations, (i.e. assume it hits instantly), and then apply a fudge factor to account for the fact that a real gust actually ramps up over a short distance much like it is shown in Fig 1. For example, the 50fps ‘sharp edged’ gust assumed by FAR Part 23 actually represents a stronger 66fps gust, but with a more gradual ramp up. All very straightforward so far, but what does this mean for the aircraft’s structure?

The effect of a gust can be split into two areas; the immediate load increase on the wings, and the effect of the ensuing gust-induced acceleration. The change in lift force produced by a gust is determined purely by the wing’s aerodynamic properties and so is, initially at least, independent of aircraft weight. This leads to some unexpected effects when determining the critical loading. For the wing structure the worst case scenario will be hitting an updraft with the aircraft at maximum weight. The gust load will add to the large lift load already required to support the aircraft, producing severe loading on the wing structure. “Nothing particularly strange about that”, I hear you say, but now consider what happens with the plane flying at minimum weight. Gust forces are independent of weight so both the light and the heavily loaded plane will experience the same increase in lift force, but thanks to Newton we know that the same force will accelerate a light object more rapidly than a heavy one so the lightly loaded plane will accelerate more sharply and thus experience a higher load factor. This confirms what we already know intuitively – light planes get thrown around more in turbulence – but there is more to it than that.

The wing structure will probably be ok at minimum weight because the increased load factor will probably be balanced out by the reduced weight of the aircraft, so the resulting loading is unlikely to be critical. But this is not true for all of the structure. Taking the engine mount as an example. It doesn’t matter whether the plane is flying heavy or light, the engine will weigh the same, but the lighter plane will experience a higher load factor due to its more rapid acceleration. If this load factor works out to be larger than the manoeuvring load factor for the plane, then it will present the critical scenario for the design of the engine mount. As can be seen in the example shown in Fig 2, the same gust produces a 60% higher load on the engine mount for the minimum weight plane compared to the maximum weight one. I’m guessing there’s a good chance that that wasn’t a result you were expecting!

Gusts Fig2 Gust2

Figure 2 – The Effect of Aircraft Weight on Gust Loading (click for larger image)

The above requirement also extends to all the other structures supporting fixed masses such as battery trays, pulley mounts, seats, even cup holders! It also demonstrates an important concept; any large acceleration, no matter what the cause, can produce loads that are critical for design. The V-n diagram will capture manoeuvre load factors and may also include gust loading, but there are other sources a designer needs to consider. If you have a hard landing your first thought will probably be for the landing gear, but a 3g landing deceleration applied to a wing with full tip tanks or pylon mounted engines is likely to produce a load in the wing spars way beyond that produced by a limit negative-g manoeuvre.

For completeness, there is another potential source of acceleration loading too, albeit one that is unlikely to be an issue for an ultralight design, and that is rotation – i.e. pitch, roll and yaw. If your aircraft is to be exposed to violent manoeuvres (or it is simply dimensionally very large) then masses mounted at the extremities of the aircraft will generate significant loading when the airframe is rotated, both due to rotational acceleration and centripetal forces.

 

Feel The Force

Last time we looked at design load factors and how they combine with the mass of an aircraft to give “limit loads”. Limit loads represent the maximum loads an aeroplane can expect to see during its operational life and so define the forces an aeroplane must be able to withstand without suffering damage or permanent deformation to its structure.

In a perfect world limit loading would be all you need worry about when designing a plane, but in the real world there is uncertainty in loading, operating conditions and manufacturing, to name but a few. So beyond the limit loading there needs to be some safety margin which leads to the concept of “ultimate loads” – the maximum forces the aircraft structure must be able to withstand without failing, but where damage or permanent deformation to the is acceptable. The ultimate load is simply the limit load multiplied by a factor of safety – but how big should the factor of safety be?

The reality for an aircraft design is that weight is critical; you simply don’t have the option of beefing everything up and relying on a large factor of safety to cover any uncertainty. So careful analysis and tight factors of safety are the order of the day. For a metal aeroplane a factor of safety of 1.5 is typical, with occasional increases to cover things like bolted joints or hard to predict control surface hinge loads. If you are familiar with aircraft design 1.5 probably sounds like a perfectly reasonable number, but if you happen to know a civil engineer try mentioning that you are designing a safety critical structure with a factor of safety of 1.5, then sit back and enjoy their reaction, (they prefer a factor of safety closer to 6!)

With such narrow factors of safety there isn’t much room for getting the design wrong, a problem which is compounded by the seemingly endless possible loading scenarios which an aircraft can experience. To make things worse engineering inevitably involves calculations, and calculations need well defined inputs. This means we have to answer tricky questions like, “How bad is a bad landing?”, and, “How strong is a wind gust?” In other words, you are faced with a lot of uncertainty. Fortunately hard won experience has made the job a whole lot easier by identifying the parts of the flight envelope which produce the extremes of loading, and also just how bad a landing our aircraft will have to tolerate! As an example let’s take a wing and look at the four critical loading scenarios which will drive much of the design – but please bear in mind I’m not considering control surface induced loads, flap loads, or even spanwise load distribution so this is not the whole story!

Figure 1 – Critical Wing Loading Scenarios (click for larger image)

Force Fig 1 - Forces

Figure 1 shows a cross section of a wing in four different loading scenarios. The airflow is fixed as coming directly from the left so any rotation of the wing cross section represents a change in angle-of-attack. I’ve chosen to gather the aerodynamic lift and drag forces acting on the wing into a total resultant force, shown acting at the centre of lift – this makes it easier to visualise what’s going on compared to reality, where the forces are actually a pressure distribution spread over the skin of the aerofoil. I’ve also shown the resultant aerodynamic force broken down into force components aligned parallel and perpendicular to the aircraft axes, which is much more convenient for structural design. For reference I’ve also reproduced the V-n Diagram from the last article, this is relevant as the four conditions shown in figure 1 correspond directly to points A, D, G & E on the V-n diagram.

Loading Fig 1 - Vn Diagram

The top left part of Figure 1 represents the positive high angle-of-attack condition. This occurs at VA the lowest speed at which a rapid application of “nose up” elevator can develop the limit g-load for the aeroplane. At lower speeds the aeroplane will enter an accelerated stall before reaching the limit load, at higher speeds the limit load will be reached at a lower angle-of-attack. This first loading scenario is notable as even though the resultant force is angled back relative to the airflow it is angled forward relative to the wing chord. Early aeroplane designers were unaware of this situation, believing that the drag force on the wing would always result in the leading edge of the wing being in tension. The resulting absence of “anti-drag” wires in the wing structure meant some early aircraft displayed an unfortunate tendency for the wings to fold forward and “clap hands” when exposed to an enthusiastic pull-up manoeuvre at fairly low airspeeds. The magnitude of this forward force depends on both the maximum lift the wing can generate and the stalling angle-of-attack at which the maximum lift occurs. The end result is this scenario usually produces the maximum compressive load on the upper surface near the leading edge and the maximum tensile load on the lower surface near the trailing edge.

As a side note, when a wing is pitched up rapidly it will reach a higher angle-of-attack before stalling than if it is pitched up gradually. How much higher is tricky (i.e. expensive!) to quantify so for structural calculations a 25% margin is added to the wing’s maximum lift coefficient and a “dynamic” stalling angle-of-attack is extrapolated from that. This is a conservative approach from a structural point of view, but not from an aerodynamic one – so don’t try this when calculating stall speed or you could be in for a nasty shock!

Getting back to Figure 1, the top right diagram shows the positive low angle-of-attack condition. This condition occurs during a limit g-load pull out from a dive at VD – the high speed allows large lift loads to be developed at a low angle-of-attack and also gives a high drag force. Combined these forces cause a large compression load on the rear upper portion of the wing and a corresponding tension on the forward lower portion. In addition the rearward location of the resultant force, positioned back around the 50% chord, produces a large nose down pitching moment, loading the wing in torsion. This may not be the maximum torsion the wing must withstand however as aircraft with flaps extended, especially flaps that increase the wing area, can produce massive torsional loads when operating at VFE (Maximum flap extended speed).

The two diagrams at the bottom of Figure 1 represent similar conditions to those already described above, but for negative angles-of-attack. For non aerobatic aircraft these primarily represent exposure to downdrafts at high and low airspeeds. As I mentioned last time the g-load limits are usually set lower for the negative angle-of-attack scenarios, mainly because most planes spend their time flying the right way up and so are likely to already be flying at +1g when a gust hits. Negative loading produces compressive forces on the lower wing structure which usually dictates the design in this area. Tensile loading occurs on the upper wing structure, but this is seldom critical when compared to the positive lift loads.

That’s it for this article, join me next time for part three where we’ll look at structure and load paths.

Shouldering the Load

It is an annoying fact of life that sometimes things break. So, if you operate a complex machine such as an aeroplane for a period of years it is virtually inevitable that you will experience a component failure at some point. What’s more, when that something does break there’s a good chance that you’ll be cursing the ineptitude of the designer responsible for producing such a flimsy engineering abomination! Thankfully though, whilst components do inevitably wear out, major structural failures are almost unheard of so the engineers must be getting it right most of the time, but how are they doing it?!

One thing that has always stuck with me from my very earliest days as an engineering student was one of the professors cautioning the new intake with the words, “Remember, 99% of engineering failures are a failure of imagination, not calculation!” He was right. Failures are not uncommon, but when they do occur it is incredibly rare for them to be a direct result of an error in calculation or analysis. Ask most engineers what their biggest challenge is when they produce a design and the answer won’t be, “the analysis”, nine times out of ten it will be, “The assumptions I have to make to perform the analysis.” This concern is with good reason, as when a component fails the cause is almost always one of two things: Either it was exposed to a condition which wasn’t allowed for in the design, or there was a defect in the manufacturing or materials which meant the part didn’t meet its designed strength. I’m going to start with the first of these problems, and examine the problem of getting the loading right.

That’s Heavy Man

Given the nature of this blog it’s fair to assume that you are familiar with aeroplanes, and so have probably noticed that, unlike bridges or buildings, aircraft are not fixed to the ground. This fact makes them much more interesting to be around, but also rather trickier to design. It’s true that bridges and aeroplanes both have to support their own weight, plus the weight of whatever they are carrying, and they also both have to deal with aerodynamic gust loads (although a civil engineer would probably just call it “wind loading”), but what really sets them apart is acceleration loads. Thanks to their mobility, aircraft can experience accelerations in almost any direction. A significant point because, as Isaac Newton pointed out (probably via your high school physics teacher), force = mass × acceleration, so the forces acting on your aeroplane depend directly on its mass and how much that mass is being accelerated.

For static structures like bridges there is only one acceleration to worry about (ignoring earthquakes!) and that’s the effect of gravity. On the Earth’s surface gravity is constantly trying to accelerate you, and everything around you, towards the centre of the planet. The rate of this acceleration is 9.81m/s² but it is more commonly referred to as ‘1g’. Multiply this 1g acceleration by your mass and you get the force which acts on the bottom of your feet, conveniently stopping you from accelerating towards the centre of the earth and usually better known as your weight! For a bridge or a house that’s pretty much the end of the story as far as  loads go; they have weight plus some loading and they transfer it to the ground which provides support. For an aircraft, it’s fair to say, there’s rather more to think about.

From a loading point of view flying straight and level is not unlike standing on the ground; gravity applies 1g and the wings generate a lift force equal to the plane’s weight, which holds everything up. Pull a sharp turn or hit an updraft however and, (as the seat of your pants will tell you), you are experiencing more than just gravity. This is because you are accelerating, and more acceleration means more force. This is where the concept of ‘load factor’ comes in. Although gravitational and manoeuvring accelerations come from completely different sources, as far as the aeroplane’s structure is concerned the effects are indistinguishable and they can be combined; perform a ‘1g’ pull-up from straight-and-level flight and you will experience ‘1g’ of gravity plus the ‘1g’ of manoeuver load so the airframe (and your bum) will experience a load factor equal to ‘2g’ – i.e. you will feel like your weight has doubled. This relationship is linear so if you now double the load factor again and pull ‘4g’ for example, you double the lift the wings have to provide and double the external loads applied to the aircraft. Pull ‘8g’ however… and the wings may snap off!

Because aircraft weight is critical and carbon fibre is expensive it’s usually not practical to make a plane ‘unbreakable’, so some rational decisions have to be made about what loading the aircraft will be designed to withstand. Of course as a designer of an experimental the choice is yours, but there are some minimums defined in FAR part 23 that are mandatory for certified aircraft and which you would be foolish not to follow. These minimums, shown in Table 1, specify the limit load factors an aeroplane must meet to qualify in each of three categories: Normal, Utility & Aerobatic.

Loading Table1 - Load FactorsTable 1 – Limit Manoeuver Load Factors (extract from Appendix A to FAR part 23 – Simplified Design Load Criteria)

Regulations like the FARs are a lifesaver when it comes to estimating loading and they go a long way to explaining why structural failures in aircraft are so rare. A hundred years of hard-won aviation design experience is distilled into these documents, which provide direction about design loads, gust loads, landing gear loads, asymmetric conditions, flutter and much more. Unfortunately regulations seldom give any explanation as to why a particular requirement exists, but at risk of sounding melodramatic, they tend to be ‘written in blood’ from previous accidents, so you would want to have a very good reason not to comply – even though they are not mandatory for experimental aircraft.

Takin’ it to the Limit

Having consulted the FARs and selected the limit load factors for a design they can then be combined with some of the aeroplane’s basic performance data to produce what is called a ‘V-n diagram’. A V-n diagram plots load factors against calibrated airspeeds and so captures the flight envelope the plane is designed to operate within and thus the loads it will have to withstand. An example V-n diagram is given in Figure 1 for an ultralight aircraft designed to meet the Utility category with limit loads of +4.4g and -2.2g. So let’s take a look and see what this diagram tells us:

Loading Fig 1 - Vn DiagramFigure 1 – An example V-n diagram for an Ultralight Aircraft (click for larger image)

Firstly, the vertical line at the left hand side of the envelope marks VS, the unaccelerated stall speed with flaps retracted, this represents the lowest speed at which the aircraft can fly in the clean configuration. As speed increases above VS the maximum load the plane can experience increases exponentially until point A on the envelope is reached, marking the point where performance becomes limited by the aircraft’s structure rather than its aerodynamics. Below VA (the design manoeuvring speed), even the most vigorous ‘positive g’ manoeuvre will be unable to overstress the airframe, as the wing will enter an accelerated stall before it can develop the rated limit load.

Loading Table2 - Airspeed AbbreviationsTable 2 – Standard Airspeed Abbreviations

For this particular example the line between points A, C and D is constant at +4.4g (the selected design limit load), however this is not the case for all aircraft. The diagonal dashed lines within the envelope represent the load factor that would be produced by 50 foot per second and 25 foot per second vertical gusts. Years of data collection by the regulating authorities have shown these gust values to be suitably conservative for design purposes and the practice is for the 50fps gust line to apply up to the design cruising speed (VC) and the 25fps line to apply at the maximum dive speed (VD). These two lines are then joined to give a decreasing limit gust load between VC & VD, representing the expectation that pilots will fly slower in turbulent conditions. For aircraft in the ‘Normal’ category with high cruise speeds or low wing loadings the 50fps gust line will often extend above the line between A and D and thus cause a peak to be added to the envelope centered around point C. In addition aircraft POHs will often specify a VNO speed, the maximum structural cruising speed, which applies in turbulent conditions to mitigate the risk of airframe damage from gust loading.

The far right of the V-n diagram is bounded by a vertical line at VD, the design diving speed, which is a little over the placarded VNE to give some margin for horizontal gusts etc. Bear in mind this margin is for the designer not the pilot, so don’t go flying at more than VNE “because the design is good for VD“, as you may well pay the price!

Finally, we get to the bottom of the envelope. This is close to a mirror image of the top half, only the negative limit loads are substantially smaller than the positive ones. This is for two reasons, firstly because most planes spend their time flying the right way up and so are likely to be flying at close to +1g load when a gust hits, and secondly, pilots are much less tolerant of negative g; not many of us would deliberately choose to support twice our own body weight on our harness shoulder straps, at lest not for an extended period!

That’s it for this post, next time we’ll look at what these load factors mean for the aeroplane’s structure, and the concept of ‘factors of safety’.