by J E Gordon
Torsion or twisting
The aeroplane was developed from an impossible object into a serious military weapon in something like ten years. This was achieved almost without benefit of science. The aircraft pioneers were often gifted amateurs and great sportsmen, but very few of them had much theoretical knowledge. Like modern car enthusiasts, they were generally more interested in their noisy and unreliable engines than they were in the supporting structure, about which they knew little and often cared less. Naturally, if you hot up the engine sufficiently, you can get almost any aeroplane into the air. Whether it stays there depends upon problems of control and stability and structural strength which are conceptually difficult.
In the early days too many brave men, like C. S. Rolls and S. F. Cody, paid with their lives for this attitude of mind. The theoretical basis of aerodynamics had been worked out by F. W. Lanchester in the 1890s, but not many practical men had the least idea what he was talking about.* A good many of the accidents to the pioneers were caused by stalls and spins, but structural failures were nearly as common. Since the early pilots seldom used parachutes, these accidents were generally fatal.
The requirement for a really reliable lightweight engineering structure was, of course, more or less a new one. In the first place, the wings of an aircraft are subject to bending forces, very much like a bridge. Since this is obvious, and since there was a good deal of precedent to go on in the matter of bridge construction, bending loads could generally be dealt with more or less safely. What was not so often realized was that the wings of an aeroplane are, in addition, subject to large torsional or twisting forces. If no proper provision is made to resist these torsions, the wings will be twisted off.
With the expansion of military flying after war broke out in 1914, the accident rate became a serious matter. In this country, luckily, such questions were dealt with by that small group of brilliant young men at Farnborough who afterwards became famous as Lord Cherwell, Sir Geoffrey Taylor, Sir Henry Tizard and ‘Jehovah’ Green. Thanks to their efforts the traditional biplane became, by 1918, one of the safest of all structures and came to be regarded as almost unbreakable. The Germans were less fortunate. Their aircraft technical authorities at that period had the reputation of being rather hidebound. At any rate they had a long run of structural accidents – many of them due to a failure to understand the problem of torsion in aircraft wings.
By the early part of 1917 the Allies had achieved a degree of air superiority on the western front, partly as a result of the technical quality of their fighters. However, in the meantime, the very able designer Antony Fokker was developing an advanced monoplane fighter – the Fokker D8 – with a performance better than anything available or in immediate prospect on the Allied side. Because of the critical tactical situation, production of the D8 was accelerated and it was issued to several of the crack German fighter squadrons without undergoing any adequate programme of test flying.
As soon as the D8 was flown under combat conditions it was found that, when the aircraft was pulled out of a dive in a dogfight, the wings came off. Since many lives were lost – including those of some of the best and most experienced German fighter pilots – this was a matter of very grave concern to the Germans at the time, and it is still instructive to study the cause of the trouble.
In those days most aircraft were biplanes, because this form of construction was lighter and also more reliable. However, for a given engine power, a monoplane will generally be faster than a biplane, because it does not have to experience the extra air resistance resulting from the aerodynamic interference which occurs between two adjacent sets of wings. There was thus a strong inducement to build monoplane fighters. However, although the reasons for the many failures were not understood, monoplanes had been known to be structurally unreliable ever since the wings of Samuel Langley’s historic aeroplane had collapsed over the Potomac river in America in 1903.
The wings of the Fokker D8, like those of most monoplanes at the time, were fabric-covered. The fabric was there solely to provide the desired aerodynamic shape. It was merely stretched over an internal structural framework and itself carried none of the main loads. The main bending loads were taken by two parallel wooden spars or cantilever beams which projected sideways from the fuselage. The two spars were connected every few inches by a series of light shaped wooden ribs, to which the doped fabric was attached (Figure 10).
As soon as the accidents to the D8 became known the German Air Force authorities very naturally ordered structural tests to be made. After the custom of the time, a complete aircraft was mounted upside down in a test-frame and the wings were loaded with piles of shot-bags, disposed so as to simulate the aerodynamic loads which occur in flight. When tested in this way the wings showed no sign of weakness, and they were broken only by a load which was equivalent to six times the total loaded weight of the aircraft. Although nowadays fighter aircraft are required to withstand a load equivalent to twelve times their own weight, in 1917 a ‘factor’ of six was considered entirely adequate and almost certainly represented a bigger load than would have occurred under the worst combat conditions at the time. In other words, the aircraft should have been perfectly safe.
Figure 10. Fabric-covered monoplane wing.
However, in the D8, when structural collapse did eventually happen on the test-rig, the failure could be seen to begin in the after of the two spars. To make quite certain, therefore, the authorities ordered the rear spars of all Fokker D8s to be replaced by thicker and stronger ones. Unfortunately, after this had been done, the accidents became more, not less, frequent, and so the German Air Ministry had to face the fact that by ‘strengthening’ the wing by adding more structural material they had actually made it weaker.
By this time it was becoming clear to Antony Fokker that he was not going to get much effective help from the official mind. He therefore loaded up another D8 under his own supervision in his own factory. This time he took care to measure the deflections which occurred in the wing when it was loaded. What he found was not only that when the wing was loaded it deflected in bending (that is to say, the wing-tips would rise with respect to the fuselage when the plane was pulled out of a dive), but also that the wings twisted although no obvious twisting loads had been applied to them. What was particularly important was that the direction of this twisting was such that the aerodynamic incidence, or angle of attack of the wing, was significantly increased.
Pondering over these results that night, it suddenly occurred to Fokker that here lay the solution to the D8 accidents and to a great many other monoplane troubles as well. When the pilot pulled the control-stick back the nose of the plane rose and so did the load on the wings. But at the same time the wings twisted, so that air loads on the wings rose disproportionately; so the wings twisted more; so the loads rose still more; and so on, until the pilot no longer had any control over the situation and the wings were twisted off. Fokker had discovered something which is called a ‘divergent condition’ – which can also be a very lethal one.
What was actually happening in terms of elasticity?
Centres of flexure and centres of pressure
Consider a pair of similar, parallel, cantilever beams or wing-spars, joined together at intervals by horizontal fore and aft ribs bridging the gap between them (Figure 10). Suppose now a single upward force to be applied at some point on one of the outer ribs. Unless this force is applied at a point which is just half-way between the two cantilever spars (Figure 11), the load will not be equally shared between the spars and the upward force will be greater on one spar than on the other. If this happens then the more heavily loaded spar must deflect upwards further than its partner (Figure 12). In such a case the ribs joining the spars will cease to be horizontal and the wing as a whole must twist. The point at which a load must be applied so as to cause no twisting in a beam-like structure is called the ‘centre of flexure’ or the ‘flexural centre’.
Figure 11. Coupled bending and tor
sion. Only if the vertical lift forces act effectively at a point called the’ flexural centre’ (in this case halfway between the two spars) will the wings bend upwards without twisting.
Naturally, if there are more than two spars, or if the spars are of differing stiffness, then the flexural centre will not be at the midpoint but at some other position along the fore and aft or chord line. However, there is always a centre of flexure associated with every sort of beam or beam-like structure. A vertical load applied at this point will not cause the beam or wing to twist; a load applied at any other fore and aft position will cause a greater or less amount of twisting or torsional deflection as well as the usual bending deflection.
So far we have argued the case in terms of a single point load applied to a beam or a wing. Naturally, the aerodynamic lifting forces which, when an aircraft is in flight, press upwards on a wing and so keep the machine in the air are diffused over the whole of the wing surface. However, for the purposes of discussion and calculation all these forces can be considered as acting together at a single point on the wing surface which is known as the ‘centre of pressure’or C.P.
Figure 12. If the lift forces act at a point away from the flexural centre (e.g. near the leading edge of a wing), then the wing (or any other beam) will twist as it bends. If this causes an increase of aerodynamic incidence the result may be fatal, as it was in the Fokker D8.
It might perhaps be supposed by the uninitiated that the C.P. of the lift forces acting on a wing in flight lay at the middle of the wing, half-way between the leading and trailing edges, that is to say, at mid-chord. Actually it is a well-known fact of aerodynamic life that this is just what does not happen. The centre of pressure of the lift forces on a wing is really not far behind the leading edge, usually near to what is called the ‘quarter-chord’ position: that is to say, 25 per cent of the chord behind the leading edge.*
It follows that, unless the structure of the wing is designed so that the flexural centre is close to the quarter-chord position, the wing must twist. The angle through which the wing will twist will naturally depend upon how stiff the wing is in torsion, but, on the whole, all wing-twisting is a bad and dangerous thing in an aeroplane and it is the designer’s aim to reduce it as much as possible. This is why the quill of a bird’s wing feather is usually located around the quarter-chord position (Figure 13).
Figure 13. Lift distribution across an aerofoil.
In a simple fabric-covered monoplane wing both the position of the centre of flexure and also the torsional stiffness depend almost entirely upon the relative bending stiffnesses of the main spars. In the Fokker D8 the centre of flexure was a long way behind the centre of pressure and much too near mid-chord. The wing had not enough stiffness to resist the resulting torsional forces and so it was twisted off. Modifications which strengthened and stiffened the rear spar had the effect of moving the flexural centre still further backwards and so made the situation even worse. When these facts dawned on Antony Fokker he took the by now obvious step of reducing the thickness and stiffness of the rear spar, thus moving the centre of flexure further forward and closer to the C.P. When this was done the D8 became, comparatively speaking, a safe machine and a menace to the Royal Hying Corps and the French Air Force.
Because of the laws of aerodynamics the C.P. of the lift forces acting on an aeroplane wing must always be near to the quarter-chord position. To reduce the torsional or twisting stresses in the wing it is therefore necessary to design the structure in such a way that the centre of flexure is well forward in the wing and lies close to the C.P. However, the ailerons (which control the aircraft in roll, that is to say, when banking) apply large up or down forces to the wing tips, and these forces act at points not far from the trailing edge and thus a long way to the rear of the centre of flexure. Thus the ailerons inevitably exert large twisting loads on the wings every time the pilot banks the aircraft. It will be seen from Figure 14 that the direction of this twist is such as to change the aerodynamic lift on the wing, as a whole, in the opposite sense to the action of the aileron and thus to reduce its effect. If the wing is not sufficiently stiff in torsion the effect of the aileron may actually be reversed, so that the pilot, wanting to roil or bank the aircraft to the right, and applying his controls in that sense, may find that the aircraft actually rolls to the left. This effect, which is not only disconcerting but also very dangerous, is called ‘aileron reversal’ and is not unknown. It is a serious problem in the design of modern fast aircraft. The cure or preventive is to ensure ample torsional stiffness in the wing structure.
Figure 14. An aileron applies large vertical loads near the trailing edge of a wing and well aft of the wing’s flexural centre. It therefore tends to twist the wing in such a way as to provide aerodynamic forces which are the opposite of those desired by the pilot.
In the early fabric-covered monoplanes, such as the D8, the torsional stiffness of the wings was almost entirely due to what is called the ‘differential bending’ of the two main spars. Not very much can be done about this and the amount of torsional stiffness which can be obtained from such a system – even with the help of a certain amount of wire rigging – is quite limited. For this reason such aircraft were always more or less dangerous – so much so that the authorities in nearly every country frowned on monoplane construction, and in some cases it was actually forbidden.
The preference for biplanes was, therefore, not due to some kind of reactionary stupidity on the part of air ministries but rather to the fact that the biplane provides what is inherently a stiffer and stronger form of construction – especially in torsion. In practice, biplanes were both lighter and safer than monoplanes for many years, and in the early days the difference in speed was not very great.
What the strutted and braced biplane construction does is to provide, in effect, a sort of cage or ‘torsion box’ which is very strong and stiff, not only in bending but also in torsion. From Figure 15 it will be seen that the four main spars (two in each wing) run along the corners of the box, while the spaces between them form a braced truss or lattice girder. One does not, of course, see the diagonal bracing on the top and bottom surfaces, because it is hidden by the fabric of the wings. However, this horizontal bracing is there all right, and its function is to take the shears which arise from the torsions in the wing structure. The manner in which such a box can resist torsion is shown diagrammatically in the figure. It will be seen that each side of the box is being sheared individually, very much like the lattice web of a trussed beam which is in bending. Notice that all four sides of the box are being sheared together and that they are mutually dependent. If one of the four sides were cut or removed there would be no resistance at all to torsion.
Figure 15. Diagram of the main structure of a pair of wire-braced biplane wings subject to torsional forces, e.g. from the ailerons. The whole affair forms what is called a ‘torsion box’.
In a biplane these shear panels are necessarily made from struts and wires. However, if the structure did not have to fly but merely had to resist torsional forces on the ground, then the lattice of wires and struts could be replaced by continuous panels of metal or sheets of plywood. From a purely structural point of view the effect would be the same, just as it would be in the web of a beam truss. Torsion can therefore be resisted by any kind of box or tube whose sides may be continuous or alternatively of openwork lattice construction. In either case the walls or sides of the tube are subject to shearing stresses. In terms of weight and strength and stiffness this is a very much more effective way of resisting torsion than depending on the differential bending of two beams.
Formulae for the strength and stiffness in torsion of various kinds of rods and tubes are given in Appendix 3. Among other things it will be noticed that the strength and stiffness in twisting of a tube or torsion box depends upon the square of the area of its cross-section. Thus a torsion box of large cross-section, such as an old-fashioned biplane, will require little material and will be light
in weight. When we build a modern monoplane, what we do is to turn the wing itself into a torsion tube with a continuous covering of metal sheet or plywood. However, even though we, perforce, use a much thicker wing than was the practice with biplanes, yet the cross-sectional area of the torsion tube, as a whole, is still much less than that of the biplane. So to get adequate torsional strength and stiffness we are forced to use comparatively thick and heavy skin. Thus a comparatively high proportion of the weight of the structure of modern aircraft has to be devoted to resisting torsion.
Although a lack of torsional stiffness is not quite as dangerous in cars as in aircraft, the character of a car’s suspension and road-holding does largely depend upon it. The pre-war vintage cars were sometimes magnificent objects, but, like vintage aircraft, they suffered from having had more attention paid to the engine and the transmission than to the structure of the frame or chassis. These chassis, in fact, usually relied for any torsional stiffness which they might have had upon the differential bending of rather flexible beams – much like the old Fokker D8. It was the lack of stiffness in the chassis which gave these cars their highly uncertain road-holding characteristics and which made them so tiring to drive.