Some Aerodynamic Musings Without Formulae

Why does an aeroplane lose height during a turn? Without drawing vector diagrams this may be a little difficult but it may be interesting to try!

The wings cause an aeroplane to turn, not the rudder. Rudder only makes the plane yaw and increases the drag. It may eventually turn but only if there is enough dihedral and rudder is held on long enough. The plane will still descend though, due to the drag causing a reduction in airspeed. But that is another story……..

Lift is always perpendicular to the wing. The turn is initiated by banking the plane left for a left turn and right for a right turn. With the plane in straight and level flight (this is the point to keep in mind) the lift force is also perpendicular to the earth`s surface and weight is vertically down. The two are now equal. As the wing banks the lift remains perpendicular to the wing with weight still straight down. A vector diagram will show that the total lift force is now less than it was but weight remains the same. The plane will now start to descend unless the lift force is increased. This is achieved by applying up elevator to increase the wings angle of attack.

In the turn the wing angle of attack changes from what it was in S&L flight but not the same for both wings. The AOA of the wing on the inside of the turn increases and that of the wing on the outside of the turn decreases. Pulling too much up elevator during a tight turn, even though full power is set, can still produce a snap roll. So beware of getting too slow at the turn onto final, even though you have a model with parallel chord wings, but it is much more dangerous with a wing with a high taper ratio where the tip chord is much smaller than the root.

Why do tail-less aircraft (flying wings) fly? A model with a conventional layout will not fly without a tailplane, everyone knows that, so why does a tail-less aircraft fly?

We hear talk of “wing sections” being symmetrical or lifting but never of “airfoil sections” being so, but all wings lift, so let`s clear up some points.

1)     A wing section is part of a whole wing. For instance, the part from the root to a point mid section, or from half span to the tip.

2)     An airfoil is the shape you would see if the wing is cut through across the chord and viewed endwise.

So we will be discussing “airfoils” and not “wing sections.”

The airfoil used on a conventional layout, ie one with a tail-plane, while producing lift, also produces a tendency for the leading edge to roll nose down and the whole airfoil to pivot about the aerodynamic centre. The stronger the lift produced the stronger is the tendency to nose down. The term used here is Cmo, the pitching moment coefficient. The tailplane produces a down force on the aircraft sufficient to balance the Cmo and hold the wing at the correct angle of attack (AOA) for that speed. When up elevator is input the down-force is increased and the aircraft pitches nose up and vice versa for a down input.

Notice the penultimate sentence. The AOA is only good for one speed.  If you increase the speed the plane will climb so if you want to increase the speed, but remain straight and level, you must change the AOA. How? By retrimming the elevator nose down. This is vice versa for a speed reduction. So then, to climb you input more RPM and to descend take some off. Generally speaking it does not require any elevator retrimming during the climb/descent stage as would be necessary on full size aircraft as there, the aircraft has to be trimmed to a specific climb/descent speed.

Back to the Cmo then……..

On a tail-less wing the airfoil has a much lower Cmo, sometimes nearing zero due to its designed shape, where the T.E curves up slightly. ie reflex. The underside is also a little different from the other airfoil in that it sometimes has a slight bulge at about thirty percent chord. There is now no, or very little, tendency to nose down and, what there is being controlled by a slight upward twisting towards the T/E in the outboard panels, the downward pressure being accentuated by the rearward sweep in the wing planform. This upward twist is called “washout” and produces the down force required to balance the Cmo. The longitudinal balance point is positioned at approximately 20 to 25% of the geometric mean chord and not at approximately 35% as in the conventional layout.

It will be found that longitudinal control is more sensitive to down inputs that to up as would be expected due to Cmo and therefore less down elevator movements are set.

As a point of interest, any wing can be made to fly without a tail so if you have an old glider wing sitting around getting in the way this could be used. The best are those from a really efficient, fast, moulded type. Devise a way to join the two panels so that they slope back at 15 to 20 degrees. Build a simple box fuselage to house the weight and radio. Balance at 20% geometric mean chord, the position being found using the graphic method. Some will know this one but for those who do not I can send/supply one. The next thing to do is to set the transmitter trims to zero and set the ailerons up a bit, the amount being a bit of an educated guess. Test fly over long grass or up in the hills over the thick heather. (But she was a lovely gal!!) You can use it as an electric powered machine or simply as a slope soarer….or both. Let us see some out there in the Spring. The resultant model will not be as efficient as one with a dedicated low Cmo airfoil but it will provide some good entertainment at low cost.

Note . The more common usage for the geometric chord is the “mean aerodynamic centre” which requires some extremely complicated math with which I am not familiar, only having seen it once. It is considered by the real aerodynamicists that the GMC is close enough for model plane balancing.

A tail-less model does not necessarily have to have a wing which is swept, as a straight wing can be made to fly. Balancing and longitudinal control may be a bit tricky but it can be done. This type of wing is called a “plank” and these use dedicated airfoils which are designed to have an even lower Cmo than for the swept type wing, even having a positive tendency to nose up instead of down as previously mentioned. In this type it is usual to have even less down elevator movement and be sure that the balance is at the fore most point or even a little more so. Elevator is reflexed but more than for the swept wing.


Mike White