Unlike conventional aircraft the longitudinal stability has to come from the wing itself.
This is not as difficult as it seems as long as the cord is large enough. The principle is the same as with any aircraft: the centre of gravity has to be ahead of the aerodynamic centre. So there must always be an aerodynamic moment keeping the tail down. When flying too fast due to an inadvertent descent, the aerodynamic forces will win over the mass forces and put the tail down and visa versa.
The aerodynamic centre with zero moment is with every section at ¼ cord. The delta has a tapered wing with sweepback, some of them have multiple sweepbacks. So finding the aerodynamic centre is not so easy. If you take the ¼ cord line and take in account every lift distribution along the span as equivalent of the cord, things can go wrong because the lift distribution is not proportional with the cord. There are parts of the wing that have a higher load than others, this depends on the planform.
Fortunately, because of the wide cord, the centre of gravity is not critical. However it is wise to start with a forward centre of gravity to be sure of positive stability.
Due to the sweepback the delta wing tends to have a higher load at half span. The air going to the half span section is sucked upwards by the air that is already flowing over the nose of the centre part. This causes a higher angle of attack here.
In a stall this can be a nusance when the wings stalls first half span. Of course this happens on one side first and the result is a spin.
The Verhees Deltas have counteracted this by making the elevons very wide at this point. When defected up, necessary for a high angle of attack, the wing load will be diminished at this section and a stall is prevented.
This shape of elevon helps also to make the lift distribution more like an ellips, giving a better efficiency.
The directional stability of a Delta is in fact the same as with conventional aircraft, with the exception that roll stabilty tends to be better as directional stability. This is due to the fact that the aircraft is short and has sweepback.
This can cause dutch roll: when the aircraft is rolled, say to the right it also slides to the right. The relative wind will “see” a longer right wing and the aircraft starts rolling left before the tail is pushed to the left, so the aircraft rolls left and slides right. This movement will repeat at the other side and the aircraft will make a funny oscillation.
In airliners this is compensated with a yaw damper, we have to do it in a natural way. The Verhees Deltas have done it by giving the wing anhedral, so on purpose diminishing the roll stability. The positive effect is also that a windgust will push the aircraft with the wing into the wind instead of the other way like with a conventional aircraft.
A delta has some particular advantages in flying. First of all the behaviour in turbulence is much nicer. In an updraft most aircraft tend to raise the nose and after that the speed falls down. A delta reacts the other way, the nose is lowered, thus keeping the altitude. This gust penetration can be calculated and it appeares also to be the practice.
Another pro is that the propwash will give a benefit. With a normal tractor propeller setup the fuselage will fly in faster air than the wings, this causes extra drag. With a delta the faster airflow over the wing causes extra lift and diminishes the induced drag, so it is a benefit.
A delta can be efficient but it is not a certainty. The wing area has to be bigger than for a conventional airplane (because you can’t use flaps, on the contrary for more lift you even have to put the elevons up), the span is shorter, giving more induced drag.
The advantage must come from having no fuselage and a lighter structure. Flying wings with fuselage are per definition less efficient than conventional aircraft.
Furthermore, because of the high induced drag, the delta has to be flown fast for good efficiency. The D2 at 100 km/h takes the same power as at 220 km/h. Because it is a fast aircraft a relative big engine is necessary, the big engine and the light weight compensate for the higher induced drag when flying slow for climbing.
Because the aircraft needs relatively much power for flying slow, there is less left for climbing. On a hot day or at high altitude the climb performance is relatively more decreased than with fi. a motorglider that needs little power to fly and has the rest to climb.
Centre of gravity
The further the centre of gravity is to the rear the less up elevon is needed to keep the nose up, so the wing will give more lift. The D1 has the same performance with almost empty tank and without luggage than with full tanks and luggage due to the tanks and luggage being after the centre of gravity. Of course, a centre of gravity too far to the rear gives an instable aircraft, although the stability is improved with the D1 and D2 by the fact that the elevons are not balanced: flying too slow and the weight of the elevon will win and push the nose down and flying too fast and the aerodynamic trim will win and the nose goes up, kind of artificial stability instead of those computers big aircraft have and are not allowed for us.