Why does instability in pitch lower trim drag for an aircraft with a tail?

Question

I have a hard time figuring out why a longitudinally unstable aircraft has a lower trim drag. This seems to be a thing especially in fighter aircraft, so does it have to do anything with supersonic flight as well?

Answer 1

It might be helpful to look at this article from Boldmethod.

The basic idea is that the farther away the center of gravity is from the center of pressure (or center of lift depending on your terminology) the more lift the horizontal stabilizer will have to generate. The more lift an airfoil has to generate will result in more induced drag. Trim drag is specifically the induced drag created by the horizontal stabilizer. The horizontally stabilizer can actually produce both positive (upward) and negative (downward) lift but the negative lift has the even worse affect of requiring the wings to create more lift to compensate for the downward lift as demonstrated in the Boldmethod article.

Having the center of gravity at the center of pressure also allows the aircraft to be more maneuverable since less force is required from the horizontal stabilizer to initiate a maneuver. This is why fighter jets tend to be longitudinally unstable and use fly-by-wire to compensate for it.

Answer 2

Longitudinal trim is achieved when the total pitching moment on the aircraft is zero. Except for some special cases, the tail (or elevons in the case of tailless aircraft) will generate some lift to trim out the pitching moment from the wingbody. Therefore, if the tail generates negative lift (thereby providing a nose up moment), the wingbody needs to work harder (i.e. higher AOA) to generate the aircraft level $C_L$ required for level flight.

At this point, let's define what trim drag actually is. Trim drag is the ensemble of: additional induced drag from tail incidence (or elevators or elevons), plus additional induced drag from the wingbody due to a higher AOA required to achieve the total $C_L$, plus additional interference/viscous drag due to control surface deflections. The first and third components are actually relatively small compared to the second component. Unless you have a big control surface deflection, the majority of the trim drag actually comes from the loss of lift!

When the aircraft is pitch stable and trimmed, there is a reduction of $C_{L_{\alpha}}$ compared to the untrimmed case. As the static margin is reduced, amount of negative lift from the tail is reduced and the lift slope improves. This also improves the trim drag.

The following graphs illustrate the effect of static margin with trimmed $C_{L}$, amount of h-stab needed to trim and trim drag, generated with typical aircraft geometries and aerodynamics:

Answer 3

It's really simple. To hold the aircraft up in the air, the TOTAL Sum of Up Lift and Down lift (plus or minus) must be equal to, and oppose, the weight of the aircraft. If the lift from the tail is pulling the aircraft down, towards the earth, (as in a positively static stable aircraft), then the lift from the wing must be higher (by twice the tail amount pulling down) to counteract it. The total lift up minus the total lift down must be equal to the aircraft weight. So since the total lift Up and Down are both producing drag, then there must be more drag.

  Say the aircraft weighs 1000 pounds and say that drag is 10% of total lift
          Wing Lift      tail Lift     Result       Total lift    Drag
 Stable    1200 lbs      -200 lbs      1000 lbs      1400 lbs    140 lbs    
 Unstable  800 lbs        200 lbs      1000 lbs      1000 lbs    100 lbs     

Answer 4

Different question, same answer. Active stability allows for the $c.g.$ to be behind the centre of lift, thereby compensating for the associated aerodynamic instability.

For passive longitudinal static stability (by aeroforces), the total centre of lift $C_N$ must be behind the centre of gravity. At all angles of attack and all velocities, with stalled wings etc. The only passive solution that is always safe in all circumstances, is the aerodynamic centre $a.c._w$ behind the $c.g.$, always creating a nose down moment which must then be compensated by an aerodynamic nose up moment from the tailplane: negative lift. So we need to compensate this by more lift from the main wing, with associated induced drag.

That's the passive, aerodynamic solution. If we allow $n.p._{fixed}$ to be in front of the $c.g.$, the tailplane will always help in creating lift, not destroy it. At cruise, we can trim the aeroplane for neutral pitching moment, but if there is a disturbance in angle of attack (like a vertical gust) the main wing will create more lift than the tailplane (it makes sense to make the main wing the most efficient one.) But that means that any disturbance in AoA will create a sudden, unstabilised nose up reaction: static instability.

The only solution to be able to use the $n.p._{fixed}$ before $c.g.$ situation, is by using active stability. Any disturbance in pitching moment is immediately counteracted by an automatic elevator deflection, like balancing a stick vertically on an open palm, or riding a unicycle.

This principle goes for both subsonic and supersonic flight. But going supersonic means that the Centre of Pressure shifts rearwards: Mach tuck. The aeroplane could be:

• passive statically stable in supersonic flight, unstable in subsonic flight.
• passive statically unstable in supersonic flight, and much more unstable in subsonic flight.

Answer 5

You need a picture of a 3rd airplane with the center of gravity right underneath the wing lift arrow. Notice the elevons would be neither up or down. This is the lowest drag configuration, as up or down elevons adds drag. Up elevons (staticly stable) are slightly more draggy (because they force the wing to work harder against their downforce) than down elevons (staticly unstable), but both are more draggy than no elevon deflection.

IMPORTANT TO DESIGN:

It is the horizontal stabilizers job to set optimal AOA of the single wing (since the 1920s) while the Hstab is at 0 (lowest drag) angle of attack in flight. The difference in incidence is called DECALAGE of the horizontal stabilizer (See B-52). The center of gravity optimally belongs DIRECTLY UNDER the center of lift. The horizontal stabilizer must have ADEQUATE VOLUME to hold that wing in place.

Next one decides how much static stability (speed stability) one wants in the plane for safety. This is dependent on weight placement of fuel and payload, as well as potential shifts in CP due to change in AOA and ENGINE THRUST torque factors. Without active stability control (computer control) this is generally set up to be positive.

Setting up for static stability and trimming aerodynamicly is usually accomplished with a small trim tab. Sadly, this seems to have lead to a belief among modern designers that a tiny horizontal tail volume is OK, and computers will solve everything.

We even have graphs showing us that creating a staticly unstable tandem (biplane) will save fuel.

Starting every morning by looking at a Piper Cub may be helpful.