# How do I achieve a lower stall speed, and capture potential CLmax without enough elevator control authority?

I am running some analysis on a uav, and the results I have found show that with proposed modifications I am unable to trim at my previous $c_{L\:max}$ and thus originally designed stall speed (experimentally determined). Ideally I want to decrease my stall speed as much as possible (for obvious reasons). Theoretically with a new flap design I can achieve higher lift coefficients however the elevator does not have enough control authority to obtain steady level flight at these conditions. Varying my cg location somewhat will allow me to capture my original $c_{L\:max}$ but it doesn't have enough range to reach the new potential $c_{L\:max}$.

What am I over looking that can help me achieve a lower stall speed? How does the propeller/power, glide slope etc effect this problem?

• Just because TRIM doesn't have that much authority shouldn't mean the ELEVATOR doesn't – TomMcW May 10 '16 at 18:16
• @PeterKämpf AFAIK it is better to avoid mathjax in the question titles, it slows down the loading of the main page and it looks weird on SEs that do not have mathjax active (if it ends up on the "hot questions" list) – Federico May 10 '16 at 18:22
• @Federico: Is this compromise acceptable? – Peter Kämpf May 10 '16 at 19:49
• @PeterKämpf I turned it into a question, otherwise I thought it was more than fine. – Federico May 10 '16 at 19:53
• Even if you maintain a force on the stick to stabilize an angle of attack, your pitch moment ($c_M$) will be zero. $c_M$ ≠ 0 means the aircraft will accelerate its pitch rate. – Peter Kämpf May 10 '16 at 20:07

It depends, partially on what you precisely mean with "trim".

Pilots use a rather narrow definition where trimming means to zero the control forces for a specific control surface deflection and speed. This is achieved by tabs or springs in the control linkage.

Engineers use it more broadly and include the ability to deflect control surfaces such that the desired attitude can be stabilized. I guess that you refer to this line of thought.

Long before the lift coefficient of a stalling airplane peaks, the flow over part of the wing will start to separate. Ideally it will do so near the trailing edge of the wing root, and the separation will slowly progress forward and outward as angle of attack increases. This separation will shift the local center of pressure back, such that the aircraft will experience an increasing nose-down moment as it approaches stall. To stabilize it at higher angles of attack will, therefore, need nonlinearly increasing elevator deflections. Depending on the position of the center of gravity, the installed elevator authority might not be sufficient to trim the aircraft all the way into the fully developed stall.

If you mean the first interpretation of "trim", then yes, most aircraft will not allow you to zero stick forces into the stationary stall. The trim range should cover the speed for steepest climb, not more. However, if the center of gravity range is wide enough, you should be able to trim an aircraft with rear c.o.g. all the way into the stall. After all, with neutral stability you can ideally trim (second interpretation) any angle of attack with the same elevator deflection angle (note that the nonlinearity explained above will require more negative elevator deflections as you approach stall even in a statically neutral aircraft).

I would rule out that the control forces are too high - after all, when stalling in level flight at 1g the aircraft will fly as slowly as possible, so stick forces should be small.

The effects of thrust depend on the engine installation. With a propeller, more power will add torque and increase the dynamic pressure at the tail. Now it depends whether the prop blast will hit the empennage - if it doesn't, the effect of adding power will at best be be an asymmetric stall.

In case you have a configuration change where the older configuration is known and the new should give the same flight characteristics, use tail volume as a sizing parameter. Horizontal tails of the same volume should give the same control power. Volume is the product of area and the lever arm between tail neutral point and the center of gravity. If the new tail has a different dihedral angle, don't forget to add the cosine of the dihedral angle.

When comparing elevators of the same size but of different flap chords, use the square root of the relative flap chord for comparison. Say the old elevator has a 20% flap and the new one 30%. The new one will have 22.5% more control power for the same deflection ($\sqrt\frac{0.3}{0.2}$).

Depending on elevator chord, at some point more deflection will not help much (typically 20° for a 25% elevator - going higher will add little control power). Now several options can be employed to increase control power:

• Change the incidence of the stabilizer. That is what airliners do to compensate the massive trim changes caused by Fowler flaps.
• Add leading edge devices on the stabilizer to make the elevator more effective. This adds a lot of complexity for a small gain, however.
• Use slotted flaps and double flaps to eke more control power and higher useful deflection angles from an existing elevator. Again, airliners with their wing flaps should point the way.

In damping, both the dihedral angle and the lever arm have a quadratic influence while they have a linear influence on control power. This way one can adjust damping and control characteristics individually.

• @spacegirl1923: Don't use the comments but edit the question. You will have more space to work with. – Peter Kämpf May 11 '16 at 6:27
• I am using morphing wing technology which makes flap chord comparison problematic at best. I cannot alter the shape of the body or the root chord location of the horizontal tail either. However you do make an excellent point with increasing the area of the htail, but currently that is not an option that I am aware of. (I have a lot of limitations) I am trying to make sure I did not miss anything in my analysis. Thanks for your help! – spacegirl1923 May 18 '16 at 21:14
• @spacegirl1923: Do you at least have the liberty to relax static stability? With a more aft cg location your necessary trim deflections become smaller. They scale linearly with static stability (= cg location ahead of the aerodynamic center). Thrust won't help, as little is needed during approach and landing. – Peter Kämpf May 18 '16 at 21:39
• Yes, see rephrased question above, it allows me to capture my original stall speed, however it doesn't allow me to utilize the potential increase in CL from the flaps. – spacegirl1923 May 18 '16 at 21:44
• @spacegirl1923 Sorry, I read the new question only after typing the comment. Can you share planform information? Do you run into maximum effective elevator deflection issues (= more deflection won't help)? It is hard for me to imagine what can be done when I don't know what is available. – Peter Kämpf May 18 '16 at 21:46

Is wing sweep an option? With inboard flaps and enough sweep, flaps can be moment neutral.

You have inadequate elevator authority to counter the moment generated by flaps. Flaps with a reduced moment require less elevator authority, thus enabling greater deflection and Cl. If inboard flaps are used with a swept wing, they can have reduced moment down to zero added moment when deflected depending on sweep, flap size, span and chord.