I'm running into a problem in the analysis of my 'wing that I don't fully understand. Rather than put a wall of text here, I'm going to give preliminary description and hope for some insight... details to come as I figure out where to poke. Let me also say that some of this is possibly an artifact of the VLM tools I'm using now... but I'm 99% convinced that it's mostly a "real" effect.
The effect I am seeing is drastically decreasing longitudinal stability of a swept flying wing at increasing angles of attack. I believe that the primary underlying cause of this is the shift in lift distribution as a function of angle of attack. That is, at high speeds = low angle of attack, the ratio of root lift to tip lift is quite high; as speed decreased, this ratio decreases. I believe that for constant stability I would want this ratio to be approximately constant.
I've been investigating this using the definition static margin = - Cmα / CLα (Raymer and others). The values this produces make sense; in particular, a basic swept flying wing using the Panknin twist formula produces the target static margin in the no-lift condition. As expected, CLα is essentially constant for the design (high aspect ratio, no modeling of vortex lift or separation). Cmα, however, is very much not so. Cmα increases linearly (linearity probably due to approximations in the VLM model) from the target value, at low angle of attack, to the absolute value of this value at high angle of attack, passing through zero at around 1.3*Vs.
Now, I think I understand the effect (but would like discussion there)... but how have other flying wings solved this, besides by either varying twist dynamically (for my design, this would imply flaps 20° required below 100 kts... makes flap failure scary) or drastically overstabilizing and using either flap reflex or significant cruise elevon deflection (inefficient).
The effect I am seeing is drastically decreasing longitudinal stability of a swept flying wing at increasing angles of attack. I believe that the primary underlying cause of this is the shift in lift distribution as a function of angle of attack. That is, at high speeds = low angle of attack, the ratio of root lift to tip lift is quite high; as speed decreased, this ratio decreases. I believe that for constant stability I would want this ratio to be approximately constant.
I've been investigating this using the definition static margin = - Cmα / CLα (Raymer and others). The values this produces make sense; in particular, a basic swept flying wing using the Panknin twist formula produces the target static margin in the no-lift condition. As expected, CLα is essentially constant for the design (high aspect ratio, no modeling of vortex lift or separation). Cmα, however, is very much not so. Cmα increases linearly (linearity probably due to approximations in the VLM model) from the target value, at low angle of attack, to the absolute value of this value at high angle of attack, passing through zero at around 1.3*Vs.
Now, I think I understand the effect (but would like discussion there)... but how have other flying wings solved this, besides by either varying twist dynamically (for my design, this would imply flaps 20° required below 100 kts... makes flap failure scary) or drastically overstabilizing and using either flap reflex or significant cruise elevon deflection (inefficient).