# How to approximate lag of roll of a bird (or RC airplane)?

When an airplane rolls using ailerons, the ailerons itself are changing their state quite instantly. However, in order for the airplane to actually start to roll, it should take a considerable amount of time for it to reach, say, 90 degrees. This holds even if we discard the mass, which is quite insignificant in the case of a bird. This lag occurs because the airplane needs to move through the air, and thus it needs the air to roll.

A RC airplane or bird does not really move fast, say, 10 m/s. I would think that the slower you go through the air, the more time it will take to roll.

I have looked around for flight dynamics formulas, but I only found formulas too complicated for a layman like me to understand. Maybe I didn't find the correct terms for it. Can you help me out with some method to approximate this roll lag?

Note: The most important thing for me to get out of this is the time it takes for an average sized bird to roll 90 degrees, with a speed of about 10 m/s. Like, is it 1 ms, 10 ms, 100 ms, 1 s, or even larger? (I would personally think somewhere between 100ms-2s)

## 1 Answer

You're talking about the longitudinal axis or "roll axis".

Its value is the "bank angle" or "roll angle". Of course there's no limit on that.

Its first derivative is the "roll rate". In fighter aircraft this is as high as 720 degrees/second. I can't think of any upper limit on this, because you could make the whole wing an aileron, and if you tilted it far enough, the whole airplane would become a propeller.

Its second derivative is the "roll acceleration". This would be limited by the inverse of the longitudinal angular moment of inertia, which could be very small, so it could be very fast.

Its third derivative is the "roll jerk". This would be limited by the rate at which ailerons can change their angle. It is a short time, but certainly not zero.

I'm not sure if you're asking about the rate or the acceleration.

• Thanks for pointing out the different terms! I will need a combination of all of them, to calculate an exact value. The analogy of the propeller is very good now that you mention it. Therefore I think the 'roll rate' will be most significant, as it will be depending most on airspeed and propeller size (which are two relatively small values for a bird). Since I only need an approximation, therefore the 'roll rate' is the one I'm looking for (if my reasoning is correct).
– Yeti
Dec 7, 2014 at 20:00
• @Yeti: You're probably only able to estimate an approximate value. There's guesswork no matter how you do it. Dec 8, 2014 at 2:08
• I found the answer: Birds, bats and insects hold secrets for aerospace engineers Thanks for getting me on the right track with the correct terms. It says that some birds may exceed a roll rate of 5000 degrees per second. Which comes down to the fact that turning 90 degrees, takes only 18 ms. Even though I still don't know roll acceleration and roll jerk, I suppose those values are in the same range.
– Yeti
Dec 8, 2014 at 13:56