# What is the sink rate of a glider during a roll?

For a glider in a steady bank at angle $\mu$, to a good approximation, the sink rate has a factor $1/\sqrt{\cos \mu}$ relative to the sink rate at zero bank angle.

What are the dynamics of the sink rate during a roll, for instance, when rolling from a bank angle of zero to a bank angle of $\mu \sim 20^{\circ}$ in one second?

I'm not looking for a very precise, quantitative answer but rather some qualitative idea of the physical effects that underlie the dynamics of the sink at such roll rates for a model plane.

Any references or guidance will be helpful, thanks!

• Would you be able to take the average of the 2 angles (start and finish)? so, the average of 0 and 20 degrees? That would be 10 degrees. so your sink rate would be using that same formula but instead of mu being 20, it would be 10.
– alex
Apr 6, 2017 at 9:26
• @alex the bank rate influence is non-linear, as seen from the 1/sqrt(cos) equation, so applying it to the average of the input (the bank angle) does not provide the average of the output
– Federico
Apr 6, 2017 at 10:06
• @Federico Clearly, it is not, but -intuitively- I believe that the form of the curve lift/bank angle is probably concave during the first half of the roll and convex during the second. Thus, the non-linearity may (roughly) cancel out... and a linear rate might be OK for a first approximation... Apr 6, 2017 at 13:21
• @xxavier "I believe that the form of the curve lift/bank angle is probably concave during the first half of the roll and convex during the second" it is not
– Federico
Apr 6, 2017 at 13:25
• @xxavier The lift will not necessarily be zero when inverted. It may be negative, or something else depending on angle of attack. Apr 6, 2017 at 15:19

• Thanks! We have a good amount of data using a model plane. The change in sink rate is about 50% for a turn from $20^{\circ}$ to $40^{\circ}$ as you guessed but the sink rate changes in both directions - it increases when we move the bank angle farther from 0 and decreases when we move it towards 0. The sign suggests this is due to unbalanced lift. This change is not affected when we have a rudder mix in our rolls so it is not due to sideslip nor is it affected when we soften our aileron deflection. We can test if it's due to roll acceleration; a reference for this will be greatly appreciated. Apr 10, 2017 at 8:32