How do I calculate the angle of bank required to achieve a radius of turn, still air, of 0.15 nm at an airspeed of 75 kts?
Answers needed to help me fulfill a nerdish desire to achieve Navigation Perfection.
I think :
Radius = (Velocity Squared / Gravity) x Tangent of Bank Angle
but you need the units to agree.
So for your case the units need to be:
NM = (NM^2/Hour^2 / NM/Hour^2).[unitless angle]
So you need to convert g (9.8 m/s^2) into NM/Hour^2
9.8 m/s^2 = 9.8 × 3600 × 3600 / 1852 = 68578.83369 NM per squared hour
So then your formula becomes:
0.15 = ( (75^2) / 68578.83369) . tan(a)
0.15 = 0.082022392.tan(a)
1.828768905 = tan(a)
tan^-1 (1.828768905) = bank angle = 61.32945813 Degrees…
Call it 60 degree bank.
Doesn’t sound great at 75 kts…
Thank you I’m so glad I asked. But more glad you gave the answer at the end.
Can you tell me what is the rate of turn in degrees per second at 60 degrees of Bank at 75kts
Rate = (1092.95 x tan(a) ) / Airspeed
Rate = (1092.95 × 1.828768905) / 75
Roughly = 26.6 Degrees per second.
And your welcome… finally I found a use for the ATPL study I did nothing with :)
60° of bank at 75 kts will bring the vast majority of non-microlights unpleasantly close to a stall. It’s equivalent to 75 / sqrt(tan 60°) = 53 kts in level flight.
It’ll be 40% on top of your stall speed.
In my Europa it would lift the stall speed to c. 60 knots in a 60 Deg bank.
75 Degrees will double the stall speed… so I’d probably do the manoeuvre in still air, but certainly not if there was anything that could flip my wing a little.
And Jude did say “still air” in the first post.
Italianjon just as well there’s no Italians in this flying competition or they may not be happy, lol.
Once again thank you
You all mean a level turn. You can trade height for g in a descending turn, eg in a valley.
I assume the aircraft is on autopilot as you do the calculations – with a “whizzwheel”, of course,. not an electronic device. 
So … what angle of bank gives the tightest turn? asuming that you maintain airspeed related to stall speed (e.g. maintaining 1,3 x Vs) and maintain level flight.
I worked that out years back, before I started sniffing 100LL and forgot all I ever learnt about infinitesimal math.
I found that although the turn gets tighter, the more you bank, there is a theoretical limit, approached asymptotically as the bank goes towards 90 degrees; and also that increasing bank beyond say 60 degrees does very little for tightening the turn (reducing turn radius).
@italianjon, if your math is fresher than mine, perhaps you can confirm?
