The easy formula, that I was given when taking IR training:
Standard rate of turn (3°/sec.): BankAngle = 10% of TAS + 5
For 100 knots, this formula suggests 15° of bank angle as an approximate standard rate turn. This formula returns a good estimate, as the "exact" bank angle is 15.38°.
Now take for instance...250 knots. If no flight director is installed, then 30 degrees of bank (using the easy formula) approximates a standard rate turn. The "exact" standard rate bank angle is 34.51° (flight directors limit bank angle to a maximum of 25° for those who do not know).
It seems this formula is good enough for slow speeds, however, when you need to know the "exact" bank angle, use this formula (find your scientific calculator!):
ROT = ( 1091 * tan a ) / TAS
"ROT" is rate of turn ("3" for 3°/second)
"a" is bank angle
"TAS" is in knots true
"*" means multiply, "/" means divide
A little bit of algebra and you have:
a = tan-1 ( (ROT * TAS) / 1091 )
Use "3" for ROT and you will have a standard rate turn. Use "1.5" and you will have half standard rate (jets, high altitude, something faster than 250 knots).
I cannot remember whether "tan-1" means arctangent or cotangent...anyway, do all the math inside the parantheses then hit "shift, tan" or "2nd, tan" on your calculator and voila!
What? No scientific calculator or tangent tables available? Then use the
chart
(PM me if you want a higher resolution copy of this chart)
TomBola: you did ask "why" and there you have it! Now if I can just be asked questions like this on my pilot candidate interviews, I could probably get my name to the top of the stack quicker.
On my most recent interview last month, I was flown to company HQ via one of their freight Learjets. In a hurry to keep a tight schedule, standard rate turn policy went out the window and 60 degrees of bank
was rolled in to get on a GPS direct course in a hurry! Tisk tisk--Learjet cowboys...well at least the freight did not mind!
Hope the information helps,
gear down props forward