View Full Version : Radius of Turn

19th Feb 2008, 14:27
Hi Guys,

Read the stuff on google/wikipedia but can't remember the rule of thumb for calculating radius of turn for a given bank angle and speed.....

Anybody any ideas?

19th Feb 2008, 14:46
Well, for a rate one turn (180 degrees per minute) the required bank angle is, approximately, (airspeed/10)+7.

For exapmle at 120 knots, the angle of bank for a rate on turn is 19 degrees.

As for radius etc. that would mean a quick revisiting of the ATPL notes.

If you have an Excel spreadsheet, paste in this:


Cell E3 is the TAS
Cell E4 is the bank angle

gives the radius in feet.

There are several threads about this.

HERE (http://www.pprune.org/forums/showthread.php?s=&threadid=159674)


HERE TOO (http://www.pprune.org/forums/showthread.php?s=&threadid=159674)

9th Mar 2008, 11:20
Hi All, given the inverse data,

speed = 160kts
radius = 3.4nm
degrees of turn = 205
can I calculate the bank angle needed?


PS not a pilot just a special fx person and I need to match some internal and external shots to a wescam plate for a movie, just in case that question seems a little dumb.

9th Mar 2008, 14:43
Good morning Vanderlay. 3.4 nm (just under 20700 ft) gives you a lot of room to turn at 160 knots. At 15 deg of bank and a 160 knot ground speed, you'd need approx 8500 feet.

A few questions, though.

Is your goal to stick precisely to a radius, stay inside it, or stay outside it?
Are we looking at a sea level location?
Is the airspeed going to be constant through the turn, and
What is the wind like in the area you are considering? For the arc you are describing, for a constant airspeed, the wind may signficantly decrease the groundspeed (and with it, radius) at one point in the turn and increase both for the other.


9th Mar 2008, 14:54
This applies for standard turns only (3deg/sec):

Radius (m) = GS(kt) x 10
Bank = TAS/10 + TAS/20

10th Mar 2008, 01:46
For a rate 1 turn the diameter of a turn is 1% of TAS
eg.TAS 220kts dia=2.2nm
radius is half that:)

10th Mar 2008, 03:18
Thank you all,

there are actually several shots, these were done with a large RC(or small UAV depending on the way you measure it I suppose.) the shots are to recreate a UAV monitoring several targets and we then add several other AC and objects to match. The data we got was all great(even GPS) with the exception of bank angle. however the BA is an easier interface to work with than computing radials etc. I will try and post some of the work in small parts if we get permission in a few months after we have done some renders.

Again thank you for your speedy and informative responses


10th Mar 2008, 06:00
Hi.. this is from the aviation formulary website.. Hope it helps..

In a steady turn, in no wind, with bank angle, b at an airspeed v
tan(b)= v^2/(R g) v= w R where g is the acceleration due to gravity, R is the radius of turn and w is the rate of turn.
Pivotal altitude h_p is given by
h = v^2/g With R in feet, v in knots, b in degrees and w in degrees/sec (inconsistent units!), numerical constants are introduced:
R =v^2/(11.23*tan(0.01745*b)) (Example) At 100 knots, with a 45 degree bank, the radius of turn is 100^2/(11.23*tan(0.01745*45))= 891 feet.
The rate of turn w is given by:
w = 96.7*v/R (Example) = 96.7*100/891= 10.9 degs/sec
The bank angle b_s for a standard rate turn is given by:
b_s = 57.3*atan(v/362.1) (Example) for 100 knots, b_s = 57.3*atan(100/362.1) = 15.4 degrees
A useful rule-of-thumb, accurate to ~1 degree for speeds less than 250 knots, is b_s= v/7 (v in knots).
The pivotal altitude is given by:
h_p = v^2/11.23 (Example) At 100 knots groundspeed the pivotal altitude is 100^2/11.23 = 890 feet.


henry crun
10th Mar 2008, 07:41
sameep: That is great rule of thumb............................... if you have a good memory and are an ace at mental arithmetic !

17th Mar 2008, 15:50
LoL.. sorry... ;-)