Radius of turn rule of thumb

[Banana Joe]

Not really sure this is the correct place, but what was the quick rule of thumb to quickly get a rough estimate of radius of turn?
Miles per minute minus 2? 240 knots would 4nm/min and minus 2 would be 2nm of radius?

[pattern_is_full]

What bank angle? What G?

Concorde used about 35nm radius to do a 180 at Mach 2.02 (1165 kts). Bank of 30° 1.15 g. Tha's just about exactly twice what your rule predicts. Rule = 19.5 nm/minute - 2 = 17.5nm, actual = 35 nm.

Anothe source says 20° bank, 1.06g, 52nm radius turn.

The Blue Angels (F-18 Hornets) had a dual maneuver I saw once. One plane in carrier-landing-config (flaps, gear, hook), the other clean at ~ 610 kts (700 mph). The fast plane would pass the slow one at the middle of the showline, and both would roll into 360-turns timed to return to the crowd at the same moment. "Slow and dirty" used about 0.4-mile radius (less than width of the Mississippi at that point), fast plane flew 3-mile+ radius way out over Arkansas. No idea what angle and G they used.

[sycamore]

Google ; csgnetwork.com/aircraft turn performance........

[Banana Joe]

I am just looking for a simple rule of thumb to use in the terminal area for a medium sized airliner (A320, 737, etc.) and that would make it easy to calculate when to turn into a DME arc and lead radial to turn off it.

[FalconFan]

See the below. I am not allowed to post the actual link at this point, delete the space before htm.
code7700.com/rot_turn_radius. htm

[stilton]

I am just looking for a simple rule of thumb to use in the terminal area for a medium sized airliner (A320, 737, etc.) and that would make it easy to calculate when to turn into a DME arc and lead radial to turn off it.


On the 727 we used to use 1% of our groundspeed added to the DME arc distance
as a lead in to start the turn to join it

[industry insider]

Old thread here

https://www.pprune.org/tech-log/159674-radius-turn-formula.html

[pineteam]

Or this thread too—> https://www.pprune.org/tech-log/390973-formula-radius-turn.html

[DaveReidUK]

One of the simplest rules-of-thumb that I've seen (assumes limiting bank angle of 25°) is to square the groundspeed (in nm/min) and then divide the result by 9, to give radius in nm.

[pineteam]

Hello DaveReidUK,

Do you mind to give an example? Not sure I understood your rule of thumb.
Thanks.

Edit: Ohhhh I think I got it: so 240kt = 4nm/min =4^2= 16/9 =1.8nm?

[DaveReidUK]

Yes, that's it.

You had me worried for a moment - I teach maths as a sideline, so I ought to be able to explain things clearly. :O

[pineteam]

Hahaha sorry my bad, I did not have enough sleep last night; Took me a while to undestand it. xD
Great tips by the way! :ok:

[Centaurus]

I find the navigation formula of "About yea" does the trick most of the time."

[HalinTexas]

1% of groundspeed, in still air, SRT.

Or, Mach number minus 2, still air SRT.

[scifi]

Using the original formula.... At 120kts = 2nm / m minus 2 is 0nm radius... Even less at lower speeds.

So best rule of thumb... Radius is 2nm.
.

[Banana Joe]

The Mach number -2 or nm/min-2 would work for speeds higher than 180 knots since we are limited to a bank angle of 25°.

I thought the other rule of thumb was TAS or GS divided by 200? 1% of GS is the diameter, isn't it?

[mcdhu]

To be clear:

TAS 140kts - Diameter 1.4nm
TAS 180kts - Diameter 1.8nm
TAS 210kts - Diameter 2.1nm

mcdhu

[eckhard]

Radius of turn for a NAT turnback:

Boeing MCP Bank limit Auto means about 15 AOB in HDG SEL:
TAS 500kts, still air, r = 15nm.

Bank limit set to 25 AOB:
TAS 500kts, still air, r = 7.5nm (which is quite handy as that means you will end up 15nm off track on the reciprocal.)

Same exercise with 100kt crosswind, doubles or halves the radius depending on direction of turn downwind or upwind.

So, to stay within 15nm, use 25 AOB and/or turn into the crosswind if you can.

[DaveReidUK]

To be clear:

TAS 140kts - Diameter 1.4nm
TAS 180kts - Diameter 1.8nm
TAS 210kts - Diameter 2.1nm

mcdhu

Subject to assumptions about turn rate and bank angle, of course.

[scifi]

Just wondering if the OPs original formula should have had a divide by 2 sign, instead of a minus 2 sign...?
Still gives about the same answer...
.

[gearlever]

Just wondering if the OPs original formula should have had a divide by 2 sign, instead of a minus 2 sign...?
Still gives about the same answer...
.

Yep, but only with 240kt.:ouch:

[Banana Joe]

Just wondering if the OPs original formula should have had a divide by 2 sign, instead of a minus 2 sign...?
Still gives about the same answer...
.
You subtrsct two. This works for Mach Number but I was wondering if it would work also for airspeed higher than 180 kts.

[KingAir1978]

Circumference of a circle = 2Πr.

r = (Half Circumference) / Π.

Rate 1 turn... 360° turn takes 2 minutes... 180° takes 1 minute. so...

Ground speed in NM/Min. 180 kts --> 3NM/min.

So in 1 minute you cover 3 NM and in this example that's half the circumference. So if you assume Π ≈ 3, your radius become ≈ 1 NM.

Ground speed in NM/Min. 120 kts --> 2NM/min.

So in 1 minute you cover 2 NM and in this example that's half the circumference. So if you assume Π ≈ 3, your radius become ≈ .66 NM.

Ground speed in NM/Min. 210 kts --> 3.5NM/min.

So in 1 minute you cover 3.5 NM and in this example that's half the circumference. So if you assume Π ≈ 3, your radius become ≈ 1.15 NM.

[Le Flaneur]

From the since rescinded US Air Force AFMAN 11-217, Volume 3, page 65:

Turn Radius Calculation. The following two relationships provide the distance required to turn an aircraft 90° using 30° of bank. This distance is the aircraft’s approximate turn radius. These formulas are particularly useful when determining lead turn points when planning to perform a radial-to-arc or arc-to-radial portion of an instrument procedure

Formula 1: Turn radius [in nm] = (True Airspeed [in knots] / 60) - 2 or (Mach × 10) – 2
Formula 2: Turn radius [in nm] R = (True airspeed [in knots] ÷ 60)^2 / 10 or Mach^2 × 10

If you are flying in against a ground-fixed reference (e.g. DME arc, VOR radial, FMS Track-to-fix or course-to-fix leg), use ground speed in lieu of true airspeed

[DaveReidUK]

Formula 1: Turn radius [in nm] = (True Airspeed [in knots] ÷ 60) - 2 or (True airspeed in nm/minute × 10) – 2
Formula 2: Turn radius [in nm] R = (True airspeed [in knots] ÷ 60)^2 ÷ 10 or (True airspeed in nm/minute)^2 × 10

Those formulae don't make sense.

In each case, the bit before the "or" is OK, but the part after should use True Mach, not TAS nm/min.

[Le Flaneur]

Those formulae don't make sense.

In each case, the bit before the "or" is OK, but the part after should use True Mach, not TAS nm/min.
Post corrected, thanks for pointing out the error

[jimjim1]

One of the simplest rules-of-thumb that I've seen (assumes limiting bank angle of 25°) is to square the groundspeed (in nm/min) and then divide the result by 9, to give radius in nm.

For your info - This is described in the link posted (in a non-link form) above

Turn Radius (http://code7700.com/rot_turn_radius.htm)

with a full proof.

Also suggests dividing by 10 as it's clearly easier and "in most cases is close enough".

To get a better approximation of dividing by 9 you could divide by 10 and add 10%.

So - taking the example of 25

25 / 9 = 2.78
25 / 10 = 2.5
2.5 + 10% = 2.75

To see the difference between 1/9 and the new approximation

1/9 = 0.111111

Dividing by 10 and adding 10% can be expressed as
0.1 * 1.1 = 0.11 which is very close to 0.11111. It's about 1% different.

[DaveReidUK]

Dividing by 10 and adding 10% can be expressed as
0.1 * 1.1 = 0.11 which is very close to 0.11111. It's about 1% different.

Close enough for government work. :O