Radius of turn rule of thumb

[gearlever]

Originally Posted by 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...
.

Yep, but only with 240kt.

[Banana Joe]

Originally Posted by 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...
.

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From the since rescinded US Air Force AFMAN 11-217, Volume 3, page 65: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

Originally Posted by Le Flaneur

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]

Originally Posted by DaveReidUK

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]

Originally Posted by 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.

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

Turn Radius

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]

Originally Posted by jimjim1

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.