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Old 18th Jan 2005, 17:24   #1 (permalink)
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Radius of turn Formula

Wondering if anyone has a simple (relatively) formula for radius of turn of commercial jets (taking into account TAS etc). The aviation formulary page is a little complicated for this guy!

Either that or a guide of radii for about 280 to 400 KTAS.

I'm asuming the TAS factor takes into account altitude.

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Old 18th Jan 2005, 17:36   #2 (permalink)
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Groundspeed (kts)

is a reasonable rule of thumb for Rate 1. Handy for working out the lead distance for turning 90 deg onto a DME arc ie radius of turn. You could substitute TAS in nil wind.

I've also seen 100 used as the denominator but that might be more applicable at much faster speeds.

You could always use the standard radius of turn formula given on the aviation formulary website to derive reasonable approximations. Start with the maximum & minimum speeds & AoB you wish to consider to derive a radius for each then work out what factor for the TAS used gives the same answer.

Depending on how much difference in speeds you use you'll be able to derive a rule of thumb for a particular speed/AoB range.
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Old 18th Jan 2005, 18:17   #3 (permalink)
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Radius of turn = TAS squared/ g x tangent of AoB

R equals Vee squared over g tan theta

Applies to anything in a steady banked turn - A380 to microlight to TypHoon.
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Old 18th Jan 2005, 18:27   #4 (permalink)
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You can try this one,

Radius (ft) = Velocity (fps) squared divided by 32.2 x Tan of Bank angle

Typical flight directors limit max bank angle to 25 degrees, but most pilots use 1/2 bank at the speeds that you are talking about so the bank angle would be 12.5 degrees, so if you whip out a scientific calculator and figure the Tangent for 12.5 degrees (0.2217) and multiply your TAS in knots by 1.687 to get fps you can work up a quickie formula.

R (ft) = V x 1.687 sq / 7.139

for 280 knots I get 31,254 feet (5.9 sm)
and 400 knots = 63,784 feet (12 sm)
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Old 18th Jan 2005, 19:20   #5 (permalink)
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How odes this sound:

V^2/R = g?((n^2)-1)

where V is True Airspeed
R is turn radius
n is load factor


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Old 18th Jan 2005, 22:16   #6 (permalink)
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If you have an Excel spreadsheet, paste in this:


Cell E3 is the TAS
Cell E4 is the bank angle

Gives the answer for the Radius in feet.
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Old 19th Jan 2005, 10:46   #7 (permalink)
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Many thanks for your replies all. The spreadsheet one worked a charm and cross checked well with Astra Driver's post. Thanks to all the others as well.
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Old 19th Jan 2005, 18:35   #8 (permalink)
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For a quickie, use IAS/100 (e.g., 250 kts => 2.5 NM) for 25-30 deg AOB. Use TAS if available. It should be close enough for estimates in the terminal area.

How does that work with all the fancy formulae?
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Old 21st Jan 2005, 14:03   #9 (permalink)

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You can check this thread: Radius of Turn

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Old 22nd Jan 2005, 17:04   #10 (permalink)
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Interesting to note that in the need to turn back over the Atlantic, depending of the wind, a single continuous turn would bring you not too far from the 30 nm offset track ... and we could almost forget about the 90 deg initial turn.
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Old 23rd Jan 2005, 02:28   #11 (permalink)

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This might be a bit more involved than you need, but here is the Pans Ops Radius of Turn formula that I use :-

Cell numbers are different from those mentioned previously, as follows :-
D2 = TAS value
F2 = Angle of bank.
Result is in NM

To convert IAS to TAS, the Pans Ops formula is :-

A2 = IAS value in NM/Hr
B2 = Altitude in Feet
C2 = Variation from ISA
Note that this formula and calculation is a prerequisite to the Pans Ops radius of turn formula and calculation.

Theoretically, the wind should be taken into account, to determine the total airspace needed to complete the turn. As an example, using the above formulae in conjunction, I made calculations for 280 and 400 knots at 10,000 feet, IAS +15, at 25 degrees AOB.

Radius at 280 KIAS = 3.507 NM with wind effect at 0.494 NM per minute of turn. The airspace used in the first 90 degrees of the turn is 4.646 NM.
Radius at 400 KIAS = 7.170 NM with wind effect at 0.706 NM per minute of turn. The airspace used in the first 90 degrees of the turn is 8.761 NM.

The total area for the first 90 degrees of the turn includes an allowance for distance travelled between the time the bank is applied and the aircraft begins to turn.
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