Radius of turn Formula
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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.
thanks.
Either that or a guide of radii for about 280 to 400 KTAS.
I'm asuming the TAS factor takes into account altitude.
thanks.
Groundspeed (kts)
-----------------
200
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.
-----------------
200
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.
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.
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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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)
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)
If you have an Excel spreadsheet, paste in this:
=ROUND(PRODUCT(E3,E3)/(11.26*TAN(E4*PI()/180)),0)
Cell E3 is the TAS
Cell E4 is the bank angle
Gives the answer for the Radius in feet.
=ROUND(PRODUCT(E3,E3)/(11.26*TAN(E4*PI()/180)),0)
Cell E3 is the TAS
Cell E4 is the bank angle
Gives the answer for the Radius in feet.
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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?
How does that work with all the fancy formulae?
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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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This might be a bit more involved than you need, but here is the Pans Ops Radius of Turn formula that I use :-
=ROUNDUP(POWER(D2,2)/((TAN(F2/(180/PI())))*68625),3)
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 :-
=ROUNDUP(A2*171233*SQRT((288+C2)-0.00198*B2)/POWER(288-(0.00198*B2),2.628),0)
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.
=ROUNDUP(POWER(D2,2)/((TAN(F2/(180/PI())))*68625),3)
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 :-
=ROUNDUP(A2*171233*SQRT((288+C2)-0.00198*B2)/POWER(288-(0.00198*B2),2.628),0)
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.
