Radius for turn Formulae
Guest
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Radius for turn Formulae
Here is the formulae I have for radius of turn:
r=V^2/(11.26*tanTHETA)
question: the value for V in V^2; is that to be in ft. per second or Knots per hour?
The second formula:
r=V^2/(32.2*tanTHETA)
I tried both of these and came up with diferent answers with each. Can anyone shed some light, perhaps with a full explanation of units required or a different formula?
Thanks
r=V^2/(11.26*tanTHETA)
question: the value for V in V^2; is that to be in ft. per second or Knots per hour?
The second formula:
r=V^2/(32.2*tanTHETA)
I tried both of these and came up with diferent answers with each. Can anyone shed some light, perhaps with a full explanation of units required or a different formula?
Thanks
Guest
Posts: n/a
Radius of turn = V²/(g.tan(bank angle))
I would normally use V in m/s, radius in metres and g in m/s/s. But your second formula is identical to mine for V in fps and radius of turn in ft (g is 32.2 fps/s).
It's important to be self-consistent with units. These formulae generally use either m, s, kg, N; or ft, s, lb, lbf. Don't mix them, and don't use mph, kph or knots which will only work with added conversion factors.
Also bear in mind that V is TAS, not EAS. To convert from EAS (or CAS, or roughly IAS) to TAS at subsonic speeds, divide by SQRT(sigma) where sigma is the relative density.
G
I would normally use V in m/s, radius in metres and g in m/s/s. But your second formula is identical to mine for V in fps and radius of turn in ft (g is 32.2 fps/s).
It's important to be self-consistent with units. These formulae generally use either m, s, kg, N; or ft, s, lb, lbf. Don't mix them, and don't use mph, kph or knots which will only work with added conversion factors.
Also bear in mind that V is TAS, not EAS. To convert from EAS (or CAS, or roughly IAS) to TAS at subsonic speeds, divide by SQRT(sigma) where sigma is the relative density.
G
Guest
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230 kn TAS = 118.22m/s (x 0.514)
tan (25°) = 0.4663
g = 9.80665 (universal(ish) constant)
Thus..
R = V²/g.tan(bank)
= 118.22² / (9.80665 x 0.4663)
= 3056.29m
= 1.65 nm (divide metres by 1850 for nm)
Thus at 5000ft sHp, 210 kn EAS (giving 230 kn TAS), a 25° banked turn will give a 1.65nm radius of turn.
If you want to turn this into turn rate, work out the circumference (2.Pi.R) = 10.37nm. At 230 kn TAS you would fly around this in (230 / 10.37 = ) 0.045 hours, or (x 60 x 60 = ) 162 seconds. That's 360° in 162 seconds, or (360 / 162 = ) 2.2°/s.
I'm sure that there are rules of thumb for all this, but being an engineer I live with a calculator in my hand anyway - and tend to use it for my flying too (I confess to struggling in CAA / JAA exams because I'm totally unused to the Dalton computer, and suchlike tools).
G
tan (25°) = 0.4663
g = 9.80665 (universal(ish) constant)
Thus..
R = V²/g.tan(bank)
= 118.22² / (9.80665 x 0.4663)
= 3056.29m
= 1.65 nm (divide metres by 1850 for nm)
Thus at 5000ft sHp, 210 kn EAS (giving 230 kn TAS), a 25° banked turn will give a 1.65nm radius of turn.
If you want to turn this into turn rate, work out the circumference (2.Pi.R) = 10.37nm. At 230 kn TAS you would fly around this in (230 / 10.37 = ) 0.045 hours, or (x 60 x 60 = ) 162 seconds. That's 360° in 162 seconds, or (360 / 162 = ) 2.2°/s.
I'm sure that there are rules of thumb for all this, but being an engineer I live with a calculator in my hand anyway - and tend to use it for my flying too (I confess to struggling in CAA / JAA exams because I'm totally unused to the Dalton computer, and suchlike tools).
G
Guest
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Or my way:-
Assume nil wind
TAS=G/S=230kt
1%=2.3nm
Now, if you wait till 2.3nm prior to start your turn onto the DME arc, you'll be as near as damn it due to inertia of the a/c.
In any event you'll be within the tracking tolerances (2nm) by a good margin.
K.I.S.S.
Assume nil wind
TAS=G/S=230kt
1%=2.3nm
Now, if you wait till 2.3nm prior to start your turn onto the DME arc, you'll be as near as damn it due to inertia of the a/c.
In any event you'll be within the tracking tolerances (2nm) by a good margin.
K.I.S.S.
Guest
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Musta, I do prefer to use the 1% rule, particularly when trying to train a new sprog.
Genghis, I must admit that I do appreciate the detail you go into with some of your posts. I have "plaigurised" (spelling) some of your material for the benefit of training also. Hope you don't mind!
It is also handy to know how many track miles to run once we are established on an arc. Remember your basic trig. from school? I think someone touched on it previously. For example,with 30 degrees to run on a 10 mile arc, you have approximately 5.5nm to the inbound track. (2 pie R divided by 360 degrees multiplied by the degrees to run). The only benefit I guess from knowing this is to help you plan the gear and flap selection. Nothing worse than dragging it in from too far out with gear and flap hanging out.
Ballpark figures:
On an 8nm arc, multiply the degrees to run by .140: 10nm arc by .174: 12nm arc by .209: and 15nm arc by .262. Makes for easy planning!
Happy new year!
Genghis, I must admit that I do appreciate the detail you go into with some of your posts. I have "plaigurised" (spelling) some of your material for the benefit of training also. Hope you don't mind!
It is also handy to know how many track miles to run once we are established on an arc. Remember your basic trig. from school? I think someone touched on it previously. For example,with 30 degrees to run on a 10 mile arc, you have approximately 5.5nm to the inbound track. (2 pie R divided by 360 degrees multiplied by the degrees to run). The only benefit I guess from knowing this is to help you plan the gear and flap selection. Nothing worse than dragging it in from too far out with gear and flap hanging out.
Ballpark figures:
On an 8nm arc, multiply the degrees to run by .140: 10nm arc by .174: 12nm arc by .209: and 15nm arc by .262. Makes for easy planning!
Happy new year!
Guest
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hi every one,
try these,
First of all i'll do the bank angle formulae. See if it make sense.
Bank angle for rate 1 turn is approximately ((TAS*0.1)+7)=Bank Angle.BUt these limited to about 25Deg.
Where as if you use a moderate bank angle the approximation is:
Bank angle= (TAS * Turn rate)/7
Eg...TAS 350, Turn Rate 1/2(1.5Deg/sec),
Bank Angle= (350*1/2)/7=25Deg
Radius of turn; At rate 1 the Turn Radius =TAS/180
Eg...TAS120, Turn radius=120/180=0.7nm.
try these,
First of all i'll do the bank angle formulae. See if it make sense.
Bank angle for rate 1 turn is approximately ((TAS*0.1)+7)=Bank Angle.BUt these limited to about 25Deg.
Where as if you use a moderate bank angle the approximation is:
Bank angle= (TAS * Turn rate)/7
Eg...TAS 350, Turn Rate 1/2(1.5Deg/sec),
Bank Angle= (350*1/2)/7=25Deg
Radius of turn; At rate 1 the Turn Radius =TAS/180
Eg...TAS120, Turn radius=120/180=0.7nm.
Guest
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Dan, if people like me got out more, there'd be nobody designing aeroplanes - then where would you be?
I never suggested taking a calculator in the air as such (although I have been known to) any more than I'd suggest doing your flight planning after, rather than before, take-off....
G
[This message has been edited by Genghis the Engineer (edited 04 January 2001).]
I never suggested taking a calculator in the air as such (although I have been known to) any more than I'd suggest doing your flight planning after, rather than before, take-off....
G
[This message has been edited by Genghis the Engineer (edited 04 January 2001).]
Guest
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Does anyone know the address for the publishers of De Principia Mathematica ?
A simple revision would, I am sure, have it selling like hot cakes among you mathematically inclined aviators.
If Sir Isaac Newton had had the foresight to express g in useful units, rather than this 32.2 ft/sec/sec; 9.81 metres/sec/sec nonsense, I am sure you would all go out right now and grab your copy of his book. And Mr Kermode would have a lot less to talk about on the subject of consistent units of measurement.
Ike should have used nautical miles/hour/hour, or Knots/hour. Then g is the easily remembered number 68600 (roughly). Just rolls off you tongue, doesn't it ?
If we bung that in the Genghis/gaga example, using PROPER measures of speed and distance, we get
tan(angle of bank) = TAS squared / (68600 * turn radius)
= (230 x 230)/(68600 x 1.65). That is, use knots and nm directly.
AOB = 25 degrees.
So everyone, repeat after me
"THE FLYING PERSONS GRAVITATIONAL CONSTANT IS 68,600 kt/hr (to about 3 places)"
And NO, I don't want to be nominated as the supplier of this week's most useless bit of information.
HAPPY NEW YEAR TO ALL
A simple revision would, I am sure, have it selling like hot cakes among you mathematically inclined aviators.
If Sir Isaac Newton had had the foresight to express g in useful units, rather than this 32.2 ft/sec/sec; 9.81 metres/sec/sec nonsense, I am sure you would all go out right now and grab your copy of his book. And Mr Kermode would have a lot less to talk about on the subject of consistent units of measurement.
Ike should have used nautical miles/hour/hour, or Knots/hour. Then g is the easily remembered number 68600 (roughly). Just rolls off you tongue, doesn't it ?
If we bung that in the Genghis/gaga example, using PROPER measures of speed and distance, we get
tan(angle of bank) = TAS squared / (68600 * turn radius)
= (230 x 230)/(68600 x 1.65). That is, use knots and nm directly.
AOB = 25 degrees.
So everyone, repeat after me
"THE FLYING PERSONS GRAVITATIONAL CONSTANT IS 68,600 kt/hr (to about 3 places)"
And NO, I don't want to be nominated as the supplier of this week's most useless bit of information.
HAPPY NEW YEAR TO ALL
Guest
Posts: n/a
No, knots per hour (admittely an unusual unit, but it works for echo tango) is a valid unit of deceleration - identical to nautical miles per hour per hour. Just as stall tests are normally done at 1 knot per second - or nautical miles per hour per second.
An aviators version of principia, an interesting idea, but I'm not convinced it would sell. Those of us whose prefered method of doing sums isn't using rules of thumb are probably in the minority.
G
An aviators version of principia, an interesting idea, but I'm not convinced it would sell. Those of us whose prefered method of doing sums isn't using rules of thumb are probably in the minority.
G
Guest
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When I needed to calculate the radius of a turn in order to fly a safe low level demo I divided the square of my indicated speed by 10 times the reading I intended to use on the g meter.
I offer four advantages for this method:
The answer is in feet.
No conversion of units is required
You barely need to know how to spell maths.
The answer is 13% pessimistic which keeps you out of trouble with the display line even with an on crowd wind (and or your off days)
Worked for me
JF
I offer four advantages for this method:
The answer is in feet.
No conversion of units is required
You barely need to know how to spell maths.
The answer is 13% pessimistic which keeps you out of trouble with the display line even with an on crowd wind (and or your off days)
Worked for me
JF