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4 Answers

Calculate Load Factor in a given Banked Angle

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General Aviation

Currently studying for my Private License. I did a sample exam and one of the questions was, what is the new stall speed of an aircraft in a given bank angle with straight and level flight stall speed provided. Eg. 50kts straight and level stall speed, if you are in a 30* banked coordinated turn, what is the new increased stall speed?

My question is, how do I calculate the load factor of the aircraft in banked, coordinated flight?

I know that Load Factor = 1/cos Bank Angle

and Stall Speed banked = Stall Speed Level / Square Root of cos Bank Angle

How do I calculate 'cos'? If I can easily find what 'cos' is then ill be sorted! I can't find a SIMPLE put way of finding or calculating 'cos'


Assistance is appreciated. Thanks

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4 Answers

  1. Aaron on Jan 22, 2014

    I memorized the cosines of 30, 45, and 60 (0.866, 0.707, and 0.5 respectively). They’re incredibly helpful in calculating wind correction angles as well as headwind components for determining a more accurate groundspeed figure on precision approaches for LOC only timing.

    Admittedly, I wouldn’t know how to answer that question otherwise, except to offer a guess that it relates to the fact that stall speed doubles in a 60* bank which should be a known fact. (cosine Of 60 is 0.5 and 1/0.5 is 2).

    Also iirc, there may have been an included figure with load factor and stall speed relationship graphed out. In that case, it is easy to understand that some practice test sources may exclude figures required to answer questions. I know I couldn’t really answer your question, but I hope I could help a little bit!

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  2. Brian on Jan 25, 2014

    “How do I calculate ‘cos’?”

    If you’re looking for a way to calculate it on paper the short answer is, you don’t. Where it comes from and how it is calculated involves a level of calculus that is beyond my understanding. If you care to see, here: http://mathworld.wolfram.com/Cosine.html

    Enter the calculator. To do this on a calculator you will need a scientific calculator that includes cos, sin, and tangent keys. The calculator on a windows and apple computers can be formatted to show this by navigating to the settings. Your phone calculator may also have these keys.

    To get an accurate calculation of cos for the purposes of this problem you will need to have the calculator set to degrees, type in the bank angle, and then press the cos button. Be sure it’s the cos, not cos ^ -1, or you will get an error message.

    As Aaron noted above, memorizing the answers for 30, 45, and 60 are helpful. He gives the answer for 30 as being 0.866. If you were to accidentally have the calculator set in radians you would get an answer of 0.15. Or if you accidentally did cos ^ -1 you would get an error.

    FWIW Cos ^ -1 is inverse cosine, meaning it works backwards. For example if you put 0.866 in and hit this button you would get an answer of 30. In other words it is a good way to double check your work.

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  3. hcourtney on Feb 22, 2014

    Thanks for the helpful answers, Can now easily calculate what I need using an electronic calculator… Ive started using an E6B Flight Computer, I worked out how to calculate square root of a load factor using it, and from that how to calculate the increased stall speed. But is it possible to find the Load Factor of a given bank angle using an E6B?? My exam is tomorrow and electronic calculators are not allowed, but E6B is allowed. I can try and memerise the load factors for given angles but you never know what angles are going to be in the exam…

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  4. Simon on Mar 03, 2017

    I think a little review of “what a cosine is” would be helpful.

    The cosine of an angle “Z”, is the ratio (one number divided by a second number) of the lengths of two sides of a right-angle triangle. To be specific, it is the ratio of the side “A”djacent to the angle Z, divided by the length of the “H”ypotenuse side of this right triangle.

    The cosine of a few common angles is easy enough to memorize.
    Imagine a triangle that has angles 30, 60 and 90 degrees.
    Have a look : http://www.mathopenref.com/triangle306090.html
    Such a triangle will have sides that have lengths in the ratio of 1:2: {squareroot(3)}.
    The hypotenuse side has length 2 units, and the other two have lengths 1 and sqrt(3) (≈1.73) units, respectively.

    You might remember the mnemonic “SOH, CAH, TOA”. This little phrase reminds us which ratio goes with which function (“sine”, “cosine” and “tangent” as below:)
    sin Z = Opposite/Hypotenuse (“SOH”)
    ** cos Z = Adjacent/Hypotenuse (“CAH”) **
    tan Z = Opposite/Adjacent (“TOA”)

    If angle Z is 30 degrees, then looking at the standard triangle, the side “Adjacent” to the 30-degrees angle has length “squarerootof3”, and the “Hypotenuse” side has length 2.
    We said cos Z = length of Adjacent side / length of Hypotenuse side (… think “CAH”)
    So cos (30 degrees) = (squarerootof3 ÷ 2)

    In the case of load factor for a given bank angle, we are told that load factor = 1 ÷ cosine of the bank angle.

    So load factor = 1 ÷ cos (30 degrees)
    So load factor = 1 ÷ [squarerootof3 ÷ 2]
    So load factor = 2 ÷ squarerootof3
    So load factor ≈ 2 ÷ 1.732
    So load factor ≈ 1.15

    It’s even easier if the bank angle is 60 degrees, because then:
    load factor = 1 ÷ cos (60 degrees)
    cos (60 degrees) is found on the special triangle by looking at what the length of the side “Adjacent” to the 60 degrees is (1) and dividing it by what the length of the “Hypotenuse” side is (2), i.e. (1÷2) = 1/2

    If load factor = 1 ÷ cos (60 degrees)
    Then load factor = 1 ÷ (1/2)
    So load factor = 2, when the bank angle is 60 degrees.

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