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vg and va changes in gross weight of an aircraft

Asked by: 8941 views Student Pilot

describe for me the changes in Vg and Va with changes in the gross weight of an aircraft?

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1 Answers



  1. Brian on Nov 30, 2015

    Disclaimer: I’ve used purely an analytical method to respond to this question. Try not to let the formula’s bellow intimidate. Instead focus on the wording between the formula’s as I attempt to explain in a simple way what they represent. If you’d prefer a different explanation or wish for clarification just ask! Enjoy.

    Both speeds are Angle of Attack (AoA) related. So let’s look at the formula for lift:

    Lift (L) = 1/2 Velocity (V) squared * Density (rho or ρ) * Wing Area (S) * Lift Coefficient (CL)

    Lift coefficient is what is important here as the specific angle of attack will result in a specific CL. Surely you’ve heard the term CLmax in reference to stall speed before. Let me rewrite this in it’s plane terms before we continue:

    L = 1⁄2 V^2 ρ S CL

    So how does weight factor in? Well lift equals weight in unaccelerated flight. This means that, for the purpose of finding our unaccelerated stall speed, we can replace the above Lift variable with Weight and we have the following:

    W = 1⁄2 V^2 ρ S CL

    Now we can move some things around and set Velocity on it’s own since that is what we are looking for:

    V = Sqrt [W / (1⁄2 ρ S CL)]

    If we now take this same formula and plug in the CLmax we have our stall formula:

    Vs = Sqrt [W / (1⁄2 ρ S CLmax)]

    We can do the same for a best glide formula by using CLbg:

    Vbg = Sqrt [W / (1⁄2 ρ S CLbg)]

    —

    In each case you’ll notice that weight variable is on top. Lift coefficient, wing area, and density are held constant for the purposes of your question. So if weight, which is on top remember, goes up then Vs and Vbg will go up as well. Vice versa if they go down.

    To calculate the effects of weight use this:

    V (corrected for weight) = Sqrt [actual weight/gross weight] * V speed at gross weight

    This formula holds true for all performance V-speeds as well as Va. All other limitation speeds are not effected by weight.

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