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I am trying to draw the V-n Diagram for a small aircraft I built, but I am stuck in the gust envelope part. I know how it is supposed to look. However, I am having a hard time calculating it. I would like to know (1) why it's composed of four lines; and (2) how to find the slope of each line. So far, I have these three equations:

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Also, (3) why do these equations describe the gust envelope, and (4) what each variable in the equations stands for?

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  • $\begingroup$ Where did you get the equations? $\endgroup$ – fooot Jul 12 '18 at 17:03
  • $\begingroup$ They are from a study guide from an aero design competition. Fairly reputable source. I've also seen them in other places, but if they are wrong, please let me know. $\endgroup$ – Unicorn Lord Jul 12 '18 at 17:06
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    $\begingroup$ @fooot Those are straight from the now deprecated FAR 23.341 and may be used in the absence of a more rational method to calculate gust loads. $\endgroup$ – Peter Kämpf Jul 13 '18 at 3:26
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The gust envelope is four lines overlaid on the flight envelope, usually the plus/minus of maximum gust at design cruising speed (Vc) and half maximum gust at maximum speed (Vd) as required by the certifying authority. This is usually +-50ft/sec (15.2m/sec) and +-25ft/sec (7.6m/sec).

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  • n is the normal acceleration in a sharp edged gust
  • K is the tailplane gust alleviation factor. In a canard this is an aggravation factor.
  • u is the airplane mass ratio

The source contains examples of how the lines are calculated. The following information (defined) is required:

enter image description here

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  • $\begingroup$ Thanks a lot for this. The only thing I didn't understand was the 2-D aerofoil lift-curve slope. Is it a tabled value different for each airfoil? If not, how do I calculate it? $\endgroup$ – Unicorn Lord Jul 12 '18 at 23:42
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    $\begingroup$ @UnicornLord It is different for each airfoil and derived from the airfoil's lift/AOA table. The reference's reference 1 shows how to calculate it. You can also google "lift curve slope" to see alternate descriptions. It usually turns out to be around 5-6/rad or about 0.1/degree. The example had 5.7/rad, oddly similar to but completely unrelated to the wing aspect ratio. $\endgroup$ – Pilothead Jul 13 '18 at 0:24

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