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Nickel vs Raymer: C-point, E-point, NP, and CG

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Aerowerx

Well-Known Member
Joined
Dec 1, 2011
Messages
6,092
Location
Marion, Ohio
I thought it would be better to start a new thread on this, instead of tacking onto the end of an old one.

I have been going through Karl Nickel's book (Tailless Aircraft), trying to understand it by doing a hypothetical design.

Besides the CG, he defines several points that he says are important to the stability of a tailless aircraft. These are the C, E, and NP. He also defines a parameter 'P', but I don't understand what it does for you.

He states that the induced drag will be minimum if the CG is at the E-point, which is the center of lift for an elliptical lift distribution. The C-point is supposed to be the center of lift for a "constant local lift coefficient", which I guess means the same airfoil used through out the wing.

The NP is as commonly accepted, except he does not give a simple formula for it. So I used Raymer's formula for the NP (page 114 in his "Simplified" book).

Taking that the CG is at the E point, Raymer's formula says that the NP is ahead of the CG, for the test cases I am using. Same thing happens when I change the sweep angle, keeping all else the same.

Now, I know that there is an error in the formula for the C-point, and have seen the errata for the book, but is there an error in the formula for the E-point? Or am I comparing "apples and oranges" in using Raymer's formula for the NP. Raymer's formula includes a term for the tail, which I set to 0.0, and a correction for the fuselage, which I am using.

Nickel states that the E-point is a constant value, independent of sweep, aspect, and taper. But the formula includes a term for the offset of the wing tip LE from the root LE (Nickel uses 'H'). Isn't that essentially defining the sweep?

By the way, Raymer's formula agrees with the graphical method of finding the NP (quarter chord point of the MAC).
 
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