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Is there some kind of a ratio or a very general rule of thumb that describes fuselage weight increase in relation to the increase of its diameter? (All other things being equal, length etc.)

Note: I took all the data from the project work "Aircraft Design Studies Based on the ATR 72". Author: Mihaela Florentina Niţă. Direct download link is here.

According to the fragments below (page 103), the estimated fuselage mass is 2323.432 kg, its diameter is 2.77 m, wetted area is 184.593 m2, dive speed 130.076 m/s.

If we increase diameter by 10%, how heavy is going to be the fuselage and why?

enter image description here

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    $\begingroup$ Hint: C = pi D $\endgroup$
    – Jim
    Dec 23, 2021 at 20:19
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    $\begingroup$ You should in addition have been supplied with a numeric value equation containing wetted surface, dive speed and fuselage diameter, all with odd exponents. This equation is derived from a statistical analysis, giving a best fit to data from existing designs. Find it, present it here, and we can give you the answer. $\endgroup$ Dec 23, 2021 at 21:36
  • $\begingroup$ @PeterKämpf Yes, I have seen much more detailed project work by the same author a long ago, but then totally forgot about it. Anyway, I have rephrased some bits and included link to the project work with more data. Please let me know if that is sufficient. Thanks and regards. $\endgroup$ Dec 25, 2021 at 13:17
  • $\begingroup$ Much better now! $\endgroup$ Dec 25, 2021 at 13:53

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Since the surface of a cylinder is circumference times length, it scales linearly with its diameter, and the same goes for a fuselage. With a diameter increase of 10%, the width, height and surface area should increase by a factor of 1.1 if the length of the fuselage remains unchanged.

Now we can use Torenbeeks fuselage mass formula where mass is proportional to surface area to the power of 1.2 and the denominator in the square root which also changes by a factor of 1.1. Since all other parameters remain unchanged, the square root becomes smaller (95.346%, to be precise) and the surface area factor grows by 1.121 for a total change of 1.069 or 6.9% to 2483.73 kg.

If you wonder why one factor shinks and the other grows: The term with the fineness ratio $\frac{l_H}{w_F+h_F}$ shrinks because a fatter fuselage is structurally more efficient while the surface area increases the mass because more material goes into building it.

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    $\begingroup$ I take issue with the number of significant digits of your results :) I don't think Torenbeek ever intended to be accurate to the gram... $\endgroup$
    – Sanchises
    Dec 25, 2021 at 23:41

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