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V-n diagram of a 2,400 lb Part 23 normal-category airplane: 23.337 maneuver factors, 23.335 design speeds and the 23.341 gust load factors

Tool	V-n Diagram and Load Factors
Source	Federal Aviation Administration (2016). Code of Federal Regulations, Title 14, Part 23, Sections 23.333, 23.335, 23.337 and 23.341 (2016 edition, Amendment 23-62). U.S. Government Publishing Office, Washington, DC; Pratt, K. G., and Walker, W. G. (1954). A Revised Gust-Load Formula and a Re-evaluation of V-G Data Taken on Civil Transport Airplanes From 1933 to 1950. NACA Report 1206, eq. (9).
Level	Undergraduate

Problem

A normal-category light airplane weighs 2,400 lb, has 160 ft² of wing (W/S = 15 lb/ft²), a mean geometric chord of 4.5 ft, a lift-curve slope of 4.5 per radian and C_Lmax = 1.6 (positive) and −1.0 (inverted) at sea level. Find the limit maneuvering load factors of 14 CFR 23.337, the minimum design speeds V_C and V_D of 23.335, the stall speeds and the corner speeds V_A and V_G, the gust load factors of 23.341 for the 50 ft/s gust at V_C and the 25 ft/s gust at V_D, and the governing positive and negative limit load factors of the combined envelope.

Inputs to Enter

Category Part 23 normal (Amdt. 23-62); maneuver n from the rule; ultimate factor 1.5
W 2,400 lb, S 160 ft², mean chord 4.5 ft, lift slope 4.5 /rad, C_Lmax 1.6 / −1.0, altitude 0 ft
Design speeds at the rule minima; gust velocities at the rule values

Open the V-n Diagram and Load Factors tool (loaded with this example)

Answers

n = 2.1 + 24,000/(2,400 + 10,000) = 4.04, capped at 3.8 (23.337(a)(1)); negative 0.4 n = −1.52 at V_C, 0 at V_D (23.333(b)(3))
V_S1 = √(2 · 15 / (0.0023769 · 1.6)) = 88.8 ft/s = 52.62 KEAS; V_Sneg = 66.56 KEAS; V_A = 52.62 √3.8 = 102.6 KEAS; V_G = 66.56 √1.52 = 82.1 KEAS
V_C,min = 33 √15 = 127.8 KEAS; V_D,min = max(1.25 V_C, 1.40 V_C,min) = 178.9 KEAS
μ_g = 2 (W/S)/(ρ c̄ a g) = 19.37, K_g = 0.88 μ_g/(5.3 + μ_g) = 0.691; Δn at V_C = K_g · 50 · 127.8 · 4.5/(498 · 15) = 2.66 → n = 3.66 / −1.66; at V_D (25 ft/s) Δn = 1.86 → 2.86 / −0.86
Governing limit load factors: +3.8 by maneuver (the V_C gust gives 3.66), −1.66 by the V_C gust (the maneuver factor is −1.52); ultimate +5.70 / −2.49

Notes

The tool's default inputs are this airplane; press Submit. Every rule constant and the K_g fit are checked in test_vn_diagram.php against the filed rule text, NACA Report 1206 Table II (nine transports' mass ratios and gust factors), six rows of the 1976 U.S. Standard Atmosphere Table IV and an independent numpy construction of the envelope (References/V-n-Diagram/checks/vn_check.py). The gust increment uses the rule's constant 498 as printed; the exact 2/(ρ₀ · 1.688) = 498.5 gives 0.1 % less.