Comet
Sailplane Project
The Comet Sailplane plan shows
the rise in the wing's tip panel to be 4-3/8" with the wing's inner panel
flat on the work table. Unfortunately, to get the proper elevation in the
wing's inner panel, the plan shows a 10.0" rise out at the tip panel, which
is awkward to get jigged up. Therefore, I wanted to determine (calculate)
the rise of inner panel at the polyhedral joint, which is much easier to set
up from a jig standpoint. When I first went through the geometry to
determine the rise of inner panel at the polyhedral joint, I made a number
of errors in my calculations %$#@& . By consulting with Sergio Montes, Jim
O'Reilly, and Alfredo Herbon, they were able to quickly straighten me out.
The correct rise of inner panel at the polyhedral joint is 3.3736". For
documentation purposes, I want to present the calculation approach, which is
shown below.
Wing Geometry Modified from Alfredo Herbon's CAD Drawing
Given:
Sc = 12.00" (Center Panel Span)
Lt = 14.40" (Tip Panel Span)
Ht = 4-3/8" (4.3750") (Tip Panel Span
Elevation)
Li = 20.00" (Inner Panel Span)
Hi' = 10.00" (Inner Panel Elevation
at Tip Panel)
Calculations:
c = ArcSin(Ht/Lt) = 17.6872 Deg
(Polyhedral Angle)
A*A = (Lt*Lt + Li*Li - 2*Lt*Li *Cos
a)
a = 180-c
Cos a = Cos(180-c) = - Cos c
A*A = (Lt*Lt + Li*Li + 2*Lt*Li *Cos
c)
A = 34.0019"
b = ArcSin(Ht/A) = 7.3927 Deg
e = ArcSin(Hi'/A) = 17.1036Deg
d = e-b = 9.7109 Deg (Dihedral Angle)
Hi = Li*Sin(d) = 3.3736"
(Rise of inner panel at the polyhedral joint)
With this information, the flat plan wing span is
calculated as [2*(14.4 + 20.0) + 12.0] = 80.80", and the projected wing span
is calculated as [2*(A*Cos e) + 12.0] = 77.00". Interesting enough, neither
one of these values agree with the 78" wing span quoted in the specification
title block on the Comet plans shown below..................Tandy
