ENGR101 West Virginia Engineering Problem Solving Excel Riemann Sum Problem Analysis I have an excel assighment that due in 16 hours. see the attachment fi

ENGR101 West Virginia Engineering Problem Solving Excel Riemann Sum Problem Analysis I have an excel assighment that due in 16 hours. see the attachment file for more infomation. WVU Fundamentals of Engineering Program
Fall 2019
ENGR 101: Engineering Problem Solving I
Excel Riemann Sum Analysis Problem
The cross-section of an aircraft wing is commonly referred to as an airfoil. Many airfoils were initially designed by the National
Advisory Committee for Aeronautics (NACA), the government agency that went on to became NASA. One of the airfoil families
developed by this agency is known as the 4 digit series, which has some symmetric (dimensions for the top surface and bottom surface
are the same) airfoils that fit the following relationship for the Upper and Lower Surfaces of the airfoil. In the equation, t represents
the maximum thickness of that particular airfoil and is traditionally between 6 and 30 percent of the total width of the airfoil, also
known as the chord length, c. This thickness needs to be entered as a fraction of the chord length, typically between 0.06 and 0.30.
±

2
3
4
=
(0.29690√ − 0.12600 − 0.35160 ( ) + 0.28430 ( ) − 0.10150 ( ) )
0.20

Equation 1
On most aircraft, the wings also serve as a major fuel tank on the plane. By making two assumptions, first that since the airfoil is
symmetric the volume on the lower half of the airfoil is equal to that of the upper half of the airfoil, thus the area between the line y=0,

and the upper surface (+ ) can be doubled to get the total area between the upper and lower surfaces of the airfoil. The second

assumption is that the wing has the same cross-section for the uniform depth of 5 meters. Thus, the volume inside the airfoil can be
estimated by using the area found from a Riemann Sum from the cross section times the depth of 5 meters.
A step by step listing of tasks that is to be completed is provided for your success on this assignment.
1. Open EXCEL and save the file as “Wing Volume Analysis ENGR101_#$%_Lastname_Firstname.xlsx” where #$% is the
three character section number of your ENGR 101 course.
2. Create a new sheet in the file and name it “Data”
3. In the Data Sheet Create
a. An area for input values of Thickness, Chord length, and Depth at the top of the sheet (Rows 1 thru 3) assign values
of 0.20 for thickness, 3 meters for the chord length, and 5 meters for the depth for the wing fuel tank.
b. In Row 5 Create Column Headings of “X/C”, “Y/C”, “X”, “Y”, “Area”
c. In the X/C column create data that starts at 0, and increments by 0.01 and ends at a value of 1
d. Use the +Y/C part of Equation 1 to calculate the Y/C column
e. Calculate the X and Y values by multiplying the X/C and Y/C columns, respectively, by the chord length using
absolute referencing
f. Use one of Left Hand Approximation, Right Hand Approximation, or Mid-Point Rule to calculate the relative area
of each rectangle in the Riemann Sum as seen in Figure 1
Figure 1: Visual representation of the Riemann Sum rectangles in the Upper Surface of a 4-digit NACA airfoil
At the top of Columns G, H and I create a table that includes ΔX in cell G1, total Area from the Riemann Sum
approximation in G2 and volume in G3 which is found by multiplying the total area by the depth of the wing fuel
tank. Calculations in H and units in I respectively.
Create an X-Y scatter plot of the upper surface of the airfoil as Y-vs-X, recall that Y is the vertical axis and X is the
horizontal axis
g.
4.
NOTE: In step:3(g), ΔX = Δ(X/C)*Chord length; Where, Δ(X/C) = increment taken in column (X/C);

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