ME465 Fall 2019
Extra Credit Project #1
Objective: Create curve-fit equations for the curves of Figure 12-21, which is the ratio, P/pmax, as
a function of Sommerfeld number, S, where 0.01 < S < 1.0.
Rules and Guidelines
1. You may work on a team of 1, 2 or 3 people.
2. Find curve-fits that have an R2 value that exceeds 0.999.
3. Use a minimum of 20 data points for each curve.
4. Use only the solid line portions of curves. For the infinity curve, the fit needs only cover 0.01 to
0.20.
5. You may use any tool you want to do this work. Excel is but one way to do this. You may try
Matlab, which has curve-fitting tools or any other program of your choosing. Feel free to explore
curve-fits other than polynomial.
Hints
1. Use a tool like Web Plot Digitizer to generate the data you will use. You may use the picture
that is found with this document.
2. To make your charts in Excel, I suggest you convert the horizontal axes from S to log10(S).
3. Try “Add Trendline…” with “Display Equation on chart” and “Display R-squared value on
chart” switched on. Polynomial fits seem to work quite well.
4. To get the coefficients of a polynomial curve fit, use the array function (CSE* function)
LINEST as follows:
Polynomial
Linear (degree = 1)
Quadratic (degree = 2)
Cubic(degree = 3)
Quartic (degree = 4)
Quintic (degree = 5)
Select Array
5 rows × 2 cols
5 rows × 3 cols
5 rows × 4 cols
5 rows × 5 cols
5 rows × 6 cols
Function
=LINEST(known_y,known_x,TRUE,TRUE)
=LINEST(known_y,known_x^{1,2},TRUE,TRUE)
=LINEST(known_y,known_x^{1,2,3},TRUE,TRUE)
=LINEST(known_y,known_x^{1,2,3,4},TRUE,TRUE)
=LINEST(known_y,known_x^{1,2,3,4,5},TRUE,TRUE)
*CSE means Control+Shift+Enter (Hold down Control and Shift before you hit Enter).
Deliverable: Turn in four equations representing the best fit of the four curves on Figure 12-21
and include the associated R2 value for each curve. If the range of validity for the curve is other
than 0.01 < S < 1.0, express that clearly.
Due: October 31, 2019, 11:59PM.