In engineering wind tunnel can be used to measure how the fo

In engineering, wind tunnel can be used to measure how the force of air resistance depends on velocity. A set of such experimental data is given in the table below. Force (F) is measured in Newton (N) and velocity (v) is by meter per second (m/s).

(a) Find TWO best-fitted curves between F and v or F(v) using the least squares method;

(b) Discuss the advantages and disadvantages of each of the TWO best formulas obtained in (a) by your judgment; [You can outline your approach first; then use excel to present your results.]

Solution

1. Approach to this problem, a equation of line y = mx+C , fit the above given data

2. Squares of errors should be least or minimum. Error = actual value - fitting value = F(V) - mx₁+C

3. You get a function S in terms of square of errors

4. For mininmum, Partial Differentiation w.r.t \" m and C\" is to be Zero.

5. Find m and C using above Obtained Equations

ADVANTAGES OF QUADRATIC FIT OVER STRAIGHT LINE FIT

1. Error of Quadratic fit is less than the straight line fit. Quadratic Fit Give Better approximation

Using Excel

1.Straight Line fit is F(V) = 19.7V -238.93

2. Quadratic Fit is  F(V) = .046V² +15.53V-169.4