Mechanical Design Handbook

I first wrote about this topic back in 2009. At that time, finding a reliable "computational engine" online was a revelation. Today, while the tools have evolved significantly, the need for quick, accurate engineering calculations remains the same. The Classic Powerhouse: Wolfram|Alpha Wolfram|Alpha 's long-term goal is to make all systematic knowledge immediately computable and accessible to everyone. Unlike a standard search engine that gives you links, Wolfram|Alpha gives you answers based on structured data and physics formulas. For a mechanical engineer, this is incredibly useful. You can simply type a natural query like: "spring force k=500 N/m x=20mm" And it will instantly compute the result using Hooke's Law ( F = kx ), handling the unit conversions (mm to m) automatically. It serves as a definitive source for factual queries. The Modern Era: AI and Large Language Models Fast forward to today, and we hav...

In the previous post , we talked about several root finding techniques. In this post, we're going to see how we can use Microsoft Excel VBA to find the roots using the Newton-Raphson Method. The Logic As we know, the Newton-Raphson Method is the most widely used of all root-locating formulas. The Newton-Raphson method uses the slope ( first derivative ) of the function to find the root. That means, in the VBA code, we have to calculate the first derivative of the function. We already discussed how to find the first derivative using numerical methods , and we will incorporate that logic here. The Newton-Raphson Method uses the Taylor series to approximate delta x as shown below: f(x) = f(x 0 ) + (x N - x 0 )f'(x 0 ) = 0 Rearranging for the new position: x N = x 0 - f(x 0 ) / f'(x 0 ) The Algorithm Guess the initial value of the root → select x 0 . Calculate the next guess ( x N ) using the formula above. Check conv...

In the previous post, Numerical Methods - First derivative using Excel formula , we know how to calculate the first derivative of functions using formula in Microsoft Excel. In this post, let's see how we can simplify it by using Excel VBA code. The VBA is just like this. ' ================================================ ' Created by Suparerg Suksai ' Mechanical Design Handbook ' http://mechanical-design-handbook.blogspot.com ' ' First Derivative - Numerical Methods ' ================================================ Function f(x As Double ) As Double   f = 5 * (x - 3) ^ 3 - 4 * x ^ 2 - Sin(2 * x) End Function Function fDeriv(x As Double ) As Double Const h = 0.00001 ' Step size fDeriv = (-f(x + 2 * h) + 8 * f(x + h) - 8 * f(x - h) + f(x - 2 * h)) / 12 / h End Function The highlighted (yellow) text is the function that we want to calculate for the first derivative. We can simply replace it with new function. The remaining c...