Sometimes you might want to put something on a specific spot on a complex shape. Like a hole for passing wires, or an instrument for measuring load, strain, acceleration, or some other phenomenon. The Problem How do I easily put a mark on some real life complex surface and know its CAD coordinates and vice…

# Category: Applied Mathematics

## Going Fast on Your Own Power – Design

In the last two posts I went over what it takes to go fast on your own power. I found that its possible to maintain world-record breaking speeds for a fit cyclist in the right vehicle, but accelerating to those speeds is nearly impossible in current vehicles unless you are a top level cyclist. In…

## Going Fast on Your Own Power – Accelerating

I previously looked at the amount of instantaneous power it would take to go 100 mph in the worlds best faired-recumbent bicycle (velomobile). It takes approximately 1,000 watts, an achievable power output for a fit cyclist. So why hasn’t anyone gone 100 mph yet? The answer appears to be acceleration. Power Again Previously I noted…

## Going Fast on Your Own Power

The fastest anyone has ever gone on their own power on land is 89 miles per hour and change, in a vehicle called the Aerovelo Eta. The first thing I noticed is the lack of apparent windscreen. If you’re also curious about that, the vehicle pilot sees with a display connected to a camera sticking…

## Vector Analysis – Parabolic Coordinates

There are many orthogonal curvilinear coordinate systems. One of those is parabolic coordinates. In this post I will look at how parabolic coordinates are related to Cartesian coordinates in 3 dimensional space. I will determine unit vectors in parabolic coordinates in terms of Cartesian coordinate unit vectors. I will determine the arc length of a moving…

## Vector Analysis – Operations, Coordinate Systems & Arc Lengths

This post is the first in a series of example evaluations of interesting (to me) vector problems. There is plenty of literature available on the how and why of vector analysis. So while this series will not be a deep exploration, hopefully some of the problems and solutions are of interest for the reader. Problem…