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Applied Math Example - Dot Product - Finding the Angle Between Two Vectors

In this Applied Math Example I'll so how to use the Dot Product, also known as the Scalar Product, to find the angle between two cables in 3D space.

Applied Math Example - Dot Product - Finding the Angle Between Two Vectors

Dot Products, also known as Scalar Products, are coincidentally one of the things I learned in Math that I actually enjoyed. I think the reason for this is I learned about them in an actual Engineering class, Statics. Rather than learning a topic in Math without knowing of a real life use, I learned about Dot Products by applying them. For many of you however, you may have encountered Scalar Products in Linear Algebra or Matrix Algebra class, in which case there is a fairly high probability that you reasonably assumed they were mostly theoretical with few real world applications. There are a few interesting things you can do with the Dot Product, and this is one of them. Today I'll be showing you how to apply a Scalar Product to find the angle between two cables in 3D space.

Take a look at the image above. Let the...

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Another Victory For The University of Tennessee Graduate Robotics Team

The second first place finish in a row for the University of Tennessee Graduate Robotics Team.

University of Tennessee Graduate Robotics Team 2014

Following our success from the SouthEastCon2013 in Jacksonville, the University of Tennessee Graduate Robotics Team took home another victory in Lexington. The first video is of the 2013 competition winning robot. The 2nd is the winner in 2014. Here's hoping we have a fun and successful 2015!

Another Article About Our Robotics Victory in 2013

Another article about our victory in the 2013 Open Hardware Competition

Another article has been published about our victory in the Robotics Competition.

http://parallax.com/news/2013-12-18/university-tennessee-graduate-robotics-team

Using Your Time Disruptively

Sometimes you have to take time away from making money now so you can make more money in the future.

One thing I do whenever I don't have a looming deadline (which is 95% of my time) is I take time to do things not directly paying me, and I invest that time in to something disruptive. I have multiple projects underway at the moment, two of which only pay me on completion. I make sure to get a lot of progress done early in order to be comfortable knowing I'll leave my clients happy with the quality and timing of my work, but sometimes I have to make the mental note that I also work for myself. Instead of taking on additional projects, I work on disrupting my income.

Imagine two people. One works nonstop on the same type of work week in and week out (Bob). Bob feels very productive and successful since each week a certain number of lines of code are written a week, clients are trained, widgets designed, whatever it...

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CFD - Bluff Body - Splitter Preliminary

In this CFD Article I show how the Diffuser of a Race Car effects the Downforce and Balance.

CFD - Bluff Body - Splitter Length Downforce Distribution

Introduction

Though Downforce is a big player in Race Car Performance, there are other factors that will determine cornering ability and ultimate handling. One of this is the Aerodynamic Balance of the Race Car. You may generate road crushing levels of Downforce, but if all that Downforce is on the Rear Tyres it won't do your lap time a whole lot of good. For the Race Car to go around the track as quickly as possible a good Aerodynamic Balance is required.

Other words used to describe a Splitter are Front Spoilers or Air Dams [1]

Hypothesis

A very simple explanation for how Splitters work is that the high pressure that develops at the front of the Race Car is trapped by the Splitter, and this high pressure is applied to the top surface of the Splitter which pushes it down. In general and...

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CFD - Bluff Body - Ride Height

In this CFD Article I show how the Ride Height of a Race Car effects the amount of Downforce generated.

CFD - Bluff Body - Ride Height

Introduction

The majority of you landing on this page most likely already have an idea of the effect that Ride Height has on Downforce for an F1 or DSR / SR2 / LeMans Prototype Race Car. In general, the lower you can get the Underbody of the Race Car to the ground, the stronger the Ground Effect will be, and this will increase Downforce. It does however get a little more complicated than that. As you get closer to the ground, Ride Height Sensitivity increases. In addition, once the Race Car Underfloor gets too low the flow underneath can be blocked and not allow enough air through the diffuser. Once this happens, Downforce plummets.

The following article will talk about these implications in Formula One and other racing series such as DSR/SR2 and LeMans or other Formula Cars or Prototypes.

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Engineering Example - Astronautics - Non Hohman LEO to LMO Transfer

In this Engineering Example we do a LEO to LMO Non Hohman Transfer finding total Delta V and Time.

Engineering Example - Astronautics - Non Hohman LEO to LMO Transfer

Lets say we are sending an object to Mars, and it has already launched and is in a Parking Orbit over Earth at an altitude of 500km. This object is said to be in LEO, or Low Earth Orbit. We want to send it to Mars, for a Circular Orbit with an altitude of 500km.

The mission can't wait for a Hohman Transfer and there is extra fuel. The object is to intercept Mars at a True Anomaly of 165 degrees. Assume no Orbital Inclination.

What Delta V is required for the 1st and 2nd burn?

This will be pretty much Greek to most of my readers, I'll provide explanations of this for those that are interested later. I just wanted to start filling out some of my Engineering Examples List and this is a problem I did years ago.

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Engineering Example - Mechanical Vibration - Undamped F1 Car Bouncing

In this Engineering Example I give you a Practice Homework Problem to help you study for your Mechanical Vibration Exam.

Engineering Example - Mechanical Vibration - Undamped F1 Car Dropped From Jacks

This Engineering Example is meant to give you some practice problem homework to help you study for your Engineering Exam. If you are in a Mechanical Vibration class, you'd be lucky if a problem this easy was on your Exam.

Lets say an F1 Race Car is pushed down 12mm, and released from a standstill. What is the equation of motion as a function of time? Ignore all friction. Here are your "givens".

Bouncing F1 Race Car Undamped Mechanical Vibration

 

Solution

 

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Engineering Examples List - Branches - Practice Problems and Exam Study Help

These Engineering Examples are not meant to teach you the specific branch of Engineering/Science. Rather, they are meant to be used as Example Practice Problems to help when studying for your Engineering Exam.

Engineering Examples List - Branches - Practice Problems and Exam Study Help

This will be a continually updated list of Engineering Examples.

These Engineering Examples are not meant to teach you the specific branch of Engineering/Science. Rather, they are meant to be used as Example Practice Problems to help when studying for your Engineering Exam.

It was my experience that too often Professors didn't provide enough worked examples and the book didn't have good examples or even any answers in the back of the book. It made me wonder if I actually knew the material or not since I had no way to check my answers, and I got the joy of finding out the truth either the day of the Engineering Exam, or a month later sometimes when the Professor finally got his TA to grade the Exams (don't get me wrong, some of my Profs were awesome).

Aerodynamics

  • Drag on Flat Plate...
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Engineering Example - Thermodynamics - Conservation of Energy F1 Car Accelerating Uphill

In this Engineering Example I give you a Thermodynamics Practice Problem to help you study for your Engineering Exam.

Engineering Example - Thermodynamics - Conservation of Energy F1 Car Accelerating Uphill

The purpose of this Engineering Example is not to teach you Thermodynamics, but rather to give you a Thermodynamics Practice Problem to help you study for your Engineering Exam.

Lets say an F1 Race Car is Accelerating up a hill. The initial velocity is 30m/s, and after traveling 1000m, a hill of 50m height is climbed at which point the velocity is 95m/s. How much Power does the F1 Race Car have when ignoring all forms of Friction?

 

Equations

 

Answer

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