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Showing posts from April, 2022

The right size pipe for falling water

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 There are a lot of engineering calculators out there and when the problem I'm dealing with isn't a simple product of units (for which I use wolfram alpha) I make good use of them. However, I recently came across a problem for which I struggled to calculate an answer and for which I struggled to find calculators. Given a reservoir of height h how thick a pipe is required to extract P power. The energy in the water is a simple calculation that comes from mgh (mass times acceleration due to gravity (9.81m/s^2) times the height the mass is raised). However, we don't want to take the whole reservoir we simply want to power something. Water through a pipe travels as a result of pressure differences between the ends of the pipe. Water pressure at a depth is independent of the total volume of water and is the same at the sides of a given depth as it is forcing downwards. This can be calculated by working out the weight of the water atop an area at a depth. The wight of a volume of...
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Space servers

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  One of the benefits of Elon Musks' Starlink space internet is that it provides a lower-latency connection between points on earth. It does this because the speed of light in a vacuum is faster than the speed of light in fibre and so even though the beams have to travel slightly further* they travel that distance faster. Although this is great for long-distance zoom chats the real financial benefit of this is to high-frequency traders who make a living from the small arbitrage opportunities that exist between geographically separate exchanges. To that end, I conjecture that not long after the public release of Starlink and its proven utility to high-frequency traders, those trading firms will start to deploy their algorithms to servers in orbit. Why? To lower the latency. If the algorithm doesn’t need to send the signal to space before it executes then it can receive the signals from both exchanges in L/2 and after deciding to trade send the trading request at L/2 leading to a bli...
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Structural engineering with cardboard

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Moving into a new flat I have ended up with a lot of cardboard and have actually struggled to get it to all be taken away. I then saw this Kickstarter on hacker news which introduced me to the idea that I could perhaps use the cardboard I had been throwing away the whole time. I have been toying with some ideas for building myself a robot, or at least a robot arm but they seem to be just ludicrously expensive and still not able to lift much weight. One of the problems with the advancement of robotics is that although processing power has come down in price at a rate that no other product ever has, the cost of actuators (The motion inducing components like motors) has remained largely the same. I want to explore an idea I have for using cheaper motors in a robotic arm in another post though. The problem I want to look at here is the possibility of being able to use cardboard, a material which can almost be considered to have a negative price, as the structure to the robot. I love the ...
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The twelve fold way

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I really struggle to remember the combinatorial rules. Do I need to use choose or do I need to use permute? How do I calculate each of them? Is this a case of stars and bars or is this something else? One of the things I want to add to my chatbot program is a way to ask which of the many systems should I be using? I did once try to build a javascript tool although I don’t think it ever really made itself into a useful state. I recently found a paper called “The twelvefold way” which explains all the different ways you put balls in boxes (or urns as is used in the paper). It really helped me to understand, at least a little better, how to calculate the different permutations of the problem. With this newfound understanding, I once again had a go at producing a program to calculate each, with a simple form-based input. One of the things that I wanted to extend this to doing was informing me of what the calculation method was. I really like the way google now lends a hand when you a...
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