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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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Some thoughts on solving transcendental equations

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My thinking here is that although transcendental equations don’t have algebraic answers are there still links between them? That theory is supported by the contour lines in the following  So I wasn’t going to look into this but sometimes I just get captured by the mathematics. I have known for a while that most equations can’t be solved. The unsolvability of most equations leads to transcendental numbers. Numbers which aren’t the result of a solvable algebraic equation like 5x+1=7 or 2x^2=3 but can be computed, at least approximately. These numbers include pi and e. There isn’t a formula for pi or e, we can define them, we can even define them without the use of geometry. As I have found out in my curious investigations both numbers seem to crop up only when calculus is involved. e is the solution to the problem of The functions that produce these two have always seemed arbitrary to me. Why is it the case that when we don’t know the answer to we just say, the answer is the answer? We
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Too whet an appetite for DRY principles

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DRY - Don't repeat yourself One of the things I did wrong when I started to write software for a career is to try and optimise before I had a chance to understand. Having worked a little longer I feel I have a better appreciation for what should be automated and when.  There are a lot of things that I felt I was repeatedly doing that according to my understanding of the DRY principles at the time, I thought I should be abstracted away, so as not to have to repeat myself. I kept telling myself that if I was finding a project boring that the boredom was a notification from my mind that there is unnecessary repetition. I still feel that there is a level of truth in the idea of boredom being the mind picking up on repetition however I now realise that is that there is a level of repetitiveness that is inherent in working as a software developer. That is not to say that we shouldn’t strive to remove the repetitiveness but that the job of a developer when working on a project must be fir
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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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