exchemist

Because a -ve "real" number squared is +ve, as you point out, there is no way the square roots of -ve numbers can be "real" numbers. For example what is √-4 ? To deal with this, back in the c.17th, it was decided to invent a square root of -1 and call it i. Once you have that, you can say that √-4 has a value of ±2i. Numbers like this with i as a factor in them are called "imaginary" numbers, as opposed to 'real" numbers. Numbers can also have both real parts and imaginary parts, e.g 1 +2i. Such numbers are called "complex" numbers. Graphically, you can plot the real numbers along a horizontal line, with zero in the middle, -ve numbers extending to the left and +ve numbers to the right, to form an 'x' axis. Imaginary numbers however would be be plotted at right angles, vertically, as if on a "y"axis, with +ve values upward and -ve values downward from the central zero. A complex number like 1+2i, with both real and imaginary parts, would be located on the graph 1 unit along the x axis to the right and 2 units up the y axis from the central zero or "origin". (Such a graph is sometimes called an Argand diagram, after the Frenchman who devised it.) Although one might at first think the notion of defining i is perhaps a bit silly and pointless, the fact that you can plot complex numbers on a graph in this way turns out to make them enormously powerful as a tool in mathematics and science. You can represent one on the Argand diagram as a line drawn from the zero (origin) to the location I have described. This line has a direction and a magnitude. It is therefore a vector, with real and imaginary components at right angles to one another. You can also define it in another way, by the length of the line and the angle that it makes with the x axis. If the length is r and the angle is 𝜽, the complex number can be written as r(cos𝜽 +i sin𝜽), where rcos𝜽 is the x component and rsin𝜽 is the y component. It turns out that angular representation opens the door to a host of applications in physics where there is "sinusoidal" periodic motion e.g. waves or the theory of alternating current in electrical circuits. There are also many connections in maths too, involving exponentials and so on but that's another story. So that is why imaginary numbers are such a fruitful idea, even though they may at first glance seem crazy and just a mathematical curiosity. (P.S. I write this as a chemist, not in any way a mathematician, so the way I express this may not be rigorous to a mathematician. It's just how I think of it. Actually, it was learning about complex numbers in the 6th form at school that first made me begin to enjoy maths. I just thought they were so cool in what they could do and how many areas of maths and physics they are able to link together.)

Right. So either this is another "dead cat" tactic by Trumpy Republicans to distract and confuse the public, or they have been infected by the paranoia that the Trump administration likes to cultivate and actually believe it. What a waste of time.

What's the evidence this is statistically significant? Could it not just be the normal incidence, given the size of these research programmes. Hofstadter's "paranoid style" in Right wing US politics was identified over 50 years ago. It is currently in the ascendant under Trump, who has encouraged conspiracist thinking as part of his drive to gaslight and bamboozle the public. We've just seen Trump announcing he's releasing a load of UFO "files", which is another load of distracting codswallop designed to make people distrust "elites", suspect conspiracies - and look in the wrong direction. In such a climate, it is any wonder that a Republican politician starts yet another hare running? It could either be a deliberate ploy or simply genuine concern on his part, if he has himself become paranoid enough as a result of all this conspiracist campaigning.

Possibly, though I’m not sure why it would be an advantage. But yes I remember dismantling and tuning SU carburettors - and also the solenoid diaphragm fuel pump. The Minor used to stall towards the top of a steep hill going out of Oxford, which I eventually traced to fuel starvation. New contacts in the pump for £1.50 and a couple of hours fiddling solved the issue.

That's interesting, because I've always felt one of Obama's biggest errors was to refer contemptuously to Putin's Russia as a "regional power". I remember wincing when he did that (probably because I'm in Europe rather than the USA). I suspect that remark was the original catalyst for Putin's revanchist drive, the fruits of which culminated in invading Ukraine. Unnecessarily pissing off psychopaths turns out to cause disproportionate trouble later on. No, that is just "bothsidesism" or false balance, giving undeserved respectability to an indefensible position. The USA offered no coherent rationale, and no evidence of any threat, to justify the attack. All we got a set of conflicting, changing and vague stories from the adminstration, ranging from regime change (justified how?) to securing nuclear material (how?), to the threat of probable retaliation against the US (how?) due to an attack Israel was in any case planning (why not instead dissuade Israel from doing that?). The evidence Trump is behaving irrationally comes from his own mouth. All you have to do is listen and you immediately see the inconsistencies from one day to the next, the vagueness, the capriciousness - and in fact the sadism, the most repulsive recent example of which was the relish with which he talked of "bombing our little hearts out". Trump would absolutely start a war for no reason if he thought he could have an excuse to hurt a lot of people. It would make him feel powerful. That's what turns him on. Trump has a rapist's mentality. And with Hegseth at the Pentagon, he has a kindred spirit.

I think it may be more to do with droplet size. My understanding is that carburettors atomise the fuel into a fine mist rather than necessarily converting all it to vapour. But for sure the heavy ends have quite a low vapour pressure so won't evaporate quickly and may start to coat the sides of the inlet manifold, for instance. (It is noticeable how messy the ground can get at filling station fuel pumps that dispense diesel fuel. Any spills hang about instead of evaporating.)

Yes and the thinking of those clever folks informed the 2015 agreement negotiated with Iran by Obama, the UN Security Council and the EU - which Trump tore up, preferring apparently to treat Iran as a caricature. Or else just because Obama was black. Very "rational", that.

I'm sure this is right. My assessment of Khamenei's policy was to enrich to just short of bomb grade and stop there, so that Iran could plausibly say they had no bomb ambition, but to have in reserve the capability to get there very quickly if conditions were to change such as to require it. They probably foresaw exactly the kind of pre-emptive attack by the USA and Israel that has just taken place. That would make them wise planners, not "mad mullahs". The notion they would invite destruction of their country in a retaliatory strike by Israel, if they were to nuke Israel first is I think quite absurd. Though it is what Israel has hysterically been working on the Americans about for years. The whole notion of mad mullahs misjudges them entirely. There is no evidence the Iranian regime is irrational. Quite the contrary, as recent events have shown. Brutal at suppressing dissent, yes, of course. Irrational, no.

Paraffinic heavy ends would resemble light luboil, so I’m not sure it would be that much of a problem. After all, diesel engines are built to a very similar design and don’t get gunged up. But there could be trouble with the carburettor, I’d have thought, with atomisation of the fuel.

Indeed, in fact 7.5:1 according to Wiki, with the original 803cc version. : https://en.wikipedia.org/wiki/BMC_A-series_engine By the time my Minor was built it was 948cc and a compression ratio of 8.3:1, eventually raised further to 8.8:1 by the time of the 1275cc version in the go-faster Minis, in the 1970s. It seems that, after the revamp to the A+ the same basic engine continued until 2000, by which time the compression ratio was 10.1:1. Power output was originally 28hp and in the final version was up to 76hp. Quite an evolution. But I think one does tend to get this with IC engines. The 16SVT in the Class 40 diesel locomotive was rated at 2000hp, 2700 in the Class 50 (with intercooling) and in the much later Class 56, 3250hp. I've seen similar progressions with marine diesels. It seems because a new engine is such a big investment, the basic fixed components like the block are often generously designed to allow a lot of subsequent development.

I had an awful feeling it might come to this. Let's hope the military professionals hold the line against insanity. I have a fair degree of faith in them. Especially since it is increasingly evident that the president is off his rocker.

That's nonsense. There is no justification for this attack. Iran posed no immediate threat of any magnitude to the USA. No credible level of threat has even been asserted, much less corroborated. Furthermore no clear war aims have been articulated. Nor is this in any way a war of perception. It is a war with very practical consequences. These include civilian deaths in Iran including a school full of little girls, serious damage to Iranian infrastructure and civic buildings and to oil, gas and American military installations in the Gulf States. It is having a major effects on economies right across the world. As for "perception", the perception is that Trump has screwed up. Badly. Thanks to this ill-conceived operation, Iran has learnt what a powerful negotiating card they have in closing the Strait of Hormuz, something they had never before attempted. And they still have the military means to do that, because all they need is a few drones, which they have been mass-producing for years and which can be launched from almost anywhere in the country, which is vast. There is almost nobody outside the White House who thinks this is going well, or that any outcome will be better than could have been achieved by the negotiations that were broken off by the US when they decided to attack. And the cost of it all is huge.

The A40 had the same A-series engine as the Minor. My Minor was 948cc though there was a 1098cc version and even, in some later Minis, a 1275cc version. But quite small engines and I suppose feasible to crank by hand. I think there was a free end of the crankshaft at the front to which a crank handle could be fitted, as your picture of the A40 shows. But I didn’t have a crank handle for it and would never have dared to try that. If the battery went flat one would get some mates to give it a push, just as my son now does with his Fiat Panda, or use jump leads.

Ah yes, that’s it. So originally all the timing adjustment was manual, without any automatic centrifugal or inlet manifold compensation. So the driver tuned it by ear, presumably optimal just before the onset of pinking. And sure, if you did not fully retard the spark when cranking, the engine could fire backwards, in which direction the ratchet would not disengage, so the handle would whizz round, potentially breaking your arm. But I can’t help thinking there may have been an intermediate point, later on, when automatic compensation had come in but there was still a need to adjust for variations in octane number of the fuel.

Yes but again nothing about how a driver would use the manual adjustment on old cars. Nice MGB GT, though. I had a teal blue roadster in the early 80s. XDL152L. I looked up the reg on DVLC a couple of years ago - and she’s still going! I sold her when I went off to Dubai in 1983.

Ah so it was indeed to do with variability in octane rating of the fuel. But would this have been in place of the kind of automatic adjustment of ignition timing I described on my Morris Minor, or just a supplementary control, to extend the range of adjustment to cope with fuel variation? I have now looked up the history and found the concept of "octane rating" appeared towards the end of the 1920s. It looks as if the run up to WW2 led to development of high octane aviation fuel. Shell apparently pioneered "100 octane" aviation fuel, which became adopted as standard in the high compression ratio turbocharged aviation engines of the time. However there was no real standardising of octane ratings in road-going motor fuel until the 1950s. So maybe this accounts for the need to alter the timing manually, depending on the quality of fuel available.

That is why one needs the ignition timing to vary with engine speed and load but my question was not that. It was about why it was apparently controlled manually on early vehicles and what would be the circumstances under which the driver would adjust it.

I am somewhat intrigued by the bit about the spark being advanced. I seem to recall the spark advance was controlled pneumatically on my old Morris Minor (1961 model) by a diaphragm in the distributor, connected to the low pressure in the inlet manifold. But I have a faint memory of being in an ancient vehicle, perhaps a school bus, in which there was a control on the dashboard with "advance" and "retard" on it, presumably so the driver could alter the ignition timing manually. Seems rather extraordinary. Was this common in the early motoring era and why was it done? I wonder if it was before fuel ignition quality (knock rating) was standardised.

So are removable oven doors. Maybe this topic will get all us oldies fessing up to various mechanical amateur repair experiences. I’m reminded of James Thurber’s comments on psychological traumas inflicted by early motor cars:”Yonder toddles an ancient who once tried to crank an old Reo with the spark advanced…”

In my limited experience, trying to repair anything with a spring-loaded mechanism is fraught with danger. There is often some kind of mechanical advantage issue, whereby the spring needs to be very powerful to exert force at what is in effect the wrong end of a lever. Fiddling with such things is a recipe for taking your finger off or something.

For some reason it seems to be only the Italians that have exploited this, in their aliscafi on the Italian Lakes (and Emilio Largo’s Disco Volante in Thunderball) I remember someone once made a hydrofoil bicycle, with a propeller driven by pedals, which could just about beat a sculler in a racing shell. The snag was it had to be launched artificially, as the energy barrier to getting it up on its foils was too much for the athlete pedalling.

I'm no physicist but I had understood there is an unresolved incompatibility between the two, i.e. as the two theories stand today if one is right then the other can't be, and that is why there is a search for a resolution that unifies them. But no doubt a physicist will show up and explain.

This "Engineering Made Easy" is a YouTube Indian woo channel: https://www.youtube.com/@EngineeringMadeEasy There is a whole bank of videos taking turd about "spirituality". It has nothing whatsoever to do with either engineering or science. I think this poster is just spamming. It certainly does not belong in the Physics section anyway.

What great flood has science proven? Please provide a reference.

Interesting example of a faux ami. I gather the English word calamity comes, via Old French, from Latin calamitas, which has no connection to calamus.