The math of faster-than-sound freefall

http://blog.wolfram.com/2012/10/24/falling-faster-than-the-speed-of-sound/

by peterbush • 14 years ago

78 27 14 years ago

blog.wolfram.com

madarco• 14 years ago

I'd like to master Mathematica like that

opminion• 14 years ago

Question for US writers:

At 39 kilometers, the horizon is roughly 439 miles away

For someone who was taught only the metric system, and told that it is good practice to avoid mixing units (centimetres with metres, milligrams with grams, etc), reading science written in the US using miles and Farenheit degrees is a bit unpleasant. Fair enough, they are called imperial for a reason :-)

But sometimes US writers mix imperial and metric units, such as in the paragraph above. I remember a talk by some NASA guy doing the same. Is there a really good reason for that?

A separate question is, if you are willing to use metric, why use imperial?

Edit: wording

TeMPOraL• 14 years ago

> But often I see US writers mixing imperial and metric units, such as in the paragraph above. I remember a talk by some NASA guy doing the same.

Well, they once crashed a Mars probe because of that.

http://en.wikipedia.org/wiki/Mars_Climate_Orbiter#Cause_of_f...

arethuza2• 14 years ago

Do Americans actually use the term "imperial" - I'd assumed, as someone from the UK, that this usage was only common in UK and what's now the Commonwealth.

NB Not being snarky - just wanted to know! :-)

carbocation• 14 years ago

Yep, we call it imperial. Also, mixing imperial and metric is really quite odd. I am not familiar with someone doing it on purpose and would distrust any mixed statement, suspecting that the units may be mislabeled.

merlincorey• 14 years ago

Americans call it the "customary" measurement system.

bane3• 14 years ago

Most people just call it "measuring" without knowing it has a particular category name.

Those that know call it "imperial".

gecko• 14 years ago

Where I grew up in the urban Midwest, they were called English units (despite everyone knowing that England is metric). Kind of reminded me how the French call French horns English horns.

barking• 14 years ago

Are they the same though. There are differences between english and American pints, for example. Also it means nothing to me when someone quotes their weight in lbs or kgs. I need stones to get an impression of how heavy they are. Where I live it's currently a mish mash of metric and imperial units but the trend is definitely towards metric. I don't think my kids think in imperial the way i do a lot of the time. Meanwhile metric means absolutely nothing to my dad.

grecy2• 14 years ago

I live in Canada very close to a border with Alaska where many cruise-ship tourists cross over on enormous buses when they don't actually have to see the border guard. Often they are unaware they are in an entirely separate country.

When we mention degrees or kilometers, the response is often "What's that in 'normal'?"

Also, these people become extremely confused when told the price of something in "dollars" that are not the dollars they are used to.

bane3• 14 years ago

It's bad form for formal technical writing. I cringe whenever I see NASA or similar doing it. Popular writing can get away with it as it's supposed to be bridging the gap between technical and average readers.

Almost all serious engineering, scientific and military matters and the majority of manufacturing are metric in the U.S.

However imperial is the customary measurement system and is familiar to most people. It's also pretty easy to estimate using various body parts and has some nice features around simple fractions.

It's actually not terribly unusual though, I've been in countries that are "100% metric" and people still communicate with their local customary measures in many contexts.

Anechoic• 14 years ago

Almost all serious engineering, scientific [..] and the majority of manufacturing are metric in the U.S.

This isn't true in my experience. Of course my experience certainly isn't comprehensive, but in my work I interact with a lot of US fields (environmental, manufacturing, civil & mechanical engineering, etc) and I almost never see metric units. The Federal Highway Administration tried to encourage state DOT's to go metric for design and engineering work back in the late 90's but they eventually gave up. If you ever worked on an American car, you still find a mix of metric and Imperial bolt sizes! About the only field where I found that metric units are used extensively is wind energy.

Heck, even my mechanical engineering PE exam used Imperial units exclusively (pounds force vs pounds-mass... sigh)

I imagine that your statement is probably most true for the military though.

jpwagner• 14 years ago

It would be easy to assume that he made a mistake, but if he did this on purpose (more likely) I suspect the reason is that the "439 miles" is supposed to be imagined, whereas the "39 km" is a measurement.

Suppose I made an example that if you were traveling at 1/3 the speed of light on Earth, you'd weigh X times your resting weight. If you are American you measure your weight in lbs, so if I quote it in kg, you just need to convert it anyway. Therefore even though I'd say you were traveling 1e8 m/s, I'd quote your supposed weight in lbs.

001sky• 14 years ago

Legal terms relating to transit (MPH) in US are in miles. Measurements are in whatever you want. So there is a bias toward using Miles in general, when talking about ~distance~ whether or not you measure in MM or Inches. Wrenches for fasteners, as an example, are not an official decision. The UK also does this. They actually use the metric for most measurements, but their roadways etc. are in miles. so its not just a US thing.

Jabbles• 14 years ago

I don't think the references to "terminal velocity" are very helpful. They're calculated from the estimates of drag coefficients and surface area, which must have reduced as he became more upright. You can't† exceed your terminal velocity without propulsion, that's why it's named as such.

†Well, I suppose if you're falling through an atmosphere that changes too rapidly, you can temporarily exceed it as the TV decreases. Perhaps it's more accurate to say "you can't accelerate if you're exceeding the terminal velocity whilst freefalling"?

rnadna• 14 years ago

I've not used mathematica in a long time, and I forgot how crazy-ugly the graphs are. The cartoonish legend in the Out[18] graph is a case in point, almost a lesson in what not to do, in terms of distracting from the content.

The syntax ain't pretty either, but one does get used to that, of course.

PS. opminion is right: the unit weaving is pretty strange. But the content of the posting is interesting enough to make me think "oh well, it's just another yank" and keep reading.

cormullion• 14 years ago

All Mathematica users hate PlotLegend...

http://mathematica.stackexchange.com/questions/4444/labeling...

jevinskie• 14 years ago

The default color palettes and line rendering is much nicer in Mathematica than MATLAB. However, tweaking the default styles is a huge pain and the labels really are bad.

blago2• 14 years ago

At 24.26 miles above the Earth, the atmosphere is very thin and cold, only about -14 degrees Fahrenheit on average.

This is way off. -14 Fahrenheit is something we get in Minnesota. Most winters :-) Any commercial flight displays temperatures in the -50 range.

Retric• 14 years ago

No, Temperature does weird things as you increase in altitude. So it's colder at 10km than 50km, then dips at 90km before rising again before dropping off in space.

http://www.aerospaceweb.org/question/atmosphere/q0090.shtml

blago2• 14 years ago

Very interesting. Thanks!

grecy2• 14 years ago

I was thinking the same thing. I rode my bike to work this morning in -14F (-25C)

The math of faster-than-sound freefall

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