Ok, so out for dinner with my OH and we got talking about a hot air balloon she had seen. She reckoned you could calculate the height of the balloon by knowing how large it was and how large it then looked (I.e. in the distance). Now at this point I'm seeing Father Ted holding a toy cow up to Father Dougal....
For me it sounded total bunkum. The angle of sight of the balloon and then variances in air pressure making the balloon different shapes would make this near impossible.
But, because she's lovely, I said I would ask in the one forum where someone might be able to, ahem, offer an opinion....
(she's spent the evening on the net looking for an equation - which she's not found)
This is what happens when you go out for dinner, rather than getting her to cook. Mind has a chance to wander from the essentials.
As far as I'm aware you could do it using trigonometry, but you need to know where it was over, so you could get the horizontal distance to where it is. You also need to know the angle from which you are viewing it, so you could then use Tan(angle)*Distance=height.
If my a-level maths serves me correctly.
The secret here is knowing how large it is, if you know that, then indeed you can work out how far away it is.
well, you can tell how far away something is if you know how big it is. In fact I have an app on my phone that does exactly that.
But... for something as far away as the hot air balloon presumably was: you're not going to get an accurate measurement of its apparent size.
And if you are looking at it from the ground then you'd need to know what size the "face" you are looking at is, rather than something more obvious like the height of the balloon.
And yes, if it is high enough then the change in atmospheric pressure would change the size/shape of the balloon.
Basically... you [i]could[/i] do it (I reckon) but you'd need a fairly complicated model and very accurate equipment to do it successfully, not high school maths.
Nah, not that complex, just treat your eye as the origin, hold a ruler at a known distance from your eye, and measure rhevapparent sizevthatbway
Nah, not that complex, just treat your eye as the origin, hold a ruler at a known distance from your eye, and measure rhevapparent sizevthatbway
Yeah, but if it is far enough away that you're struggling to tell if the apparent size is 1mm or 2mm then you have a pretty massive scope for error right there.
The angle / face of view was what was troubling me. Knowing how big the balloon was on the ground wouldn't help, you'd need to know how big it looked from the view you'd have of it while in the air..
Also air pressure as it rose would make a difference to the shape.
I appreciate the school boy error involved in letting a lady talk maths, but she is lovely, and i would not be too sorry if someone could sort this. But, my knowledge of maths suggests she's likely stuffed.
I'll start another thread "how to tell a loved one they've had a stupid idea"
But... for something as far away as the hot air balloon presumably was: you're not going to get an accurate measurement of its apparent size.
You can do it with stars, so you could probably do it for a hot air balloon.
http://en.wikipedia.org/wiki/Parallax
In fact I think it's how they measured distances in war for firing various missiles before they had lasers and radar and such (so think catapults, canons, etc.)
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Quite simple really.
The angle / face of view was what was troubling me. Knowing how big the balloon was on the ground wouldn't help, you'd need to know how big it looked from the view you'd have of it while in the air..Also air pressure as it rose would make a difference to the shape.
Tiny differences. You still get a pretty accurate estimate is you know the angle subtended from your viewing position. Measuring that angle is the tricky bit.
Knowing how big the balloon was on the ground wouldn't help, you'd need to know how big it looked from the view you'd have of it while in the air..
Yep, but you could work that out if you knew its dimensions.
Also air pressure as it rose would make a difference to the shape.
Yep, but you could work that out too if you knew enough about the air pressure at ground and at height, relative temperatures, elasticity of the balloon fabric ....
Like I said.. complex!
(Actually I can't decide if it does significantly change shape at height or not. Any balloonists on?)
You can do it with stars, so you could probably do it for a hot air balloon.
See [i]"very accurate equipment"[/i] - no one does it with stars by holding a ruler up in front of their eye 😀
Higher = bigger balloon (less pressure outside), this is why you chose flacid balloons in a balloon race on the school fate, they burst at higher altitude.
Higher = bigger balloon, this is why you chose flacid balloons in a balloon race on the school fate, they burst at higher altitude.
Yeah but those balloons are sealed. A hot-air balloon is open.
See "very accurate equipment" - no one does it with stars by holding a ruler up in front of their eye
Actually, you can do it without a ruler. You need a calculator (ideally), and some way of measuring an angle fairly accurately (a protractor would do, but it won't be that accurate). To measure the distance to a star you'd need to spend 2 minutes, write a couple of numbers down, then wait 6 months, repeat, then do a few simple calculations, and bam, you have an estimate.
To do the same with a hot air balloon, a meter stick with two protractors glued at each end would do a fairly decent job I'd imagine. Not going to try and quote how accurate the figure would be, but it would be ok. If you used a bigger stick it would get more accurate.
you have an estimate
Which relies on knowing how far away the "near star" is.
How do you work that out?
Which relies on knowing how far away the "near star" is.
The estimate [b]is[/b] how far away the near star is...?
Basically, we know the distance between us and the sun. So we look at the star, and measure the angle it makes with us by comparing it to very very distance stars (the background). We then have a distance and two angles, so we can work out everything else.
With the hot air balloon example, the meter stick represents the distance between the earth and the earth 6 months later.
http://lcogt.net/spacebook/parallax-and-distance-measurement
Couldn't you just shoot it down and time how long it takes to hit the ground?
(I mean theoretically. Obviously. This'd be one of them theoretical physics experiments. I am in no way suggesting you ACTUALLY shoot it down.)
Oh god Jennifer Anniston is so hot.
The estimate is how far away the near star is...?
Ah right, I misunderstood your diagram - thought it showed you using the known distance to the near star to calculate the distance to distant stars.
But actually it relies on the distant stars being far enough away that they are more or less unaffected by the parallax motion.
Metre stick idea seems more feasible now - but I suspect the inaccuracies in a physical measurement projected over that distance would multiply up to a pretty large potential error.
You could take out the size due to pressure query by knowing that the wicker basket Rupert is standing in beneath the balloon,at five foot eight inches tall,measures four foot deep.
Oh wait,hot air balloon baskets compress the higher they get (waterproof at 3 miles high) so that theory is out the window.
But actually it relies on the distant stars being far enough away that they are more or less unaffected by the parallax motion.
Yeah, but the distances they do actually move relative to our vision makes less of an error then things like the atmosphere, or errors in the angle measurements. For proper measurements of stars you're better off using the red shift method thing, I think. Or I think there's some other way of doing it using the known frequency of the star - as long as you know what type of star it is? It's been a while.
But yeah, using a meter stick you can measure distances fairly well within 100m or so.
Oh wait,hot air balloon baskets compress the higher they get (waterproof at 3 miles high) so that theory is out the window.
I doubt this thing changed shape very much:
http://www.flickr.com/photos/symonmreynolds/6805444460/
Certainly not to the extent that you could measure the change from 3 miles away with the naked eye!
Do hot air balloons change shaped with altitude? Obviously a sealed helium balloon would get bigger, but a hot air balloon is open so the pressure inside the balloon with be the same as outside...wouldn't it?
Spooky is right IMO, hot air balloons don't change shape with altitude........if they do it's a tiny percent of their size.
Ok then, method 2, put two stick in the ground a know distance apart. Each of you stand behind them so that the stick is directly between you and the balloon. From that you can calculate the distance to the balloon
I don't think they change shape as the air will just come in/go out the bottom. Additionally it's the volume which would change by a tiny amount, so the linear distance (you'd be measuring) would only vary with the cube root of that change, pretty negligible. So get a ruler, hold it at arms length, measure your arm length and the apparent balloon dims, if you know the actual balloon dims its just some trigonometry
That would give you an estimate of the distance to the balloon - you'd still need to do something else to get the altitude - could measure the angle to the balloon over the horizon and the height would be distance * sin(angle).
Disclaimer - first coffee of the morning being consumed - trigonometry may be ropey.
The secret here is knowing how large it is, if you know that, then indeed you can work out how far away it is.
Correct, this is sometimes used when ranging targets with rifles.
The secret here is knowing how large it is, if you know that, then indeed you can work out how far away it is.
[url= http://www.thedambusters.org.uk/sight.html ]It's the same principal the Dambusters used[/url], knowing how wide the towers were on the dams they could simply* fly straight towards the dam, and when the sticks matched up the distance was right.
* Simply: ignoring it was at night, over enemy territory, etc.