Math question / weather balloons

[MilwaukeeLion]

Interesting history of weather balloons, couple early balloonists with craters named after them on mars & moon.   https://www.highaltitudescience.com/pages/intro-to-weather-balloons

 

Can diameter of balloon below be estimated - is it ordinary balloon or weather balloon?  I first thought it was a larger weather balloon because you can make out the cord, figured it had to be bit thick to be focused enough to see.  Was windy yesterday and ordinary string would probably not remain vertical but be blowing around, could just be ordinary balloon with thicker cord or small weight attached I guess.  Perhaps one of those mylar balloons.  Weather balloons are launched twice a day from a few locations within 100km from me. 

Only data I have:

asi174mm 5.86um pixel size

roi 912x912

ED80 480mm fl

Ordinary balloons burst near 10km while weather balloons burst near 30-39km. 

Ordinary balloon diameters in inches 9,10,11,12,16,18. Balloons near 5 inches and smaller don't hold enough helium to float.

Weather balloons mostly go by weight but can purchase sizes online of 3 ft, 8 ft, 16 ft diameter.  

Guessing cord dimensions to balloon dimensions not much help.

Time and sun position below, late afternoon sun had crossed meridian heading west.

[vlaiv]

Actually you can do some math to help you narrow down possible answer.

In general case you don't know how far away something is by its angular size (if you don't have exact measures of object). But you can do the following:

1. based on measured angular size on frames and known balloon sizes determine their respective distance (distance that they need to be in order to be of that angular size).

This online resource might help with that:

http://www.1728.org/angsize.htm

Next thing to do once you have above relationship is to calculate height above ground for each distance - this should be solvable, not sure if you can approximate earth as flat (probably) or do you need to account for curvature. You have the position of the sun from recording - you can find out alt/az coordinates. Using alt you can ask the following question - how high must object be if it is X far away to appear to be ALT degrees above horizon.

For each of above distances you will get height. Cross reference with bursting height in order to see if something cancels out (regular balloon too high).

There is another "forensic" method that you might try, but that one is very complicated, and made difficult by changing seeing - measure defocus blur on cord. Your scope was effectively focused to infinity (well not quite but very close) - so anything closer will be out of focus. Cord at that distance is in essence thin line (in focus), so any measured width of cord is defocus blur. Depending on parameters of scope and camera you can figure out how much blur corresponds to how much distance to scope - look up Circle of confusion in regular photography - you should be able to find some formulae to help you with this.

[vlaiv]

Btw, I forgot to say - by looking at the cord, it looks to me it is a weather balloon - cord is too thin (not far out of focus) to be close object.

[furrysocks2]

Nice capture.

Reminds me I did some maths on someone's video frames on here of what we reckon was a bird crossing the disc of Jupiter. Using the perceived wingbeat frequency (discounted it being a bat), I guessed a range for the mass and size, and therefore distance, altitude and flight speed.

Probability of getting this capture must be pretty low, as was the bird-Jupiter capture, so well done for that at least! Very nice.

[vlaiv]

Hm, according to angular size 18 inch balloon would be around 5.3km away. !6ft weather balloon should at a distance of 56.2Km.

If we apply trigonometry, and Alt is 55 degrees (and assume flat earth - never thought I would assume something like that ) - height of object for distance of 56.2Km would be 46km - above bursting height!

So we know it's not 16ft weather balloon

 

[vlaiv]

8ft weather balloon checks out. - 23km high, below burst height.

3 minutes ago, furrysocks2 said:

Nice capture.

Reminds me I did some maths on someone's video frames on here of what we reckon was a bird crossing the disc of Jupiter. Using the perceived wingbeat frequency (discounted it being a bat), I guessed a range for the mass and size, and therefore distance, altitude and flight speed.

Probability of getting this capture must be pretty low, as was the bird-Jupiter capture, so well done for that at least! Very nice.

Great idea - we can use frame rate and angular movement to determine speed at particular distance, after determining distance for each balloon type, and thus height - we check weather record for particular day to see wind speeds at given height!

Problem solved, great detective work

 

[MilwaukeeLion]

2 hours ago, vlaiv said:

8ft weather balloon checks out. - 23km high, below burst height.

Great idea - we can use frame rate and angular movement to determine speed at particular distance, after determining distance for each balloon type, and thus height - we check weather record for particular day to see wind speeds at given height!

Problem solved, great detective work

 

Amazing, great job !  Wind gusts at 30 km and 12 km yesterday according to ventusky.com were 20mph.  Frame rate set at 30 fps max, which is what it was captured at.  It takes 65 frames from time its first seen until it disappears.

[MilwaukeeLion]

8 hours ago, vlaiv said:

Actually you can do some math to help you narrow down possible answer.

In general case you don't know how far away something is by its angular size (if you don't have exact measures of object). But you can do the following:

1. based on measured angular size on frames and known balloon sizes determine their respective distance (distance that they need to be in order to be of that angular size).

This online resource might help with that:

http://www.1728.org/angsize.htm

Next thing to do once you have above relationship is to calculate height above ground for each distance - this should be solvable, not sure if you can approximate earth as flat (probably) or do you need to account for curvature. You have the position of the sun from recording - you can find out alt/az coordinates. Using alt you can ask the following question - how high must object be if it is X far away to appear to be ALT degrees above horizon.

For each of above distances you will get height. Cross reference with bursting height in order to see if something cancels out (regular balloon too high).

There is another "forensic" method that you might try, but that one is very complicated, and made difficult by changing seeing - measure defocus blur on cord. Your scope was effectively focused to infinity (well not quite but very close) - so anything closer will be out of focus. Cord at that distance is in essence thin line (in focus), so any measured width of cord is defocus blur. Depending on parameters of scope and camera you can figure out how much blur corresponds to how much distance to scope - look up Circle of confusion in regular photography - you should be able to find some formulae to help you with this.

This is great, I can now get altitude of my collection of jets crossing sun.  For arc sec / pixel which would be more accurate, measuring wingspan, diameter or length of fuelselage?

[vlaiv]

15 hours ago, MilwaukeeLion said:

Amazing, great job !  Wind gusts at 30 km and 12 km yesterday according to ventusky.com were 20mph.  Frame rate set at 30 fps max, which is what it was captured at.  It takes 65 frames from time its first seen until it disappears.

So 65 frames is roughly 2 seconds - around 840 arcseconds for two seconds, this means 420 arc seconds per second.

At a distance of 8ft balloon this gives about 57.5 meters per second or in miles per hour quite high: 128mph

Let's try 3ft balloon, and see if it fits:

distance: 10600m

altitude: ~8700m

Speed: 21.6m/s = 48mph (this might match)

18inch balloon:

distance: 5400m

altitude: ~4400m

Speed: 11m/s = 24mph

Hm, it looks, based on wind data, that weather balloons are out of the picture

With above information, I would say best match is regular balloon (not sure about diameter because as you calculate for smaller diameters you get more conservative values - like height and speed so we can't apply upper bound to exclude results).

9 hours ago, MilwaukeeLion said:

This is great, I can now get altitude of my collection of jets crossing sun.  For arc sec / pixel which would be more accurate, measuring wingspan, diameter or length of fuelselage?

I think your best bet for doing arc/second per pixel is to go with Sun itself - airplane will be moving and there will be a slight motion blur in each frame. With Sun you have large target to measure (greater SNR due to more "signal") and you have exact apparent diameter in arc seconds.

I did a quick check to see if image you posted was binned or could I use it for measurements - arcsec/pixel based on equipment specs (5.86um pixel and 480mm FL) gives 2.52"/pixel - I roughly measured 2.55"/pixel (using 1920" sun diameter approximation - I did not check actual sun apparent diameter at your location for given footage time).

As for measuring angular size of airplane, and if you want to be precise about it (provided that you can identify aircraft model) - do a series of measurements - on each frame, use both length of fuselage and wing span and calculate mean value between frames (you can even use standard deviation for error calculation if you wish).

This will give you angular value that you must somehow correct for plane orientation in each frame to compare to actual airplane size (fuselage at 90 degrees will be of exact length, but flying at 45 degrees towards you will have 1/2^0.5 apparent length).

When you determine angular measure and true measure (from aircraft specs) - you will have distance, same ALT calculation will give you flight level. Speed will also depend on distance and angle (we did not account for angle above because there is no way to determine orientation - so we assumed it flu straight across).